Effects of structural nonlinearity on subsonic aeroelastic characteristics of an aircraft wing with control surface

NASA Astrophysics Data System (ADS)

Bae, J.-S.; Inman, D. J.; Lee, I.

2004-07-01

The nonlinear aeroelastic characteristics of an aircraft wing with a control surface are investigated. A doublet-hybrid method is used for the calculation of subsonic unsteady aerodynamic forces and the minimum-state approximation is used for the approximation of aerodynamic forces. A free vibration analysis is performed using the finite element and the fictitious mass methods. The structural nonlinearity in the control surface hinge is represented by both free-play and a bilinear nonlinearity. These nonlinearities are linearized using the describing function method. From the nonlinear flutter analysis, various types of limit cycle oscillations and periodic motions are observed in a wide range of air speeds below the linear flutter boundary. The effects of structural nonlinearities on aeroelastic characteristics are investigated.

Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. III. Twist Number Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Y.; Pariat, E.; Moraitis, K.

We study the writhe, twist, and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free Titov–Démoulin equilibrium solution, non-force-free magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by the Berger–Prior formula, which is suitable for arbitrary geometry and both force-free and non-force-free models. The magnetic helicity is estimated by the twistmore » multiplied by the square of the axial magnetic flux. We compare the obtained values with those derived by a finite volume helicity estimation method. We find that the magnetic helicity obtained with the twist method agrees with the helicity carried by the purely current-carrying part of the field within uncertainties for most test cases. It is also found that the current-carrying part of the model field is relatively significant at the very location of the magnetic flux rope. This qualitatively explains the agreement between the magnetic helicity computed by the twist method and the helicity contributed purely by the current-carrying magnetic field.« less

Efficient Nonlinear Atomization Model for Thin 3D Free Liquid Films

NASA Astrophysics Data System (ADS)

Mehring, Carsten

2007-03-01

Reviewed is a nonlinear reduced-dimension thin-film model developed by the author and aimed at the prediction of spray formation from thin films such as those found in gas-turbine engines (e.g., prefilming air-blast atomizers), heavy-fuel-oil burners (e.g., rotary-cup atomizers) and in the paint industry (e.g., flat-fan atomizers). Various implementations of the model focusing on different model-aspects, i.e., effect of film geometry, surface tension, liquid viscosity, coupling with surrounding gas-phase flow, influence of long-range intermolecular forces during film rupture are reviewed together with a validation of the nonlinear wave propagation characteristics predicted by the model for inviscid planar films using a two-dimensional vortex- method. An extension and generalization of the current nonlinear film model for implementation into a commercial flow- solver is outlined.

Special class of nonlinear damping models in flexible space structures

NASA Technical Reports Server (NTRS)

Hu, Anren; Singh, Ramendra P.; Taylor, Lawrence W.

1991-01-01

A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.

Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1988-01-01

The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.

Growth and wall-transpiration control of nonlinear unsteady Görtler vortices forced by free-stream vortical disturbances

NASA Astrophysics Data System (ADS)

Marensi, Elena; Ricco, Pierre

2017-11-01

The generation, nonlinear evolution, and wall-transpiration control of unsteady Görtler vortices in an incompressible boundary layer over a concave plate is studied theoretically and numerically. Görtler rolls are initiated and driven by free-stream vortical perturbations of which only the low-frequency components are considered because they penetrate the most into the boundary layer. The formation and development of the disturbances are governed by the nonlinear unsteady boundary-region equations with the centrifugal force included. These equations are subject to appropriate initial and outer boundary conditions, which account for the influence of the upstream and free-stream forcing in a rigorous and mutually consistent manner. Numerical solutions show that the stabilizing effect on nonlinearity, which also occurs in flat-plate boundary layers, is significantly enhanced in the presence of centrifugal forces. Sufficiently downstream, the nonlinear vortices excited at different free-stream turbulence intensities Tu saturate at the same level, proving that the initial amplitude of the forcing becomes unimportant. At low Tu, the disturbance exhibits a quasi-exponential growth with the growth rate being intensified for more curved plates and for lower frequencies. At higher Tu, in the typical range of turbomachinery applications, the Görtler vortices do not undergo a modal stage as nonlinearity saturates rapidly, and the wall curvature does not affect the boundary-layer response. Good quantitative agreement with data from direct numerical simulations and experiments is obtained. Steady spanwise-uniform and spanwise-modulated zero-mass-flow-rate wall transpiration is shown to attenuate the growth of the Görtler vortices significantly. A novel modified version of the Fukagata-Iwamoto-Kasagi identity, used for the first time to study a transitional flow, reveals which terms in the streamwise momentum balance are mostly affected by the wall transpiration, thus offering insight into the increased nonlinear growth of the wall-shear stress.

Casting the Coronal Magnetic Field Reconstructions with Magnetic Field Constraints above the Photosphere in 3D Using MHD Bifrost Model

NASA Astrophysics Data System (ADS)

Fleishman, G. D.; Anfinogentov, S.; Loukitcheva, M.; Mysh'yakov, I.; Stupishin, A.

2017-12-01

Measuring and modeling coronal magnetic field, especially above active regions (ARs), remains one of the central problems of solar physics given that the solar coronal magnetism is the key driver of all solar activity. Nowadays the coronal magnetic field is often modelled using methods of nonlinear force-free field reconstruction, whose accuracy has not yet been comprehensively assessed. Given that the coronal magnetic probing is routinely unavailable, only morphological tests have been applied to evaluate performance of the reconstruction methods and a few direct tests using available semi-analytical force-free field solution. Here we report a detailed casting of various tools used for the nonlinear force-free field reconstruction, such as disambiguation methods, photospheric field preprocessing methods, and volume reconstruction methods in a 3D domain using a 3D snapshot of the publicly available full-fledged radiative MHD model. We take advantage of the fact that from the realistic MHD model we know the magnetic field vector distribution in the entire 3D domain, which enables us to perform "voxel-by-voxel" comparison of the restored magnetic field and the true magnetic field in the 3D model volume. Our tests show that the available disambiguation methods often fail at the quiet sun areas, where the magnetic structure is dominated by small-scale magnetic elements, while they work really well at the AR photosphere and (even better) chromosphere. The preprocessing of the photospheric magnetic field, although does produce a more force-free boundary condition, also results in some effective `elevation' of the magnetic field components. The effective `elevation' height turns out to be different for the longitudinal and transverse components of the magnetic field, which results in a systematic error in absolute heights in the reconstructed magnetic data cube. The extrapolation performed starting from actual AR photospheric magnetogram (i.e., without preprocessing) are free from this systematic error, while have other metrics either comparable or only marginally worse than those estimated for extrapolations from the preprocessed magnetograms. This finding favors the use of extrapolations from the original photospheric magnetogram without preprocessing.

Discrete-vortex model for the symmetric-vortex flow on cones

NASA Technical Reports Server (NTRS)

Gainer, Thomas G.

1990-01-01

A relatively simple but accurate potential flow model was developed for studying the symmetric vortex flow on cones. The model is a modified version of the model first developed by Bryson, in which discrete vortices and straight-line feeding sheets were used to represent the flow field. It differs, however, in the zero-force condition used to position the vortices and determine their circulation strengths. The Bryson model imposed the condition that the net force on the feeding sheets and discrete vortices must be zero. The proposed model satisfies this zero-force condition by having the vortices move as free vortices, at a velocity equal to at the local crossflow velocity at their centers. When the free-vortex assumption is made, a solution is obtained in the form of two nonlinear algebraic equations that relate the vortex center coordinates and vortex strengths to the cone angle and angle of attack. The vortex center locations calculated using the model are in good agreement with experimental values. The cone normal forces as well as center locations are in good agreement with the vortex cloud method of calculating symmetric flow fields.

Fresnel formulas for the forced electromagnetic pulses and their application for optical-to-terahertz conversion in nonlinear crystals.

PubMed

Bakunov, M I; Maslov, A V; Bodrov, S B

2007-11-16

We show that the usual Fresnel formulas for a free-propagating pulse are not applicable for a forced terahertz electromagnetic pulse supported by an optical pulse at the end of a nonlinear crystal. The correct linear reflection and transmission coefficients that we derive show that such pulses can experience a gain or loss at the boundary. This energy change depends on linear dielectric constants only. We also predict a regime where a complete disappearance of the forced pulse under oblique incidence occurs, an effect that has no counterpart for free-propagating pulses.

Characterization of structural connections using free and forced response test data

NASA Technical Reports Server (NTRS)

Lawrence, Charles; Huckelbridge, Arthur A.

1989-01-01

The accurate prediction of system dynamic response often has been limited by deficiencies in existing capabilities to characterize connections adequately. Connections between structural components often are complex mechanically, and difficult to accurately model analytically. Improved analytical models for connections are needed to improve system dynamic preditions. A procedure for identifying physical connection properties from free and forced response test data is developed, then verified utilizing a system having both a linear and nonlinear connection. Connection properties are computed in terms of physical parameters so that the physical characteristics of the connections can better be understood, in addition to providing improved input for the system model. The identification procedure is applicable to multi-degree of freedom systems, and does not require that the test data be measured directly at the connection locations.

Dynamics of ultraharmonic resonances in spiral galaxies

NASA Technical Reports Server (NTRS)

Artymowicz, Pawel; Lubow, Stephen H.

1992-01-01

The mildly nonlinear response of a fluid disk with pressure, viscosity, and self-gravity to spiral stellar forcing is considered as a model of the interstellar medium in spiral galaxies. Nonlinear effects are analyzed through a quasi-linear flow analysis ordered by successive powers of a dimensionless spiral perturbing force, which is the ratio of imposed nonaxisymmetric gravitational to axisymmetric gravitational forces. Waves with mn arms are launched from a position where the wavenumber of a free wave matches n times the wavenumber of the spiral forcing. The launched short wave in the gas is an interarm feature that is more tightly wrapped than the stellar wave. The gas wave extracts energy and angular momentum from the stellar wave, causing it to damp. The application of the results to the stellar disk alone reveals even stronger damping, as stars undergo Landau damping of the short wave. For parameters in M81, damping times are less than 10 exp 9 yr.

Identification of nonlinear modes using phase-locked-loop experimental continuation and normal form

NASA Astrophysics Data System (ADS)

Denis, V.; Jossic, M.; Giraud-Audine, C.; Chomette, B.; Renault, A.; Thomas, O.

2018-06-01

In this article, we address the model identification of nonlinear vibratory systems, with a specific focus on systems modeled with distributed nonlinearities, such as geometrically nonlinear mechanical structures. The proposed strategy theoretically relies on the concept of nonlinear modes of the underlying conservative unforced system and the use of normal forms. Within this framework, it is shown that without internal resonance, a valid reduced order model for a nonlinear mode is a single Duffing oscillator. We then propose an efficient experimental strategy to measure the backbone curve of a particular nonlinear mode and we use it to identify the free parameters of the reduced order model. The experimental part relies on a Phase-Locked Loop (PLL) and enables a robust and automatic measurement of backbone curves as well as forced responses. It is theoretically and experimentally shown that the PLL is able to stabilize the unstable part of Duffing-like frequency responses, thus enabling its robust experimental measurement. Finally, the whole procedure is tested on three experimental systems: a circular plate, a chinese gong and a piezoelectric cantilever beam. It enable to validate the procedure by comparison to available theoretical models as well as to other experimental identification methods.

Magnetic diffusion and flare energy buildup

NASA Technical Reports Server (NTRS)

Wu, S. T.; Yin, C. L.; Yang, W.-H.

1992-01-01

Photospheric motion shears or twists solar magnetic fields to increase magnetic energy in the corona, because this process may change a current-free state of a coronal field to force-free states which carry electric current. This paper analyzes both linear and nonlinear 2D force-free magnetic field models and derives relations of magnetic energy buildup with photospheric velocity field. When realistic data of solar magnetic field and photospheric velocity field are used, it is found that 3-4 hours are needed to create an amount of free magnetic energy which is of the order of the current-free field energy. Furthermore, the paper studies situations in which finite magnetic diffusivities in photospheric plasma are introduced. The shearing motion increases coronal magnetic energy, while the photospheric diffusion reduces the energy. The variation of magnetic energy in the coronal region, then, depends on which process dominates.

One-dimensional Vlasov-Maxwell equilibrium for the force-free Harris sheet.

PubMed

Harrison, Michael G; Neukirch, Thomas

2009-04-03

In this Letter, the first nonlinear force-free Vlasov-Maxwell equilibrium is presented. One component of the equilibrium magnetic field has the same spatial structure as the Harris sheet, but whereas the Harris sheet is kept in force balance by pressure gradients, in the force-free solution presented here force balance is maintained by magnetic shear. Magnetic pressure, plasma pressure and plasma density are constant. The method used to find the equilibrium is based on the analogy of the one-dimensional Vlasov-Maxwell equilibrium problem to the motion of a pseudoparticle in a two-dimensional conservative potential. The force-free solution can be generalized to a complete family of equilibria that describe the transition between the purely pressure-balanced Harris sheet to the force-free Harris sheet.

Violent transient sloshing-wave interaction with a baffle in a three-dimensional numerical tank

NASA Astrophysics Data System (ADS)

Xue, Mi-An; Zheng, Jinhai; Lin, Pengzhi; Xiao, Zhong

2017-08-01

A finite difference model for solving Navier Stokes equations with turbulence taken into account is used to investigate viscous liquid sloshing-wave interaction with baffles in a tank. The volume-of-fluid and virtual boundary force methods are employed to simulate free surface flow interaction with structures. A liquid sloshing experimental apparatus was established to evaluate the accuracy of the proposed model, as well as to study nonlinear sloshing in a prismatic tank with the baffles. Damping effects of sloshing in a rectangular tank with bottom-mounted vertical baffles and vertical baffles touching the free surface are studied numerically and experimentally. Good agreement is obtained between the present numerical results and experimental data. The numerical results match well with the current experimental data for strong nonlinear sloshing with large free surface slopes. The reduction in sloshing-wave elevation and impact pressure induced by the bottom-mounted vertical baffle and the vertical baffle touching the free surface is estimated by varying the external excitation frequency and the location and height of the vertical baffle under horizontal excitation.

Nonlinear vibration of a traveling belt with non-homogeneous boundaries

NASA Astrophysics Data System (ADS)

Ding, Hu; Lim, C. W.; Chen, Li-Qun

2018-06-01

Free and forced nonlinear vibrations of a traveling belt with non-homogeneous boundary conditions are studied. The axially moving materials in operation are always externally excited and produce strong vibrations. The moving materials with the homogeneous boundary condition are usually considered. In this paper, the non-homogeneous boundaries are introduced by the support wheels. Equilibrium deformation of the belt is produced by the non-homogeneous boundaries. In order to solve the equilibrium deformation, the differential and integral quadrature methods (DIQMs) are utilized to develop an iterative scheme. The influence of the equilibrium deformation on free and forced nonlinear vibrations of the belt is explored. The DIQMs are applied to solve the natural frequencies and forced resonance responses of transverse vibration around the equilibrium deformation. The Galerkin truncation method (GTM) is utilized to confirm the DIQMs' results. The numerical results demonstrate that the non-homogeneous boundary conditions cause the transverse vibration to deviate from the straight equilibrium, increase the natural frequencies, and lead to coexistence of square nonlinear terms and cubic nonlinear terms. Moreover, the influence of non-homogeneous boundaries can be exacerbated by the axial speed. Therefore, non-homogeneous boundary conditions of axially moving materials especially should be taken into account.

Peeling off an elastica from a smooth attractive substrate

NASA Astrophysics Data System (ADS)

Oyharcabal, Xabier; Frisch, Thomas

2005-03-01

Using continuum mechanics, we study theoretically the unbinding of an inextensible rod with free ends attracted by a smooth substrate and submitted to a vertical force. We use the elastica model in a medium-range van der Waals potential. We numerically solve a nonlinear boundary value problem and obtain the force-stretching relation at zero temperature. We obtain the critical force for which the rod unbinds from the substrate as a function of three dimensionless parameters, and we find two different regimes of adhesion. We study analytically the contact potential case as the van der Waals radius goes to zero.

Large Deflection of Ideal Pseudo-Elastic Shape Memory Alloy Cantilever Beam

NASA Astrophysics Data System (ADS)

Cui, Shitang; Hu, Liming; Yan, Jun

This paper deals with the large deflections of pseudo-elastic shape memory alloy cantilever beams subjected to a concentrated load at the free end. Because of the large deflections, geometry nonlinearity arises and this analysis employs the nonlinear bending theory. The exact expression of curvature is used in the moment-curvature relationship. As a vertical force at the tip of cantilever, curvature and bending moment distribution expressions are deduced. The curvature changed distinctly when the surface material undergoes phase transformation. The length of phase transformation region was affected greatly with the force at the free end.

Nonlinear time-periodic models of the longitudinal flight dynamics of desert locusts Schistocerca gregaria

PubMed Central

Taylor, Graham K; Żbikowski, Rafał

2005-01-01

Previous studies of insect flight control have been statistical in approach, simply correlating wing kinematics with body kinematics or force production. Kinematics and forces are linked by Newtonian mechanics, so adopting a dynamics-based approach is necessary if we are to place the study of insect flight on its proper physical footing. Here we develop semi-empirical models of the longitudinal flight dynamics of desert locusts Schistocerca gregaria. We use instantaneous force–moment measurements from individual locusts to parametrize the nonlinear rigid body equations of motion. Since the instantaneous forces are approximately periodic, we represent them using Fourier series, which are embedded in the equations of motion to give a nonlinear time-periodic (NLTP) model. This is a proper mathematical generalization of an earlier linear-time invariant (LTI) model of locust flight dynamics, developed using previously published time-averaged versions of the instantaneous force recordings. We perform various numerical simulations, within the fitted range of the model, and across the range of body angles used by free-flying locusts, to explore the likely behaviour of the locusts upon release from the tether. Solutions of the NLTP models are compared with solutions of the nonlinear time-invariant (NLTI) models to which they reduce when the periodic terms are dropped. Both sets of models are unstable and therefore fail to explain locust flight stability fully. Nevertheless, whereas the measured forces include statistically significant harmonic content up to about the eighth harmonic, the simulated flight trajectories display no harmonic content above the fundamental forcing frequency. Hence, manoeuvre control in locusts will not directly reflect subtle changes in the higher harmonics of the wing beat, but must operate on a coarser time-scale. A state-space analysis of the NLTP models reveals orbital trajectories that are impossible to capture in the LTI and NLTI models, and inspires the hypothesis that asymptotic orbital stability is the proper definition of stability in flapping flight. Manoeuvre control on the scale of more than one wing beat would then consist in exciting transients from one asymptotically stable orbit to another. We summarize these hypotheses by proposing a limit-cycle analogy for flapping flight control and suggest experiments for verification of the limit-cycle control analogy hypothesis. PMID:16849180

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1987-01-01

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

Nonparametric identification of nonlinear dynamic systems using a synchronisation-based method

NASA Astrophysics Data System (ADS)

Kenderi, Gábor; Fidlin, Alexander

2014-12-01

The present study proposes an identification method for highly nonlinear mechanical systems that does not require a priori knowledge of the underlying nonlinearities to reconstruct arbitrary restoring force surfaces between degrees of freedom. This approach is based on the master-slave synchronisation between a dynamic model of the system as the slave and the real system as the master using measurements of the latter. As the model synchronises to the measurements, it becomes an observer of the real system. The optimal observer algorithm in a least-squares sense is given by the Kalman filter. Using the well-known state augmentation technique, the Kalman filter can be turned into a dual state and parameter estimator to identify parameters of a priori characterised nonlinearities. The paper proposes an extension of this technique towards nonparametric identification. A general system model is introduced by describing the restoring forces as bilateral spring-dampers with time-variant coefficients, which are estimated as augmented states. The estimation procedure is followed by an a posteriori statistical analysis to reconstruct noise-free restoring force characteristics using the estimated states and their estimated variances. Observability is provided using only one measured mechanical quantity per degree of freedom, which makes this approach less demanding in the number of necessary measurement signals compared with truly nonparametric solutions, which typically require displacement, velocity and acceleration signals. Additionally, due to the statistical rigour of the procedure, it successfully addresses signals corrupted by significant measurement noise. In the present paper, the method is described in detail, which is followed by numerical examples of one degree of freedom (1DoF) and 2DoF mechanical systems with strong nonlinearities of vibro-impact type to demonstrate the effectiveness of the proposed technique.

Non-linear dynamic analysis of geared systems, part 2

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

PubMed

Frey Law, Laura A; Shields, Richard K

2006-03-01

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

Elastohydrodynamics of microfilament under distributed body actuation

NASA Astrophysics Data System (ADS)

Singh, T. Sonamani; Yadava, R. D. S.

2018-05-01

The dynamics of an active filament in low Reynolds (Re) number regime is analyzed under distributed body actuation represented by the sliding filament model. The governing elastohydrodynamic equations are formulated by assuming the resistive force theory (RFT). The effect of geometric nonlinearity in bending stiffness on the propulsive thrust has been analyzed where the former is introduced by cross-sectional tapering. Two types of boundary conditions (clamped-free and hinged-free) are analyzed. A comparison with the uniform filament dynamics reveals that the tapering enhances the thrust under both types of boundary conditions.

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.

Influence of impeller shroud forces on turbopump rotor dynamics

NASA Technical Reports Server (NTRS)

Williams, J. P.; Childs, Dara W.

1993-01-01

The shrouded-impeller leakage path forces calculated by Childs have been analyzed to answer two questions. First, because of certain characteristics or the results of Childs, the forces could not be modeled with traditional approaches. Therefore, an approach has been devised to include the forces in conventional rotordynamic analyses. The forces were found to be well-modeled with this approach. Finally, the effect these forces had on a simple rotor-bearing system was analyzed, and, therefore, they, in addition to seal forces, were applied to a Jeffcott rotor. The traditional methods of dynamic system analysis were modified to incorporate the impeller forces and yielded results for the eigenproblem, frequency response, critical speed, transient response, and an iterative technique for finding the frequency of free vibration as well as system stability. All results lead to the conclusion that the forces have little influence on natural frequency but can have appreciable effects on system stability. Specifically, at higher values of fluid swirl at the leakage path entrance, relative stability is reduced. The only unexpected response characteristics that occurred are attributed to the nonlinearity of the model.

Modeling the free energy surfaces of electron transfer in condensed phases

NASA Astrophysics Data System (ADS)

Matyushov, Dmitry V.; Voth, Gregory A.

2000-10-01

We develop a three-parameter model of electron transfer (ET) in condensed phases based on the Hamiltonian of a two-state solute linearly coupled to a harmonic, classical solvent mode with different force constants in the initial and final states (a classical limit of the quantum Kubo-Toyozawa model). The exact analytical solution for the ET free energy surfaces demonstrates the following features: (i) the range of ET reaction coordinates is limited by a one-sided fluctuation band, (ii) the ET free energies are infinite outside the band, and (iii) the free energy surfaces are parabolic close to their minima and linear far from the minima positions. The model provides an analytical framework to map physical phenomena conflicting with the Marcus-Hush two-parameter model of ET. Nonlinear solvation, ET in polarizable charge-transfer complexes, and configurational flexibility of donor-acceptor complexes are successfully mapped onto the model. The present theory leads to a significant modification of the energy gap law for ET reactions.

Nonlinear aeroservoelastic analysis of a controlled multiple-actuated-wing model with free-play

NASA Astrophysics Data System (ADS)

Huang, Rui; Hu, Haiyan; Zhao, Yonghui

2013-10-01

In this paper, the effects of structural nonlinearity due to free-play in both leading-edge and trailing-edge outboard control surfaces on the linear flutter control system are analyzed for an aeroelastic model of three-dimensional multiple-actuated-wing. The free-play nonlinearities in the control surfaces are modeled theoretically by using the fictitious mass approach. The nonlinear aeroelastic equations of the presented model can be divided into nine sub-linear modal-based aeroelastic equations according to the different combinations of deflections of the leading-edge and trailing-edge outboard control surfaces. The nonlinear aeroelastic responses can be computed based on these sub-linear aeroelastic systems. To demonstrate the effects of nonlinearity on the linear flutter control system, a single-input and single-output controller and a multi-input and multi-output controller are designed based on the unconstrained optimization techniques. The numerical results indicate that the free-play nonlinearity can lead to either limit cycle oscillations or divergent motions when the linear control system is implemented.

Three-dimensional simulation of the motion of a single particle under a simulated turbulent velocity field

NASA Astrophysics Data System (ADS)

Moreno-Casas, P. A.; Bombardelli, F. A.

2015-12-01

A 3D Lagrangian particle tracking model is coupled to a 3D channel velocity field to simulate the saltation motion of a single sediment particle moving in saltation mode. The turbulent field is a high-resolution three dimensional velocity field that reproduces a by-pass transition to turbulence on a flat plate due to free-stream turbulence passing above de plate. In order to reduce computational costs, a decoupled approached is used, i.e., the turbulent flow is simulated independently from the tracking model, and then used to feed the 3D Lagrangian particle model. The simulations are carried using the point-particle approach. The particle tracking model contains three sub-models, namely, particle free-flight, a post-collision velocity and bed representation sub-models. The free-flight sub-model considers the action of the following forces: submerged weight, non-linear drag, lift, virtual mass, Magnus and Basset forces. The model also includes the effect of particle angular velocity. The post-collision velocities are obtained by applying conservation of angular and linear momentum. The complete model was validated with experimental results from literature within the sand range. Results for particle velocity time series and distribution of particle turbulent intensities are presented.

Origin and structures of solar eruptions II: Magnetic modeling

NASA Astrophysics Data System (ADS)

Guo, Yang; Cheng, Xin; Ding, MingDe

2017-07-01

The topology and dynamics of the three-dimensional magnetic field in the solar atmosphere govern various solar eruptive phenomena and activities, such as flares, coronal mass ejections, and filaments/prominences. We have to observe and model the vector magnetic field to understand the structures and physical mechanisms of these solar activities. Vector magnetic fields on the photosphere are routinely observed via the polarized light, and inferred with the inversion of Stokes profiles. To analyze these vector magnetic fields, we need first to remove the 180° ambiguity of the transverse components and correct the projection effect. Then, the vector magnetic field can be served as the boundary conditions for a force-free field modeling after a proper preprocessing. The photospheric velocity field can also be derived from a time sequence of vector magnetic fields. Three-dimensional magnetic field could be derived and studied with theoretical force-free field models, numerical nonlinear force-free field models, magnetohydrostatic models, and magnetohydrodynamic models. Magnetic energy can be computed with three-dimensional magnetic field models or a time series of vector magnetic field. The magnetic topology is analyzed by pinpointing the positions of magnetic null points, bald patches, and quasi-separatrix layers. As a well conserved physical quantity, magnetic helicity can be computed with various methods, such as the finite volume method, discrete flux tube method, and helicity flux integration method. This quantity serves as a promising parameter characterizing the activity level of solar active regions.

Modelling of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

Lehmann, M.; Schmidt, J.; Salo, H.

2014-04-01

Density wave theory, originally proposed to explain the spiral structure of galactic disks, has been applied to explain parts of the complex sub-structure in Saturn's rings, such as the wavetrains excited at the inner Lindblad resonances (ILR) of various satellites. The linear theory for the excitation and damping of density waves in Saturn's rings is fairly well developed (e.g. Goldreich & Tremaine [1979]; Shu [1984]). However, it fails to describe certain aspects of the observed waves. The non-applicability of the linear theory is already indicated by the "cusplike" shape of many of the observed wave profiles. This is a typical nonlinear feature which is also present in overstability wavetrains (Schmidt & Salo [2003]; Latter & Ogilvie [2010]). In particular, it turns out that the detailed damping mechanism, as well as the role of different nonlinear effects on the propagation of density waves remain intransparent. First attemps are being made to investigate the excitation and propagation of nonlinear density waves within a hydrodynamical formalism, which is also the natural formalism for describing linear density waves. A simple weakly nonlinear model, derived from a multiple-scale expansion of the hydrodynamic equations, is presented. This model describes the damping of "free" spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients, where the effects of the hydrodynamic nonlinearities are included. The model predicts that density waves are linearly unstable in a ring region where the conditions for viscous overstability are met, which translates to a steep dependence of the shear viscosity with respect to the disk's surface density. The possibility that this dependence could lead to a growth of density waves with increasing distance from the resonance, was already mentioned in Goldreich & Tremaine [1978]. Sufficiently far away from the ILR, the surface density perturbation caused by the wave, is predicted to saturate to a constant value due to the effects of nonlinear viscous damping. A qualitatively similar behaviour has also been predicted for the damping of nonlinear density waves, as described within a streamline formalism (Borderies, Goldreich & Tremaine [1985]). The damping lengths which follow from the weakly nonlinear model depend more or less strongly on a set of different input parameters, such as the viscosity and the surface density of the unperturbed ring state. Further, they depend on the wave's amplitude at resonance. For a real wave, which has been excited by an external satellite, this amplitude can be deduced from the magnitude of the satellite's forcing potential. Appart from that, hydrodynamical simulations are being developed to study the nonlinear damping of resonantly forced density waves.

A new class of exact, nonlinear solutions to the Grad-Shafranov equation

NASA Technical Reports Server (NTRS)

Roumeliotis, George

1993-01-01

We have constructed a new class of exact, nonlinear solutions to the Grad-Shafranov equation, representing force-free magnetic fields with translational symmetry. These exact solutions are pertinent to the study of magnetic structures in the solar corona that are subjected to photospheric shearing motions.

Effect of Second-Order and Fully Nonlinear Wave Kinematics on a Tension-Leg-Platform Wind Turbine in Extreme Wave Conditions: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robertson, Amy N; Jonkman, Jason; Pegalajar-Jurado, Antonio

In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equation for the hydrodynamic forcing. The wave kinematics are computed from either theoretical or measured signals of free-surface elevation. The numerical results from each model are compared to results from wave basin tests on a scaled prototype. The comparison shows that sub and superharmonic responses can be introduced by second-order and fully nonlinear wave kinematics. The response at themore » wave frequency range is better reproduced when kinematics are generated from the measured surface elevation. In the future, the numerical response may be further improved by replacing the global, constant damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping.« less

Effect of Second-Order and Fully Nonlinear Wave Kinematics on a Tension-Leg-Platform Wind Turbine in Extreme Wave Conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Robertson, Amy N; Jonkman, Jason; Pegalajar-Jurado, Antonio

In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equation for the hydrodynamic forcing. The wave kinematics are computed from either theoretical or measured signals of free-surface elevation. The numerical results from each model are compared to results from wave basin tests on a scaled prototype. The comparison shows that sub and superharmonic responses can be introduced by second-order and fully nonlinear wave kinematics. The response at themore » wave frequency range is better reproduced when kinematics are generated from the measured surface elevation. In the future, the numerical response may be further improved by replacing the global, constant damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping.« less

Nonlinear microrheology of dense colloidal suspensions: A mode-coupling theory

NASA Astrophysics Data System (ADS)

Gazuz, I.; Fuchs, M.

2013-03-01

A mode-coupling theory for the motion of a strongly forced probe particle in a dense colloidal suspension is presented. Starting point is the Smoluchowski equation for N bath and a single probe particle. The probe performs Brownian motion under the influence of a strong constant and uniform external force Fex. It is immersed in a dense homogeneous bath of (different) particles also performing Brownian motion. Fluid and glass states are considered; solvent flow effects are neglected. Based on a formally exact generalized Green-Kubo relation, mode coupling approximations are performed and an integration through transients approach applied. A microscopic theory for the nonlinear velocity-force relations of the probe particle in a dense fluid and for the (de-) localized probe in a glass is obtained. It extends the mode coupling theory of the glass transition to strongly forced tracer motion and describes active microrheology experiments. A force threshold is identified which needs to be overcome to pull the probe particle free in a glass. For the model of hard sphere particles, the microscopic equations for the threshold force and the probability density of the localized probe are solved numerically. Neglecting the spatial structure of the theory, a schematic model is derived which contains two types of bifurcation, the glass transition and the force-induced delocalization, and which allows for analytical and numerical solutions. We discuss its phase diagram, forcing effects on the time-dependent correlation functions, and the friction increment. The model was successfully applied to simulations and experiments on colloidal hard sphere systems [Gazuz , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.102.248302 102, 248302 (2009)], while we provide detailed information on its derivation and general properties.

Reaction Force of Micro-scale Liquid Droplets Constrained Between Parallel Plates through CFD

NASA Astrophysics Data System (ADS)

Free, Robert; Hekiri, Haider; Hawa, Takumi

2012-02-01

Micro-scale liquid droplets responding to depression between parallel plates are investigated analytically and numerically. The functional dependence of the reaction force accrued in such droplets on droplet size, surface tension, depression amount, and contact angle is explored. For both the 2D and 3D case, an analytical model is developed based on first principles. Computational fluid dynamics is then utilized to evaluate the validity of these models. The reaction force is highly nonlinear, initially increasing very slowly with increasing depression of the droplet, but eventually moving asymptotically to infinity. The force scales linearly with both the droplet free radius and surface tension of the liquid, but has a much more complicated dependence on the contact angle and depression. Explicit expressions for the reaction force have been determined, showing these dependencies. The 3D model has been largely supported by the CFD results. It very accurately predicts the reaction force on the upper plate as the droplet is crushed, accounting for the effect of contact angle, surface tension, and droplet size.

Electrostatic and aerodynamic forced vibrations of a thin flexible electrode: Quasi-periodic vs. chaotic oscillations.

PubMed

Madanu, Sushma B; Barbel, Stanley I; Ward, Thomas

2016-06-01

In this paper, transverse vibrations of an electrostatically actuated thin flexible cantilever perturbed by low-speed air flow are studied using both experiments and numerical modeling. In the experiments, the dynamic characteristics of the cantilever are studied by supplying a DC voltage with an AC component for electrostatic forcing and a constant uniform air flow around the cantilever system for aerodynamic forcing. A range of control parameters leading to stable vibrations are established using a dimensionless operating parameter that is the ratio of the induced and the free stream velocities. Numerical results are validated with experimental data. Assuming the amplitude of vibrations are small, then a non-linear dynamic Euler-Bernoulli beam equation with viscous damping and gravitational effects is used to model the equation of motion. Aerodynamic forcing is modelled as a temporally sinusoidal and uniform force acting perpendicular to the beam length. The forcing amplitude is found to be proportional to the square of the air flow velocity. Numerical results strongly agree with the experiments predicting accurate vibration amplitude, displacement frequency, and quasi-periodic displacement of the cantilever tip.

Development of a piezo-actuated micro-teleoperation system for cell manipulation.

PubMed

Zareinejad, M; Rezaei, S M; Abdullah, A; Shiry Ghidary, S

2009-03-01

Intracytoplasmic sperm injection (ICSI) requires long training and has low success rates, primarily due to poor control over the injection force. Making force feedback available to the operator will improve the success rate of the injection task. A macro-micro-teleoperation system bridges the gap between the task performed at the micro-level and the macroscopic movements of the operator. The teleoperation slave manipulator should accurately position a needle to precisely penetrate a cell membrane. Piezoelectric actuators are widely used in micromanipulation applications; however, hysteresis non-linearity limits the accuracy of these actuators. This paper presents a novel approach for utilizing a piezoelectric nano-stage as slave manipulator of a teleoperation system. The Prandtl-Ishlinskii (PI) model is used to model actuator hysteresis in a feedforward scheme to cancel out this non-linearity. To deal with the influence of parametric uncertainties, unmodelled dynamics and PI identification error, a perturbation term is added to the slave model and applies a sliding mode-based impedance control with perturbation estimation. The stability of entire system is guaranteed by Llewellyn's absolute stability criterion. The performance of the proposed controller was investigated through experiments for cell membrane penetration. The experimental results verified the accurate position tracking in free motion and simultaneous position and force tracking in contact with a low stiffness environment.

Screening fifth forces in k-essence and DBI models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brax, Philippe; Burrage, Clare; Davis, Anne-Christine, E-mail: Philippe.Brax@cea.fr, E-mail: Clare.Burrage@nottingham.ac.uk, E-mail: A.C.Davis@damtp.cam.ac.uk

New fifth forces have not yet been detected in the laboratory or in the solar system, hence it is typically difficult to introduce new light scalar fields that would mediate such forces. In recent years it has been shown that a number of non-linear scalar field theories allow for a dynamical mechanism, such as the Vainshtein and chameleon ones, that suppresses the strength of the scalar fifth force in experimental environments. This is known as screening, however it is unclear how common screening is within non-linear scalar field theories. k-essence models are commonly studied examples of non-linear models, with DBImore » as the best motivated example, and so we ask whether these non-linearities are able to screen a scalar fifth force. We find that a Vainshtein-like screening mechanism exists for such models although with limited applicability. For instance, we cannot find a screening mechanism for DBI models. On the other hand, we construct a large class of k-essence models which lead to the acceleration of the Universe in the recent past for which the fifth force mediated by the scalar can be screened.« less

New LMI based gain-scheduling control for recovering contact-free operation of a magnetically levitated rotor

NASA Astrophysics Data System (ADS)

Wang, M.; Cole, M. O. T.; Keogh, P. S.

2017-11-01

A new approach for the recovery of contact-free levitation of a rotor supported by active magnetic bearings (AMB) is assessed through control strategy design, system modelling and experimental verification. The rotor is considered to make contact with a touchdown bearing (TDB), which may lead to entrapment in a bi-stable nonlinear response. A linear matrix inequality (LMI) based gain-scheduling H∞ control technique is introduced to recover the rotor to a contact-free state. The controller formulation involves a time-varying effective stiffness parameter, which can be evaluated in terms of forces transmitted through the TDB. Rather than measuring these forces directly, an observer is introduced with a model of the base structure to transform base acceleration signals using polytopic coordinates for controller adjustment. Force transmission to the supporting base structure will occur either through an AMB alone without contact, or through the AMB and TDB with contact and this must be accounted for in the observer design. The controller is verified experimentally in terms of (a) non-contact robust stability and vibration suppression performance; (b) control action for contact-free recovery at typical running speeds with various unbalance and TDB misalignment conditions; and (c) coast-down experimental tests. The results demonstrate the effectiveness of the AMB control action whenever it operates within its dynamic load capacity.

Nonlinear Acoustic Propagation into the Seafloor

NASA Astrophysics Data System (ADS)

McDonald, B. Edward

2006-05-01

Explosions near the seafloor result in shock waves entering a much more complicated medium than water or air. Nonlinearities may be increased by two processes inherent to granular media: (1) a poroelastic nonlinearity comparable to the addition of bubbles to water, and (2) the Hertz force resulting from elastic deformation of grains, proportional to the Youngs modulus of the grains times the strain rate to the power 3/2. These two types of nonlinearity for shock propagation into the seafloor are investigated using a variant of the NPE model. The traditional Taylor series expansion of the equation of state (pressure as a function of density) is not appropriate to the Hertz force in the limit of small strain. We present a simple nonlinear wave equation model for compressional waves in marine sediments that retains the Hertz force explicitly with overdensity to the power 3/2. Numerical results for shock propagation are compared with similarity solutions for quadratic nonlinearity and for the fractional nonlinearity of the Hertz force.

A dynamic load estimation method for nonlinear structures with unscented Kalman filter

NASA Astrophysics Data System (ADS)

Guo, L. N.; Ding, Y.; Wang, Z.; Xu, G. S.; Wu, B.

2018-02-01

A force estimation method is proposed for hysteretic nonlinear structures. The equation of motion for the nonlinear structure is represented in state space and the state variable is augmented by the unknown the time history of external force. Unscented Kalman filter (UKF) is improved for the force identification in state space considering the ill-condition characteristic in the computation of square roots for the covariance matrix. The proposed method is firstly validated by a numerical simulation study of a 3-storey nonlinear hysteretic frame excited by periodic force. Each storey is supposed to follow a nonlinear hysteretic model. The external force is identified and the measurement noise is considered in this case. Then a case of a seismically isolated building subjected to earthquake excitation and impact force is studied. The isolation layer performs nonlinearly during the earthquake excitation. Impact force between the seismically isolated structure and the retaining wall is estimated with the proposed method. Uncertainties such as measurement noise, model error in storey stiffness and unexpected environmental disturbances are considered. A real-time substructure testing of an isolated structure is conducted to verify the proposed method. In the experimental study, the linear main structure is taken as numerical substructure while the one of the isolations with additional mass is taken as the nonlinear physical substructure. The force applied by the actuator on the physical substructure is identified and compared with the measured value from the force transducer. The method proposed in this paper is also validated by shaking table test of a seismically isolated steel frame. The acceleration of the ground motion as the unknowns is identified by the proposed method. Results from both numerical simulation and experimental studies indicate that the UKF based force identification method can be used to identify external excitations effectively for the nonlinear structure with accurate results even with measurement noise, model error and environmental disturbances.

The role of nonlinear torsional contributions on the stability of flexural-torsional oscillations of open-cross section beams

NASA Astrophysics Data System (ADS)

Di Egidio, Angelo; Contento, Alessandro; Vestroni, Fabrizio

2015-12-01

An open-cross section thin-walled beam model, already developed by the authors, has been conveniently simplified while maintaining the capacity of accounting for the significant nonlinear warping effects. For a technical range of geometrical and mechanical characteristics of the beam, the response is characterized by the torsional curvature prevailing over the flexural ones. A Galerkin discretization is performed by using a suitable expansion of displacements based on shape functions. The attention is focused on the dynamic response of the beam to a harmonic force, applied at the free end of the cantilever beam. The excitation is directed along the symmetry axis of the beam section. The stability of the one-component oscillations has been investigated using the analytical model, showing the importance of the internal resonances due to the nonlinear warping coupling terms. Comparison with the results provided by a computational finite element model has been performed. The good agreement among the results of the analytical and the computational models confirms the effectiveness of the simplified model of a nonlinear open-cross section thin-walled beam and overall the important role of the warping and of the torsional elongation in the study of the one-component dynamic oscillations and their stability.

Invisibility of Solar Active Region Umbra-to-Umbra Coronal Loops: New Evidence that Magnetoconvection Drives Solar-Stellar Coronal Heating

NASA Technical Reports Server (NTRS)

Tiwari, Sanjiv K.; Thalmann, Julia K.; Panesar, Navdeep K.; Moore, Ronald L.; Winebarger, Amy R.

2017-01-01

Coronal heating generally increases with increasing magnetic field strength: the EUV/X-ray corona in active regions is 10--100 times more luminous and 2--4 times hotter than that in quiet regions and coronal holes, which are heated to only about 1.5 MK, and have fields that are 10--100 times weaker than that in active regions. From a comparison of a nonlinear force-free model of the three-dimensional active region coronal field to observed extreme-ultraviolet loops, we find that (1) umbra-to-umbra coronal loops, despite being rooted in the strongest magnetic flux, are invisible, and (2) the brightest loops have one foot in an umbra or penumbra and the other foot in another sunspot's penumbra or in unipolar or mixed-polarity plage. The invisibility of umbra-to-umbra loops is new evidence that magnetoconvection drives solar-stellar coronal heating: evidently, the strong umbral field at both ends quenches the magnetoconvection and hence the heating. Our results from EUV observations and nonlinear force-free modeling of coronal magnetic field imply that, for any coronal loop on the Sun or on any other convective star, as long as the field can be braided by convection in at least one loop foot, the stronger the field in the loop, the stronger the coronal heating.

Hyper-resistive forced magnetic reconnection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vekstein, G., E-mail: g.vekstein@manchester.ac.uk

We study Taylor's model of forced magnetic reconnection mediated by plasma hyper-resistivity. This includes both linear and nonlinear regimes of the process. It is shown how the onset of plasmoid instability occurs in the strongly nonlinear regime of forced reconnection.

Sensor-less force-reflecting macro-micro telemanipulation systems by piezoelectric actuators.

PubMed

Amini, H; Farzaneh, B; Azimifar, F; Sarhan, A A D

2016-09-01

This paper establishes a novel control strategy for a nonlinear bilateral macro-micro teleoperation system with time delay. Besides position and velocity signals, force signals are additionally utilized in the control scheme. This modification significantly improves the poor transparency during contact with the environment. To eliminate external force measurement, a force estimation algorithm is proposed for the master and slave robots. The closed loop stability of the nonlinear micro-micro teleoperation system with the proposed control scheme is investigated employing the Lyapunov theory. Consequently, the experimental results verify the efficiency of the new control scheme in free motion and during collision between the slave robot and the environment of slave robot with environment, and the efficiency of the force estimation algorithm. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Analytical Model of the Nonlinear Dynamics of Cantilever Tip-Sample Surface Interactions for Various Acoustic-Atomic Force Microscopies

NASA Technical Reports Server (NTRS)

Cantrell, John H., Jr.; Cantrell, Sean A.

2008-01-01

A comprehensive analytical model of the interaction of the cantilever tip of the atomic force microscope (AFM) with the sample surface is developed that accounts for the nonlinearity of the tip-surface interaction force. The interaction is modeled as a nonlinear spring coupled at opposite ends to linear springs representing cantilever and sample surface oscillators. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a standard iteration procedure. Solutions are obtained for the phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) techniques including force modulation microscopy, atomic force acoustic microscopy, ultrasonic force microscopy, heterodyne force microscopy, resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM), and the commonly used intermittent contact mode (TappingMode) generally available on AFMs. The solutions are used to obtain a quantitative measure of image contrast resulting from variations in the Young modulus of the sample for the amplitude and phase images generated by the A-AFM techniques. Application of the model to RDF-AFUM and intermittent soft contact phase images of LaRC-cp2 polyimide polymer is discussed. The model predicts variations in the Young modulus of the material of 24 percent from the RDF-AFUM image and 18 percent from the intermittent soft contact image. Both predictions are in good agreement with the literature value of 21 percent obtained from independent, macroscopic measurements of sheet polymer material.

High Frequency Chandler Wobble Excitation

NASA Astrophysics Data System (ADS)

Seitz, F.; Stuck, J.; Thomas, M.

2003-04-01

Variations of Earth rotation on sub-daily to secular timescales are caused by mass redistributions in the Earth system as a consequence of geophysical processes and gravitational influences. Forced oscillations of polar motion are superposed by free oscillations of the Earth, i.e. the Chandler wobble and the free core nutation. In order to study the interactions between externally induced polar motion and the Earth's free oscillations, a non-linear gyroscopic model has been developed. In most of the former investigations on polar motion, the Chandler wobble is introduced as a damped oscillation with predetermined frequency and amplitude. However, as the effect of rotational deformation is a backcoupling mechanism of polar motion on the Earth's rotational dynamics, both period and amplitude of the Chandler wobble are time-dependent when regarding additional excitations from, e.g., atmospheric or oceanic mass redistributions. The gyroscopic model is free of any explicit information concerning amplitude, phase, and period of free oscillations. The characteristics of the Earth's free oscillation is reproduced by the model from rheological and geometrical parameters and rotational deformation is taken into account. This enables to study the time variable Chandler oscillation when the gyro is forced with atmospheric and oceanic angular momentum from the global atmospheric ECHAM3-T21 general circulation model together with the ocean model for circulation and tides OMCT driven by ECHAM including surface pressure. Besides, mass redistributions in the Earth's body due to gravitational and loading deformations are regarded and external torques exerted by Moon and Sun are considered. The numerical results of the gyro are significantly related with the geodetically observed time series of polar motion published by the IERS. It is shown that the consistent excitation is capable to counteract the damping and thus to maintain the Chandler amplitude. Spectral analyses of the ECHAM and OMCT forcing fields give no hint for increased excitation power in the Chandler band. Thus it is assumed, that continuous high frequency excitation due to stochastic weather phenomena is responsible for the perpetuation of the Chandler wobble.

Casting the Coronal Magnetic Field Reconstruction Tools in 3D Using the MHD Bifrost Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fleishman, Gregory D.; Loukitcheva, Maria; Anfinogentov, Sergey

Quantifying the coronal magnetic field remains a central problem in solar physics. Nowadays, the coronal magnetic field is often modeled using nonlinear force-free field (NLFFF) reconstructions, whose accuracy has not yet been comprehensively assessed. Here we perform a detailed casting of the NLFFF reconstruction tools, such as π -disambiguation, photospheric field preprocessing, and volume reconstruction methods, using a 3D snapshot of the publicly available full-fledged radiative MHD model. Specifically, from the MHD model, we know the magnetic field vector in the entire 3D domain, which enables us to perform a “voxel-by-voxel” comparison of the restored and the true magnetic fieldsmore » in the 3D model volume. Our tests show that the available π -disambiguation methods often fail in the quiet-Sun areas dominated by small-scale magnetic elements, while they work well in the active region (AR) photosphere and (even better) chromosphere. The preprocessing of the photospheric magnetic field, although it does produce a more force-free boundary condition, also results in some effective “elevation” of the magnetic field components. This “elevation” height is different for the longitudinal and transverse components, which results in a systematic error in absolute heights in the reconstructed magnetic data cube. The extrapolations performed starting from the actual AR photospheric magnetogram are free from this systematic error, while other metrics are comparable with those for extrapolations from the preprocessed magnetograms. This finding favors the use of extrapolations from the original photospheric magnetogram without preprocessing. Our tests further suggest that extrapolations from a force-free chromospheric boundary produce measurably better results than those from a photospheric boundary.« less

MJO: Asymptotically-Nondivergent Nonlinear Wave?: A Review

NASA Astrophysics Data System (ADS)

Yano, J. I.

2014-12-01

MJO is often considered a convectively-coupled wave. The present talk is going to argue that it is best understood primarily as a nonlinear solitary wave dominated by vorticity. Role of convection is secondary,though likely catalytic. According to Charney's (1963) scale analysis, the large-scale tropical circulations are nondivergent to the leading order, i.e., dominated by rotational flows. Yano et al (2009) demonstrate indeed that is the case for a period dominated by three MJO events. The scale analysis of Yano and Bonazzola (2009, JAS) demonstrates such an asymptotically nondivergent regime is a viable alternative to the traditionally-believed equatorial-wave regime. Wedi and Smolarkiewicz (2010, JAS) in turn, show by numerical computations of a dry system that a MJO-like oscillation for a similar period can indeed be generated by free solitary nonlinear equatorial Rossby-wave dynamicswithout any convective forcing to a system. Unfortunately, this perspective is slow to be accepted with people's mind so much fixed on the role of convection. This situation may be compared to a slow historical process of acceptance of Eady and Charney's baroclinicinstability simply because it does not invoke any convection Ironically, once the nonlinear free-wave view for MJO is accepted, interpretations can more easily be developed for a recent series of numerical model experiments under a global channel configuration overthe tropics with a high-resolution of 5-50 km with or without convection parameterization. All those experiments tend to reproduce observed large-scale circulations associated with MJO rather well, though most of time, they fail to reproduce convective coherency associated with MJO.These large-scale circulations appear to be generated by lateral forcing imposed at the latitudinal walls. These lateral boundaries are reasonably far enough (30NS) to induce any direct influence to the tropics. There is no linear dry equatorial wave that supports this period either. In Wedi and Smolarkiewicz's analysis, such a lateral forcing is essential in order to obtain their nonlinear solitary wave solution. Thus is the leading-order solution for MJO in the same sense as the linear baroclinic instability is a leading-order solution to the midlatitude synoptic-scale storm.

Wind Tunnel Database Development using Modern Experiment Design and Multivariate Orthogonal Functions

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.; DeLoach, Richard

2003-01-01

A wind tunnel experiment for characterizing the aerodynamic and propulsion forces and moments acting on a research model airplane is described. The model airplane called the Free-flying Airplane for Sub-scale Experimental Research (FASER), is a modified off-the-shelf radio-controlled model airplane, with 7 ft wingspan, a tractor propeller driven by an electric motor, and aerobatic capability. FASER was tested in the NASA Langley 12-foot Low-Speed Wind Tunnel, using a combination of traditional sweeps and modern experiment design. Power level was included as an independent variable in the wind tunnel test, to allow characterization of power effects on aerodynamic forces and moments. A modeling technique that employs multivariate orthogonal functions was used to develop accurate analytic models for the aerodynamic and propulsion force and moment coefficient dependencies from the wind tunnel data. Efficient methods for generating orthogonal modeling functions, expanding the orthogonal modeling functions in terms of ordinary polynomial functions, and analytical orthogonal blocking were developed and discussed. The resulting models comprise a set of smooth, differentiable functions for the non-dimensional aerodynamic force and moment coefficients in terms of ordinary polynomials in the independent variables, suitable for nonlinear aircraft simulation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wiegelmann, T.; Solanki, S. K.; Barthol, P.

Magneto-static models may overcome some of the issues facing force-free magnetic field extrapolations. So far they have seen limited use and have faced problems when applied to quiet-Sun data. Here we present a first application to an active region. We use solar vector magnetic field measurements gathered by the IMaX polarimeter during the flight of the Sunrise balloon-borne solar observatory in 2013 June as boundary conditions for a magneto-static model of the higher solar atmosphere above an active region. The IMaX data are embedded in active region vector magnetograms observed with SDO /HMI. This work continues our magneto-static extrapolation approach,more » which was applied earlier to a quiet-Sun region observed with Sunrise I. In an active region the signal-to-noise-ratio in the measured Stokes parameters is considerably higher than in the quiet-Sun and consequently the IMaX measurements of the horizontal photospheric magnetic field allow us to specify the free parameters of the model in a special class of linear magneto-static equilibria. The high spatial resolution of IMaX (110–130 km, pixel size 40 km) enables us to model the non-force-free layer between the photosphere and the mid-chromosphere vertically by about 50 grid points. In our approach we can incorporate some aspects of the mixed beta layer of photosphere and chromosphere, e.g., taking a finite Lorentz force into account, which was not possible with lower-resolution photospheric measurements in the past. The linear model does not, however, permit us to model intrinsic nonlinear structures like strongly localized electric currents.« less

The nonlinear wave equation for higher harmonics in free-electron lasers

NASA Technical Reports Server (NTRS)

Colson, W. B.

1981-01-01

The nonlinear wave equation and self-consistent pendulum equation are generalized to describe free-electron laser operation in higher harmonics; this can significantly extend their tunable range to shorter wavelengths. The dynamics of the laser field's amplitude and phase are explored for a wide range of parameters using families of normalized gain curves applicable to both the fundamental and harmonics. The electron phase-space displays the fundamental physics driving the wave, and this picture is used to distinguish between the effects of high gain and Coulomb forces.

Non-normal perturbation growth in idealised island and headland wakes

NASA Astrophysics Data System (ADS)

Aiken, C. M.; Moore, A. M.; Middleton, J. H.

2003-12-01

Generalised linear stability theory is used to calculate the linear perturbations that furnish most rapid growth in energy in a model of a steady recirculating island wake. This optimal peturbation is found to be antisymmetric and to evolve into a von Kármán vortex street. Eigenanalysis of the linearised system reveals that the eigenmodes corresponding to vortex sheet formation are damped, so the growth of the perturbation is understood through the non-normality of the linearised system. Qualitatively similar perturbation growth is shown to occur in a non-linear model of stochastically-forced subcritical flow, resulting in transition to an unsteady wake. Free-stream variability with amplitude 8% of the mean inflow speed sustains vortex street structures in the non-linear model with perturbation velocities the order of the inflow speed, suggesting that environmental stochastic forcing may similarly be capable of exciting growing disturbances in real island wakes. To support this, qualitatively similar perturbation growth is demonstrated in the straining wake of a realistic island obstacle. It is shown that for the case of an idealised headland, where the vortex street eigenmodes are lacking, vortex sheets are produced through a similar non-normal process.

Techniques for forced response involving discrete nonlinearities. I - Theory. II - Applications

NASA Astrophysics Data System (ADS)

Avitabile, Peter; Callahan, John O.

Several new techniques developed for the forced response analysis of systems containing discrete nonlinear connection elements are presented and compared to the traditional methods. In particular, the techniques examined are the Equivalent Reduced Model Technique (ERMT), Modal Modification Response Technique (MMRT), and Component Element Method (CEM). The general theory of the techniques is presented, and applications are discussed with particular reference to the beam nonlinear system model using ERMT, MMRT, and CEM; frame nonlinear response using the three techniques; and comparison of the results obtained by using the ERMT, MMRT, and CEM models.

Equivalent linear damping characterization in linear and nonlinear force-stiffness muscle models.

PubMed

Ovesy, Marzieh; Nazari, Mohammad Ali; Mahdavian, Mohammad

2016-02-01

In the current research, the muscle equivalent linear damping coefficient which is introduced as the force-velocity relation in a muscle model and the corresponding time constant are investigated. In order to reach this goal, a 1D skeletal muscle model was used. Two characterizations of this model using a linear force-stiffness relationship (Hill-type model) and a nonlinear one have been implemented. The OpenSim platform was used for verification of the model. The isometric activation has been used for the simulation. The equivalent linear damping and the time constant of each model were extracted by using the results obtained from the simulation. The results provide a better insight into the characteristics of each model. It is found that the nonlinear models had a response rate closer to the reality compared to the Hill-type models.

Electrostatic and aerodynamic forced vibrations of a thin flexible electrode: Quasi-periodic vs. chaotic oscillations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Madanu, Sushma B.; Barbel, Stanley I.; Ward, Thomas

In this paper, transverse vibrations of an electrostatically actuated thin flexible cantilever perturbed by low-speed air flow are studied using both experiments and numerical modeling. In the experiments, the dynamic characteristics of the cantilever are studied by supplying a DC voltage with an AC component for electrostatic forcing and a constant uniform air flow around the cantilever system for aerodynamic forcing. A range of control parameters leading to stable vibrations are established using a dimensionless operating parameter that is the ratio of the induced and the free stream velocities. Numerical results are validated with experimental data. Assuming the amplitude ofmore » vibrations are small, then a non-linear dynamic Euler-Bernoulli beam equation with viscous damping and gravitational effects is used to model the equation of motion. Aerodynamic forcing is modelled as a temporally sinusoidal and uniform force acting perpendicular to the beam length. The forcing amplitude is found to be proportional to the square of the air flow velocity. Numerical results strongly agree with the experiments predicting accurate vibration amplitude, displacement frequency, and quasi-periodic displacement of the cantilever tip.« less

Force-Free Magnetic Fields Calculated from Automated Tracing of Coronal Loops with AIA/SDO

NASA Astrophysics Data System (ADS)

Aschwanden, M. J.

2013-12-01

One of the most realistic magnetic field models of the solar corona is a nonlinear force-free field (NLFFF) solution. There exist about a dozen numeric codes that compute NLFFF solutions based on extrapolations of photospheric vector magnetograph data. However, since the photosphere and lower chromosphere is not force-free, a suitable correction has to be applied to the lower boundary condition. Despite of such "pre-processing" corrections, the resulting theoretical magnetic field lines deviate substantially from observed coronal loop geometries. - Here we developed an alternative method that fits an analytical NLFFF approximation to the observed geometry of coronal loops. The 2D coordinates of the geometry of coronal loop structures observed with AIA/SDO are traced with the "Oriented Coronal CUrved Loop Tracing" (OCCULT-2) code, an automated pattern recognition algorithm that has demonstrated the fidelity in loop tracing matching visual perception. A potential magnetic field solution is then derived from a line-of-sight magnetogram observed with HMI/SDO, and an analytical NLFFF approximation is then forward-fitted to the twisted geometry of coronal loops. We demonstrate the performance of this magnetic field modeling method for a number of solar active regions, before and after major flares observed with SDO. The difference of the NLFFF and the potential field energies allows us then to compute the free magnetic energy, which is an upper limit of the energy that is released during a solar flare.

Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

PubMed

Rigatos, Gerasimos G

2016-06-01

It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

Stress Induced in Periodontal Ligament under Orthodontic Loading (Part II): A Comparison of Linear Versus Non-Linear Fem Study.

PubMed

Hemanth, M; Deoli, Shilpi; Raghuveer, H P; Rani, M S; Hegde, Chatura; Vedavathi, B

2015-09-01

Simulation of periodontal ligament (PDL) using non-linear finite element method (FEM) analysis gives better insight into understanding of the biology of tooth movement. The stresses in the PDL were evaluated for intrusion and lingual root torque using non-linear properties. A three-dimensional (3D) FEM model of the maxillary incisors was generated using Solidworks modeling software. Stresses in the PDL were evaluated for intrusive and lingual root torque movements by 3D FEM using ANSYS software. These stresses were compared with linear and non-linear analyses. For intrusive and lingual root torque movements, distribution of stress over the PDL was within the range of optimal stress value as proposed by Lee, but was exceeding the force system given by Proffit as optimum forces for orthodontic tooth movement with linear properties. When same force load was applied in non-linear analysis, stresses were more compared to linear analysis and were beyond the optimal stress range as proposed by Lee for both intrusive and lingual root torque. To get the same stress as linear analysis, iterations were done using non-linear properties and the force level was reduced. This shows that the force level required for non-linear analysis is lesser than that of linear analysis.

Analyses of Multishaft Rotor-Bearing Response

NASA Technical Reports Server (NTRS)

Nelson, H. D.; Meacham, W. L.

1985-01-01

Method works for linear and nonlinear systems. Finite-element-based computer program developed to analyze free and forced response of multishaft rotor-bearing systems. Acronym, ARDS, denotes Analysis of Rotor Dynamic Systems. Systems with nonlinear interconnection or support bearings or both analyzed by numerically integrating reduced set of coupledsystem equations. Linear systems analyzed in closed form for steady excitations and treated as equivalent to nonlinear systems for transient excitation. ARDS is FORTRAN program developed on an Amdahl 470 (similar to IBM 370).

Spacetimes dressed with stealth electromagnetic fields

NASA Astrophysics Data System (ADS)

Smolić, Ivica

2018-04-01

Stealth field configurations by definition have a vanishing energy-momentum tensor, and thus do not contribute to the gravitational field equations. While only trivial fields can be stealth in Maxwell's electrodynamics, nontrivial stealth fields appear in some nonlinear models of electromagnetism. We find the necessary and sufficient conditions for the electromagnetic fields to be stealth and analyze which models admit such configurations. Furthermore, we present some concrete exact solutions, featuring a class of black holes dressed with the stealth electromagnetic hair, closely related to force-free solutions. Stealth hair does not alter the generalized Smarr formula, but may contribute to the Komar charges.

Nonlinear Force-free Coronal Magnetic Stereoscopy

NASA Astrophysics Data System (ADS)

Chifu, Iulia; Wiegelmann, Thomas; Inhester, Bernd

2017-03-01

Insights into the 3D structure of the solar coronal magnetic field have been obtained in the past by two completely different approaches. The first approach are nonlinear force-free field (NLFFF) extrapolations, which use photospheric vector magnetograms as boundary condition. The second approach uses stereoscopy of coronal magnetic loops observed in EUV coronal images from different vantage points. Both approaches have their strengths and weaknesses. Extrapolation methods are sensitive to noise and inconsistencies in the boundary data, and the accuracy of stereoscopy is affected by the ability of identifying the same structure in different images and by the separation angle between the view directions. As a consequence, for the same observational data, the 3D coronal magnetic fields computed with the two methods do not necessarily coincide. In an earlier work (Paper I) we extended our NLFFF optimization code by including stereoscopic constrains. The method was successfully tested with synthetic data, and within this work, we apply the newly developed code to a combined data set from SDO/HMI, SDO/AIA, and the two STEREO spacecraft. The extended method (called S-NLFFF) contains an additional term that monitors and minimizes the angle between the local magnetic field direction and the orientation of the 3D coronal loops reconstructed by stereoscopy. We find that when we prescribe the shape of the 3D stereoscopically reconstructed loops, the S-NLFFF method leads to a much better agreement between the modeled field and the stereoscopically reconstructed loops. We also find an appreciable decrease by a factor of two in the angle between the current and the magnetic field. This indicates the improved quality of the force-free solution obtained by S-NLFFF.

Nonlinear convective analysis of a rotating Oldroyd-B nanofluid layer under thermal non-equilibrium utilizing Al2O3-EG colloidal suspension

NASA Astrophysics Data System (ADS)

Agarwal, Shilpi; Rana, Puneet

2016-04-01

In this paper, we examine a layer of Oldroyd-B nanofluid for linear and nonlinear regimes under local thermal non-equilibrium conditions for the classical Rayleigh-Bénard problem. The free-free boundary condition has been implemented with the flux for nanoparticle concentration being zero at edges. The Oberbeck-Boussinesq approximation holds good and for the rotational effect Coriolis term is included in the momentum equation. A two-temperature model explains the effect of local thermal non-equilibrium among the particle and fluid phases. The criteria for onset of stationary convection has been derived as a function of the non-dimensionalized parameters involved including the Taylor number. The assumed boundary conditions negate the possibility of overstability due to the absence of opposing forces responsible for it. The thermal Nusselt number has been obtained utilizing a weak nonlinear theory in terms of various pertinent parameters in the steady and transient mode, and has been depicted graphically. The main findings signify that the rotation has a stabilizing effect on the system. The stress relaxation parameter λ_1 inhibits whereas the strain retardation parameter λ_2 exhibits heat transfer utilizing Al2O3 nanofluids.

Modeling the two-way feedback between contractility and matrix realignment reveals a nonlinear mode of cancer cell invasion

PubMed Central

Ahmadzadeh, Hossein; Webster, Marie R.; Behera, Reeti; Jimenez Valencia, Angela M.; Wirtz, Denis; Weeraratna, Ashani T.; Shenoy, Vivek B.

2017-01-01

Cancer cell invasion from primary tumors is mediated by a complex interplay between cellular adhesions, actomyosin-driven contractility, and the physical characteristics of the extracellular matrix (ECM). Here, we incorporate a mechanochemical free-energy–based approach to elucidate how the two-way feedback loop between cell contractility (induced by the activity of chemomechanical interactions such as Ca2+ and Rho signaling pathways) and matrix fiber realignment and strain stiffening enables the cells to polarize and develop contractile forces to break free from the tumor spheroids and invade into the ECM. Interestingly, through this computational model, we are able to identify a critical stiffness that is required by the matrix to break intercellular adhesions and initiate cell invasion. Also, by considering the kinetics of the cell movement, our model predicts a biphasic invasiveness with respect to the stiffness of the matrix. These predictions are validated by analyzing the invasion of melanoma cells in collagen matrices of varying concentration. Our model also predicts a positive correlation between the elongated morphology of the invading cells and the alignment of fibers in the matrix, suggesting that cell polarization is directly proportional to the stiffness and alignment of the matrix. In contrast, cells in nonfibrous matrices are found to be rounded and not polarized, underscoring the key role played by the nonlinear mechanics of fibrous matrices. Importantly, our model shows that mechanical principles mediated by the contractility of the cells and the nonlinearity of the ECM behavior play a crucial role in determining the phenotype of the cell invasion. PMID:28196892

Standard electrode potential, Tafel equation, and the solvation thermodynamics.

PubMed

Matyushov, Dmitry V

2009-06-21

Equilibrium in the electronic subsystem across the solution-metal interface is considered to connect the standard electrode potential to the statistics of localized electronic states in solution. We argue that a correct derivation of the Nernst equation for the electrode potential requires a careful separation of the relevant time scales. An equation for the standard metal potential is derived linking it to the thermodynamics of solvation. The Anderson-Newns model for electronic delocalization between the solution and the electrode is combined with a bilinear model of solute-solvent coupling introducing nonlinear solvation into the theory of heterogeneous electron transfer. We therefore are capable of addressing the question of how nonlinear solvation affects electrochemical observables. The transfer coefficient of electrode kinetics is shown to be equal to the derivative of the free energy, or generalized force, required to shift the unoccupied electronic level in the bulk. The transfer coefficient thus directly quantifies the extent of nonlinear solvation of the redox couple. The current model allows the transfer coefficient to deviate from the value of 0.5 of the linear solvation models at zero electrode overpotential. The electrode current curves become asymmetric in respect to the change in the sign of the electrode overpotential.

A discrete model for geometrically nonlinear transverse free constrained vibrations of beams with various end conditions

NASA Astrophysics Data System (ADS)

Rahmouni, A.; Beidouri, Z.; Benamar, R.

2013-09-01

The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions. The development of an adequate discrete model including the effect of the axial strains induced by large displacement amplitudes, which is predominant in geometrically nonlinear transverse constrained vibrations of beams [1]. The investigation of the results such a discrete model may lead to in the case of nonlinear free vibrations. The development of the analogy between the previously developed models of geometrically nonlinear vibrations of Euler-Bernoulli continuous beams, and multidof system models made of N masses placed at the end of elastic bars connected by linear spiral springs, presenting the beam flexural rigidity. The validation of the new model via the analysis of the convergence conditions of the nonlinear frequencies obtained by the N-dof system, when N increases, and those obtained in previous works using a continuous description of the beam. In addition to the above points, the models developed in the present work, may constitute, in our opinion, a good illustration, from the didactic point of view, of the origin of the geometrical nonlinearity induced by large transverse vibration amplitudes of constrained continuous beams, which may appear as a Pythagorean Theorem effect. The first step of the work presented here was the formulation of the problem of nonlinear vibrations of the discrete system shown in Fig. 1 in terms of the semi-analytical method, denoted as SAA, developed in the early 90's by Benamar and coauthors [3], and discussed for example in [6,7]. This method has been applied successfully to various types of geometrically nonlinear problems of structural dynamics [1-3,6-8,10-12] and the objective here was to use it in order to develop a flexible discrete nonlinear model which may be useful for presenting in further works geometrically nonlinear vibrations of real beams with discontinuities in the mass, the section, or the stiffness distributions. The purpose in the present work was restricted to developing and validating the model, via comparison of the obtained dependence of the resonance frequencies of such a system on the amplitude of vibration, with the results obtained previously by continuous beams nonlinear models. In the SAA method, the dynamic system under consideration is described by the mass matrix [M], the rigidity matrix [K], and the nonlinear rigidity matrix [B], which depends on the amplitude of vibration, and involves a fourth-order nonlinearity tensor bijkl. Details are given below, corresponding to the definition of the tensors mentioned above. The analogy between the classical continuous Euler-Bernoulli model of beams and the present discrete model is developed, leading to the expressions for the equivalent spiral and axial stiffness, in terms of the continuous beam geometrical and mechanical characteristics. Some numerical results are also given, showing the amplitude dependence of the frequencies on the amplitude of vibration, and compared to the backbone curves obtained previously by the continuous nonlinear classical beam theory, presented for example in [3,5,8,15-22]. A convergence study is performed by increasing the number of masses and bars, showing a good convergence to the theoretical values of continuous beams.

Nonlinear response and bistability of driven ion acoustic waves

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-08-01

The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.

Nonlinear Dynamics of Cantilever-Sample Interactions in Atomic Force Microscopy

NASA Technical Reports Server (NTRS)

Cantrell, John H.; Cantrell, Sean A.

2010-01-01

The interaction of the cantilever tip of an atomic force microscope (AFM) with the sample surface is obtained by treating the cantilever and sample as independent systems coupled by a nonlinear force acting between the cantilever tip and a volume element of the sample surface. The volume element is subjected to a restoring force from the remainder of the sample that provides dynamical equilibrium for the combined systems. The model accounts for the positions on the cantilever of the cantilever tip, laser probe, and excitation force (if any) via a basis set of set of orthogonal functions that may be generalized to account for arbitrary cantilever shapes. The basis set is extended to include nonlinear cantilever modes. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a matrix iteration procedure. The effects of oscillatory excitation forces applied either to the cantilever or to the sample surface (or to both) are obtained from the solution set and applied to the to the assessment of phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) modalities. The influence of bistable cantilever modes of on AFM signal generation is discussed. The effects on the cantilever-sample surface dynamics of subsurface features embedded in the sample that are perturbed by surface-generated oscillatory excitation forces and carried to the cantilever via wave propagation are accounted by the Bolef-Miller propagating wave model. Expressions pertaining to signal generation and image contrast in A-AFM are obtained and applied to amplitude modulation (intermittent contact) atomic force microscopy and resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM). The influence of phase accumulation in A-AFM on image contrast is discussed, as is the effect of hard contact and maximum nonlinearity regimes of A-AFM operation.

Nonlinear effects in the radiation force generated by amplitude-modulated focused beams

NASA Astrophysics Data System (ADS)

González, Nuria; Jiménez, Noé; Redondo, Javier; Roig, Bernardino; Picó, Rubén; Sánchez-Morcillo, Víctor; Konofagou, Elisa E.; Camarena, Francisco

2012-10-01

Harmonic Motion Imaging (HMI) uses an amplitude-modulated (AM) beam to induce an oscillatory radiation force before, during and after ablation. In this paper, the findings from a numerical analysis of the effects related with the nonlinear propagation of AM focused ultrasonic beams in water on the radiation force and the location of its maxima will be presented. The numerical modeling is performed using the KZK nonlinear parabolic equation. The radiation force is generated by a focused transducer with a gain of 18, a carrier frequency of 1 MHz and a modulation frequency of 25 kHz. The modulated excitation generates a spatially-invariant force proportional to the intensity. Regarding the nonlinear wave propagation, the force is no longer proportional to the intensity, reaching a factor of eight between the nonlinear and linear estimations. Also, a 9 mm shift in the on-axis force peak occurs when the initial pressure increased from 1 to 300 kPa. This spatial shift, due to the nonlinear effects, becomes dynamic in AM focused beams, as the different signal periods have different amplitudes. This study shows that both the value and the spatial position of the force peak are affected by the nonlinear propagation of the ultrasonic waves.

Self-Supervised Dynamical Systems

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Transient Characteristics of Free Piston Vuilleurnier Cycle Heat Pumps

NASA Astrophysics Data System (ADS)

Matsue, Junji; Fujimoto, Norioki; Shirai, Hiroyuki

A dynamic analysis of a free piston Vuilleumier cycle heat pump was performed using a time-stepping integration method to investigate transient characteristics under power controlling. The nonlinear relationship between displacement and force for pistons was taken into account for the motion of reciprocating components. The force for pistons is mainly caused by the pressure change of working gas varying with piston displacements; moreover nonlinear viscous dissipative force due to the oscillating flow of working gas in heat exchangers and discontinuous damping force caused by solid friction at piston seals and rod seals are included. The displacements of pistons and pressure changes in the Vuilleumier cycle heat pump were integrated by an ideal isothermal thermodynamic relationship. It was assumed that the flow friction was proportional to the kinematic pressure of working gas, and that the solid friction at the seals was due to the functions of the working gas pressure and the tension of seal springs. In order to investigate the transient characteristics of a proposed free piston Vuilleumier cycle heat pump machine when hot-side working gas temperatures and alternate force were changed, some calculations were performed and discussed. These calculation results make clear transient characteristics at starting and power controlling. It was further found that only a small amount of starter power is required in particular conditions. During controlling, the machine becomes unstable when there is ar elatively large reduction in cooling or heating power. Therefore, an auxiliary device is additionally needed to obtain stable operation, such as al inear motor.

Soft tissue modelling through autowaves for surgery simulation.

PubMed

Zhong, Yongmin; Shirinzadeh, Bijan; Alici, Gursel; Smith, Julian

2006-09-01

Modelling of soft tissue deformation is of great importance to virtual reality based surgery simulation. This paper presents a new methodology for simulation of soft tissue deformation by drawing an analogy between autowaves and soft tissue deformation. The potential energy stored in a soft tissue as a result of a deformation caused by an external force is propagated among mass points of the soft tissue by non-linear autowaves. The novelty of the methodology is that (i) autowave techniques are established to describe the potential energy distribution of a deformation for extrapolating internal forces, and (ii) non-linear materials are modelled with non-linear autowaves other than geometric non-linearity. Integration with a haptic device has been achieved to simulate soft tissue deformation with force feedback. The proposed methodology not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply changing diffusion coefficients.

Full non-linear treatment of the global thermospheric wind system. I - Mathematical method and analysis of forces. II - Results and comparison with observations

NASA Technical Reports Server (NTRS)

Blum, P. W.; Harris, I.

1975-01-01

The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In Part I the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analyzed. Results of the method given in Part I are presented with comparison with previous calculations and observations of upper atmospheric winds. Conclusions are that nonlinear effects are only significant in the equatorial region, especially at solstice conditions and that nonlinear effects do not produce any superrotation.

Rigorous Model Reduction for a Damped-Forced Nonlinear Beam Model: An Infinite-Dimensional Analysis

NASA Astrophysics Data System (ADS)

Kogelbauer, Florian; Haller, George

2018-06-01

We use invariant manifold results on Banach spaces to conclude the existence of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces of the linearized beam equation. Reduction in the governing PDE to SSMs provides an explicit low-dimensional model which captures the correct asymptotics of the full, infinite-dimensional dynamics. Our approach is general enough to admit extensions to other types of continuum vibrations. The model-reduction procedure we employ also gives guidelines for a mathematically self-consistent modeling of damping in PDEs describing structural vibrations.

Measurement of nonlinear normal modes using multi-harmonic stepped force appropriation and free decay

NASA Astrophysics Data System (ADS)

Ehrhardt, David A.; Allen, Matthew S.

2016-08-01

Nonlinear Normal Modes (NNMs) offer tremendous insight into the dynamic behavior of a nonlinear system, extending many concepts that are familiar in linear modal analysis. Hence there is interest in developing methods to experimentally and numerically determine a system's NNMs for model updating or simply to characterize its dynamic response. Previous experimental work has shown that a mono-harmonic excitation can be used to isolate a system's dynamic response in the neighborhood of a NNM along the main backbones of a system. This work shows that a multi-harmonic excitation is needed to isolate a NNM when well separated linear modes of a structure couple to produce an internal resonance. It is shown that one can tune the multiple harmonics of the input excitation using a plot of the input force versus the response velocity until the area enclosed by the force-velocity curve is minimized. Once an appropriated NNM is measured, one can increase the force level and retune the frequency to obtain a NNM at a higher amplitude or remove the excitation and measure the structure's decay down a NNM backbone. This work explores both methods using simulations and measurements of a nominally-flat clamped-clamped beam excited at a single point with a magnetic force. Numerical simulations are used to validate the method in a well defined environment and to provide comparison with the experimentally measured NNMs. The experimental results seem to produce a good estimate of two NNMs along their backbone and part of an internal resonance branch. Full-field measurements are then used to further explore the couplings between the underlying linear modes along the identified NNMs.

An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations for marginally unstable systems

NASA Technical Reports Server (NTRS)

Hinata, S.

1989-01-01

An approximate analytic solution of a set of nonlinear model alpha-omega-dynamo equations is obtained. The reaction of the Lorentz force on the velocity shear which stretches and, hence, amplifies the magnetic field is incorporated into the model. To single out the effect of the Lorentz force on the omega-effect, the effect of the Lorentz force on the alpha-effect is neglected in this study. The solution represents a nonlinear oscillation with the amplitude and period determined by the dynamo number N. The amplitude is proportional to N - 1, while the period is almost exactly the same as the dissipation time of the unstable mode (proportional to N).

A Nonlinear Elasticity Model of Macromolecular Conformational Change Induced by Electrostatic Forces

PubMed Central

Zhou, Y. C.; Holst, Michael; McCammon, J. Andrew

2008-01-01

In this paper we propose a nonlinear elasticity model of macromolecular conformational change (deformation) induced by electrostatic forces generated by an implicit solvation model. The Poisson-Boltzmann equation for the electrostatic potential is analyzed in a domain varying with the elastic deformation of molecules, and a new continuous model of the electrostatic forces is developed to ensure solvability of the nonlinear elasticity equations. We derive the estimates of electrostatic forces corresponding to four types of perturbations to an electrostatic potential field, and establish the existance of an equilibrium configuration using a fixed-point argument, under the assumption that the change in the ionic strength and charges due to the additional molecules causing the deformation are sufficiently small. The results are valid for elastic models with arbitrarily complex dielectric interfaces and cavities, and can be generalized to large elastic deformation caused by high ionic strength, large charges, and strong external fields by using continuation methods. PMID:19461946

Finite-time adaptive sliding mode force control for electro-hydraulic load simulator based on improved GMS friction model

NASA Astrophysics Data System (ADS)

Kang, Shuo; Yan, Hao; Dong, Lijing; Li, Changchun

2018-03-01

This paper addresses the force tracking problem of electro-hydraulic load simulator under the influence of nonlinear friction and uncertain disturbance. A nonlinear system model combined with the improved generalized Maxwell-slip (GMS) friction model is firstly derived to describe the characteristics of load simulator system more accurately. Then, by using particle swarm optimization (PSO) algorithm ​combined with the system hysteresis characteristic analysis, the GMS friction parameters are identified. To compensate for nonlinear friction and uncertain disturbance, a finite-time adaptive sliding mode control method is proposed based on the accurate system model. This controller has the ability to ensure that the system state moves along the nonlinear sliding surface to steady state in a short time as well as good dynamic properties under the influence of parametric uncertainties and disturbance, which further improves the force loading accuracy and rapidity. At the end of this work, simulation and experimental results are employed to demonstrate the effectiveness of the proposed sliding mode control strategy.

The force-free configuration of flux ropes in geomagnetotail: Cluster observations

NASA Astrophysics Data System (ADS)

Yang, Y. Y.; Shen, C.; Zhang, Y. C.; Rong, Z. J.; Li, X.; Dunlop, M.; Ma, Y. H.; Liu, Z. X.; Carr, C. M.; Rème, H.

2014-08-01

Unambiguous knowledge of magnetic field structure and the electric current distribution is critical for understanding the origin, evolution, and related dynamic properties of magnetic flux ropes (MFRs). In this paper, a survey of 13 MFRs in the Earth's magnetotail are conducted by Cluster multipoint analysis, so that their force-free feature, i.e., the kind of magnetic field structure satisfying J × B = 0, can be probed directly. It is showed that the selected flux ropes with the bipolar signature of the south-north magnetic field component generally lie near the equatorial plane, as expected, and that the magnetic field gradient is rather weak near the axis center, where the curvature radius is large. The current density (up to several tens of nA/m2) reaches their maximum values as the center is approached. It is found that the stronger the current density, the smaller the angles between the magnetic field and current in MFRs. The direct observations show that only quasi force-free structure is observed, and it tends to appear in the low plasma beta regime (in agreement with the theoretic results). The quasi force-free region is generally found to be embedded in the central portion of the MFRs, where the current is approximately field aligned and proportional to the strength of core field. It is shown that ~60% of surveyed MFRs can be globally approximated as force free. The force-free factor α is found to be nonconstantly varied through the quasi force-free MFR, suggesting that the force-free structure is nonlinear.

Nonlinear dynamic analysis of a rotor-bearing-seal system under two loading conditions

NASA Astrophysics Data System (ADS)

Ma, Hui; Li, Hui; Niu, Heqiang; Song, Rongze; Wen, Bangchun

2013-11-01

The operating speed of the rotating machinery often exceeds the second or even higher order critical speeds to pursue higher efficiency. Thus, how to restrain the higher order mode instability caused by the nonlinear oil-film force and seal force at high speed as far as possible has become more and more important. In this study, a lumped mass model of a rotor-bearing-seal system considering the gyroscopic effect is established. The graphite self-lubricating bearing and the sliding bearing are simulated by a spring-damping model and a nonlinear oil-film force model based on the assumption of short bearings, respectively. The seal is simulated by Muszynska nonlinear seal force model. Effects of the seal force and oil-film force on the first and second mode instabilities are investigated under two loading conditions which are determined by API Standard 617 (Axial and Centrifugal Compressors and Expander-compressors for Petroleum, Chemical and Gas Industry Services, Seventh Edition). The research focuses on the effects of exciting force forms and their magnitudes on the first and second mode whips in a rotor-bearing-seal system by using the spectrum cascades, vibration waveforms, orbits and Poincaré maps. The first and second mode instability laws are compared by including and excluding the seal effect in a rotor system with single-diameter shaft and two same discs. Meanwhile, the instability laws are also verified in a rotor system with multi-diameter shaft and two different discs. The results show that the second loading condition (out-of-phase unbalances of two discs) and the nonlinear seal force can mainly restrain the first mode instability and have slight effects on the second mode instability. This study may contribute to a further understanding about the higher order mode instability of such a rotor system with fluid-induced forces from the oil-film bearings and seals.

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

NASA Astrophysics Data System (ADS)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially.

Nonlinear oscillation of a rigid body over high- Tc superconductors supported by electro-magnetic forces

NASA Astrophysics Data System (ADS)

Sugiura, T.; Ogawa, S.; Ura, H.

2005-10-01

Characteristics of high- Tc superconducting levitation systems are no contact support and stable levitation without control. They can be applied to supporting mechanisms in machines, such as linear-drives and magnetically levitated trains. But small damping due to noncontact support and nonlinearity in the magnetic force can easily cause complicated phenomena of nonlinear dynamics. This research deals with nonlinear oscillation of a rigid bar supported at its both ends by electro-magnetic forces between superconductors and permanent magnets as a simple modeling of the above application. Deriving the equation of motion, we discussed an effect of nonlinearity in the magnetic force on dynamics of the levitated body: occurrence of combination resonance in the asymmetrical system. Numerical analyses and experiments were also carried out, and their results confirmed the above theoretical prediction.

Lagrangian particle drift and surface deformation in a rotating wave on a free liquid surface

NASA Astrophysics Data System (ADS)

Fontana, Paul W.; Francois, Nicolas; Xia, Hua; Punzmann, Horst; Shats, Michael

2017-11-01

A nonlinear model of a rotating wave on the free surface of a liquid is presented. The flow is assumed to be inviscid and irrotational. The wave is constructed as a superposition of two perpendicular, monochromatic standing Stokes waves and is standing-wave-like, but with ``antinodes'' or cells consisting of rotating surface gradients of alternating polarity. Lagrangian fluid particle trajectories show a rotational drift about each cell in the direction of wave rotation, corresponding to a rotating Stokes drift. Each cell therefore has a circulating flow and localized angular momentum even though the Eulerian flow is irrotational. Meanwhile, the wave sets up a static displacement of the free surface, making a trough in each cell. This static surface gradient provides a centripetal force that may account for additional rotation seen in experiments.

Nonlinear tapping dynamics of multi-walled carbon nanotube tipped atomic force microcantilevers

NASA Astrophysics Data System (ADS)

Lee, S. I.; Howell, S. W.; Raman, A.; Reifenberger, R.; Nguyen, C. V.; Meyyappan, M.

2004-05-01

The nonlinear dynamics of an atomic force microcantilever (AFM) with an attached multi-walled carbon nanotube (MWCNT) tip is investigated experimentally and theoretically. We present the experimental nonlinear frequency response of a MWCNT tipped microcantilever in the tapping mode. Several unusual features in the response distinguish it from those traditionally observed for conventional tips. The MWCNT tipped AFM probe is apparently immune to conventional imaging instabilities related to the coexistence of attractive and repulsive tapping regimes. A theoretical interaction model for the system using an Euler elastica MWCNT model is developed and found to predict several unusual features of the measured nonlinear response.

On the nonlinear forced response of the North Atlantic atmosphere to meridional shifts of the Gulf Stream path

NASA Astrophysics Data System (ADS)

Seo, H.; Kwon, Y. O.; Joyce, T. M.; Ummenhofer, C.

2016-12-01

This study examines the North Atlantic atmospheric circulation response to the meridional shift of Gulf Stream path using a large-ensemble, high-resolution, and hemispheric-scale WRF simulations. The model is forced with wintertime SST anomalies derived from a wide range of Gulf Stream shift scenarios. The key result of the model experiments, supported in part by an independent analysis of a reanalysis data set, is that the large-scale, quasi-steady North Atlantic circulation response is unambiguously nonlinear about the sign and amplitude of chosen SST anomalies. This nonlinear response prevails over the weak linear response and resembles the negative North Atlantic Oscillation, the leading intrinsic mode of variability in the model and the observations. Further analysis of the associated dynamics reveals that the nonlinear responses are accompanied by the anomalous southward shift of the North Atlantic eddy-driven jet stream, which is reinforced nearly equally by the high-frequency transient eddy feedback and the low-frequency high-latitude wave breaking events. The result highlights the importance of the intrinsically nonlinear transient eddy dynamics and eddy-mean flow interactions in generating the nonlinear forced response to the meridional shift in the Gulf Stream.

Numerical calculation of nonlinear ultrashort laser pulse propagation in transparent Kerr media

NASA Astrophysics Data System (ADS)

Arnold, Cord L.; Heisterkamp, Alexander; Ertmer, Wolfgang; Lubatschowski, Holger

2005-03-01

In the focal region of tightly focused ultrashort laser pulses, sufficient high intensities to initialize nonlinear ionization processes are easily achieved. Due to these nonlinear ionization processes, mainly multiphoton ionization and cascade ionization, free electrons are generated in the focus resulting in optical breakdown. A model including both nonlinear pulse propagation and plasma generation is used to calculate numerically the interaction of ultrashort pulses with their self-induced plasma in the vicinity of the focus. The model is based on a (3+1)-dimensional nonlinear Schroedinger equation describing the pulse propagation coupled to a system of rate equations covering the generation of free electrons. It is applicable to any transparent Kerr medium, whose linear and nonlinear optical parameters are known. Numerical calculations based on this model are used to understand nonlinear side effects, such as streak formation, occurring in addition to optical breakdown during short pulse refractive eye surgeries like fs-LASIK. Since the optical parameters of water are a good first-order approximation to those of corneal tissue, water is used as model substance. The free electron density distribution induced by focused ultrashort pulses as well as the pulses spatio-temporal behavior are studied in the low-power regime around the critical power for self-focusing.

Time domain nonlinear SMA damper force identification approach and its numerical validation

NASA Astrophysics Data System (ADS)

Xin, Lulu; Xu, Bin; He, Jia

2012-04-01

Most of the currently available vibration-based identification approaches for structural damage detection are based on eigenvalues and/or eigenvectors extracted from vibration measurements and, strictly speaking, are only suitable for linear system. However, the initiation and development of damage in engineering structures under severe dynamic loadings are typical nonlinear procedure. Studies on the identification of restoring force which is a direct indicator of the extent of the nonlinearity have received increasing attention in recent years. In this study, a date-based time domain identification approach for general nonlinear system was developed. The applied excitation and the corresponding response time series of the structure were used for identification by means of standard least-square techniques and a power series polynomial model (PSPM) which was utilized to model the nonlinear restoring force (NRF). The feasibility and robustness of the proposed approach was verified by a 2 degree-of-freedoms (DOFs) lumped mass numerical model equipped with a shape memory ally (SMA) damper mimicking nonlinear behavior. The results show that the proposed data-based time domain method is capable of identifying the NRF in engineering structures without any assumptions on the mass distribution and the topology of the structure, and provides a promising way for damage detection in the presence of structural nonlinearities.

Fuzzy control for nonlinear structure with semi-active friction damper

NASA Astrophysics Data System (ADS)

Zhao, Da-Hai; Li, Hong-Nan

2007-04-01

The implementation of semi-active friction damper for vibration mitigation of seismic structure generally requires an efficient control strategy. In this paper, the fuzzy logic based on Takagi-Sugeno model is proposed for controlling a semi-active friction damper that is installed on a nonlinear building subjected to strong earthquakes. The continuous Bouc-Wen hysteretic model for the stiffness is used to describe nonlinear characteristic of the building. The optimal sliding force with friction damper is determined by nonlinear time history analysis under normal earthquakes. The Takagi-Sugeno fuzzy logic model is employed to adjust the clamping force acted on the friction damper according to the semi-active control strategy. Numerical simulation results demonstrate that the proposed method is very efficient in reducing the peak inter-story drift and acceleration of the nonlinear building structure under earthquake excitations.

Highway traffic estimation of improved precision using the derivative-free nonlinear Kalman Filter

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Zervos, Nikolaos; Melkikh, Alexey

2015-12-01

The paper proves that the PDE dynamic model of the highway traffic is a differentially flat one and by applying spatial discretization its shows that the model's transformation into an equivalent linear canonical state-space form is possible. For the latter representation of the traffic's dynamics, state estimation is performed with the use of the Derivative-free nonlinear Kalman Filter. The proposed filter consists of the Kalman Filter recursion applied on the transformed state-space model of the highway traffic. Moreover, it makes use of an inverse transformation, based again on differential flatness theory which enables to obtain estimates of the state variables of the initial nonlinear PDE model. By avoiding approximate linearizations and the truncation of nonlinear terms from the PDE model of the traffic's dynamics the proposed filtering methods outperforms, in terms of accuracy, other nonlinear estimators such as the Extended Kalman Filter. The article's theoretical findings are confirmed through simulation experiments.

Force-free field modeling of twist and braiding-induced magnetic energy in an active-region corona

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thalmann, J. K.; Tiwari, S. K.; Wiegelmann, T., E-mail: julia.thalmann@uni-graz.at

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 withmore » 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.« less

Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates

PubMed Central

Batra, Romesh C.; Porfiri, Maurizio; Spinello, Davide

2008-01-01

We study the influence of von Kármán nonlinearity, van der Waals force, and thermal stresses on pull-in instability and small vibrations of electrostatically actuated microplates. We use the Galerkin method to develop a tractable reduced-order model for electrostatically actuated clamped rectangular microplates in the presence of van der Waals forces and thermal stresses. More specifically, we reduce the governing two-dimensional nonlinear transient boundary-value problem to a single nonlinear ordinary differential equation. For the static problem, the pull-in voltage and the pull-in displacement are determined by solving a pair of nonlinear algebraic equations. The fundamental vibration frequency corresponding to a deflected configuration of the microplate is determined by solving a linear algebraic equation. The proposed reduced-order model allows for accurately estimating the combined effects of van der Waals force and thermal stresses on the pull-in voltage and the pull-in deflection profile with an extremely limited computational effort. PMID:27879752

Study on longitudinal force simulation of heavy-haul train

NASA Astrophysics Data System (ADS)

Chang, Chongyi; Guo, Gang; Wang, Junbiao; Ma, Yingming

2017-04-01

The longitudinal dynamics model of heavy-haul trains and air brake model used in the longitudinal train dynamics (LTDs) are established. The dry friction damping hysteretic characteristic of steel friction draft gears is simulated by the equation which describes the suspension forces in truck leaf springs. The model of draft gears introduces dynamic loading force, viscous friction of steel friction and the damping force. Consequently, the numerical model of the draft gears is brought forward. The equation of LTDs is strongly non-linear. In order to solve the response of the strongly non-linear system, the high-precision and equilibrium iteration method based on the Newmark-β method is presented and numerical analysis is made. Longitudinal dynamic forces of the 20,000 tonnes heavy-haul train are tested, and models and solution method provided are verified by the test results.

Force-free electrodynamics in dynamical curved spacetimes

NASA Astrophysics Data System (ADS)

McWilliams, Sean

2015-04-01

We present results on our study of force-free electrodynamics in curved spacetimes. Specifically, we present several improvements to what has become the established set of evolution equations, and we apply these to study the nonlinear stability of analytically known force-free solutions for the first time. We implement our method in a new pseudo-spectral code built on top of the SpEC code for evolving dynamic spacetimes. Finally, we revisit these known solutions and attempt to clarify some interesting properties that render them analytically tractable. Finally, we preview some new work that similarly revisits the established approach to solving another problem in numerical relativity: the post-merger recoil from asymmetric gravitational-wave emission. These new results may have significant implications for the parameter dependence of recoils, and consequently on the statistical expectations for recoil velocities of merged systems.

Computation of Relative Magnetic Helicity in Spherical Coordinates

NASA Astrophysics Data System (ADS)

Moraitis, Kostas; Pariat, Étienne; Savcheva, Antonia; Valori, Gherardo

2018-06-01

Magnetic helicity is a quantity of great importance in solar studies because it is conserved in ideal magnetohydrodynamics. While many methods for computing magnetic helicity in Cartesian finite volumes exist, in spherical coordinates, the natural coordinate system for solar applications, helicity is only treated approximately. We present here a method for properly computing the relative magnetic helicity in spherical geometry. The volumes considered are finite, of shell or wedge shape, and the three-dimensional magnetic field is considered to be fully known throughout the studied domain. Testing of the method with well-known, semi-analytic, force-free magnetic-field models reveals that it has excellent accuracy. Further application to a set of nonlinear force-free reconstructions of the magnetic field of solar active regions and comparison with an approximate method used in the past indicates that the proposed method can be significantly more accurate, thus making our method a promising tool in helicity studies that employ spherical geometry. Additionally, we determine and discuss the applicability range of the approximate method.

Vibration isolation using extreme geometric nonlinearity

NASA Astrophysics Data System (ADS)

Virgin, L. N.; Santillan, S. T.; Plaut, R. H.

2008-08-01

A highly deformed, slender beam (or strip), attached to a vertically oscillating base, is used in a vibration isolation application to reduce the motion of a supported mass. The isolator is a thin strip that is bent so that the two ends are clamped together, forming a loop. The clamped ends are attached to an excitation source and the supported system is attached at the loop midpoint directly above the base. The strip is modeled as an elastica, and the resulting nonlinear boundary value problem is solved numerically using a shooting method. First the equilibrium shapes of the loop with varying static loads and lengths are studied. The analysis reveals a large degree of stiffness tunability; the stiffness is dependent on the geometric configuration, which itself is determined by the supported mass, loop length, and loop self-weight. Free vibration frequencies and mode shapes are also found. Finally, the case of forced vibration is studied, and the displacement transmissibility over a large range of forcing frequencies is determined for varying parameter values. Experiments using polycarbonate strips are conducted to verify equilibrium and dynamic behavior.

Buckling analysis of carbon nanotube bundles under axial compressive, bending and torsional loadings via a structural mechanics model

NASA Astrophysics Data System (ADS)

Lashkari Zadeh, Ali; Shariati, Mahmoud; Torabi, Hamid

2012-11-01

A structural mechanics model is employed for the investigation of the buckling behavior of carbon nanotube bundles of three single-walled carbon nanotubes (SWCNTs) under axial compressive, bending and torsional loadings. The effects of van der Waals (vdW) forces are further modeled using a nonlinear spring element.The effects of different types of boundary conditions are studied for nanotubes with various aspect ratios. The results reveal that bundles comprising longer SWCNTs exhibit lower critical buckling load. Moreover, for the fixed-free boundary condition the rate of critical buckling load reduction is highest, while the lowest critical buckling load occurs. Simulations show good agreement between our model and molecular dynamics results.

Nonlinear modeling of forced magnetic reconnection in slab geometry with NIMROD

NASA Astrophysics Data System (ADS)

Beidler, M. T.; Callen, J. D.; Hegna, C. C.; Sovinec, C. R.

2017-05-01

The nonlinear, extended-magnetohydrodynamic (MHD) code NIMROD is benchmarked with the theory of time-dependent forced magnetic reconnection induced by small resonant fields in slab geometry in the context of visco-resistive MHD modeling. Linear computations agree with time-asymptotic, linear theory of flow screening of externally applied fields. The inclusion of flow in nonlinear computations can result in mode penetration due to the balance between electromagnetic and viscous forces in the time-asymptotic state, which produces bifurcations from a high-slip state to a low-slip state as the external field is slowly increased. We reproduce mode penetration and unlocking transitions by employing time-dependent externally applied magnetic fields. Mode penetration and unlocking exhibit hysteresis and occur at different magnitudes of applied field. We also establish how nonlinearly determined flow screening of the resonant field is affected by the square of the magnitude of the externally applied field. These results emphasize that the inclusion of nonlinear physics is essential for accurate prediction of the reconnected field in a flowing plasma.

Multibody dynamic analysis using a rotation-free shell element with corotational frame

NASA Astrophysics Data System (ADS)

Shi, Jiabei; Liu, Zhuyong; Hong, Jiazhen

2018-03-01

Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore, the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model.

Full nonlinear treatment of the global thermospheric wind system. Part 1: Mathematical method and analysis of forces

NASA Technical Reports Server (NTRS)

Blum, P. W.; Harris, I.

1973-01-01

The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all the nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In part 1 the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analysed.

Efficient techniques for forced response involving linear modal components interconnected by discrete nonlinear connection elements

NASA Astrophysics Data System (ADS)

Avitabile, Peter; O'Callahan, John

2009-01-01

Generally, response analysis of systems containing discrete nonlinear connection elements such as typical mounting connections require the physical finite element system matrices to be used in a direct integration algorithm to compute the nonlinear response analysis solution. Due to the large size of these physical matrices, forced nonlinear response analysis requires significant computational resources. Usually, the individual components of the system are analyzed and tested as separate components and their individual behavior may essentially be linear when compared to the total assembled system. However, the joining of these linear subsystems using highly nonlinear connection elements causes the entire system to become nonlinear. It would be advantageous if these linear modal subsystems could be utilized in the forced nonlinear response analysis since much effort has usually been expended in fine tuning and adjusting the analytical models to reflect the tested subsystem configuration. Several more efficient techniques have been developed to address this class of problem. Three of these techniques given as: equivalent reduced model technique (ERMT);modal modification response technique (MMRT); andcomponent element method (CEM); are presented in this paper and are compared to traditional methods.

Stability, Nonlinearity and Reliability of Electrostatically Actuated MEMS Devices

PubMed Central

Zhang, Wen-Ming; Meng, Guang; Chen, Di

2007-01-01

Electrostatic micro-electro-mechanical system (MEMS) is a special branch with a wide range of applications in sensing and actuating devices in MEMS. This paper provides a survey and analysis of the electrostatic force of importance in MEMS, its physical model, scaling effect, stability, nonlinearity and reliability in detail. It is necessary to understand the effects of electrostatic forces in MEMS and then many phenomena of practical importance, such as pull-in instability and the effects of effective stiffness, dielectric charging, stress gradient, temperature on the pull-in voltage, nonlinear dynamic effects and reliability due to electrostatic forces occurred in MEMS can be explained scientifically, and consequently the great potential of MEMS technology could be explored effectively and utilized optimally. A simplified parallel-plate capacitor model is proposed to investigate the resonance response, inherent nonlinearity, stiffness softened effect and coupled nonlinear effect of the typical electrostatically actuated MEMS devices. Many failure modes and mechanisms and various methods and techniques, including materials selection, reasonable design and extending the controllable travel range used to analyze and reduce the failures are discussed in the electrostatically actuated MEMS devices. Numerical simulations and discussions indicate that the effects of instability, nonlinear characteristics and reliability subjected to electrostatic forces cannot be ignored and are in need of further investigation.

Mathematical models of human paralyzed muscle after long-term training.

PubMed

Law, L A Frey; Shields, R K

2007-01-01

Spinal cord injury (SCI) results in major musculoskeletal adaptations, including muscle atrophy, faster contractile properties, increased fatigability, and bone loss. The use of functional electrical stimulation (FES) provides a method to prevent paralyzed muscle adaptations in order to sustain force-generating capacity. Mathematical muscle models may be able to predict optimal activation strategies during FES, however muscle properties further adapt with long-term training. The purpose of this study was to compare the accuracy of three muscle models, one linear and two nonlinear, for predicting paralyzed soleus muscle force after exposure to long-term FES training. Further, we contrasted the findings between the trained and untrained limbs. The three models' parameters were best fit to a single force train in the trained soleus muscle (N=4). Nine additional force trains (test trains) were predicted for each subject using the developed models. Model errors between predicted and experimental force trains were determined, including specific muscle force properties. The mean overall error was greatest for the linear model (15.8%) and least for the nonlinear Hill Huxley type model (7.8%). No significant error differences were observed between the trained versus untrained limbs, although model parameter values were significantly altered with training. This study confirmed that nonlinear models most accurately predict both trained and untrained paralyzed muscle force properties. Moreover, the optimized model parameter values were responsive to the relative physiological state of the paralyzed muscle (trained versus untrained). These findings are relevant for the design and control of neuro-prosthetic devices for those with SCI.

The Effect of Systematic Error in Forced Oscillation Testing

NASA Technical Reports Server (NTRS)

Williams, Brianne Y.; Landman, Drew; Flory, Isaac L., IV; Murphy, Patrick C.

2012-01-01

One of the fundamental problems in flight dynamics is the formulation of aerodynamic forces and moments acting on an aircraft in arbitrary motion. Classically, conventional stability derivatives are used for the representation of aerodynamic loads in the aircraft equations of motion. However, for modern aircraft with highly nonlinear and unsteady aerodynamic characteristics undergoing maneuvers at high angle of attack and/or angular rates the conventional stability derivative model is no longer valid. Attempts to formulate aerodynamic model equations with unsteady terms are based on several different wind tunnel techniques: for example, captive, wind tunnel single degree-of-freedom, and wind tunnel free-flying techniques. One of the most common techniques is forced oscillation testing. However, the forced oscillation testing method does not address the systematic and systematic correlation errors from the test apparatus that cause inconsistencies in the measured oscillatory stability derivatives. The primary objective of this study is to identify the possible sources and magnitude of systematic error in representative dynamic test apparatuses. Sensitivities of the longitudinal stability derivatives to systematic errors are computed, using a high fidelity simulation of a forced oscillation test rig, and assessed using both Design of Experiments and Monte Carlo methods.

Free magnetic energy and relative magnetic helicity diagnostics for the quality of NLFF field extrapolations

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.

Analysis of Nonlinear Dynamics in Linear Compressors Driven by Linear Motors

NASA Astrophysics Data System (ADS)

Chen, Liangyuan

2018-03-01

The analysis of dynamic characteristics of the mechatronics system is of great significance for the linear motor design and control. Steady-state nonlinear response characteristics of a linear compressor are investigated theoretically based on the linearized and nonlinear models. First, the influence factors considering the nonlinear gas force load were analyzed. Then, a simple linearized model was set up to analyze the influence on the stroke and resonance frequency. Finally, the nonlinear model was set up to analyze the effects of piston mass, spring stiffness, driving force as an example of design parameter variation. The simulating results show that the stroke can be obtained by adjusting the excitation amplitude, frequency and other adjustments, the equilibrium position can be adjusted by adjusting the DC input, and to make the more efficient operation, the operating frequency must always equal to the resonance frequency.

Application of viscous and Iwan modal damping models to experimental measurements from bolted structures

DOE PAGES

Deaner, Brandon J.; Allen, Matthew S.; Starr, Michael James; ...

2015-01-20

Measurements are presented from a two-beam structure with several bolted interfaces in order to characterize the nonlinear damping introduced by the joints. The measurements (all at force levels below macroslip) reveal that each underlying mode of the structure is well approximated by a single degree-of-freedom (SDOF) system with a nonlinear mechanical joint. At low enough force levels, the measurements show dissipation that scales as the second power of the applied force, agreeing with theory for a linear viscously damped system. This is attributed to linear viscous behavior of the material and/or damping provided by the support structure. At larger forcemore » levels, the damping is observed to behave nonlinearly, suggesting that damping from the mechanical joints is dominant. A model is presented that captures these effects, consisting of a spring and viscous damping element in parallel with a four-parameter Iwan model. As a result, the parameters of this model are identified for each mode of the structure and comparisons suggest that the model captures the stiffness and damping accurately over a range of forcing levels.« less

A model for flexi-bar to evaluate intervertebral disc and muscle forces in exercises.

PubMed

Abdollahi, Masoud; Nikkhoo, Mohammad; Ashouri, Sajad; Asghari, Mohsen; Parnianpour, Mohamad; Khalaf, Kinda

2016-10-01

This study developed and validated a lumped parameter model for the FLEXI-BAR, a popular training instrument that provides vibration stimulation. The model which can be used in conjunction with musculoskeletal-modeling software for quantitative biomechanical analyses, consists of 3 rigid segments, 2 torsional springs, and 2 torsional dashpots. Two different sets of experiments were conducted to determine the model's key parameters including the stiffness of the springs and the damping ratio of the dashpots. In the first set of experiments, the free vibration of the FLEXI-BAR with an initial displacement at its end was considered, while in the second set, forced oscillations of the bar were studied. The properties of the mechanical elements in the lumped parameter model were derived utilizing a non-linear optimization algorithm which minimized the difference between the model's prediction and the experimental data. The results showed that the model is valid (8% error) and can be used for simulating exercises with the FLEXI-BAR for excitations in the range of the natural frequency. The model was then validated in combination with AnyBody musculoskeletal modeling software, where various lumbar disc, spinal muscles and hand muscles forces were determined during different FLEXI-BAR exercise simulations. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

Effect of buoyancy on appearance and characteristics of surface tension repeated auto-oscillations.

PubMed

Kovalchuk, N M; Vollhardt, D

2005-08-11

The effect of buoyancy on spontaneous repeated nonlinear oscillations of surface tension, which appear at the free liquid interface by dissolution of a surfactant droplet under the interface, is considered on the basis of direct numerical simulation of the model system behavior. The oscillations are the result of periodically rising and fading Marangoni instability. The buoyancy force per se cannot lead to the oscillatory behavior in the considered system, but it influences strongly both the onset and decay of the instability and therefore, affects appearance and characteristics of the oscillations. If the surfactant solution density is smaller than the density of the pure liquid, then the buoyancy force leads to a considerable decrease of the induction period and the period of oscillations. The buoyancy force affects also the dependence of the oscillation characteristics on the system dimensions. The results of the simulations are compared with the available experimental data.

Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Freitas, Celso, E-mail: cbnfreitas@gmail.com; Macau, Elbert, E-mail: elbert.macau@inpe.br; Pikovsky, Arkady, E-mail: pikovsky@uni-potsdam.de

2015-04-15

We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the fullmore » synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones.« less

Nonlinear finite-element analysis of nanoindentation of viral capsids

NASA Astrophysics Data System (ADS)

Gibbons, Melissa M.; Klug, William S.

2007-03-01

Recent atomic force microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity. To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity. Homogeneous, isotropic, elastic, thick-shell models are proposed for two capsids: the spherical cowpea chlorotic mottle virus (CCMV), and the ellipsocylindrical bacteriophage ϕ29 . As analyzed by the finite-element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions. The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive particulars, and greatly influenced by geometric and kinematic details. Nonlinear stiffening and softening of the force response is dependent on the AFM tip dimensions and shell thickness. Fits of the models capture the roughly linear behavior observed in experimental measurements and result in estimates of Young’s moduli of ≈280-360MPa for CCMV and ≈4.5GPa for ϕ29 .

High angle of attack control law development for a free-flight wind tunnel model using direct eigenstructure assignment

NASA Technical Reports Server (NTRS)

Wendel, Thomas R.; Boland, Joseph R.; Hahne, David E.

1991-01-01

Flight-control laws are developed for a wind-tunnel aircraft model flying at a high angle of attack by using a synthesis technique called direct eigenstructure assignment. The method employs flight guidelines and control-power constraints to develop the control laws, and gain schedules and nonlinear feedback compensation provide a framework for considering the nonlinear nature of the attack angle. Linear and nonlinear evaluations show that the control laws are effective, a conclusion that is further confirmed by a scale model used for free-flight testing.

A displacement-based approach for determining non-linear effects on pre-tensioned-cable cross-braced structures

NASA Astrophysics Data System (ADS)

Giaccu, Gian Felice; Caracoglia, Luca

2017-04-01

Pre-tensioned-cable bracing systems are widely employed in structural engineering to limit lateral deflections and stabilize structures. A suitable configuration of the pre-tensioned-cable bracing systems in a structure is an important issue since the internal force distribution, emerging from the interaction with the existing structure, significantly affects the structural dynamic behavior. The design, however, is often based on the intuition and the previous experience of the engineer. In recent years, the authors have been investigating the non-linear dynamic response of cable systems, installed on cable-stayed bridges, and in particular the so-called "cable-cross-tie systems" forming a cable network. The bracing cables (cross-ties) can exhibit slackening or snapping. Therefore, a non-linear unilateral model, combined with the taut-cable theory, is required to simulate the incipient slackening conditions in the stays. Capitalizing from this work on non-linear cable dynamics, this paper proposes a new approach to analyze, in laterally- braced truss structures, the unilateral effects and dynamic response accounting for the loss in the pre-tensioning force imparted to the bracing cables. This effect leads to non-linear vibration of the structure. In this preliminary study, the free vibrations of the structure are investigated by using the "Equivalent Linearization Method". A performance coefficient, a real positive number between 0.5 and 1.0, is defined and employed to monitor the relative reduction in the apparent stiffness of the braces during structural vibration, "mode by mode". It is shown that the system can exhibit alternate unilateral behavior of the cross-braces. A reduction of the performance coefficient close to fifty percent is observed in the braces when the initial pre-tensioning force is small. On the other hand the performance coefficient tends to one in the case of a high level of pre-stress. It is concluded that the performance coefficient may possibly be used as an indicator for the design of the braces since a suitable selection of the initial pre-tensioning force can avoid slackening in the braces.

Unstable force analysis for induction motor eccentricity

NASA Astrophysics Data System (ADS)

Han, Xu; Palazzolo, Alan

2016-05-01

The increasing popularity of motors in machinery trains has led to an intensified interest in the forces they produce that may influence machinery vibration. Motor design typically assumes a uniform air gap, however in practice all motors operate with the rotor slightly displaced from the motor centerline in what is referred to as an eccentric position. Rotor center eccentricity can cause a radially unbalanced magnetic field when the motor is operating. This will results in both a radial force pulling the motor further away from the center, and a tangential force which can induce a vibration stability problem. In this paper, a magnetic equivalent circuit MEC modeling method is proposed to calculate both the radial and tangential motor eccentric force. The treatment of tangential force determination is rarely addressed, but it is very important for rotordynamic vibration stability evaluation. The proposed model is also coupled with the motor electric circuit model to provide capability for transient vibration simulations. FEM is used to verify the MEC model. A parametric study is performed on the motor radial and tangential eccentric forces. Also a Jeffcott rotor model is used to study the influence of the motor eccentric force on mechanical vibration stability and nonlinear behavior. Furthermore, a stability criteria for the bearing damping is provided. The motor radial and tangential eccentric forces are both curved fitted to include their nonlinearity in time domain transient simulation for both a Jeffcott rotor model and a geared machinery train with coupled torsional-lateral motion. Nonlinear motions are observed, including limit cycles and bifurcation induced vibration amplitude jumps.

Nonlinear force propagation, anisotropic stiffening and non-affine relaxation in a model cytoskeleton

NASA Astrophysics Data System (ADS)

Mizuno, Daisuke; Head, David; Ikebe, Emi; Nakamasu, Akiko; Kinoshita, Suguru; Peijuan, Zhang; Ando, Shoji

2013-03-01

Forces are generated heterogeneously in living cells and transmitted through cytoskeletal networks that respond highly non-linearly. Here, we carry out high-bandwidth passive microrheology on vimentin networks reconstituted in vitro, and observe the nonlinear mechanical response due to forces propagating from a local source applied by an optical tweezer. Since the applied force is constant, the gel becomes equilibrated and the fluctuation-dissipation theorem can be employed to deduce the viscoelasticity of the local environment from the thermal fluctuations of colloidal probes. Our experiments unequivocally demonstrate the anisotropic stiffening of the cytoskeletal network behind the applied force, with greater stiffening in the parallel direction. Quantitative agreement with an affine continuum model is obtained, but only for the response at certain frequency ~ 10-1000 Hz which separates the high-frequency power law and low-frequency elastic behavior of the network. We argue that the failure of the model at lower frequencies is due to the presence of non-affinity, and observe that zero-frequency changes in particle separation can be fitted when an independently-measured, empirical nonaffinity factor is applied.

Inheritance of Cell-Cycle Duration in the Presence of Periodic Forcing

NASA Astrophysics Data System (ADS)

Mosheiff, Noga; Martins, Bruno M. C.; Pearl-Mizrahi, Sivan; Grünberger, Alexander; Helfrich, Stefan; Mihalcescu, Irina; Kohlheyer, Dietrich; Locke, James C. W.; Glass, Leon; Balaban, Nathalie Q.

2018-04-01

Periodic forcing of nonlinear oscillators leads to a large number of dynamic behaviors. The coupling of the cell cycle to the circadian clock provides a biological realization of such forcing. A previous model of forcing leads to nontrivial relations between correlations along cell lineages. Here, we present a simplified two-dimensional nonlinear map for the periodic forcing of the cell cycle. Using high-throughput single-cell microscopy, we have studied the correlations between cell-cycle duration in discrete lineages of several different organisms, including those with known coupling to a circadian clock and those without known coupling to a circadian clock. The model reproduces the paradoxical correlations and predicts new features that can be compared with the experimental data. By fitting the model to the data, we extract the important parameters that govern the dynamics. Interestingly, the model reproduces bimodal distributions for cell-cycle duration, as well as the gating of cell division by the phase of the clock, without having been explicitly fed into the model. In addition, the model predicts that circadian coupling may increase cell-to-cell variability in a clonal population of cells. In agreement with this prediction, deletion of the circadian clock reduces variability. Our results show that simple correlations can identify systems under periodic forcing and that studies of nonlinear coupling of biological oscillators provide insight into basic cellular processes of growth.

Parametric model of servo-hydraulic actuator coupled with a nonlinear system: Experimental validation

NASA Astrophysics Data System (ADS)

Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.

2018-05-01

Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.

Study on the impulsive pressure of tank oscillating by force towards multiple degrees of freedom

NASA Astrophysics Data System (ADS)

Hibi, Shigeyuki

2018-06-01

Impulsive loads should be excited under nonlinear phenomena with free surface fluctuating severely such as sloshing and slamming. Estimating impulsive loads properly are important to recent numerical simulations. But it is still difficult to rely on the results of simulations perfectly because of the nonlinearity of the phenomena. In order to develop the algorithm of numerical simulations experimental results of nonlinear phenomena are needed. In this study an apparatus which can oscillate a tank by force was introduced in order to investigate impulsive pressure on the wall of the tank. This apparatus can oscillate it simultaneously towards 3 degrees of freedom with each phase differences. The impulsive pressure under the various combinations of oscillation direction was examined and the specific phase differences to appear the largest peak values of pressure were identified. Experimental results were verified through FFT analysis and statistical methods.

Nonlinear zero-sum differential game analysis by singular perturbation methods

NASA Technical Reports Server (NTRS)

Sinar, J.; Farber, N.

1982-01-01

A class of nonlinear, zero-sum differential games, exhibiting time-scale separation properties, can be analyzed by singular-perturbation techniques. The merits of such an analysis, leading to an approximate game solution, as well as the 'well-posedness' of the formulation, are discussed. This approach is shown to be attractive for investigating pursuit-evasion problems; the original multidimensional differential game is decomposed to a 'simple pursuit' (free-stream) game and two independent (boundary-layer) optimal-control problems. Using multiple time-scale boundary-layer models results in a pair of uniformly valid zero-order composite feedback strategies. The dependence of suboptimal strategies on relative geometry and own-state measurements is demonstrated by a three dimensional, constant-speed example. For game analysis with realistic vehicle dynamics, the technique of forced singular perturbations and a variable modeling approach is proposed. Accuracy of the analysis is evaluated by comparison with the numerical solution of a time-optimal, variable-speed 'game of two cars' in the horizontal plane.

Mixed models and reduced/selective integration displacement models for nonlinear analysis of curved beams

NASA Technical Reports Server (NTRS)

Noor, A. K.; Peters, J. M.

1981-01-01

Simple mixed models are developed for use in the geometrically nonlinear analysis of deep arches. A total Lagrangian description of the arch deformation is used, the analytical formulation being based on a form of the nonlinear deep arch theory with the effects of transverse shear deformation included. The fundamental unknowns comprise the six internal forces and generalized displacements of the arch, and the element characteristic arrays are obtained by using Hellinger-Reissner mixed variational principle. The polynomial interpolation functions employed in approximating the forces are one degree lower than those used in approximating the displacements, and the forces are discontinuous at the interelement boundaries. Attention is given to the equivalence between the mixed models developed herein and displacement models based on reduced integration of both the transverse shear and extensional energy terms. The advantages of mixed models over equivalent displacement models are summarized. Numerical results are presented to demonstrate the high accuracy and effectiveness of the mixed models developed and to permit a comparison of their performance with that of other mixed models reported in the literature.

Hands-on Force Spectroscopy: Weird Springs and Protein Folding

ERIC Educational Resources Information Center

Euler, Manfred

2008-01-01

A force spectroscopy model experiment is presented using a low-cost tensile apparatus described earlier. Force-extension measurements of twisted rubber bands are obtained. They exhibit a complex nonlinear elastic behaviour that resembles atomic force spectroscopy investigations of molecules of titin, a muscle protein. The model experiments open up…

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

NASA Astrophysics Data System (ADS)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

Cogging force investigation of a free piston permanent magnet linear generator

NASA Astrophysics Data System (ADS)

Abdalla, I. I.; Zainal, A. E. Z.; Ramlan, N. A.; Firmansyah; Aziz, A. R. A.; Heikal, M. R.

2017-10-01

Better performance and higher efficiency of the vehicles can be achieved by using free piston engine, in which the piston is connected directly to the linear generator and waiving of any mechanical means. The free piston engine has the ability to overcome or reduce many of the challenges, such as the carbon dioxide (CO2) emission and fossil fuel consumption. The cogging force produces undesired vibration and acoustic noise in the generator. However, the cogging force must be minimized as much as possible, in order to have a high performance. This paper studies the effects of ferromagnetic materials on the cogging force of the permanent magnet linear generator (PMLG) to be used in a free piston engine using nonlinear finite-element analysis (FEA) under ANSYS Maxwell. The comparisons have been established for the cogging force of the PMLG under various translator velocities and three different ferromagnetic materials for the stator core, namely, Silicon Steel laminations, Mild Steel and Somaloy. It has been shown that the PMLG with a stator core made of Somaloy has a lower cogging force among them. Furthermore, the induced voltage of the PMLG at different accelerations has been studied. It is found that the PMLG with Mild Steel and Somaloy, respectively give larger induced voltage. Moreover, as the translator speed increase the induced voltage increased.

Dry wind tunnel system

NASA Technical Reports Server (NTRS)

Chen, Ping-Chih (Inventor)

2013-01-01

This invention is a ground flutter testing system without a wind tunnel, called Dry Wind Tunnel (DWT) System. The DWT system consists of a Ground Vibration Test (GVT) hardware system, a multiple input multiple output (MIMO) force controller software, and a real-time unsteady aerodynamic force generation software, that is developed from an aerodynamic reduced order model (ROM). The ground flutter test using the DWT System operates on a real structural model, therefore no scaled-down structural model, which is required by the conventional wind tunnel flutter test, is involved. Furthermore, the impact of the structural nonlinearities on the aeroelastic stability can be included automatically. Moreover, the aeroservoelastic characteristics of the aircraft can be easily measured by simply including the flight control system in-the-loop. In addition, the unsteady aerodynamics generated computationally is interference-free from the wind tunnel walls. Finally, the DWT System can be conveniently and inexpensively carried out as a post GVT test with the same hardware, only with some possible rearrangement of the shakers and the inclusion of additional sensors.

Algebraic motion of vertically displacing plasmas

NASA Astrophysics Data System (ADS)

Bhattacharjee, Amitava; Pfefferle, David; Hirvijoki, Eero

2017-10-01

The vertical displacement of tokamak plasmas is modelled during the non-linear phase by a free-moving current-carrying rod coupled to a set of fixed conducting wires and a cylindrical conducting shell. The models capture the leading term in a Taylor expansion of the Green's function for the interaction between the plasma column and the vacuum vessel. The plasma is assumed not to vary during the VDE such that it behaves as a rigid body. In the limit of perfectly conducting structures, the plasma is prevented from coming in contact with the wall due to steep effective potential barriers by the eddy currents, and will hence oscillate at Alfvénic frequencies about a given force-free position. In addition to damping oscillations, resistivity allows for the column to drift towards the vessel on slow flux penetration timescales. The initial exponential motion of the plasma, i.e. the resistive vertical instability, is succeeded by a non-linear sinking behaviour, that is shown analytically to be algebraic and decelerative. The acceleration of the plasma column often observed in experiments is thus conjectured to originate from an early sharing of toroidal current between the core, the halo plasma and the wall or from the thermal quench dynamics precipitating loss of plasma current

Force Control and Nonlinear Master-Slave Force Profile to Manage an Admittance Type Multi-Fingered Haptic User Interface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anthony L. Crawford

2012-08-01

Natural movements and force feedback are important elements in using teleoperated equipment if complex and speedy manipulation tasks are to be accomplished in remote and/or hazardous environments, such as hot cells, glove boxes, decommissioning, explosives disarmament, and space to name a few. In order to achieve this end the research presented in this paper has developed an admittance type exoskeleton like multi-fingered haptic hand user interface that secures the user’s palm and provides 3-dimensional force feedback to the user’s fingertips. Atypical to conventional haptic hand user interfaces that limit themselves to integrating the human hand’s characteristics just into the system’smore » mechanical design this system also perpetuates that inspiration into the designed user interface’s controller. This is achieved by manifesting the property differences of manipulation and grasping activities as they pertain to the human hand into a nonlinear master-slave force relationship. The results presented in this paper show that the admittance-type system has sufficient bandwidth that it appears nearly transparent to the user when the user is in free motion and when the system is subjected to a manipulation task, increased performance is achieved using the nonlinear force relationship compared to the traditional linear scaling techniques implemented in the vast majority of systems.« less

Nonlinear regional warming with increasing CO2 concentrations

NASA Astrophysics Data System (ADS)

Good, Peter; Lowe, Jason A.; Andrews, Timothy; Wiltshire, Andrew; Chadwick, Robin; Ridley, Jeff K.; Menary, Matthew B.; Bouttes, Nathaelle; Dufresne, Jean Louis; Gregory, Jonathan M.; Schaller, Nathalie; Shiogama, Hideo

2015-02-01

When considering adaptation measures and global climate mitigation goals, stakeholders need regional-scale climate projections, including the range of plausible warming rates. To assist these stakeholders, it is important to understand whether some locations may see disproportionately high or low warming from additional forcing above targets such as 2 K (ref. ). There is a need to narrow uncertainty in this nonlinear warming, which requires understanding how climate changes as forcings increase from medium to high levels. However, quantifying and understanding regional nonlinear processes is challenging. Here we show that regional-scale warming can be strongly superlinear to successive CO2 doublings, using five different climate models. Ensemble-mean warming is superlinear over most land locations. Further, the inter-model spread tends to be amplified at higher forcing levels, as nonlinearities grow--especially when considering changes per kelvin of global warming. Regional nonlinearities in surface warming arise from nonlinearities in global-mean radiative balance, the Atlantic meridional overturning circulation, surface snow/ice cover and evapotranspiration. For robust adaptation and mitigation advice, therefore, potentially avoidable climate change (the difference between business-as-usual and mitigation scenarios) and unavoidable climate change (change under strong mitigation scenarios) may need different analysis methods.

3D WHOLE-PROMINENCE FINE STRUCTURE MODELING

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gunár, Stanislav; Mackay, Duncan H.

2015-04-20

We present the first 3D whole-prominence fine structure model. The model combines a 3D magnetic field configuration of an entire prominence obtained from nonlinear force-free field simulations, with a detailed description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model. Through the use of a novel radiative transfer visualization technique for the Hα line such plasma-loaded magnetic field model produces synthetic images of the modeled prominence comparable with high-resolution observations. This allows us for the first time to use a single technique tomore » consistently study, in both emission on the limb and absorption against the solar disk, the fine structures of prominences/filaments produced by a magnetic field model.« less

A contact stress model for multifingered grasps of rough objects

NASA Technical Reports Server (NTRS)

Sinha, Pramath Raj; Abel, Jacob M.

1990-01-01

The model developed utilizes a contact-stress analysis of an arbitrarily shaped object in a multifingered grasp. The fingers and the object are all treated as elastic bodies, and the region of contact is modeled as a deformable surface patch. The relationship between the friction and normal forces is nonlocal and nonlinear in nature and departs from the Coulomb approximation. The nature of the constraints arising out of conditions for compatibility and static equilibrium motivated the formulation of the model as a nonlinear constrained minimization problem. The model is able to predict the magnitude of the inwardly directed normal forces and both the magnitude and direction of the tangential (friction) forces at each finger-object interface for grasped objects in static equilibrium.

Dynamic contact forces on leukocyte microvilli and their penetration of the endothelial glycocalyx.

PubMed Central

Zhao, Y; Chien, S; Weinbaum, S

2001-01-01

We develop a theoretical model to examine the combined effect of gravity and microvillus length heterogeneity on tip contact force (F(m)(z)) during free rolling in vitro, including the initiation of L-, P-, and E-selectin tethers and the threshold behavior at low shear. F (m)(z) grows nonlinearly with shear. At shear stress of 1 dyn/cm(2), F(m)(z) is one to two orders of magnitude greater than the 0.1 pN force for gravitational settling without flow. At shear stresses > 0.2 dyn/cm(2) only the longest microvilli contact the substrate; hence at the shear threshold (0.4 dyn/cm(2) for L-selectin), only 5% of microvilli can initiate tethering interaction. The characteristic time for tip contact is surprisingly short, typically 0.1-1 ms. This model is then applied in vivo to explore the free-rolling interaction of leukocyte microvilli with endothelial glycocalyx and the necessary conditions for glycocalyx penetration to initiate cell rolling. The model predicts that for arteriolar capillaries even the longest microvilli cannot initiate rolling, except in regions of low shear or flow reversal. In postcapillary venules, where shear stress is approximately 2 dyn/cm(2), tethering interactions are highly likely, provided that there are some relatively long microvilli. Once tethering is initiated, rolling tends to ensue because F(m)(z) and contact duration will both increase substantially to facilitate glycocalyx penetration by the shorter microvilli. PMID:11222278

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables

NASA Astrophysics Data System (ADS)

Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino

2013-12-01

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables.

PubMed

Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino

2013-12-07

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.

Comment on "Scaling regimes and linear/nonlinear responses of last millennium climate to volcanic and solar forcing" by S. Lovejoy and C. Varotsos (2016)

NASA Astrophysics Data System (ADS)

Rypdal, Kristoffer; Rypdal, Martin

2016-07-01

Lovejoy and Varotsos (2016) (L&V) analyse the temperature response to solar, volcanic, and solar plus volcanic forcing in the Zebiak-Cane (ZC) model, and to solar and solar plus volcanic forcing in the Goddard Institute for Space Studies (GISS) E2-R model. By using a simple wavelet filtering technique they conclude that the responses in the ZC model combine subadditively on timescales from 50 to 1000 years. Nonlinear response on shorter timescales is claimed by analysis of intermittencies in the forcing and the temperature signal for both models. The analysis of additivity in the ZC model suffers from a confusing presentation of results based on an invalid approximation, and from ignoring the effect of internal variability. We present tests without this approximation which are not able to detect nonlinearity in the response, even without accounting for internal variability. We also demonstrate that internal variability will appear as subadditivity if it is not accounted for. L&V's analysis of intermittencies is based on a mathematical result stating that the intermittencies of forcing and response are the same if the response is linear. We argue that there are at least three different factors that may invalidate the application of this result for these data. It is valid only for a power-law response function; it assumes power-law scaling of structure functions of forcing as well as temperature signal; and the internal variability, which is strong at least on the short timescales, will exert an influence on temperature intermittence which is independent of the forcing. We demonstrate by a synthetic example that the differences in intermittencies observed by L&V easily can be accounted for by these effects under the assumption of a linear response. Our conclusion is that the analysis performed by L&V does not present valid evidence for a detectable nonlinear response in the global temperature in these climate models.

Nonlinear 2D arm dynamics in response to continuous and pulse-shaped force perturbations.

PubMed

Happee, Riender; de Vlugt, Erwin; van Vliet, Bart

2015-01-01

Ample evidence exists regarding the nonlinearity of the neuromuscular system but linear models are widely applied to capture postural dynamics. This study quantifies the nonlinearity of human arm postural dynamics applying 2D continuous force perturbations (0.2-40 Hz) inducing three levels of hand displacement (5, 15, 45 mm RMS) followed by force-pulse perturbations inducing large hand displacements (up to 250 mm) in a position task (PT) and a relax task (RT) recording activity of eight shoulder and elbow muscles. The continuous perturbation data were used to analyze the 2D endpoint dynamics in the frequency domain and to identify reflexive and intrinsic parameters of a linear neuromuscular shoulder-elbow model. Subsequently, it was assessed to what extent the large displacements in response to force pulses could be predicted from the 'small amplitude' linear neuromuscular model. Continuous and pulse perturbation responses with varying amplitudes disclosed highly nonlinear effects. In PT, a larger continuous perturbation induced stiffening with a factor of 1.5 attributed to task adaptation evidenced by increased co-contraction and reflexive activity. This task adaptation was even more profound in the pulse responses where reflexes and displacements were strongly affected by the presence and amplitude of preceding continuous perturbations. In RT, a larger continuous perturbation resulted in yielding with a factor of 3.8 attributed to nonlinear mechanical properties as no significant reflexive activity was found. Pulse perturbations always resulted in yielding where a model fitted to the preceding 5-mm continuous perturbations predicted only 37% of the recorded peak displacements in RT and 79% in PT. This demonstrates that linear neuromuscular models, identified using continuous perturbations with small amplitudes, strongly underestimate displacements in pulse-shaped (e.g., impact) loading conditions. The data will be used to validate neuromuscular models including nonlinear muscular (e.g., Hill and Huxley) and reflexive components.

Spin contribution to the ponderomotive force in a plasma.

PubMed

Brodin, G; Misra, A P; Marklund, M

2010-09-03

The concept of a ponderomotive force due to the intrinsic spin of electrons is developed. An expression containing both the classical as well as the spin-induced ponderomotive force is derived. The results are used to demonstrate that an electromagnetic pulse can induce a spin-polarized plasma. Furthermore, it is shown that, for certain parameters, the nonlinear backreaction on the electromagnetic pulse from the spin magnetization current can be larger than that from the classical free current. Suitable parameter values for a direct test of this effect are presented.

Inefficient epidemic spreading in scale-free networks

NASA Astrophysics Data System (ADS)

Piccardi, Carlo; Casagrandi, Renato

2008-02-01

Highly heterogeneous degree distributions yield efficient spreading of simple epidemics through networks, but can be inefficient with more complex epidemiological processes. We study diseases with nonlinear force of infection whose prevalences can abruptly collapse to zero while decreasing the transmission parameters. We find that scale-free networks can be unable to support diseases that, on the contrary, are able to persist at high endemic levels in homogeneous networks with the same average degree.

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

DOE PAGES

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

2015-03-11

Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with thesemore » quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.« less

Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carlberg, Kevin; Tuminaro, Ray; Boggs, Paul

Our work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model retains key properties such as energy conservation and symplectic time-evolution maps. We focus on parameterized simple mechanical systems subjected to Rayleigh damping and external forces, and consider an application to nonlinear structural dynamics. To preserve structure, the method first approximates the system's “Lagrangian ingredients''---the Riemannian metric, the potential-energy function, the dissipation function, and the external force---and subsequently derives reduced-order equations of motion by applying the (forced) Euler--Lagrange equation with thesemore » quantities. Moreover, from the algebraic perspective, key contributions include two efficient techniques for approximating parameterized reduced matrices while preserving symmetry and positive definiteness: matrix gappy proper orthogonal decomposition and reduced-basis sparsification. Our results for a parameterized truss-structure problem demonstrate the practical importance of preserving Lagrangian structure and illustrate the proposed method's merits: it reduces computation time while maintaining high accuracy and stability, in contrast to existing nonlinear model-reduction techniques that do not preserve structure.« less

Vertical Distribution of Radiation Stress for Non-linear Shoaling Waves

NASA Astrophysics Data System (ADS)

Webb, B. M.; Slinn, D. N.

2004-12-01

The flux of momentum directed shoreward by an incident wave field, commonly referred to as the radiation stress, plays a significant role in nearshore circulation and, therefore, has a profound impact on the transport of pollutants, biota, and sediment in nearshore systems. Having received much attention since the seminal work of Longuet-Higgins and Stewart in the early 1960's, use of the radiation stress concept continues to be refined and evidence of its utility is widespread in literature pertaining to coastal and ocean science. A number of investigations, both numerical and analytical in nature, have used the concept of the radiation stress to derive appropriate forcing mechanisms that initiate cross-shore and longshore circulation, but typically in a depth-averaged sense due to a lack of information concerning the vertical distribution of the wave stresses. While depth-averaged nearshore circulation models are still widely used today, advancements in technology have permitted the adaptation of three-dimensional (3D) modeling techniques to study flow properties of complex nearshore circulation systems. It has been shown that the resulting circulation in these 3D models is very sensitive to the vertical distribution of the nearshore forcing, which have often been implemented as either depth-uniform or depth-linear distributions. Recently, analytical expressions describing the vertical structure of radiation stress components have appeared in the literature (see Mellor, 2003; Xia et al., 2004) but do not fully describe the magnitude and structure in the region bound by the trough and crest of non-linear, propagating waves. Utilizing a three-dimensional, non-linear, numerical model that resolves the time-dependent free surface, we present mean flow properties resulting from a simulation of Visser's (1984, 1991) laboratory experiment on uniform longshore currents. More specifically, we provide information regarding the vertical distribution of radiation stress components (Sxx and Sxy) resulting from obliquely incident, non-linear shoaling waves. Vertical profiles of the radiation stress components predicted by the numerical model are compared with published analytical solutions, expressions given by linear theory, and observations from an investigation employing second-order cnoidal wave theory.

Analysis of radial and longitudinal force of plasma wakefield generated by a chirped pulse laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghasemi, Leila; Afhami, Saeedeh; Eslami, Esmaeil, E-mail: eeslami@iust.ac.ir

2015-08-15

In present paper, the chirp effect of an electromagnetic pulse via an analytical model of wakefield generation is studied. Different types of chirps are employed in this study. Our results show that by the use of nonlinear chirped pulse the longitudinal wakefield and focusing force is stronger than that of linear chirped pulse. It is indicated that quadratic nonlinear chirped pulses are globally much efficient than periodic nonlinear chirped pulses. Our calculations also predict that in nonlinear chirped pulse case, the overlap of focusing and accelerating regions is broader than that achieved in linear chirped pulse.

Nonlinear force feedback control of piezoelectric-hydraulic pump actuator for automotive transmission shift control

NASA Astrophysics Data System (ADS)

Kim, Gi-Woo; Wang, K. W.

2008-03-01

In recent years, researchers have investigated the feasibility of utilizing piezoelectric-hydraulic pump based actuation systems for automotive transmission controls. This new concept could eventually reduce the complexity, weight, and fuel consumption of the current transmissions. In this research, we focus on how to utilize this new approach on the shift control of automatic transmissions (AT), which generally requires pressure profiling for friction elements during the operation. To illustrate the concept, we will consider the 1--> 2 up shift control using band brake friction elements. In order to perform the actuation force tracking for AT shift control, nonlinear force feedback control laws are designed based on the sliding mode theory for the given nonlinear system. This paper will describe the modeling of the band brake actuation system, the design of the nonlinear force feedback controller, and simulation and experimental results for demonstration of the new concept.

A Computer Code for Dynamic Stress Analysis of Media-Structure Problems with Nonlinearities (SAMSON). Volume III. User’s Manual.

DTIC Science & Technology

NONLINEAR SYSTEMS, LINEAR SYSTEMS, SUBROUTINES , SOIL MECHANICS, INTERFACES, DYNAMICS, LOADS(FORCES), FORCE(MECHANICS), DAMPING, ACCELERATION, ELASTIC...PROPERTIES, PLASTIC PROPERTIES, CRACKS , REINFORCING MATERIALS , COMPOSITE MATERIALS , FAILURE(MECHANICS), MECHANICAL PROPERTIES, INSTRUCTION MANUALS, DIGITAL COMPUTERS...STRESSES, *COMPUTER PROGRAMS), (*STRUCTURES, STRESSES), (*DATA PROCESSING, STRUCTURAL PROPERTIES), SOILS , STRAIN(MECHANICS), MATHEMATICAL MODELS

Experiments with a Magnetically Controlled Pendulum

ERIC Educational Resources Information Center

Kraftmakher, Yaakov

2007-01-01

A magnetically controlled pendulum is used for observing free and forced oscillations, including nonlinear oscillations and chaotic motion. A data-acquisition system stores the data and displays time series of the oscillations and related phase plane plots, Poincare maps, Fourier spectra and histograms. The decay constant of the pendulum can be…

Tethered swimming can be used to evaluate force contribution for short-distance swimming performance.

PubMed

Morouço, Pedro G; Marinho, Daniel A; Keskinen, Kari L; Badillo, Juan J; Marques, Mário C

2014-11-01

The purpose of this study was two-fold: (a) to compare stroke and the physiological responses between maximal tethered and free front crawl swimming and (b) to evaluate the contribution of force exertion for swimming performance over short distances. A total of 34 male swimmers, representing various levels of competitive performance, participated in this study. Each participant was tested in both a 30-second maximal tethered swimming test and a 50-m free swimming test. The tethered force parameters, the swimming speed, stroke (stroke rate [SR]), and the physiological responses (increase in blood lactate concentration [ΔBLa], heart rate, and rate of perceived exertion) were recorded and calculated. The results showed no differences in stroke and the physiological responses between tethered and free swimming, with a high level of agreement for the SR and ΔBLa. A strong correlation was obtained between the maximum impulse of force per stroke and the speed (r = 0.91; p < 0.001). Multiple regression analysis revealed that the maximum impulse and SR in the tethered condition explained 84% of the free swimming performance. The relationship between the swimming speed and maximum force tended to be nonlinear, whereas linear relationships were observed with the maximum impulse. This study demonstrates that tethered swimming does not significantly alter stroke and the physiological responses compared with free swimming, and that the maximum impulse per stroke should be used to evaluate the balance between force and the ability to effectively apply force during sprint swimming. Consequently, coaches can rely on tethered forces to identify strength deficits and improve swimming performance over short distances.

EXTRAPOLATION OF THE SOLAR CORONAL MAGNETIC FIELD FROM SDO/HMI MAGNETOGRAM BY A CESE-MHD-NLFFF CODE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang Chaowei; Feng Xueshang, E-mail: cwjiang@spaceweather.ac.cn, E-mail: fengx@spaceweather.ac.cn

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 activemore » 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.« less

A Boussinesq-scaled, pressure-Poisson water wave model

NASA Astrophysics Data System (ADS)

Donahue, Aaron S.; Zhang, Yao; Kennedy, Andrew B.; Westerink, Joannes J.; Panda, Nishant; Dawson, Clint

2015-02-01

Through the use of Boussinesq scaling we develop and test a model for resolving non-hydrostatic pressure profiles in nonlinear wave systems over varying bathymetry. A Green-Nagdhi type polynomial expansion is used to resolve the pressure profile along the vertical axis, this is then inserted into the pressure-Poisson equation, retaining terms up to a prescribed order and solved using a weighted residual approach. The model shows rapid convergence properties with increasing order of polynomial expansion which can be greatly improved through the application of asymptotic rearrangement. Models of Boussinesq scaling of the fully nonlinear O (μ2) and weakly nonlinear O (μN) are presented, the analytical and numerical properties of O (μ2) and O (μ4) models are discussed. Optimal basis functions in the Green-Nagdhi expansion are determined through manipulation of the free-parameters which arise due to the Boussinesq scaling. The optimal O (μ2) model has dispersion accuracy equivalent to a Padé [2,2] approximation with one extra free-parameter. The optimal O (μ4) model obtains dispersion accuracy equivalent to a Padé [4,4] approximation with two free-parameters which can be used to optimize shoaling or nonlinear properties. In comparison to experimental results the O (μ4) model shows excellent agreement to experimental data.

Liquid jet impingement normal to a disk in zero gravity. Ph.D. Thesis Toledo Univ.

NASA Technical Reports Server (NTRS)

Labus, T. L.

1977-01-01

The free surface shapes of circular liquid jets impinging normal to sharp-edged disks in zero gravity are determined. Zero gravity drop tower experiments yielded three distinct flow patterns that were classified in terms of the relative effects of surface tension and inertial forces. An order of magnitude analysis was conducted that indicated regions where viscous forces were not significant in the computation of free surface shapes. The free surface analysis was simplified by transforming the governing potential flow equations and boundary conditions into the inverse plane, where the stream function and velocity potential became the coordinates. The resulting nonlinear equations were solved by standard finite difference methods, and comparisons were made with the experimental data for the inertia dominated regime.

A nonlinear eigenvalue problem for self-similar spherical force-free magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 betweenmore » 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 discussed in the Appendix.« less

Dynamic modeling of moment wheel assemblies with nonlinear rolling bearing supports

NASA Astrophysics Data System (ADS)

Wang, Hong; Han, Qinkai; Luo, Ruizhi; Qing, Tao

2017-10-01

Moment wheel assemblies (MWA) have been widely used in spacecraft attitude control and large angle slewing maneuvers over the years. Understanding and controlling vibration of MWAs is a crucial factor to achieving the desired level of payload performance. Dynamic modeling of a MWA with nonlinear rolling bearing supports is conducted. An improved load distribution analysis is proposed to more accurately obtain the contact deformations and angles between the rolling balls and raceways. Then, the bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. The effects of preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication could all be reflected in the nonlinear bearing forces. Considering the mass imbalances of the flywheel, flexibility of supporting structures and rolling bearing nonlinearity, the dynamic model of a typical MWA is established based upon the energy theorem. Dynamic tests are conducted to verify the nonlinear dynamic model. The influences of flywheel mass eccentricity and inner/outer waviness amplitudes on the dynamic responses are discussed in detail. The obtained results would be useful for the design and vibration control of the MWA system.

Ultrasound shear wave simulation based on nonlinear wave propagation and Wigner-Ville Distribution analysis

NASA Astrophysics Data System (ADS)

Bidari, Pooya Sobhe; Alirezaie, Javad; Tavakkoli, Jahan

2017-03-01

This paper presents a method for modeling and simulation of shear wave generation from a nonlinear Acoustic Radiation Force Impulse (ARFI) that is considered as a distributed force applied at the focal region of a HIFU transducer radiating in nonlinear regime. The shear wave propagation is simulated by solving the Navier's equation from the distributed nonlinear ARFI as the source of the shear wave. Then, the Wigner-Ville Distribution (WVD) as a time-frequency analysis method is used to detect the shear wave at different local points in the region of interest. The WVD results in an estimation of the shear wave time of arrival, its mean frequency and local attenuation which can be utilized to estimate medium's shear modulus and shear viscosity using the Voigt model.

Analytical modeling of soliton interactions in a nonlocal nonlinear medium analogous to gravitational force

NASA Astrophysics Data System (ADS)

Zeng, Shihao; Chen, Manna; Zhang, Ting; Hu, Wei; Guo, Qi; Lu, Daquan

2018-01-01

We illuminate an analytical model of soliton interactions in lead glass by analogizing to a gravitational force system. The orbits of spiraling solitons under a long-range interaction are given explicitly and demonstrated to follow Newton's second law of motion and the Binet equation by numerical simulations. The condition for circular orbits is obtained and the oscillating orbits are proved not to be closed. We prove the analogy between the nonlocal nonlinear optical system and gravitational system and specify the quantitative relation of the quantity between the two models.

A Weakly Nonlinear Model for the Damping of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki

2016-10-01

In this paper, we address the stability of resonantly forced density waves in dense planetary rings. Goldreich & Tremaine have already argued that density waves might be unstable, depending on the relationship between the ring’s viscosity and the surface mass density. In the recent paper Schmidt et al., we have pointed out that when—within a fluid description of the ring dynamics—the criterion for viscous overstability is satisfied, forced spiral density waves become unstable as well. In this case, linear theory fails to describe the damping, but nonlinearity of the underlying equations guarantees a finite amplitude and eventually a damping of the wave. We apply the multiple scale formalism to derive a weakly nonlinear damping relation from a hydrodynamical model. This relation describes the resonant excitation and nonlinear viscous damping of spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients. The model consistently predicts density waves to be (linearly) unstable in a ring region where the conditions for viscous overstability are met. Sufficiently far away from the Lindblad resonance, the surface mass density perturbation is predicted to saturate to a constant value due to nonlinear viscous damping. The wave’s damping lengths of the model depend on certain input parameters, such as the distance to the threshold for viscous overstability in parameter space and the ground state surface mass density.

A nonlinear Kalman filtering approach to embedded control of turbocharged diesel engines

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Siano, Pierluigi; Arsie, Ivan

2014-10-01

The development of efficient embedded control for turbocharged Diesel engines, requires the programming of elaborated nonlinear control and filtering methods. To this end, in this paper nonlinear control for turbocharged Diesel engines is developed with the use of Differential flatness theory and the Derivative-free nonlinear Kalman Filter. It is shown that the dynamic model of the turbocharged Diesel engine is differentially flat and admits dynamic feedback linearization. It is also shown that the dynamic model can be written in the linear Brunovsky canonical form for which a state feedback controller can be easily designed. To compensate for modeling errors and external disturbances the Derivative-free nonlinear Kalman Filter is used and redesigned as a disturbance observer. The filter consists of the Kalman Filter recursion on the linearized equivalent of the Diesel engine model and of an inverse transformation based on differential flatness theory which enables to obtain estimates for the state variables of the initial nonlinear model. Once the disturbances variables are identified it is possible to compensate them by including an additional control term in the feedback loop. The efficiency of the proposed control method is tested through simulation experiments.

Confinement properties of tokamak plasmas with extended regions of low magnetic shear

NASA Astrophysics Data System (ADS)

Graves, J. P.; Cooper, W. A.; Kleiner, A.; Raghunathan, M.; Neto, E.; Nicolas, T.; Lanthaler, S.; Patten, H.; Pfefferle, D.; Brunetti, D.; Lutjens, H.

2017-10-01

Extended regions of low magnetic shear can be advantageous to tokamak plasmas. But the core and edge can be susceptible to non-resonant ideal fluctuations due to the weakened restoring force associated with magnetic field line bending. This contribution shows how saturated non-linear phenomenology, such as 1 / 1 Long Lived Modes, and Edge Harmonic Oscillations associated with QH-modes, can be modelled accurately using the non-linear stability code XTOR, the free boundary 3D equilibrium code VMEC, and non-linear analytic theory. That the equilibrium approach is valid is particularly valuable because it enables advanced particle confinement studies to be undertaken in the ordinarily difficult environment of strongly 3D magnetic fields. The VENUS-LEVIS code exploits the Fourier description of the VMEC equilibrium fields, such that full Lorenzian and guiding centre approximated differential operators in curvilinear angular coordinates can be evaluated analytically. Consequently, the confinement properties of minority ions such as energetic particles and high Z impurities can be calculated accurately over slowing down timescales in experimentally relevant 3D plasmas.

Non-linear dynamic analysis of geared systems. Final Report Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

1990-01-01

Under driving conditions, a typical geared system may be subjected to large dynamic loads. Also, the vibration level of the geared system is directly related to the noise radiated from the gear box. The steady state dynamic behavior of the system is examined in order to design reliable and quiet transmissions. The scope is limited to a system containing a spur gear pair with backlash and periodically time varying mesh stiffness, and rolling element bearings with clearance type nonlinearities. The internal static transmission error at the gear mesh, which is of importance from high frequency noise and vibration control view point, is considered in the formulation in sinusoidal or periodic form. A dynamic finite element model of the linear time invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and forced vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solutions with the finite element model results. Using the reduced order formulations, a three degree of freedom dynamic model is developed which includes nonlinearities associated with radical clearances in the radial rolling element bearings, backlash between a spur gear pair and periodically varying gear mesh stiffness. As a limiting case, a single degree of freedom model of the spur gear pair with backlash is considered and mathematical conditions for tooth separation and back collision are defined. Both digital simulation technique and analytical models such as method of harmonic balance and the method of multiple scales were used to develop the steady state frequency response characteristics for various nonlinear and/or time varying cases.

MAGNETO-FRICTIONAL MODELING OF CORONAL NONLINEAR FORCE-FREE FIELDS. I. TESTING WITH ANALYTIC SOLUTIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Y.; Keppens, R.; Xia, C.

2016-09-10

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 thatmore » 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.« less

Experimental validation of a novel stictionless magnetorheological fluid isolator

NASA Astrophysics Data System (ADS)

Kelso, Shawn P.; Denoyer, Keith K.; Blankinship, Ross M.; Potter, Kenneth; Lindler, Jason E.

2003-07-01

Magnetorheological (MR) fluid damper design typically constitutes a piston/dashpot configuration. During reciprocation, the fluid is circulated through the device with the generated pressure providing viscous damping. In addition, the damper is also intended to accommodate off-axis loading; i.e., rotation moments and lateral loads orthogonal to the axis of operation. Typically two sets of seals, one where the piston shaft enters and exits the device and one between the piston and the cylinder wall, maintain alignment of the damper and seal the fluid from leaking. With MR fluid, these seals can act as sources of non-linear friction effects (stiction) and oftentimes possess a shorter lifespan due to the abrasive nature of the ferrous particles suspended in the fluid. Intelligently controlling damping forces must also accommodate the non-linear stiction behavior, which degrades performance. A new, unique MR fluid isolator was designed, fabricated and tested that directly addresses these concerns. The goal of this research was the development of a stiction-free MR isolator whose damping force can be predicted and precisely controlled. This paper presents experimental results for a prototype device and compares those results to model predictions.

A Nonlinear Dynamic Model and Free Vibration Analysis of Deployable Mesh Reflectors

NASA Technical Reports Server (NTRS)

Shi, H.; Yang, B.; Thomson, M.; Fang, H.

2011-01-01

This paper presents a dynamic model of deployable mesh reflectors, in which geometric and material nonlinearities of such a space structure are fully described. Then, by linearization around an equilibrium configuration of the reflector structure, a linearized model is obtained. With this linearized model, the natural frequencies and mode shapes of a reflector can be computed. The nonlinear dynamic model of deployable mesh reflectors is verified by using commercial finite element software in numerical simulation. As shall be seen, the proposed nonlinear model is useful for shape (surface) control of deployable mesh reflectors under thermal loads.

Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams

NASA Astrophysics Data System (ADS)

Kluger, Jocelyn M.; Sapsis, Themistoklis P.; Slocum, Alexander H.

2015-04-01

In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is composed of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly on the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces. To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized by the cantilever-surface mechanism. The optimization results show that the 2DOF nonlinear system presents the best average performance when the excitation signals have three possible forms. Moreover, we observe that while for the linear systems the optimal performance is obtained for small values of the electromagnetic damping, for the 2DOF nonlinear system optimal performance is achieved for large values of damping. This feature is of particular importance for the system's robustness to parasitic damping.

Towards a footwear design tool: influence of shoe midsole properties and ground stiffness on the impact force during running.

PubMed

Ly, Quoc Hung; Alaoui, Amina; Erlicher, Silvano; Baly, Laurent

2010-01-19

Several spring-damper-mass models of the human body have been developed in order to reproduce the measured ground vertical reaction forces during human running (McMahon and Cheng, 1990; Ferris et al., 1999; Liu and Nigg, 2000). In particular, Liu and Nigg introduced at the lower level of their model, i.e. at the interface between the human body and the ground, a nonlinear element representing simultaneously the shoe midsoles and the ground flexibility. The ground reaction force is modelled as the force supported by this nonlinear element, whose parameters are identified from several sets of experimental data. This approach proved to be robust and quite accurate. However, it does not explicitly take into account the shoe and the ground properties. It turns out to be impossible to study the influence of shoe materials on the impact force, for instance for footwear design purposes. In this paper, a modification of the Liu and Nigg's model is suggested, where the original nonlinear element is replaced with a bi-layered spring-damper-mass model: the first layer represents the shoe midsole and the second layer is associated with the ground. Ground is modelled as an infinite elastic half-space. We have assumed a viscoelastic behaviour of the shoe material, so the damping of shoe material is taken into account. A methodology for the shoe-soles characterization is proposed and used together with the proposed model. A parametric study is then conducted and the influence of the shoe properties on the impact force is quantified. Moreover, it is shown that impact forces are strongly affected by the ground stiffness, which should therefore be considered as an essential parameter in the footwear design. Copyright 2009 Elsevier Ltd. All rights reserved.

Modeling and analysis of Galfenol cantilever vibration energy harvester with nonlinear magnetic force

NASA Astrophysics Data System (ADS)

Cao, Shuying; Sun, Shuaishuai; Zheng, Jiaju; Wang, Bowen; Wan, Lili; Pan, Ruzheng; Zhao, Ran; Zhang, Changgeng

2018-05-01

Galfenol traditional cantilever energy harvesters (TCEHs) have bigger electrical output only at resonance and exhibit nonlinear mechanical-magnetic-electric coupled (NMMEC) behaviors. To increase low-frequency broadband performances of a TCEH, an improved CEH (ICEH) with magnetic repulsive force is studied. Based on the magnetic dipole model, the nonlinear model of material, the Faraday law and the dynamic principle, a lumped parameter NMMEC model of the devices is established. Comparisons between the calculated and measured results show that the proposed model can provide reasonable data trends of TCEH under acceleration, bias field and different loads. Simulated results show that ICEH exhibits low-frequency resonant, hard spring and bistable behaviors, thus can harvest more low-frequency broadband vibration energy than TCEH, and can elicit snap-through and generate higher voltage even under weak noise. The proposed structure and model are useful for improving performances of the devices.

A method for reducing the order of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Masri, S. F.; Miller, R. K.; Sassi, H.; Caughey, T. K.

1984-06-01

An approximate method that uses conventional condensation techniques for linear systems together with the nonparametric identification of the reduced-order model generalized nonlinear restoring forces is presented for reducing the order of discrete multidegree-of-freedom dynamic systems that possess arbitrary nonlinear characteristics. The utility of the proposed method is demonstrated by considering a redundant three-dimensional finite-element model half of whose elements incorporate hysteretic properties. A nonlinear reduced-order model, of one-third the order of the original model, is developed on the basis of wideband stationary random excitation and the validity of the reduced-order model is subsequently demonstrated by its ability to predict with adequate accuracy the transient response of the original nonlinear model under a different nonstationary random excitation.

Subharmonic Oscillations and Chaos in Dynamic Atomic Force Microscopy

NASA Technical Reports Server (NTRS)

Cantrell, John H.; Cantrell, Sean A.

2015-01-01

The increasing use of dynamic atomic force microscopy (d-AFM) for nanoscale materials characterization calls for a deeper understanding of the cantilever dynamics influencing scan stability, predictability, and image quality. Model development is critical to such understanding. Renormalization of the equations governing d- AFM provides a simple interpretation of cantilever dynamics as a single spring and mass system with frequency dependent cantilever stiffness and damping parameters. The renormalized model is sufficiently robust to predict the experimentally observed splitting of the free-space cantilever resonance into multiple resonances upon cantilever-sample contact. Central to the model is the representation of the cantilever sample interaction force as a polynomial expansion with coefficients F(sub ij) (i,j = 0, 1, 2) that account for the effective interaction stiffness parameter, the cantilever-to-sample energy transfer, and the amplitude of cantilever oscillation. Application of the Melnikov method to the model equation is shown to predict a homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos and loss of image quality. The threshold value of the drive displacement amplitude necessary to initiate subharmonic generation depends on the acoustic drive frequency, the effective damping coefficient, and the nonlinearity of the cantilever-sample interaction force. For parameter values leading to displacement amplitudes below threshold for homoclinic bifurcation other bifurcation scenarios can occur, some of which lead to chaos.

Reliable and accurate extraction of Hamaker constants from surface force measurements.

PubMed

Miklavcic, S J

2018-08-15

A simple and accurate closed-form expression for the Hamaker constant that best represents experimental surface force data is presented. Numerical comparisons are made with the current standard least squares approach, which falsely assumes error-free separation measurements, and a nonlinear version assuming independent measurements of force and separation are subject to error. The comparisons demonstrate that not only is the proposed formula easily implemented it is also considerably more accurate. This option is appropriate for any value of Hamaker constant, high or low, and certainly for any interacting system exhibiting an inverse square distance dependent van der Waals force. Copyright © 2018 Elsevier Inc. All rights reserved.

Nonlinear dynamic modeling of rotor system supported by angular contact ball bearings

NASA Astrophysics Data System (ADS)

Wang, Hong; Han, Qinkai; Zhou, Daning

2017-02-01

In current bearing dynamic models, the displacement coordinate relations are usually utilized to approximately obtain the contact deformations between the rolling element and raceways, and then the nonlinear restoring forces of the rolling bearing could be calculated accordingly. Although the calculation efficiency is relatively higher, the accuracy is lower as the contact deformations should be solved through iterative analysis. Thus, an improved nonlinear dynamic model is presented in this paper. Considering the preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication, load distribution analysis is solved iteratively to more accurately obtain the contact deformations and angles between the rolling balls and raceways. The bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. Dynamic tests upon a typical rotor system supported by two angular contact ball bearings are conducted to verify the model. Through comparisons, the differences between the nonlinear dynamic model and current models are also pointed out. The effects of axial preload, rotor eccentricity and inner/outer waviness amplitudes on the dynamic response are discussed in detail.

Representing grounding line migration in synchronous coupling between a marine ice sheet model and a z-coordinate ocean model

NASA Astrophysics Data System (ADS)

Goldberg, D. N.; Snow, K.; Holland, P.; Jordan, J. R.; Campin, J.-M.; Heimbach, P.; Arthern, R.; Jenkins, A.

2018-05-01

Synchronous coupling is developed between an ice sheet model and a z-coordinate ocean model (the MITgcm). A previously-developed scheme to allow continuous vertical movement of the ice-ocean interface of a floating ice shelf ("vertical coupling") is built upon to allow continuous movement of the grounding line, or point of floatation of the ice sheet ("horizontal coupling"). Horizontal coupling is implemented through the maintenance of a thin layer of ocean ( ∼ 1 m) under grounded ice, which is inflated into the real ocean as the ice ungrounds. This is accomplished through a modification of the ocean model's nonlinear free surface evolution in a manner akin to a hydrological model in the presence of steep bathymetry. The coupled model is applied to a number of idealized geometries and shown to successfully represent ocean-forced marine ice sheet retreat while maintaining a continuous ocean circulation.

Novel nonlinear knowledge-based mean force potentials based on machine learning.

PubMed

Dong, Qiwen; Zhou, Shuigeng

2011-01-01

The prediction of 3D structures of proteins from amino acid sequences is one of the most challenging problems in molecular biology. An essential task for solving this problem with coarse-grained models is to deduce effective interaction potentials. The development and evaluation of new energy functions is critical to accurately modeling the properties of biological macromolecules. Knowledge-based mean force potentials are derived from statistical analysis of proteins of known structures. Current knowledge-based potentials are almost in the form of weighted linear sum of interaction pairs. In this study, a class of novel nonlinear knowledge-based mean force potentials is presented. The potential parameters are obtained by nonlinear classifiers, instead of relative frequencies of interaction pairs against a reference state or linear classifiers. The support vector machine is used to derive the potential parameters on data sets that contain both native structures and decoy structures. Five knowledge-based mean force Boltzmann-based or linear potentials are introduced and their corresponding nonlinear potentials are implemented. They are the DIH potential (single-body residue-level Boltzmann-based potential), the DFIRE-SCM potential (two-body residue-level Boltzmann-based potential), the FS potential (two-body atom-level Boltzmann-based potential), the HR potential (two-body residue-level linear potential), and the T32S3 potential (two-body atom-level linear potential). Experiments are performed on well-established decoy sets, including the LKF data set, the CASP7 data set, and the Decoys “R”Us data set. The evaluation metrics include the energy Z score and the ability of each potential to discriminate native structures from a set of decoy structures. Experimental results show that all nonlinear potentials significantly outperform the corresponding Boltzmann-based or linear potentials, and the proposed discriminative framework is effective in developing knowledge-based mean force potentials. The nonlinear potentials can be widely used for ab initio protein structure prediction, model quality assessment, protein docking, and other challenging problems in computational biology.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

PubMed

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

A theoretical model of strong and moderate El Niño regimes

NASA Astrophysics Data System (ADS)

Takahashi, Ken; Karamperidou, Christina; Dewitte, Boris

2018-02-01

The existence of two regimes for El Niño (EN) events, moderate and strong, has been previously shown in the GFDL CM2.1 climate model and also suggested in observations. The two regimes have been proposed to originate from the nonlinearity in the Bjerknes feedback, associated with a threshold in sea surface temperature (T_c ) that needs to be exceeded for deep atmospheric convection to occur in the eastern Pacific. However, although the recent 2015-16 EN event provides a new data point consistent with the sparse strong EN regime, it is not enough to statistically reject the null hypothesis of a unimodal distribution based on observations alone. Nevertheless, we consider the possibility suggestive enough to explore it with a simple theoretical model based on the nonlinear Bjerknes feedback. In this study, we implemented this nonlinear mechanism in the recharge-discharge (RD) ENSO model and show that it is sufficient to produce the two EN regimes, i.e. a bimodal distribution in peak surface temperature (T) during EN events. The only modification introduced to the original RD model is that the net damping is suppressed when T exceeds T_c , resulting in a weak nonlinearity in the system. Due to the damping, the model is globally stable and it requires stochastic forcing to maintain the variability. The sustained low-frequency component of the stochastic forcing plays a key role for the onset of strong EN events (i.e. for T>T_c ), at least as important as the precursor positive heat content anomaly (h). High-frequency forcing helps some EN events to exceed T_c , increasing the number of strong events, but the rectification effect is small and the overall number of EN events is little affected by this forcing. Using the Fokker-Planck equation, we show how the bimodal probability distribution of EN events arises from the nonlinear Bjerknes feedback and also propose that the increase in the net feedback with increasing T is a necessary condition for bimodality in the RD model. We also show that the damping strength determines both the adjustment time-scale and equilibrium value of the ensemble spread associated with the stochastic forcing.

Nonlinear forcing in the resolvent analysis of wall-turbulence

NASA Astrophysics Data System (ADS)

Rosenberg, Kevin; Lozano Duran, Adrian; Towne, Aaron; McKeon, Beverley

2016-11-01

The resolvent analysis of McKeon and Sharma formulates the Navier-Stokes equations as an input/output system in which the nonlinearity is treated as a forcing that acts upon the linear dynamics to yield a velocity response across wavenumber/frequency space. DNS data for a low Reynolds number turbulent channel (Reτ = 180) is used to investigate the structure of the nonlinear forcing directly. Specifically, we explore the spatio-temporal scales where the forcing is active and analyze its interplay with the linear amplification mechanisms present in the resolvent operator. This work could provide insight into self-sustaining processes in wall-turbulence and inform the modeling of scale interactions in large eddy simulations. We gratefully acknowledge Stanford's Center for Turbulence Research for support of this work.

Linear and nonlinear winter atmospheric responses to extreme phases of low frequency Pacific sea surface temperature variability

NASA Astrophysics Data System (ADS)

Cao, Dandan; Wu, Qigang; Hu, Aixue; Yao, Yonghong; Liu, Shizuo; Schroeder, Steven R.; Yang, Fucheng

2018-02-01

This study examines Northern Hemisphere winter (DJFM) atmospheric responses to opposite strong phases of interdecadal (low frequency, LF) Pacific sea surface temperature (SST) forcing, which resembles El Niño-Southern Oscillation (ENSO) on a longer time scale, in observations and GFDL and CAM4 model simulations. Over the Pacific-North America (PNA) sector, linear observed responses of 500-hPa height (Z500) anomalies resemble the PNA teleconnection pattern, but show a PNA-like nonlinear response because of a westward Z500 shift in the negative (LF-) relative to the positive LF (LF+) phase. Significant extratropical linear responses include a North Atlantic Oscillation (NAO)-like Z500 anomaly, a dipole-like Z500 anomaly over northern Eurasia associated with warming over mid-high latitude Eurasia, and a Southern Annular anomaly pattern associated with warming in southern land areas. Significant nonlinear Z500 responses also include a NAO-like anomaly pattern. Models forced by LF+ and LF- SST anomalies reproduce many aspects of observed linear and nonlinear responses over the Pacific-North America sector, and linear responses over southern land, but not in the North Atlantic-European sector and Eurasia. Both models simulate PNA-like linear responses in the North Pacific-North America region similar to observed, but show larger PNA-like LF+ responses, resulting in a PNA nonlinear response. The nonlinear PNA responses result from both nonlinear western tropical Pacific rainfall changes and extratropical transient eddy feedbacks. With LF tropical Pacific forcing only (LFTP+ and LFTP-, climatological SST elsewhere), CAM4 simulates a significant NAO response to LFTP-, including a linear negative and nonlinear positive NAO response.

Damping of Resonantly Forced Density Waves in Dense Planetary Rings

NASA Astrophysics Data System (ADS)

Lehmann, Marius; Schmidt, Jürgen; Salo, Heikki

2016-10-01

We address the stability of resonantly forced density waves in dense planetary rings.Already by Goldreich and Tremaine (1978) it has been argued that density waves might be unstable, depending on the relationship between the ring's viscosity and the surface mass density. In the recent paper (Schmidt et al. 2016) we have pointed out that when - within a fluid description of the ring dynamics - the criterion for viscous overstability is satisfied, forced spiral density waves become unstable as well. In this case, linear theory fails to describe the damping.We apply the multiple scale formalism to derive a weakly nonlinear damping relation from a hydrodynamical model.This relation describes the resonant excitation and nonlinear viscous damping of spiral density waves in a vertically integrated fluid disk with density dependent transport coefficients. The model consistently predicts linear instability of density waves in a ring region where the conditions for viscous overstability are met. In this case, sufficiently far away from the Lindblad resonance, the surface mass density perturbation is predicted to saturate to a constant value due to nonlinear viscous damping. In general the model wave damping lengths depend on a set of input parameters, such as the distance to the threshold for viscous overstability and the ground state surface mass density.Our new model compares reasonably well with the streamline model for nonlinear density waves of Borderies et al. 1986.Deviations become substantial in the highly nonlinear regime, corresponding to strong satellite forcing.Nevertheless, we generally observe good or at least qualitative agreement between the wave amplitude profiles of both models. The streamline approach is superior at matching the total wave profile of waves observed in Saturn's rings, while our new damping relation is a comparably handy tool to gain insight in the evolution of the wave amplitude with distance from resonance, and the different regimes of wave formation and the dependence on the parameters of the model.

Characterization of a hydro-pneumatic suspension strut with gas-oil emulsion

NASA Astrophysics Data System (ADS)

Yin, Yuming; Rakheja, Subhash; Yang, Jue; Boileau, Paul-Emile

2018-06-01

The nonlinear stiffness and damping properties of a simple and low-cost design of a hydro-pneumatic suspension (HPS) strut that permits entrapment of gas into the hydraulic oil are characterized experimentally and analytically. The formulation of gas-oil emulsion is studied in the laboratory, and the variations in the bulk modulus and mass density of the emulsion are formulated as a function of the gas volume fraction. An analytical model of the HPS is formulated considering polytropic change in the gas state, seal friction, and the gas-oil emulsion flows through orifices and valves. The model is formulated considering one and two bleed orifices configurations of the strut. The measured data acquired under a nearly constant temperature are used to identify gas volume fraction of the emulsion, and friction and flow discharge coefficients as functions of the strut velocity and fluid pressure. The results suggested that single orifice configuration, owing to high fluid pressure, causes greater gas entrapment within the oil and thus significantly higher compressibility of the gas-oil emulsion. The model results obtained under different excitations in the 0.1-8 Hz frequency range showed reasonably good agreements with the measured stiffness and damping properties of the HPS strut. The results show that the variations in fluid compressibility and free gas volume cause increase in effective stiffness but considerable reduction in the damping in a highly nonlinear manner. Increasing the gas volume fraction resulted in substantial hysteresis in the force-deflection and force-velocity characteristics of the strut.

Multi-wavelength Observations and Modeling of Solar Flares: Magnetic Structures

NASA Astrophysics Data System (ADS)

Su, Y.

2017-12-01

We present a review of our recent investigations on multi-wavelength observations and magnetic field modeling of solar flares. High-resolution observations taken by NVST and BBSO/NST reveal unprecedented fine structures of the flaring regions. Observations by SDO, IRIS, and GOES provide the complementary information. The magnetic field models are constructed using either non-linear force free field extrapolations or flux rope insertion method. Our studies have shown that the flaring regions often consist of double or multiple flux ropes, which often exist at different heights. The fine flare ribbon structures may be due to the magnetic reconnection in the complex quasi separatrix layers. The magnetic field modeling of several large flares suggests that the so called hot-channel structure is corresponding to the erupting flux rope above the X-point in a magnetic configuration with Hyperbolic Flux Tube.

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

NASA Astrophysics Data System (ADS)

Ansari, R.; Faraji Oskouie, M.; Gholami, R.

2016-01-01

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

On the real-time estimation of the wheel-rail contact force by means of a new nonlinear estimator design model

NASA Astrophysics Data System (ADS)

Strano, Salvatore; Terzo, Mario

2018-05-01

The dynamics of the railway vehicles is strongly influenced by the interaction between the wheel and the rail. This kind of contact is affected by several conditioning factors such as vehicle speed, wear, adhesion level and, moreover, it is nonlinear. As a consequence, the modelling and the observation of this kind of phenomenon are complex tasks but, at the same time, they constitute a fundamental step for the estimation of the adhesion level or for the vehicle condition monitoring. This paper presents a novel technique for the real time estimation of the wheel-rail contact forces based on an estimator design model that takes into account the nonlinearities of the interaction by means of a fitting model functional to reproduce the contact mechanics in a wide range of slip and to be easily integrated in a complete model based estimator for railway vehicle.

An optimal pole-matching observer design for estimating tyre-road friction force

NASA Astrophysics Data System (ADS)

Faraji, Mohammad; Johari Majd, Vahid; Saghafi, Behrooz; Sojoodi, Mahdi

2010-10-01

In this paper, considering the dynamical model of tyre-road contacts, we design a nonlinear observer for the on-line estimation of tyre-road friction force using the average lumped LuGre model without any simplification. The design is the extension of a previously offered observer to allow a muchmore realistic estimation by considering the effect of the rolling resistance and a term related to the relative velocity in the observer. Our aim is not to introduce a new friction model, but to present a more accurate nonlinear observer for the assumed model. We derive linear matrix equality conditions to obtain an observer gain with minimum pole mismatch for the desired observer error dynamic system. We prove the convergence of the observer for the non-simplified model. Finally, we compare the performance of the proposed observer with that of the previously mentioned nonlinear observer, which shows significant improvement in the accuracy of estimation.

Towards the stabilization of the low density elements in topology optimization with large deformation

NASA Astrophysics Data System (ADS)

Lahuerta, Ricardo Doll; Simões, Eduardo T.; Campello, Eduardo M. B.; Pimenta, Paulo M.; Silva, Emilio C. N.

2013-10-01

This work addresses the treatment of lower density regions of structures undergoing large deformations during the design process by the topology optimization method (TOM) based on the finite element method. During the design process the nonlinear elastic behavior of the structure is based on exact kinematics. The material model applied in the TOM is based on the solid isotropic microstructure with penalization approach. No void elements are deleted and all internal forces of the nodes surrounding the void elements are considered during the nonlinear equilibrium solution. The distribution of design variables is solved through the method of moving asymptotes, in which the sensitivity of the objective function is obtained directly. In addition, a continuation function and a nonlinear projection function are invoked to obtain a checkerboard free and mesh independent design. 2D examples with both plane strain and plane stress conditions hypothesis are presented and compared. The problem of instability is overcome by adopting a polyconvex constitutive model in conjunction with a suggested relaxation function to stabilize the excessive distorted elements. The exact tangent stiffness matrix is used. The optimal topology results are compared to the results obtained by using the classical Saint Venant-Kirchhoff constitutive law, and strong differences are found.

Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes

DTIC Science & Technology

2016-04-20

10 5.1 Results for Four Models with Different Nonlinearities ..................................................11 5.2 Effects of...Force Research Laboratory or the U.S. Government. 1.0 SUMMARY In this report, the effects of incorporating nonlinearities in sequential relative orbit...exactly. Huxel and Bishop [1] discussed the effects of using both inertial range measurements from tracking stations and relative range measurements

Effects of Inertial and Geometric Nonlinearities in the Simulation of Flexible Aircraft Dynamics

NASA Astrophysics Data System (ADS)

Bun Tse, Bosco Chun

This thesis examines the relative importance of the inertial and geometric nonlinearities in modelling the dynamics of a flexible aircraft. Inertial nonlinearities are derived by employing an exact definition of the velocity distribution and lead to coupling between the rigid body and elastic motions. The geometric nonlinearities are obtained by applying nonlinear theory of elasticity to the deformations. Peters' finite state unsteady aerodynamic model is used to evaluate the aerodynamic forces. Three approximate models obtained by excluding certain combinations of nonlinear terms are compared with that of the complete dynamics equations to obtain an indication of which terms are required for an accurate representation of the flexible aircraft behavior. A generic business jet model is used for the analysis. The results indicate that the nonlinear terms have a significant effect for more flexible aircraft, especially the geometric nonlinearities which leads to increased damping in the dynamics.

A non-linear study of fluctuating fluid flow on MHD mixed convection through a vertical permeable plate

NASA Astrophysics Data System (ADS)

Babu, R. Suresh; Rushi Kumar, B.

2017-11-01

In this paper, an analytical solution for an unsteady (independent of time), MHD mixed convection, two-dimensional (x and y), laminar, viscous flow of an incompressible fluid through a vertical permeable plate in a porous medium was developed with these assumptions:(i) the suction velocity (which is normal to the plate)and the free stream velocity both fluctuate with respect to time with a fixed mean; (ii) the wall temperature is constant;(iii) difference between the temperature of the plate and the free stream is moderately large due to the free convection currents. Based on the physical configuration of the model, the governing equations are derived and are non-dimensionalize using dimensionless parameters. The resultant nonlinear partial differential equations are solved using double regular perturbation technique analytically. The results are computed numerically to understand the behaviour of the fluid (i.e., effects of MHD, viscosity, body force etc.) for various non-dimensional parameters involving like Grashof number Gr, Prandtl number Pr, Hartmann number M, Eckert number E, the Viscous ratio λ and so on for velocity and temperature. These results are found to be in good agreement with known results available in the literature in the absence of few physical parameters. The numerical values of the above said flow is discussed through graphs on velocity and temperature.

A theoretical investigation of the aerodynamics of low-aspect-ratio wings with partial leading-edge separation

NASA Technical Reports Server (NTRS)

Mehrotra, S. C.; Lan, C. E.

1978-01-01

A numerical method is developed to predict distributed and total aerodynamic characteristics for low aspect-ratio wings with partial leading-edge separation. The flow is assumed to be steady and inviscid. The wing boundary condition is formulated by the quasi-vortex-lattice method. The leading-edge separated vortices are represented by discrete free vortex elements which are aligned with the local velocity vector at mid-points to satisfy the force free condition. The wake behind the trailing-edge is also force free. The flow tangency boundary condition is satisfied on the wing, including the leading- and trailing-edges. Comparison of the predicted results with complete leading-edge separation has shown reasonably good agreement. For cases with partial leading-edge separation, the lift is found to be highly nonlinear with angle of attack.

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 magnetic nonequilibrium can disrupt sheared coronal arcades, and that helmet streamers can disrupt, leading to coronal mass ejections. Our model has significantly extended the realism with which the coronal magnetic field can be inferred from actual observations. In a subsequent contract awarded by NASA, we have continued to apply and improve the evolutionary technique, to study the physical properties of active regions, and to develop theoretical models of magnetic fields.

Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction

NASA Astrophysics Data System (ADS)

Smelyanskiy, V. N.; Luchinsky, D. G.; Stefanovska, A.; McClintock, P. V.

2005-03-01

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.

Dynamic analysis of nonlinear rotor-housing systems

NASA Technical Reports Server (NTRS)

Noah, Sherif T.

1988-01-01

Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.

Control of AUVs using differential flatness theory and the derivative-free nonlinear Kalman Filter

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos; Raffo, Guilerme

2015-12-01

The paper proposes nonlinear control and filtering for Autonomous Underwater Vessels (AUVs) based on differential flatness theory and on the use of the Derivative-free nonlinear Kalman Filter. First, it is shown that the 6-DOF dynamic model of the AUV is a differentially flat one. This enables its transformation into the linear canonical (Brunovsky) form and facilitates the design of a state feedback controller. A problem that has to be dealt with is the uncertainty about the parameters of the AUV's dynamic model, as well the external perturbations which affect its motion. To cope with this, it is proposed to use a disturbance observer which is based on the Derivative-free nonlinear Kalman Filter. The considered filtering method consists of the standard Kalman Filter recursion applied on the linearized model of the vessel and of an inverse transformation based on differential flatness theory, which enables to obtain estimates of the state variables of the initial nonlinear model of the vessel. The Kalman Filter-based disturbance observer performs simultaneous estimation of the non-measurable state variables of the AUV and of the perturbation terms that affect its dynamics. By estimating such disturbances, their compensation is also succeeded through suitable modification of the feedback control input. The efficiency of the proposed AUV control and estimation scheme is confirmed through simulation experiments.

New modified multi-level residue harmonic balance method for solving nonlinearly vibrating double-beam problem

NASA Astrophysics Data System (ADS)

Rahman, Md. Saifur; Lee, Yiu-Yin

2017-10-01

In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined.

Solving the aerodynamics of fungal flight: How air viscosity slows spore motion

PubMed Central

Fischer, Mark W. F.; Stolze-Rybczynski, Jessica L.; Davis, Diana J.; Cui, Yunluan; Money, Nicholas P.

2010-01-01

Viscous drag causes the rapid deceleration of fungal spores after high-speed launches and limits discharge distance. Stokes' law posits a linear relationship between drag force and velocity. It provides an excellent fit to experimental measurements of the terminal velocity of free-falling spores and other instances of low Reynolds number motion (Re<1). More complex, non-linear drag models have been devised for movements characterized by higher Re, but their effectiveness for modeling the launch of fast-moving fungal spores has not been tested. In this paper, we use data on spore discharge processes obtained from ultra-high-speed video recordings to evaluate the effects of air viscosity predicted by Stokes' law and a commonly used non-linear drag model. We find that discharge distances predicted from launch speeds by Stokes' model provide a much better match to measured distances than estimates from the more complex drag model. Stokes' model works better over a wide range projectile sizes, launch speeds, and discharge distances, from microscopic mushroom ballistospores discharged at <1 m/s over a distance of <0.1 mm (Re<1.0), to macroscopic sporangia of Pilobolus that are launched at >10 m/s and travel as far as 2.5 m (Re>100). PMID:21036338

Nonlinear force-free field modeling of the solar magnetic carpet and comparison with SDO/HMI and Sunrise/IMAX observations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chitta, L. P.; Kariyappa, R.; Van Ballegooijen, A. A.

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 nonlinearmore » 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.« less

Nonlinear Modeling by Assembling Piecewise Linear Models

NASA Technical Reports Server (NTRS)

Yao, Weigang; Liou, Meng-Sing

2013-01-01

To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.

Data-based fault-tolerant control of high-speed trains with traction/braking notch nonlinearities and actuator failures.

PubMed

Song, Qi; Song, Yong-Duan

2011-12-01

This paper investigates the position and velocity tracking control problem of high-speed trains with multiple vehicles connected through couplers. A dynamic model reflecting nonlinear and elastic impacts between adjacent vehicles as well as traction/braking nonlinearities and actuation faults is derived. Neuroadaptive fault-tolerant control algorithms are developed to account for various factors such as input nonlinearities, actuator failures, and uncertain impacts of in-train forces in the system simultaneously. The resultant control scheme is essentially independent of system model and is primarily data-driven because with the appropriate input-output data, the proposed control algorithms are capable of automatically generating the intermediate control parameters, neuro-weights, and the compensation signals, literally producing the traction/braking force based upon input and response data only--the whole process does not require precise information on system model or system parameter, nor human intervention. The effectiveness of the proposed approach is also confirmed through numerical simulations.

Growth and nonlinear response of driven water bells

NASA Astrophysics Data System (ADS)

Kolinski, John M.; Aharoni, Hillel; Fineberg, Jay; Sharon, Eran

2017-04-01

A water bell forms when a fluid jet impacts upon a target and separates into a two-dimensional sheet. Depending on the angle of separation from the target, the sheet can curve into a variety of different geometries. We show analytically that harmonic perturbations of water bells have linear wave solutions with geometry-dependent growth. We test the predictions of this model experimentally with a custom target system, and observe growth in agreement with the model below a critical forcing amplitude. Once the critical forcing amplitude is exceeded, a nonlinear transcritical bifurcation occurs; the response amplitude increases linearly with increasing forcing amplitude, albeit with a fundamentally different spatial form, and distinct nodes appear in the amplitude envelope.

A combined averaging and frequency mixing approach for force identification in weakly nonlinear high-Q oscillators: Atomic force microscope

NASA Astrophysics Data System (ADS)

Sah, Si Mohamed; Forchheimer, Daniel; Borgani, Riccardo; Haviland, David

2018-02-01

We present a polynomial force reconstruction of the tip-sample interaction force in Atomic Force Microscopy. The method uses analytical expressions for the slow-time amplitude and phase evolution, obtained from time-averaging over the rapidly oscillating part of the cantilever dynamics. The slow-time behavior can be easily obtained in either the numerical simulations or the experiment in which a high-Q resonator is perturbed by a weak nonlinearity and a periodic driving force. A direct fit of the theoretical expressions to the simulated and experimental data gives the best-fit parameters for the force model. The method combines and complements previous works (Platz et al., 2013; Forchheimer et al., 2012 [2]) and it allows for computationally more efficient parameter mapping with AFM. Results for the simulated asymmetric piecewise linear force and VdW-DMT force models are compared with the reconstructed polynomial force and show a good agreement. It is also shown that the analytical amplitude and phase modulation equations fit well with the experimental data.

Economic policy optimization based on both one stochastic model and the parametric control theory

NASA Astrophysics Data System (ADS)

Ashimov, Abdykappar; Borovskiy, Yuriy; Onalbekov, Mukhit

2016-06-01

A nonlinear dynamic stochastic general equilibrium model with financial frictions is developed to describe two interacting national economies in the environment of the rest of the world. Parameters of nonlinear model are estimated based on its log-linearization by the Bayesian approach. The nonlinear model is verified by retroprognosis, estimation of stability indicators of mappings specified by the model, and estimation the degree of coincidence for results of internal and external shocks' effects on macroeconomic indicators on the basis of the estimated nonlinear model and its log-linearization. On the base of the nonlinear model, the parametric control problems of economic growth and volatility of macroeconomic indicators of Kazakhstan are formulated and solved for two exchange rate regimes (free floating and managed floating exchange rates)

Comparing Numerical Spall Simulations with a Nonlinear Spall Formation Model

NASA Astrophysics Data System (ADS)

Ong, L.; Melosh, H. J.

2012-12-01

Spallation accelerates lightly shocked ejecta fragments to speeds that can exceed the escape velocity of the parent body. We present high-resolution simulations of nonlinear shock interactions in the near surface. Initial results show the acceleration of near-surface material to velocities up to 1.8 times greater than the peak particle velocity in the detached shock, while experiencing little to no shock pressure. These simulations suggest a possible nonlinear spallation mechanism to produce the high-velocity, low show pressure meteorites from other planets. Here we pre-sent the numerical simulations that test the production of spall through nonlinear shock interactions in the near sur-face, and compare the results with a model proposed by Kamegai (1986 Lawrence Livermore National Laboratory Report). We simulate near-surface shock interactions using the SALES_2 hydrocode and the Murnaghan equation of state. We model the shock interactions in two geometries: rectangular and spherical. In the rectangular case, we model a planar shock approaching the surface at a constant angle phi. In the spherical case, the shock originates at a point below the surface of the domain and radiates spherically from that point. The angle of the shock front with the surface is dependent on the radial distance of the surface point from the shock origin. We model the target as a solid with a nonlinear Murnaghan equation of state. This idealized equation of state supports nonlinear shocks but is tem-perature independent. We track the maximum pressure and maximum velocity attained in every cell in our simula-tions and compare them to the Hugoniot equations that describe the material conditions in front of and behind the shock. Our simulations demonstrate that nonlinear shock interactions in the near surface produce lightly shocked high-velocity material for both planar and cylindrical shocks. The spall is the result of the free surface boundary condi-tion, which forces a pressure gradient from the peak shock pressure to the zero pressure boundary. The nonlinear shock interactions occur where the pressure contours curve to accommodate the free surface. The material within this spall zone is ejected at speeds up to 1.8 km s-1 for an imposed pulse of 1 km s-1. Where the ejection velocities are highest, the maximum pressure attained in each cell is effectively zero. We compare our simulation results with a model for nonlinear shock interactions proposed by Kamegai (1986). This model recognizes that the material behind the shock is compressed and has a higher soundspeed than the mate-rial in front of the shock. As the rarefaction wave moves behind the shock, its increased velocity through the com-pressed material combines with the residual particle velocity behind the shock to "catch up" with the shock. This occurs in the near surface where the sum of the compressed sound speed and the residual particle velocity is greater than or equal to the shock velocity. Initial results for the spherical shocks qualitatively match the volume described by this model, but differ significantly in the quantitative slope of the curve defining the region of interaction. We continue to test the Kamegai model with high-resolution numerical simulations of shock interactions to determine its potential application to planetary spallation.

An experimental nonlinear low dynamic stiffness device for shock isolation

NASA Astrophysics Data System (ADS)

Francisco Ledezma-Ramirez, Diego; Ferguson, Neil S.; Brennan, Michael J.; Tang, Bin

2015-07-01

The problem of shock generated vibration is very common in practice and difficult to isolate due to the high levels of excitation involved and its transient nature. If not properly isolated it could lead to large transmitted forces and displacements. Typically, classical shock isolation relies on the use of passive stiffness elements to absorb energy by deformation and some damping mechanism to dissipate residual vibration. The approach of using nonlinear stiffness elements is explored in this paper, focusing in providing an isolation system with low dynamic stiffness. The possibilities of using such a configuration for a shock mount are studied experimentally following previous theoretical models. The model studied considers electromagnets and permanent magnets in order to obtain nonlinear stiffness forces using different voltage configurations. It is found that the stiffness nonlinearities could be advantageous in improving shock isolation in terms of absolute displacement and acceleration response when compared with linear elastic elements.

Quasi-Linear Parameter Varying Representation of General Aircraft Dynamics Over Non-Trim Region

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob

2007-01-01

For applying linear parameter varying (LPV) control synthesis and analysis to a nonlinear system, it is required that a nonlinear system be represented in the form of an LPV model. In this paper, a new representation method is developed to construct an LPV model from a nonlinear mathematical model without the restriction that an operating point must be in the neighborhood of equilibrium points. An LPV model constructed by the new method preserves local stabilities of the original nonlinear system at "frozen" scheduling parameters and also represents the original nonlinear dynamics of a system over a non-trim region. An LPV model of the motion of FASER (Free-flying Aircraft for Subscale Experimental Research) is constructed by the new method.

Computing Incompressible Flows With Free Surfaces

NASA Technical Reports Server (NTRS)

Kothe, D.

1994-01-01

RIPPLE computer program models transient, two-dimensional flows of incompressible fluids with surface tension on free surfaces of general shape. Surface tension modeled as volume force derived from continuum-surface-force model, giving RIPPLE both robustness and accuracy in modeling surface-tension effects at free surface. Also models wall adhesion effects. Written in FORTRAN 77.

Nonlinear state-space modelling of the kinematics of an oscillating circular cylinder in a fluid flow

NASA Astrophysics Data System (ADS)

Decuyper, J.; De Troyer, T.; Runacres, M. C.; Tiels, K.; Schoukens, J.

2018-01-01

The flow-induced vibration of bluff bodies is an important problem of many marine, civil, or mechanical engineers. In the design phase of such structures, it is vital to obtain good predictions of the fluid forces acting on the structure. Current methods rely on computational fluid dynamic simulations (CFD), with a too high computational cost to be effectively used in the design phase or for control applications. Alternative methods use heuristic mathematical models of the fluid forces, but these lack the accuracy (they often assume the system to be linear) or flexibility to be useful over a wide operating range. In this work we show that it is possible to build an accurate, flexible and low-computational-cost mathematical model using nonlinear system identification techniques. This model is data driven: it is trained over a user-defined region of interest using data obtained from experiments or simulations, or both. Here we use a Van der Pol oscillator as well as CFD simulations of an oscillating circular cylinder to generate the training data. Then a discrete-time polynomial nonlinear state-space model is fit to the data. This model relates the oscillation of the cylinder to the force that the fluid exerts on the cylinder. The model is finally validated over a wide range of oscillation frequencies and amplitudes, both inside and outside the so-called lock-in region. We show that forces simulated by the model are in good agreement with the data obtained from CFD.

Scientific study of data analysis

NASA Technical Reports Server (NTRS)

Wu, S. T.

1990-01-01

We present a comparison between two numerical methods for the extrapolation of nonlinear force-free magnetic fields, the Iterative Method (IM) and the Progressive Extension Method (PEM). The advantages and disadvantages of these two methods are summarized and the accuracy and numerical instability are discussed. On the basis of this investigation, we claim that the two methods do resemble each other qualitatively.

A conformal approach for the analysis of the non-linear stability of radiation cosmologies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Luebbe, Christian, E-mail: c.luebbe@ucl.ac.uk; Department of Mathematics, University of Leicester, University Road, LE1 8RH; Valiente Kroon, Juan Antonio, E-mail: j.a.valiente-kroon@qmul.ac.uk

2013-01-15

The conformal Einstein equations for a trace-free (radiation) perfect fluid are derived in terms of the Levi-Civita connection of a conformally rescaled metric. These equations are used to provide a non-linear stability result for de Sitter-like trace-free (radiation) perfect fluid Friedman-Lemaitre-Robertson-Walker cosmological models. The solutions thus obtained exist globally towards the future and are future geodesically complete. - Highlights: Black-Right-Pointing-Pointer We study the Einstein-Euler system in General Relativity using conformal methods. Black-Right-Pointing-Pointer We analyze the structural properties of the associated evolution equations. Black-Right-Pointing-Pointer We establish the non-linear stability of pure radiation cosmological models.

Development of a Subject-Specific Foot-Ground Contact Model for Walking.

PubMed

Jackson, Jennifer N; Hass, Chris J; Fregly, Benjamin J

2016-09-01

Computational walking simulations could facilitate the development of improved treatments for clinical conditions affecting walking ability. Since an effective treatment is likely to change a patient's foot-ground contact pattern and timing, such simulations should ideally utilize deformable foot-ground contact models tailored to the patient's foot anatomy and footwear. However, no study has reported a deformable modeling approach that can reproduce all six ground reaction quantities (expressed as three reaction force components, two center of pressure (CoP) coordinates, and a free reaction moment) for an individual subject during walking. This study proposes such an approach for use in predictive optimizations of walking. To minimize complexity, we modeled each foot as two rigid segments-a hindfoot (HF) segment and a forefoot (FF) segment-connected by a pin joint representing the toes flexion-extension axis. Ground reaction forces (GRFs) and moments acting on each segment were generated by a grid of linear springs with nonlinear damping and Coulomb friction spread across the bottom of each segment. The stiffness and damping of each spring and common friction parameter values for all springs were calibrated for both feet simultaneously via a novel three-stage optimization process that used motion capture and ground reaction data collected from a single walking trial. The sequential three-stage process involved matching (1) the vertical force component, (2) all three force components, and finally (3) all six ground reaction quantities. The calibrated model was tested using four additional walking trials excluded from calibration. With only small changes in input kinematics, the calibrated model reproduced all six ground reaction quantities closely (root mean square (RMS) errors less than 13 N for all three forces, 25 mm for anterior-posterior (AP) CoP, 8 mm for medial-lateral (ML) CoP, and 2 N·m for the free moment) for both feet in all walking trials. The largest errors in AP CoP occurred at the beginning and end of stance phase when the vertical ground reaction force (vGRF) was small. Subject-specific deformable foot-ground contact models created using this approach should enable changes in foot-ground contact pattern to be predicted accurately by gait optimization studies, which may lead to improvements in personalized rehabilitation medicine.

Development of a Subject-Specific Foot-Ground Contact Model for Walking

PubMed Central

Jackson, Jennifer N.; Hass, Chris J.; Fregly, Benjamin J.

2016-01-01

Computational walking simulations could facilitate the development of improved treatments for clinical conditions affecting walking ability. Since an effective treatment is likely to change a patient's foot-ground contact pattern and timing, such simulations should ideally utilize deformable foot-ground contact models tailored to the patient's foot anatomy and footwear. However, no study has reported a deformable modeling approach that can reproduce all six ground reaction quantities (expressed as three reaction force components, two center of pressure (CoP) coordinates, and a free reaction moment) for an individual subject during walking. This study proposes such an approach for use in predictive optimizations of walking. To minimize complexity, we modeled each foot as two rigid segments—a hindfoot (HF) segment and a forefoot (FF) segment—connected by a pin joint representing the toes flexion–extension axis. Ground reaction forces (GRFs) and moments acting on each segment were generated by a grid of linear springs with nonlinear damping and Coulomb friction spread across the bottom of each segment. The stiffness and damping of each spring and common friction parameter values for all springs were calibrated for both feet simultaneously via a novel three-stage optimization process that used motion capture and ground reaction data collected from a single walking trial. The sequential three-stage process involved matching (1) the vertical force component, (2) all three force components, and finally (3) all six ground reaction quantities. The calibrated model was tested using four additional walking trials excluded from calibration. With only small changes in input kinematics, the calibrated model reproduced all six ground reaction quantities closely (root mean square (RMS) errors less than 13 N for all three forces, 25 mm for anterior–posterior (AP) CoP, 8 mm for medial–lateral (ML) CoP, and 2 N·m for the free moment) for both feet in all walking trials. The largest errors in AP CoP occurred at the beginning and end of stance phase when the vertical ground reaction force (vGRF) was small. Subject-specific deformable foot-ground contact models created using this approach should enable changes in foot-ground contact pattern to be predicted accurately by gait optimization studies, which may lead to improvements in personalized rehabilitation medicine. PMID:27379886

Vibration computer programs E13101, E13102, E13104, and E13112 and application to the NERVA program. Project 187: Methodology documentation

NASA Technical Reports Server (NTRS)

Mironenko, G.

1972-01-01

Programs for the analyses of the free or forced, undamped vibrations of one or two elastically-coupled lumped parameter teams are presented. Bearing nonlinearities, casing and rotor distributed mass and elasticity, rotor imbalance, forcing functions, gyroscopic moments, rotary inertia, and shear and flexural deformations are all included in the system dynamics analysis. All bearings have nonlinear load displacement characteristics, the solution is achieved by iteration. Rotor imbalances allowed by such considerations as pilot tolerances and runouts as well as bearing clearances (allowing concail or cylindrical whirl) determine the forcing function magnitudes. The computer programs first obtain a solution wherein the bearings are treated as linear springs of given spring rates. Then, based upon the computed bearing reactions, new spring rates are predicted and another solution of the modified system is made. The iteration is continued until the changes to bearing spring rates and bearing reactions become negligibly small.

Baroclinic Adjustment of the Eddy-Driven Jet

NASA Astrophysics Data System (ADS)

Novak, Lenka; Ambaum, Maarten H. P.; Harvey, Ben J.

2017-04-01

The prediction of poleward shift in the midlatitude eddy-driven jets due to anthropogenic climate change is now a robust feature of climate models, but the magnitude of this shift or the processes responsible for it are less certain. This uncertainty comes from the complex response in storm tracks to large-scale forcing and their nonlinear modulation of the jet. This study uses global circulation models to reveal a relationship between eddy growth rate (referred to as baroclinicity) and eddy activity, whereby baroclinicity responds most rapidly to an eddy-dissipating forcing whereas eddy activity responds most rapidly to a baroclinicity-replenishing forcing. This nonlinearity can be generally explained using a two-dimensional dynamical system essentially describing the baroclinic adjustment as a predator-prey relationship. Despite this nonlinearity, the barotropic changes in the eddy-driven jet appear to be of a comparable magnitude for the ranges of both types of forcing tested in this study. It is implied that while changes in eddy activity or baroclinicity may indicate the sign of latitudinal jet shifting, the precise magnitude of this shifting is a result of a balance between these two quantities.

Analysis of stochastic model for non-linear volcanic dynamics

NASA Astrophysics Data System (ADS)

Alexandrov, D.; Bashkirtseva, I.; Ryashko, L.

2014-12-01

Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al. (2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random trajectories are scattered on both sides of the deterministic cycle or grouped on its internal side only. It is shown that dispersions are highly inhomogeneous along cycles in the presence of noises. The effects of noise-induced shifts, pressure stabilization and localization of random trajectories have been revealed with increasing the noise intensity. The plug velocity, pressure and displacement are highly dependent of noise intensity as well. These new stochastic phenomena are related with the nonlinear peculiarities of the deterministic phase portrait. It is demonstrated that the repetitive stick-slip motions of the magma-plug system in the case of stochastic forcing can be connected with drumbeat earthquakes.

Robophysical study of jumping dynamics on granular media

NASA Astrophysics Data System (ADS)

Aguilar, Jeffrey; Goldman, Daniel I.

2016-03-01

Characterizing forces on deformable objects intruding into sand and soil requires understanding the solid- and fluid-like responses of such substrates and their effect on the state of the object. The most detailed studies of intrusion in dry granular media have revealed that interactions of fixed-shape objects during free impact (for example, cannonballs) and forced slow penetration can be described by hydrostatic- and hydrodynamic-like forces. Here we investigate a new class of granular interactions: rapid intrusions by objects that change shape (self-deform) through passive and active means. Systematic studies of a simple spring-mass robot jumping on dry granular media reveal that jumping performance is explained by an interplay of nonlinear frictional and hydrodynamic drag as well as induced added mass (unaccounted by traditional intrusion models) characterized by a rapidly solidified region of grains accelerated by the foot. A model incorporating these dynamics reveals that added mass degrades the performance of certain self-deformations owing to a shift in optimal timing during push-off. Our systematic robophysical experiment reveals both new soft-matter physics and principles for robotic self-deformation and control, which together provide principles of movement in deformable terrestrial environments.

Measuring the nonlinear elastic properties of tissue-like phantoms.

PubMed

Erkamp, Ramon Q; Skovoroda, Andrei R; Emelianov, Stanislav Y; O'Donnell, Matthew

2004-04-01

A direct mechanical system simultaneously measuring external force and deformation of samples over a wide dynamic range is used to obtain force-displacement curves of tissue-like phantoms under plain strain deformation. These measurements, covering a wide deformation range, then are used to characterize the nonlinear elastic properties of the phantom materials. The model assumes incompressible media, in which several strain energy potentials are considered. Finite-element analysis is used to evaluate the performance of this material characterization procedure. The procedures developed allow calibration of nonlinear elastic phantoms for elasticity imaging experiments and finite-element simulations.

Recent Applications of Higher-Order Spectral Analysis to Nonlinear Aeroelastic Phenomena

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Hajj, Muhammad R.; Dunn, Shane; Strganac, Thomas W.; Powers, Edward J.; Stearman, Ronald

2005-01-01

Recent applications of higher-order spectral (HOS) methods to nonlinear aeroelastic phenomena are presented. Applications include the analysis of data from a simulated nonlinear pitch and plunge apparatus and from F-18 flight flutter tests. A MATLAB model of the Texas A&MUniversity s Nonlinear Aeroelastic Testbed Apparatus (NATA) is used to generate aeroelastic transients at various conditions including limit cycle oscillations (LCO). The Gaussian or non-Gaussian nature of the transients is investigated, related to HOS methods, and used to identify levels of increasing nonlinear aeroelastic response. Royal Australian Air Force (RAAF) F/A-18 flight flutter test data is presented and analyzed. The data includes high-quality measurements of forced responses and LCO phenomena. Standard power spectral density (PSD) techniques and HOS methods are applied to the data and presented. The goal of this research is to develop methods that can identify the onset of nonlinear aeroelastic phenomena, such as LCO, during flutter testing.

A phenomenological force model of Li-ion battery packs for enhanced performance and health management

NASA Astrophysics Data System (ADS)

Oh, Ki-Yong; Epureanu, Bogdan I.

2017-10-01

A 1-D phenomenological force model of a Li-ion battery pack is proposed to enhance the control performance of Li-ion battery cells in pack conditions for efficient performance and health management. The force model accounts for multiple swelling sources under the operational environment of electric vehicles to predict swelling-induced forces in pack conditions, i.e. mechanically constrained. The proposed force model not only incorporates structural nonlinearities due to Li-ion intercalation swelling, but also separates the overall range of states of charge into three ranges to account for phase transitions. Moreover, an approach to study cell-to-cell variations in pack conditions is proposed with serial and parallel combinations of linear and nonlinear stiffness, which account for battery cells and other components in the battery pack. The model is shown not only to accurately estimate the reaction force caused by swelling as a function of the state of charge, battery temperature and environmental temperature, but also to account for cell-to-cell variations due to temperature variations, SOC differences, and local degradation in a wide range of operational conditions of electric vehicles. Considering that the force model of Li-ion battery packs can account for many possible situations in actual operation, the proposed approach and model offer potential utility for the enhancement of current battery management systems and power management strategies.

Nonlinear friction modelling and compensation control of hysteresis phenomena for a pair of tendon-sheath actuated surgical robots

NASA Astrophysics Data System (ADS)

Do, T. N.; Tjahjowidodo, T.; Lau, M. W. S.; Phee, S. J.

2015-08-01

Natural Orifice Transluminal Endoscopic Surgery (NOTES) is a special method that allows surgical operations via natural orifices like mouth, anus, and vagina, without leaving visible scars. The use of flexible tendon-sheath mechanism (TSM) is common in these systems because of its light weight in structure, flexibility, and easy transmission of power. However, nonlinear friction and backlash hysteresis pose many challenges to control of such systems; in addition, they do not provide haptic feedback to assist the surgeon in the operation of the systems. In this paper, we propose a new dynamic friction model and backlash hysteresis nonlinearity for a pair of TSM to deal with these problems. The proposed friction model, unlike current approaches in the literature, is smooth and able to capture the force at near zero velocity when the system is stationary or operates at small motion. This model can be used to estimate the friction force for haptic feedback purpose. To improve the system tracking performances, a backlash hysteresis model will be introduced, which can be used in a feedforward controller scheme. The controller involves a simple computation of the inverse hysteresis model. The proposed models are configuration independent and able to capture the nonlinearities for arbitrary tendon-sheath shapes. A representative experimental setup is used to validate the proposed models and to demonstrate the improvement in position tracking accuracy and the possibility of providing desired force information at the distal end of a pair of TSM slave manipulator for haptic feedback to the surgeons.

New force replica exchange method and protein folding pathways probed by force-clamp technique.

PubMed

Kouza, Maksim; Hu, Chin-Kun; Li, Mai Suan

2008-01-28

We have developed a new extended replica exchange method to study thermodynamics of a system in the presence of external force. Our idea is based on the exchange between different force replicas to accelerate the equilibrium process. This new approach was applied to obtain the force-temperature phase diagram and other thermodynamical quantities of the three-domain ubiquitin. Using the C(alpha)-Go model and the Langevin dynamics, we have shown that the refolding pathways of single ubiquitin depend on which terminus is fixed. If the N end is fixed then the folding pathways are different compared to the case when both termini are free, but fixing the C terminal does not change them. Surprisingly, we have found that the anchoring terminal does not affect the pathways of individual secondary structures of three-domain ubiquitin, indicating the important role of the multidomain construction. Therefore, force-clamp experiments, in which one end of a protein is kept fixed, can probe the refolding pathways of a single free-end ubiquitin if one uses either the polyubiquitin or a single domain with the C terminus anchored. However, it is shown that anchoring one end does not affect refolding pathways of the titin domain I27, and the force-clamp spectroscopy is always capable to predict folding sequencing of this protein. We have obtained the reasonable estimate for unfolding barrier of ubiquitin, using the microscopic theory for the dependence of unfolding time on the external force. The linkage between residue Lys48 and the C terminal of ubiquitin is found to have the dramatic effect on the location of the transition state along the end-to-end distance reaction coordinate, but the multidomain construction leaves the transition state almost unchanged. We have found that the maximum force in the force-extension profile from constant velocity force pulling simulations depends on temperature nonlinearly. However, for some narrow temperature interval this dependence becomes linear, as have been observed in recent experiments.

Nonlinear damping for vibration isolation of microsystems using shear thickening fluid

NASA Astrophysics Data System (ADS)

Iyer, S. S.; Vedad-Ghavami, R.; Lee, H.; Liger, M.; Kavehpour, H. P.; Candler, R. N.

2013-06-01

This work reports the measurement and analysis of nonlinear damping of micro-scale actuators immersed in shear thickening fluids (STFs). A power-law damping term is added to the linear second-order model to account for the shear-dependent viscosity of the fluid. This nonlinear model is substantiated by measurements of oscillatory motion of a torsional microactuator. At high actuation forces, the vibration velocity amplitude saturates. The model accurately predicts the nonlinear damping characteristics of the STF using a power-law index extracted from independent rheology experiments. This result reveals the potential to use STFs as adaptive, passive dampers for vibration isolation of microelectromechanical systems.

Experimental characterization of deployable trusses and joints

NASA Technical Reports Server (NTRS)

Ikegami, R.; Church, S. M.; Keinholz, D. A.; Fowler, B. L.

1987-01-01

The structural dynamic properties of trusses are strongly affected by the characteristics of joints connecting the individual beam elements. Joints are particularly significant in that they are often the source of nonlinearities and energy dissipation. While the joints themselves may be physically simple, direct measurement is often necessary to obtain a mathematical description suitable for inclusion in a system model. Force state mapping is a flexible, practical test method for obtaining such a description, particularly when significant nonlinear effects are present. It involves measurement of the relationship, nonlinear or linear, between force transmitted through a joint and the relative displacement and velocity across it. An apparatus and procedure for force state mapping are described. Results are presented from tests of joints used in a lightweight, composite, deployable truss built by the Boeing Aerospace Company. The results from the joint tests are used to develop a model of a full 4-bay truss segment. The truss segment was statically and dynamically tested. The results of the truss tests are presented and compared with the analytical predictions from the model.

The elastic free energy of a tandem modular protein under force.

PubMed

Valle-Orero, Jessica; Eckels, Edward C; Stirnemann, Guillaume; Popa, Ionel; Berkovich, Ronen; Fernandez, Julio M

2015-05-01

Recent studies have provided a theoretical framework for including entropic elasticity in the free energy landscape of proteins under mechanical force. Accounting for entropic elasticity using polymer physics models has helped explain the hopping behavior seen in single molecule experiments in the low force regime. Here, we expand on the construction of the free energy of a single protein domain under force proposed by Berkovich et al. to provide a free energy landscape for N tandem domains along a continuous polypeptide. Calculation of the free energy of individual domains followed by their concatenation provides a continuous free energy landscape whose curvature is dominated by the worm-like chain at forces below 20 pN. We have validated our free energy model using Brownian dynamics and reproduce key features of protein folding. This free energy model can predict the effects of changes in the elastic properties of a multidomain protein as a consequence of biological modifications such as phosphorylation or the formation of disulfide bonds. This work lays the foundations for the modeling of tissue elasticity, which is largely determined by the properties of tandem polyproteins. Copyright © 2015. Published by Elsevier Inc.

On the nonlinear aerodynamic and stability characteristics of a generic chine-forebody slender-wing fighter configuration

NASA Technical Reports Server (NTRS)

Erickson, Gary E.; Brandon, Jay M.

1987-01-01

An exploratory investigation was conducted of the nonlinear aerodynamic and stability characteristics of a tailless generic fighter configuration featuring a chine-shaped forebody coupled to a slender cropped delta wing in the NASA Langley Research Center's 12-Foot Low-Speed Wind Tunnel. Forebody and wing vortex flow mechanisms were identified through off-body flow visualizations to explain the trends in the longitudinal and lateral-directional characteristics at extreme attitudes (angles of attack and sideslip). The interactions of the vortical motions with centerline and wing-mounted vertical tail surfaces were studied and the flow phenomena were correlated with the configuration forces and moments. Single degree of freedom, free-to-roll tests were used to study the wing rock susceptibility of the generic fighter model. Modifications to the nose region of the chine forebody were examined and fluid mechanisms were established to account for their ineffectiveness in modulating the highly interactive forebody and wing vortex systems.

A numerical study of linear and nonlinear kinematic models in fish swimming with the DSD/SST method

NASA Astrophysics Data System (ADS)

Tian, Fang-Bao

2015-03-01

Flow over two fish (modeled by two flexible plates) in tandem arrangement is investigated by solving the incompressible Navier-Stokes equations numerically with the DSD/SST method to understand the differences between the geometrically linear and nonlinear models. In the simulation, the motions of the plates are reconstructed from a vertically flowing soap film tunnel experiment with linear and nonlinear kinematic models. Based on the simulations, the drag, lift, power consumption, vorticity and pressure fields are discussed in detail. It is found that the linear and nonlinear models are able to reasonably predict the forces and power consumption of a single plate in flow. Moreover, if multiple plates are considered, these two models yield totally different results, which implies that the nonlinear model should be used. The results presented in this work provide a guideline for future studies in fish swimming.

Design and analysis of coiled fiber reinforced soft pneumatic actuator.

PubMed

Singh, Gaurav; Xiao, Chenzhang; Hsiao-Wecksler, Elizabeth T; Krishnan, Girish

2018-04-18

Fiber reinforced elastomeric enclosures (FREEs) are soft pneumatic actuators that can contract and generate forces upon pressurization. Typical engineering applications utilize FREEs in their straight cylindrical configuration and derive actuation displacement and forces from their ends. However, there are several instances in nature, such as an elephant trunk, snakes and grapevine tendrils, where a spiral configuration of muscle systems is used for gripping, thereby establishing a mechanical connection with uniform force distribution. Inspired by these examples, this paper investigates the constricting behavior of a contracting FREE actuator deployed in a spiral or coiled configuration around a cylindrical object. Force balance is used to model the blocked force of the FREE, which is then related to the constriction force using a string model. The modeling and experimental findings reveal an attenuation in the blocked force, and thus the constriction force caused by the coupling of peripheral contact forces acting in the spiral configuration. The usefulness of the coiled FREE configuration is demonstrated in a soft arm orthosis for crutch users that provides a constriction force around the forearm. This design minimizes injury risk by reducing wrist load and improving wrist posture.

RIPPLE - A new model for incompressible flows with free surfaces

NASA Technical Reports Server (NTRS)

Kothe, D. B.; Mjolsness, R. C.

1991-01-01

A new free surface flow model, RIPPLE, is summarized. RIPPLE obtains finite difference solutions for incompressible flow problems having strong surface tension forces at free surfaces of arbitrarily complex topology. The key innovation is the continuum surface force model which represents surface tension as a (strongly) localized volume force. Other features include a higher-order momentum advection model, a volume-of-fluid free surface treatment, and an efficient two-step projection solution method. RIPPLE's unique capabilities are illustrated with two example problems: low-gravity jet-induced tank flow, and the collision and coalescence of two cylindrical rods.

Water entry and exit of horizontal circular cylinders

NASA Astrophysics Data System (ADS)

Greenhow, M.; Moyo, S.

This paper describes fully nonlinear two-dimensional numerical calculations of the free-surface deformations of initially calm water caused by the forced motion of totally or partially submerged horizontal circular cylinders. The paper considers the following. (i) Totally submerged cylinders moving with constant velocity in vertical, horizontal or combined motions. Results are compared with the small-time asymptotic solution obtained by Tyvand and Milohin 1995. Their results, which are taken to third-order (which is when gravity terms first appear in the expansions), are in excellent agreement with the numerical calculations for small times; beyond this only the numerical method gives accurate results until the free surface breaks or the cylinder emerges from the free surface. Breaking can occur during exit due to strongly negative pressures arising on the cylinder surface, or during the downwards motion causing a free-surface depression which closes up rapidly, forming splashes. Downwards motion is also shown to give rise to high-frequency waves in some cases. (ii) The free-surface deformations, pressures and forces acting on a cylinder in vertical or oblique forced motion during engulfment when it submerges from being initially half-submerged. The initial stages, when the cylinder still pierces the free surface, specify the initial conditions for a separate program for a completely submerged body, thereby allowing complete engulfment to be studied. The free surface closes up violently over the top of the cylinder resulting in jet flow, which, while difficult to handle numerically, has been shown to be insignificant for the bulk flow and the cylinder pressures and forces.

Non-linear modelling and control of semi-active suspensions with variable damping

NASA Astrophysics Data System (ADS)

Chen, Huang; Long, Chen; Yuan, Chao-Chun; Jiang, Hao-Bin

2013-10-01

Electro-hydraulic dampers can provide variable damping force that is modulated by varying the command current; furthermore, they offer advantages such as lower power, rapid response, lower cost, and simple hardware. However, accurate characterisation of non-linear f-v properties in pre-yield and force saturation in post-yield is still required. Meanwhile, traditional linear or quarter vehicle models contain various non-linearities. The development of a multi-body dynamics model is very complex, and therefore, SIMPACK was used with suitable improvements for model development and numerical simulations. A semi-active suspension was built based on a belief-desire-intention (BDI)-agent model framework. Vehicle handling dynamics were analysed, and a co-simulation analysis was conducted in SIMPACK and MATLAB to evaluate the BDI-agent controller. The design effectively improved ride comfort, handling stability, and driving safety. A rapid control prototype was built based on dSPACE to conduct a real vehicle test. The test and simulation results were consistent, which verified the simulation.

Internal Resonance in a Vibrating Beam: A Zoo of Nonlinear Resonance Peaks

PubMed Central

Mangussi, Franco

2016-01-01

In oscillating mechanical systems, nonlinearity is responsible for the departure from proportionality between the forces that sustain their motion and the resulting vibration amplitude. Such effect may have both beneficial and harmful effects in a broad class of technological applications, ranging from microelectromechanical devices to edifice structures. The dependence of the oscillation frequency on the amplitude, in particular, jeopardizes the use of nonlinear oscillators in the design of time-keeping electronic components. Nonlinearity, however, can itself counteract this adverse response by triggering a resonant interaction between different oscillation modes, which transfers the excess of energy in the main oscillation to higher harmonics, and thus stabilizes its frequency. In this paper, we examine a model for internal resonance in a vibrating elastic beam clamped at its two ends. In this case, nonlinearity occurs in the form of a restoring force proportional to the cube of the oscillation amplitude, which induces resonance between modes whose frequencies are in a ratio close to 1:3. The model is based on a representation of the resonant modes as two Duffing oscillators, coupled through cubic interactions. Our focus is put on illustrating the diversity of behavior that internal resonance brings about in the dynamical response of the system, depending on the detailed form of the coupling forces. The mathematical treatment of the model is developed at several approximation levels. A qualitative comparison of our results with previous experiments and numerical calculations on elastic beams is outlined. PMID:27648829

Path Integral Computation of Quantum Free Energy Differences Due to Alchemical Transformations Involving Mass and Potential.

PubMed

Pérez, Alejandro; von Lilienfeld, O Anatole

2011-08-09

Thermodynamic integration, perturbation theory, and λ-dynamics methods were applied to path integral molecular dynamics calculations to investigate free energy differences due to "alchemical" transformations. Several estimators were formulated to compute free energy differences in solvable model systems undergoing changes in mass and/or potential. Linear and nonlinear alchemical interpolations were used for the thermodynamic integration. We find improved convergence for the virial estimators, as well as for the thermodynamic integration over nonlinear interpolation paths. Numerical results for the perturbative treatment of changes in mass and electric field strength in model systems are presented. We used thermodynamic integration in ab initio path integral molecular dynamics to compute the quantum free energy difference of the isotope transformation in the Zundel cation. The performance of different free energy methods is discussed.

An Analysis of the Stress induced in the Periodontal Ligament during Extrusion and Rotation Movements- Part II: A Comparison of Linear vs Nonlinear FEM Study.

PubMed

Hemanth, M; Raghuveer, H P; Rani, M S; Hegde, Chathura; Kabbur, Karthik J; Chaithra, D; Vedavathi, B

2015-10-01

Optimal orthodontic forces are those which stimulate tooth movement with minimal biological trauma to the tooth, periodontal ligament (PDL) during and alveolar bone. Among various types of tooth movements, extrusion and rotational movements are seen to be associated with the least amount of root resorption and have not been studied in detail. The mechanical behavior of the PDL is known to be nonlinear elastic and thus a nonlinear simulation of the PDL provides precision to the calculated stress values. Therefore in this study, the stress patterns in the PDL were evaluated with extrusion and rotational movements using the nonlinear finite element method (FEM). A three-dimensional (3D) FEM model of the maxillary incisors was generated using SOLIDWORKS modelling software. Stresses in the PDL were evaluated with extrusive and rotational movements by a 3D FEM using ANSYS software with nonlinear material properties. It was observed that with the application of extrusive load, the tensile stresses were seen at the apex whereas the compressive stress was distributed at the cervical margin. With the application of rotational movements, maximum compressive stress was distributed at the apex and cervical third whereas the tensile stress was distributed on cervical third of the PDL on the lingual surface. For rotational and extrusion movements, stress values over the periodontal ligament was within the range of optimal stress value as proposed by Lee, with a given force system by Proffit as optimum forces for orthodontic tooth movement using nonlinear properties. During rotation there are stresses concentrated at the apex, hence due to the concentration of the compressive forces at the apex a clinician must avoid placing heavy stresses during tooth movement.

Nonlinear dynamical model of human gait

NASA Astrophysics Data System (ADS)

West, Bruce J.; Scafetta, Nicola

2003-05-01

We present a nonlinear dynamical model of the human gait control system in a variety of gait regimes. The stride-interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the fluctuations becomes more pronounced under both an increase and decrease in the average gait. Moreover, the long-range memory in these fluctuations is lost when the gait is keyed on a metronome. Human locomotion is controlled by a network of neurons capable of producing a correlated syncopated output. The central nervous system is coupled to the motocontrol system, and together they control the locomotion of the gait cycle itself. The metronomic gait is simulated by a forced nonlinear oscillator with a periodic external force associated with the conscious act of walking in a particular way.

Tethered satellite system control using electromagnetic forces and reaction wheels

NASA Astrophysics Data System (ADS)

Alandi Hallaj, Mohammad Amin; Assadian, Nima

2015-12-01

In this paper a novel non-rotating space tethered configuration is introduced which its relative positions controlled using electromagnetic forces. The attitude dynamics is controlled by three reaction wheels in the body axes. The nonlinear coupled orbital dynamics of a dumbbell tethered satellite formation flight are derived through a constrained Lagrangian approach. These equations are presented in the leader satellite orbital frame. The tether is assumed to be mass-less and straight, and the J2 perturbation is included to the analysis. The forces and the moments of the electromagnetic coils are modeled based on the far-filed model of the magnetic dipoles. A guidance scheme for generating the desired positions as a function of time in Cartesian form is presented. The satellite tethered formation with variable length is controlled utilizing a linear controller. This approach is applied to a specified scenario and it is shown that the nonlinear guidance method and the linear controller can control the nonlinear system of the tethered formation and the results are compared with optimal control approach.

Effects of van der Waals Force and Thermal Stresses on Pull-in Instability of Clamped Rectangular Microplates.

PubMed

Batra, Romesh C; Porfiri, Maurizio; Spinello, Davide

2008-02-15

We study the influence of von Karman nonlinearity, van der Waals force, and a athermal stresses on pull-in instability and small vibrations of electrostatically actuated mi-croplates. We use the Galerkin method to develop a tractable reduced-order model for elec-trostatically actuated clamped rectangular microplates in the presence of van der Waals forcesand thermal stresses. More specifically, we reduce the governing two-dimensional nonlineartransient boundary-value problem to a single nonlinear ordinary differential equation. For thestatic problem, the pull-in voltage and the pull-in displacement are determined by solving apair of nonlinear algebraic equations. The fundamental vibration frequency corresponding toa deflected configuration of the microplate is determined by solving a linear algebraic equa-tion. The proposed reduced-order model allows for accurately estimating the combined effectsof van der Waals force and thermal stresses on the pull-in voltage and the pull-in deflectionprofile with an extremely limited computational effort.

Reynolds Number Effect on Spatial Development of Viscous Flow Induced by Wave Propagation Over Bed Ripples

NASA Astrophysics Data System (ADS)

Dimas, Athanassios A.; Kolokythas, Gerasimos A.

Numerical simulations of the free-surface flow, developing by the propagation of nonlinear water waves over a rippled bottom, are performed assuming that the corresponding flow is two-dimensional, incompressible and viscous. The simulations are based on the numerical solution of the Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and appropriate bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. For the spatial discretization, a hybrid scheme is used where central finite-differences, in the horizontal direction, and a pseudo-spectral approximation method with Chebyshev polynomials, in the vertical direction, are applied. A fractional time-step scheme is used for the temporal discretization. Over the rippled bed, the wave boundary layer thickness increases significantly, in comparison to the one over flat bed, due to flow separation at the ripple crests, which generates alternating circulation regions. The amplitude of the wall shear stress over the ripples increases with increasing ripple height or decreasing Reynolds number, while the corresponding friction force is insensitive to the ripple height change. The amplitude of the form drag forces due to dynamic and hydrostatic pressures increase with increasing ripple height but is insensitive to the Reynolds number change, therefore, the percentage of friction in the total drag force decreases with increasing ripple height or increasing Reynolds number.

Analytical modeling of large amplitude free vibration of non-uniform beams carrying a both transversely and axially eccentric tip mass

NASA Astrophysics Data System (ADS)

Malaeke, Hasan; Moeenfard, Hamid

2016-03-01

The objective of this paper is to study large amplitude flexural-extensional free vibration of non-uniform cantilever beams carrying a both transversely and axially eccentric tip mass. The effects of variable axial force is also taken into account. Hamilton's principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. A numerical finite difference scheme is proposed to find the natural frequencies and mode shapes of the system which is validated specifically for a beam with linearly varying cross section. Using a single mode approximation in conjunction with the Lagrange method, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. These temporal coupled equations are then solved analytically using the multiple time scales perturbation technique. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. The qualitative and quantitative knowledge resulting from this research is expected to enable the study of the effects of eccentric tip mass and non-uniformity on the large amplitude flexural-extensional vibration of beams for improved dynamic performance.

Brownian dynamics simulations with stiff finitely extensible nonlinear elastic-Fraenkel springs as approximations to rods in bead-rod models.

PubMed

Hsieh, Chih-Chen; Jain, Semant; Larson, Ronald G

2006-01-28

A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and FENE-Fraenkel (FF) springs yield a random-walk configuration at equilibrium. We compare the simulation results of the free-draining bead-FF-spring model with those for the bead-rod model in relaxation, start-up of uniaxial extensional, and simple shear flows, and find that both methods generate nearly identical results. The computational cost per time step for a free-draining BD simulation with the proposed bead-FF-spring model is about twice as high as the traditional bead-rod model with the midpoint algorithm of Liu [J. Chem. Phys. 90, 5826 (1989)]. Nevertheless, computations with the bead-FF-spring model are as efficient as those with the bead-rod model in extensional flow because the former allows larger time steps. Moreover, the Brownian contribution to the stress for the bead-FF-spring model is isotropic and therefore simplifies the calculation of the polymer stresses. In addition, hydrodynamic interaction can more easily be incorporated into the bead-FF-spring model than into the bead-rod model since the metric force arising from the non-Cartesian coordinates used in bead-rod simulations is absent from bead-spring simulations. Finally, with our newly developed bead-FF-spring model, existing computer codes for the bead-spring models can trivially be converted to ones for effective bead-rod simulations merely by replacing the usual FENE or Cohen spring law with a FENE-Fraenkel law, and this convertibility provides a very convenient way to perform multiscale BD simulations.

Brownian dynamics simulations with stiff finitely extensible nonlinear elastic-Fraenkel springs as approximations to rods in bead-rod models

NASA Astrophysics Data System (ADS)

Hsieh, Chih-Chen; Jain, Semant; Larson, Ronald G.

2006-01-01

A very stiff finitely extensible nonlinear elastic (FENE)-Fraenkel spring is proposed to replace the rigid rod in the bead-rod model. This allows the adoption of a fast predictor-corrector method so that large time steps can be taken in Brownian dynamics (BD) simulations without over- or understretching the stiff springs. In contrast to the simple bead-rod model, BD simulations with beads and FENE-Fraenkel (FF) springs yield a random-walk configuration at equilibrium. We compare the simulation results of the free-draining bead-FF-spring model with those for the bead-rod model in relaxation, start-up of uniaxial extensional, and simple shear flows, and find that both methods generate nearly identical results. The computational cost per time step for a free-draining BD simulation with the proposed bead-FF-spring model is about twice as high as the traditional bead-rod model with the midpoint algorithm of Liu [J. Chem. Phys. 90, 5826 (1989)]. Nevertheless, computations with the bead-FF-spring model are as efficient as those with the bead-rod model in extensional flow because the former allows larger time steps. Moreover, the Brownian contribution to the stress for the bead-FF-spring model is isotropic and therefore simplifies the calculation of the polymer stresses. In addition, hydrodynamic interaction can more easily be incorporated into the bead-FF-spring model than into the bead-rod model since the metric force arising from the non-Cartesian coordinates used in bead-rod simulations is absent from bead-spring simulations. Finally, with our newly developed bead-FF-spring model, existing computer codes for the bead-spring models can trivially be converted to ones for effective bead-rod simulations merely by replacing the usual FENE or Cohen spring law with a FENE-Fraenkel law, and this convertibility provides a very convenient way to perform multiscale BD simulations.

Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance.

PubMed

Ramananarivo, Sophie; Godoy-Diana, Ramiro; Thiria, Benjamin

2011-04-12

Saving energy and enhancing performance are secular preoccupations shared by both nature and human beings. In animal locomotion, flapping flyers or swimmers rely on the flexibility of their wings or body to passively increase their efficiency using an appropriate cycle of storing and releasing elastic energy. Despite the convergence of many observations pointing out this feature, the underlying mechanisms explaining how the elastic nature of the wings is related to propulsive efficiency remain unclear. Here we use an experiment with a self-propelled simplified insect model allowing to show how wing compliance governs the performance of flapping flyers. Reducing the description of the flapping wing to a forced oscillator model, we pinpoint different nonlinear effects that can account for the observed behavior--in particular a set of cubic nonlinearities coming from the clamped-free beam equation used to model the wing and a quadratic damping term representing the fluid drag associated to the fast flapping motion. In contrast to what has been repeatedly suggested in the literature, we show that flapping flyers optimize their performance not by especially looking for resonance to achieve larger flapping amplitudes with less effort, but by tuning the temporal evolution of the wing shape (i.e., the phase dynamics in the oscillator model) to optimize the aerodynamics.

Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance

PubMed Central

Ramananarivo, Sophie; Godoy-Diana, Ramiro; Thiria, Benjamin

2011-01-01

Saving energy and enhancing performance are secular preoccupations shared by both nature and human beings. In animal locomotion, flapping flyers or swimmers rely on the flexibility of their wings or body to passively increase their efficiency using an appropriate cycle of storing and releasing elastic energy. Despite the convergence of many observations pointing out this feature, the underlying mechanisms explaining how the elastic nature of the wings is related to propulsive efficiency remain unclear. Here we use an experiment with a self-propelled simplified insect model allowing to show how wing compliance governs the performance of flapping flyers. Reducing the description of the flapping wing to a forced oscillator model, we pinpoint different nonlinear effects that can account for the observed behavior—in particular a set of cubic nonlinearities coming from the clamped-free beam equation used to model the wing and a quadratic damping term representing the fluid drag associated to the fast flapping motion. In contrast to what has been repeatedly suggested in the literature, we show that flapping flyers optimize their performance not by especially looking for resonance to achieve larger flapping amplitudes with less effort, but by tuning the temporal evolution of the wing shape (i.e., the phase dynamics in the oscillator model) to optimize the aerodynamics. PMID:21444774

Free-carrier-induced soliton fission unveiled by in situ measurements in nanophotonic waveguides

DOE Office of Scientific and Technical Information (OSTI.GOV)

Husko, Chad; Wulf, Matthias; Lefrancois, Simon

Solitons are localized waves formed by a balance of focusing and defocusing effects. These nonlinear waves exist in diverse forms of matter yet exhibit similar properties including stability, periodic recurrence and particle-like trajectories. One important property is soliton fission, a process by which an energetic higher-order soliton breaks apart due to dispersive or nonlinear perturbations. Here we demonstrate through both experiment and theory that nonlinear photocarrier generation can induce soliton fission. Using near-field measurements, we directly observe the nonlinear spatial and temporal evolution of optical pulses in situ in a nanophotonic semiconductor waveguide. We develop an analytic formalism describing themore » free-carrier dispersion (FCD) perturbation and show the experiment exceeds the minimum threshold by an order of magnitude. We confirm these observations with a numerical nonlinear Schrodinger equation model. Finally, these results provide a fundamental explanation and physical scaling of optical pulse evolution in free-carrier media and could enable improved supercontinuum sources in gas based and integrated semiconductor waveguides.« less

Free-carrier-induced soliton fission unveiled by in situ measurements in nanophotonic waveguides

DOE PAGES

Husko, Chad; Wulf, Matthias; Lefrancois, Simon; ...

2016-04-15

Solitons are localized waves formed by a balance of focusing and defocusing effects. These nonlinear waves exist in diverse forms of matter yet exhibit similar properties including stability, periodic recurrence and particle-like trajectories. One important property is soliton fission, a process by which an energetic higher-order soliton breaks apart due to dispersive or nonlinear perturbations. Here we demonstrate through both experiment and theory that nonlinear photocarrier generation can induce soliton fission. Using near-field measurements, we directly observe the nonlinear spatial and temporal evolution of optical pulses in situ in a nanophotonic semiconductor waveguide. We develop an analytic formalism describing themore » free-carrier dispersion (FCD) perturbation and show the experiment exceeds the minimum threshold by an order of magnitude. We confirm these observations with a numerical nonlinear Schrodinger equation model. Finally, these results provide a fundamental explanation and physical scaling of optical pulse evolution in free-carrier media and could enable improved supercontinuum sources in gas based and integrated semiconductor waveguides.« less

Ultrasonic Nondestructive Characterization of Adhesive Bonds

NASA Technical Reports Server (NTRS)

Qu, Jianmin

1997-01-01

Qualitative measurements of adhesion or binding forces can be accomplished, for example, by using the reflection coefficient of an ultrasound or by using thermal waves (Light and Kwun, 1989, Achenbach and Parikh, 1991, and Bostrom and wickham, 1991). However, a quantitative determination of binding forces is rather difficult. It has been observed that higher harmonics of the fundamental frequency are generated when an ultrasound passes through a nonlinear material. It seems that such non-linearity can be effectively used to characterize the bond strength. Several theories have been developed to model this nonlinear effect (Adler and Nagy, 1991; Achenbach and Parikh, 1991; Parikh and Achenbach, 1992; and Hirose and Kitahara, 1992; Anastasi and Roberts, 1992). Based on a microscopic description of the nonlinear interface binding force, a quantitative method was presented by Pangraz and Arnold (1994). Recently, Tang, Cheng and Achenbach (1997) made a comparison between the experimental and simulated results based on this theoretical model. A water immersion mode-converted shear wave through-transmission setup was used by Berndt and Green (1997) to analyze the nonlinear acoustic behavior of the adhesive bond. In this project, the nonlinear responses of an adhesive joint was investigated through transmission tests of ultrasonic wave and analyzed by the finite element simulations. The higher order harmonics were obtained in the tests. It is found that the amplitude of higher harmonics increases as the aging increases, especially the 3dorder harmonics. Results from the numerical simulation show that the material nonlinearity does indeed generate higher order harmonics. In particular, the elastic-perfect plastic behavior generates significant 3rd and 5th order harmonics.

Intense electromagnetic outbursts from collapsing hypermassive neutron stars

NASA Astrophysics Data System (ADS)

Lehner, Luis; Palenzuela, Carlos; Liebling, Steven L.; Thompson, Christopher; Hanna, Chad

2012-11-01

We study the gravitational collapse of a magnetized neutron star using a novel numerical approach able to capture both the dynamics of the star and the behavior of the surrounding plasma. In this approach, a fully general relativistic magnetohydrodynamics implementation models the collapse of the star and provides appropriate boundary conditions to a force-free model which describes the stellar exterior. We validate this strategy by comparing with known results for the rotating monopole and aligned rotator solutions and then apply it to study both rotating and nonrotating stellar collapse scenarios and contrast the behavior with what is obtained when employing the electrovacuum approximation outside the star. The nonrotating electrovacuum collapse is shown to agree qualitatively with a Newtonian model of the electromagnetic field outside a collapsing star. We illustrate and discuss a fundamental difference between the force-free and electrovacuum solutions, involving the appearance of large zones of electric-dominated field in the vacuum case. This provides a clear demonstration of how dissipative singularities appear generically in the nonlinear time evolution of force-free fluids. In both the rotating and nonrotating cases, our simulations indicate that the collapse induces a strong electromagnetic transient, which leaves behind an uncharged, unmagnetized Kerr black hole. In the case of submillisecond rotation, the magnetic field experiences strong winding, and the transient carries much more energy. This result has important implications for models of gamma-ray bursts. Even when the neutron star is surrounded by an accretion torus (as in binary merger and collapsar scenarios), a magnetosphere may emerge through a dynamo process operating in a surface shear layer. When this rapidly rotating magnetar collapses to a black hole, the electromagnetic energy released can compete with the later output in a Blandford-Znajek jet. Much less electromagnetic energy is released by a massive magnetar that is (initially) gravitationally stable: its rotational energy is dissipated mainly by internal torques. A distinct plasmoid structure is seen in our nonrotating simulations, which will generate a radio transient with subluminal expansion and greater synchrotron efficiency than is expected in shock models. Closely related phenomena appear to be at work in the giant flares of Galactic magnetars.

Vibrational dynamics of vocal folds using nonlinear normal modes.

PubMed

Pinheiro, Alan P; Kerschen, Gaëtan

2013-08-01

Many previous works involving physical models, excised and in vivo larynges have pointed out nonlinear vibration in vocal folds during voice production. Moreover, theoretical studies involving mechanical modeling of these folds have tried to gain a profound understanding of the observed nonlinear phenomena. In this context, the present work uses the nonlinear normal mode theory to investigate the nonlinear modal behavior of 16 subjects using a two-mass mechanical modeling of the vocal folds. The free response of the conservative system at different energy levels is considered to assess the impact of the structural nonlinearity of the vocal fold tissues. The results show very interesting and complex nonlinear phenomena including frequency-energy dependence, subharmonic regimes and, in some cases, modal interactions, entrainment and bifurcations. Copyright © 2012 IPEM. Published by Elsevier Ltd. All rights reserved.

Energy Accumulation and Emanation at Low Latitudes. Part II: Nonlinear Response to Strong Episodic Equatorial Forcing.

NASA Astrophysics Data System (ADS)

Chang, Hai-Ru; Webster, Peter J.

1990-11-01

A fully nonlinear model is used to reexamine the impact of a zonally varying basic state on the propagation characteristics of latitudinally equatorially trapped modes. Linear studies have shown that such modes are longitudinally trapped in regions of negative stretching deformation of the equatorial time-mean zonal flow (i.e., where Ux < 0) forming `accumulation' regions of wave action flux. Furthermore, the accumulation regions tend to act as local emanation regions to the extratropics. These physical communications between the tropics and extratropics are referred to as fast teleconnections due to their rapidity (periods of days to weeks) compared to the much slower climatological differences in the mean states such as occur between El Niño and La Niña. The latter form of communication between low and high latitudes, which is induced by very low frequency SST changes, is referred to as a slow teleconnection.It is generally found that accumulation and emanation regions are present in the nonlinear regime with much the same character as with the linear model. The similarity exists even when realistic forcing functions are used with amplitudes and temporal and spatial characteristics that correspond to impulsive convection in the western Pacific Ocean. A description of the convection is given. A diagnosis of the linear and nonlinear results shows that, in the tropics, the linear advection by the mean flow plays a dominant role and probably is the reason for the great similarity of the linear and nonlinear tropical atmosphere. However, there are some differences between the linear and nonlinear results. Nonlinear waves appear to propagate more rapidly through the maximum westerlies along the equator and with less difficulty than linear waves. The differences that do occur arise from the nonlinear changes in the tropical mass field, especially in the accumulation zone. Differences between linear and nonlinear responses in the midlatitude response to equatorial forcing appear to reflect changes in the tropics. Nonlinear maxima occur poleward of the region of tropical westerlies but only after accumulation has occurred along the equator.The results of the study are used to discuss the problem of why there is considerable similarity between simple linear models and more sophisticated nonlinear models. Such similarity would probably explain why the NMC and the NEPRF global models exhibit phase locked responses in the middle latitudes to imposed and impulsive tropical forcing. The role of fast teleconnenions in the longer term general circulation of the atmosphere is discussed, especially during El Niño and La Niña. Whereas an aggregate role for the fast teleconnections in producing very slowly evolving climate features remains obscure, it does appear that the accumulation-emanation theory may infer different routings for transient communications between the tropics and higher latitudes and vice vera depending upon the state of the basic flow.

MMS Examination of FTEs at the Earth's Subsolar Magnetopause

NASA Astrophysics Data System (ADS)

Akhavan-Tafti, M.; Slavin, J. A.; Le, G.; Eastwood, J. P.; Strangeway, R. J.; Russell, C. T.; Nakamura, R.; Baumjohann, W.; Torbert, R. B.; Giles, B. L.; Gershman, D. J.; Burch, J. L.

2018-02-01

Determining the magnetic field structure, electric currents, and plasma distributions within flux transfer event (FTE)-type flux ropes is critical to the understanding of their origin, evolution, and dynamics. Here the Magnetospheric Multiscale mission's high-resolution magnetic field and plasma measurements are used to identify FTEs in the vicinity of the subsolar magnetopause. The constant-α flux rope model is used to identify quasi-force free flux ropes and to infer the size, the core magnetic field strength, the magnetic flux content, and the spacecraft trajectories through these structures. Our statistical analysis determines a mean diameter of 1,700 ± 400 km ( 30 ± 9 di) and an average magnetic flux content of 100 ± 30 kWb for the quasi-force free FTEs at the Earth's subsolar magnetopause which are smaller than values reported by Cluster at high latitudes. These observed nonlinear size and magnetic flux content distributions of FTEs appear consistent with the plasmoid instability theory, which relies on the merging of neighboring, small-scale FTEs to generate larger structures. The ratio of the perpendicular to parallel components of current density, RJ, indicates that our FTEs are magnetically force-free, defined as RJ < 1, in their core regions (<0.6 Rflux rope). Plasma density is shown to be larger in smaller, newly formed FTEs and dropping with increasing FTE size. It is also shown that parallel ion velocity dominates inside FTEs with largest plasma density. Field-aligned flow facilitates the evacuation of plasma inside newly formed FTEs, while their core magnetic field strengthens with increasing FTE size.

Influence of mechanically-induced dilatation on the shape memory behavior of amorphous polymers at large deformation

NASA Astrophysics Data System (ADS)

Hanzon, Drew W.; Lu, Haibao; Yakacki, Christopher M.; Yu, Kai

2018-01-01

In this study, we explore the influence of mechanically-induced dilatation on the thermomechanical and shape memory behavior of amorphous shape memory polymers (SMPs) at large deformation. The uniaxial tension, glass transition, stress relaxation and free recovery behaviors are examined with different strain levels (up to 340% engineering strain). A multi-branched constitutive model that incorporates dilatational effects on the polymer relaxation time is established and applied to assist in discussions and understand the nonlinear viscoelastic behaviors of SMPs. It is shown that the volumetric dilatation results in an SMP network with lower viscosity, faster relaxation, and lower Tg. The influence of the dilatational effect on the thermomechanical behaviors is significant when the polymers are subject to large deformation or in a high viscosity state. The dilation also increases the free recovery rate of SMP at a given recovery temperature. Even though the tested SMPs are far beyond their linear viscoelastic region when a large programming strain is applied, the free recovery behavior still follows the time-temperature superposition (TTSP) if the dilatational effect is considered during the transformation of time scales; however, if the programming strain is different, TTSP fails in predicting the recovery behavior of SMPs because the network has different entropy state and driving force during shape recovery. Since most soft active polymers are subject to large deformation in practice, this study provides a theoretical basis to better understand their nonlinear viscoelastic behaviors, and optimize their performance in engineering applications.

Research on parallel load sharing principle of piezoelectric six-dimensional heavy force/torque sensor

NASA Astrophysics Data System (ADS)

Liu, Wei; Li, Ying-jun; Jia, Zhen-yuan; Zhang, Jun; Qian, Min

2011-01-01

In working process of huge heavy-load manipulators, such as the free forging machine, hydraulic die-forging press, forging manipulator, heavy grasping manipulator, large displacement manipulator, measurement of six-dimensional heavy force/torque and real-time force feedback of the operation interface are basis to realize coordinate operation control and force compliance control. It is also an effective way to raise the control accuracy and achieve highly efficient manufacturing. Facing to solve dynamic measurement problem on six-dimensional time-varying heavy load in extremely manufacturing process, the novel principle of parallel load sharing on six-dimensional heavy force/torque is put forward. The measuring principle of six-dimensional force sensor is analyzed, and the spatial model is built and decoupled. The load sharing ratios are analyzed and calculated in vertical and horizontal directions. The mapping relationship between six-dimensional heavy force/torque value to be measured and output force value is built. The finite element model of parallel piezoelectric six-dimensional heavy force/torque sensor is set up, and its static characteristics are analyzed by ANSYS software. The main parameters, which affect load sharing ratio, are analyzed. The experiments for load sharing with different diameters of parallel axis are designed. The results show that the six-dimensional heavy force/torque sensor has good linearity. Non-linearity errors are less than 1%. The parallel axis makes good effect of load sharing. The larger the diameter is, the better the load sharing effect is. The results of experiments are in accordance with the FEM analysis. The sensor has advantages of large measuring range, good linearity, high inherent frequency, and high rigidity. It can be widely used in extreme environments for real-time accurate measurement of six-dimensional time-varying huge loads on manipulators.

Exact static solutions for discrete phi4 models free of the Peierls-Nabarro barrier: discretized first-integral approach.

PubMed

Dmitriev, S V; Kevrekidis, P G; Yoshikawa, N; Frantzeskakis, D J

2006-10-01

We propose a generalization of the discrete Klein-Gordon models free of the Peierls-Nabarro barrier derived in Spreight [Nonlinearity 12, 1373 (1999)] and Barashenkov [Phys. Rev. E 72, 035602(R) (2005)], such that they support not only kinks but a one-parameter set of exact static solutions. These solutions can be obtained iteratively from a two-point nonlinear map whose role is played by the discretized first integral of the static Klein-Gordon field, as suggested by Dmitriev [J. Phys. A 38, 7617 (2005)]. We then discuss some discrete phi4 models free of the Peierls-Nabarro barrier and identify for them the full space of available static solutions, including those derived recently by Cooper [Phys. Rev. E 72, 036605 (2005)] but not limited to them. These findings are also relevant to standing wave solutions of discrete nonlinear Schrödinger models. We also study stability of the obtained solutions. As an interesting aside, we derive the list of solutions to the continuum phi4 equation that fill the entire two-dimensional space of parameters obtained as the continuum limit of the corresponding space of the discrete models.

Estimation of Handgrip Force from SEMG Based on Wavelet Scale Selection.

PubMed

Wang, Kai; Zhang, Xianmin; Ota, Jun; Huang, Yanjiang

2018-02-24

This paper proposes a nonlinear correlation-based wavelet scale selection technology to select the effective wavelet scales for the estimation of handgrip force from surface electromyograms (SEMG). The SEMG signal corresponding to gripping force was collected from extensor and flexor forearm muscles during the force-varying analysis task. We performed a computational sensitivity analysis on the initial nonlinear SEMG-handgrip force model. To explore the nonlinear correlation between ten wavelet scales and handgrip force, a large-scale iteration based on the Monte Carlo simulation was conducted. To choose a suitable combination of scales, we proposed a rule to combine wavelet scales based on the sensitivity of each scale and selected the appropriate combination of wavelet scales based on sequence combination analysis (SCA). The results of SCA indicated that the scale combination VI is suitable for estimating force from the extensors and the combination V is suitable for the flexors. The proposed method was compared to two former methods through prolonged static and force-varying contraction tasks. The experiment results showed that the root mean square errors derived by the proposed method for both static and force-varying contraction tasks were less than 20%. The accuracy and robustness of the handgrip force derived by the proposed method is better than that obtained by the former methods.

A Large Signal Model for CMUT Arrays with Arbitrary Membrane Geometries Operating in Non-Collapsed Mode

PubMed Central

Satir, Sarp; Zahorian, Jaime; Degertekin, F. Levent

2014-01-01

A large signal, transient model has been developed to predict the output characteristics of a CMUT array operated in the non-collapse mode. The model is based on separation of the nonlinear electrostatic voltage-to-force relation and the linear acoustic array response. For linear acoustic radiation and crosstalk effects, the boundary element method is used. The stiffness matrix in the vibroacoustics calculations is obtained using static finite element analysis of a single membrane which can have arbitrary geometry and boundary conditions. A lumped modeling approach is used to reduce the order of the system for modeling the transient nonlinear electrostatic actuation. To accurately capture the dynamics of the non-uniform electrostatic force distribution over the CMUT electrode during large deflections, the membrane electrode is divided into patches shaped to match higher order membrane modes, each introducing a variable to the system model. This reduced order nonlinear lumped model is solved in the time domain using Simulink. The model has two linear blocks to calculate the displacement profile of the electrode patches and the output pressure for a given force distribution over the array, respectively. The force to array displacement block uses the linear acoustic model, and the Rayleigh integral is evaluated to calculate the pressure at any field point. Using the model, the transient transmitted pressure can be simulated for different large signal drive signal configurations. The acoustic model is verified by comparison to harmonic FEA in vacuum and fluid for high and low aspect ratio membranes as well as mass-loaded membranes. The overall Simulink model is verified by comparison to transient 3D FEA and experimental results for different large drive signals; and an example for a phased array simulation is given. PMID:24158297

Does Hooke's law work in helical nanosprings?

PubMed

Ben, Sudong; Zhao, Junhua; Rabczuk, Timon

2015-08-28

Hooke's law is a principle of physics that states that the force needed to extend a spring by some distance is proportional to that distance. The law is always valid for an initial portion of the elastic range for nearly all helical macrosprings. Here we report the sharp nonlinear force-displacement relation of tightly wound helical carbon nanotubes at even small displacement via a molecular mechanics model. We demonstrate that the van der Waals (vdW) interaction between the intertube walls dominates the nonlinear relation based on our analytical expressions. This study provides physical insights into the origin of huge nonlinearity of the helical nanosprings.

Chaos in a 4D dissipative nonlinear fermionic model

NASA Astrophysics Data System (ADS)

Aydogmus, Fatma

2015-12-01

Gursey Model is the only possible 4D conformally invariant pure fermionic model with a nonlinear self-coupled spinor term. It has been assumed to be similar to the Heisenberg's nonlinear generalization of Dirac's equation, as a possible basis for a unitary description of elementary particles. Gursey Model admits particle-like solutions for the derived classical field equations and these solutions are instantonic in character. In this paper, the dynamical nature of damped and forced Gursey Nonlinear Differential Equations System (GNDES) are studied in order to get more information on spinor type instantons. Bifurcation and chaos in the system are observed by constructing the bifurcation diagrams and Poincaré sections. Lyapunov exponent and power spectrum graphs of GNDES are also constructed to characterize the chaotic behavior.

Mapping the conformational free energy of aspartic acid in the gas phase and in aqueous solution.

PubMed

Comitani, Federico; Rossi, Kevin; Ceriotti, Michele; Sanz, M Eugenia; Molteni, Carla

2017-04-14

The conformational free energy landscape of aspartic acid, a proteogenic amino acid involved in a wide variety of biological functions, was investigated as an example of the complexity that multiple rotatable bonds produce even in relatively simple molecules. To efficiently explore such a landscape, this molecule was studied in the neutral and zwitterionic forms, in the gas phase and in water solution, by means of molecular dynamics and the enhanced sampling method metadynamics with classical force-fields. Multi-dimensional free energy landscapes were reduced to bi-dimensional maps through the non-linear dimensionality reduction algorithm sketch-map to identify the energetically stable conformers and their interconnection paths. Quantum chemical calculations were then performed on the minimum free energy structures. Our procedure returned the low energy conformations observed experimentally in the gas phase with rotational spectroscopy [M. E. Sanz et al., Phys. Chem. Chem. Phys. 12, 3573 (2010)]. Moreover, it provided information on higher energy conformers not accessible to experiments and on the conformers in water. The comparison between different force-fields and quantum chemical data highlighted the importance of the underlying potential energy surface to accurately capture energy rankings. The combination of force-field based metadynamics, sketch-map analysis, and quantum chemical calculations was able to produce an exhaustive conformational exploration in a range of significant free energies that complements the experimental data. Similar protocols can be applied to larger peptides with complex conformational landscapes and would greatly benefit from the next generation of accurate force-fields.

Mapping the conformational free energy of aspartic acid in the gas phase and in aqueous solution

NASA Astrophysics Data System (ADS)

Comitani, Federico; Rossi, Kevin; Ceriotti, Michele; Sanz, M. Eugenia; Molteni, Carla

2017-04-01

The conformational free energy landscape of aspartic acid, a proteogenic amino acid involved in a wide variety of biological functions, was investigated as an example of the complexity that multiple rotatable bonds produce even in relatively simple molecules. To efficiently explore such a landscape, this molecule was studied in the neutral and zwitterionic forms, in the gas phase and in water solution, by means of molecular dynamics and the enhanced sampling method metadynamics with classical force-fields. Multi-dimensional free energy landscapes were reduced to bi-dimensional maps through the non-linear dimensionality reduction algorithm sketch-map to identify the energetically stable conformers and their interconnection paths. Quantum chemical calculations were then performed on the minimum free energy structures. Our procedure returned the low energy conformations observed experimentally in the gas phase with rotational spectroscopy [M. E. Sanz et al., Phys. Chem. Chem. Phys. 12, 3573 (2010)]. Moreover, it provided information on higher energy conformers not accessible to experiments and on the conformers in water. The comparison between different force-fields and quantum chemical data highlighted the importance of the underlying potential energy surface to accurately capture energy rankings. The combination of force-field based metadynamics, sketch-map analysis, and quantum chemical calculations was able to produce an exhaustive conformational exploration in a range of significant free energies that complements the experimental data. Similar protocols can be applied to larger peptides with complex conformational landscapes and would greatly benefit from the next generation of accurate force-fields.

Parametrically excited motion of a levitated rigid bar over high- Tc superconducting bulks

NASA Astrophysics Data System (ADS)

Shimizu, T.; Sugiura, T.; Ogawa, S.

2006-10-01

High-Tc superconducting levitation systems achieve, under no contact support, stable levitation without control. This feature can be applied to flywheels, magnetically levitated trains, and so on. But no contact support has small damping. So these mechanisms can show complicated phenomena of dynamics due to nonlinearity in their magnetic force. For application to large-scale machines, we need to analyze dynamics of a large levitated body supported at multiple points. This research deals with nonlinearly coupled oscillation of a homogeneous and symmetric rigid bar supported at its both ends by equal electromagnetic forces between superconductors and permanent magnets. In our past study, using a rigid bar, we found combination resonance. Combination resonance happens owing to the asymmetry of the system. But, even if support forces are symmetric, parametric resonance can happen. With a simple symmetric model, this research focuses on especially the parametric resonance, and evaluates nonlinear effect of the symmetric support forces by experiment and numerical analysis. Obtained results show that two modes, caused by coupling of horizontal translation and roll motion, can be excited nonlinearly when the superconductor is excited vertically in the neighborhood of twice the natural frequencies of those modes. We confirmed these resonances have nonlinear characteristics of soft-spring, hysteresis and so on.

Improved modeling of turbulent forced convection heat transfer in straight ducts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rokni, M.; Sunden, B.

1999-08-01

This investigation concerns numerical calculation of turbulent forced convective heat transfer and fluid flow in their fully developed state at low Reynolds number. The authors have developed a low Reynolds number version of the nonlinear {kappa}-{epsilon} model combined with the heat flux models of simple eddy diffusivity (SED), low Reynolds number version of generalized gradient diffusion hypothesis (GGDH), and wealth {proportional_to} earning {times} time (WET) in general three-dimensional geometries. The numerical approach is based on the finite volume technique with a nonstaggered grid arrangement and the SIMPLEC algorithm. Results have been obtained with the nonlinear {kappa}-{epsilon} model, combined with themore » Lam-Bremhorst and the Abe-Kondoh-Nagano damping functions for low Reynolds numbers.« less

Solving the aerodynamics of fungal flight: how air viscosity slows spore motion.

PubMed

Fischer, Mark W F; Stolze-Rybczynski, Jessica L; Davis, Diana J; Cui, Yunluan; Money, Nicholas P

2010-01-01

Viscous drag causes the rapid deceleration of fungal spores after high-speed launches and limits discharge distance. Stokes' law posits a linear relationship between drag force and velocity. It provides an excellent fit to experimental measurements of the terminal velocity of free-falling spores and other instances of low Reynolds number motion (Re<1). More complex, non-linear drag models have been devised for movements characterized by higher Re, but their effectiveness for modeling the launch of fast-moving fungal spores has not been tested. In this paper, we use data on spore discharge processes obtained from ultra-high-speed video recordings to evaluate the effects of air viscosity predicted by Stokes' law and a commonly used non-linear drag model. We find that discharge distances predicted from launch speeds by Stokes' model provide a much better match to measured distances than estimates from the more complex drag model. Stokes' model works better over a wide range projectile sizes, launch speeds, and discharge distances, from microscopic mushroom ballistospores discharged at <1 m s(-1) over a distance of <0.1mm (Re<1.0), to macroscopic sporangia of Pilobolus that are launched at >10 m s(-1) and travel as far as 2.5m (Re>100). Copyright © 2010 The British Mycological Society. Published by Elsevier Ltd. All rights reserved.

The hydrodynamics of swimming at intermediate Reynolds numbers in the water boatman (Corixidae).

PubMed

Ngo, Victoria; McHenry, Matthew James

2014-08-01

The fluid forces that govern propulsion determine the speed and energetic cost of swimming. These hydrodynamics are scale dependent and it is unclear what forces matter to the tremendous diversity of aquatic animals that are between a millimeter and a centimeter in length. Animals at this scale generally operate within the regime of intermediate Reynolds numbers, where both viscous and inertial fluid forces have the potential to play a role in propulsion. The present study aimed to resolve which forces create thrust and drag in the paddling of the water boatman (Corixidae), an animal that spans much of the intermediate regime (10

An accurate front capturing scheme for tumor growth models with a free boundary limit

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Tang, Min; Wang, Li; Zhou, Zhennan

2018-07-01

We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when the pressure-density relationship becomes highly nonlinear. In particular, the constitutive law connecting pressure p and density ρ is p (ρ) = m/m-1 ρ m - 1, and when m ≫ 1, the cell density ρ may evolve its support according to a pressure-driven geometric motion with sharp interface along its boundary. The nonlinearity and degeneracy in the diffusion bring great challenges in numerical simulations. Prior to the present paper, there is lack of standard mechanism to numerically capture the front propagation speed as m ≫ 1. In this paper, we develop a numerical scheme based on a novel prediction-correction reformulation that can accurately approximate the front propagation even when the nonlinearity is extremely strong. We show that the semi-discrete scheme naturally connects to the free boundary limit equation as m → ∞. With proper spatial discretization, the fully discrete scheme has improved stability, preserves positivity, and can be implemented without nonlinear solvers. Finally, extensive numerical examples in both one and two dimensions are provided to verify the claimed properties in various applications.

An experimentally validated model for geometrically nonlinear plucking-based frequency up-conversion in energy harvesting

NASA Astrophysics Data System (ADS)

Kathpalia, B.; Tan, D.; Stern, I.; Erturk, A.

2018-01-01

It is well known that plucking-based frequency up-conversion can enhance the power output in piezoelectric energy harvesting by enabling cyclic free vibration at the fundamental bending mode of the harvester even for very low excitation frequencies. In this work, we present a geometrically nonlinear plucking-based framework for frequency up-conversion in piezoelectric energy harvesting under quasistatic excitations associated with low-frequency stimuli such as walking and similar rigid body motions. Axial shortening of the plectrum is essential to enable plucking excitation, which requires a nonlinear framework relating the plectrum parameters (e.g. overlap length between the plectrum and harvester) to the overall electrical power output. Von Kármán-type geometrically nonlinear deformation of the flexible plectrum cantilever is employed to relate the overlap length between the flexible (nonlinear) plectrum and the stiff (linear) harvester to the transverse quasistatic tip displacement of the plectrum, and thereby the tip load on the linear harvester in each plucking cycle. By combining the nonlinear plectrum mechanics and linear harvester dynamics with two-way electromechanical coupling, the electrical power output is obtained directly in terms of the overlap length. Experimental case studies and validations are presented for various overlap lengths and a set of electrical load resistance values. Further analysis results are reported regarding the combined effects of plectrum thickness and overlap length on the plucking force and harvested power output. The experimentally validated nonlinear plectrum-linear harvester framework proposed herein can be employed to design and optimize frequency up-conversion by properly choosing the plectrum parameters (geometry, material, overlap length, etc) as well as the harvester parameters.

Nonlinear model of a rotating hub-beams structure: Equations of motion

NASA Astrophysics Data System (ADS)

Warminski, Jerzy

2018-01-01

Dynamics of a rotating structure composed of a rigid hub and flexible beams is presented in the paper. A nonlinear model of a beam takes into account bending, extension and nonlinear curvature. The influence of geometric nonlinearity and nonconstant angular velocity on dynamics of the rotating structure is presented. The exact equations of motion and associated boundary conditions are derived on the basis of the Hamilton's principle. The simplification of the exact nonlinear mathematical model is proposed taking into account the second order approximation. The reduced partial differential equations of motion together with associated boundary conditions can be used to study natural or forced vibrations of a rotating structure considering constant or nonconstant angular speed of a rigid hub and an arbitrary number of flexible blades.

DAISY: a new software tool to test global identifiability of biological and physiological systems.

PubMed

Bellu, Giuseppina; Saccomani, Maria Pia; Audoly, Stefania; D'Angiò, Leontina

2007-10-01

A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/.

nonlinMIP contribution to CMIP6: model intercomparison project for non-linear mechanisms: physical basis, experimental design and analysis principles (v1.0)

NASA Astrophysics Data System (ADS)

Good, Peter; Andrews, Timothy; Chadwick, Robin; Dufresne, Jean-Louis; Gregory, Jonathan M.; Lowe, Jason A.; Schaller, Nathalie; Shiogama, Hideo

2016-11-01

nonlinMIP provides experiments that account for state-dependent regional and global climate responses. The experiments have two main applications: (1) to focus understanding of responses to CO2 forcing on states relevant to specific policy or scientific questions (e.g. change under low-forcing scenarios, the benefits of mitigation, or from past cold climates to the present day), or (2) to understand the state dependence (non-linearity) of climate change - i.e. why doubling the forcing may not double the response. State dependence (non-linearity) of responses can be large at regional scales, with important implications for understanding mechanisms and for general circulation model (GCM) emulation techniques (e.g. energy balance models and pattern-scaling methods). However, these processes are hard to explore using traditional experiments, which explains why they have had so little attention in previous studies. Some single model studies have established novel analysis principles and some physical mechanisms. There is now a need to explore robustness and uncertainty in such mechanisms across a range of models (point 2 above), and, more broadly, to focus work on understanding the response to CO2 on climate states relevant to specific policy/science questions (point 1). nonlinMIP addresses this using a simple, small set of CO2-forced experiments that are able to separate linear and non-linear mechanisms cleanly, with a good signal-to-noise ratio - while being demonstrably traceable to realistic transient scenarios. The design builds on the CMIP5 (Coupled Model Intercomparison Project Phase 5) and CMIP6 DECK (Diagnostic, Evaluation and Characterization of Klima) protocols, and is centred around a suite of instantaneous atmospheric CO2 change experiments, with a ramp-up-ramp-down experiment to test traceability to gradual forcing scenarios. In all cases the models are intended to be used with CO2 concentrations rather than CO2 emissions as the input. The understanding gained will help interpret the spread in policy-relevant scenario projections. Here we outline the basic physical principles behind nonlinMIP, and the method of establishing traceability from abruptCO2 to gradual forcing experiments, before detailing the experimental design, and finally some analysis principles. The test of traceability from abruptCO2 to transient experiments is recommended as a standard analysis within the CMIP5 and CMIP6 DECK protocols.

Extracting Leading Nonlinear Modes of Changing Climate From Global SST Time Series

NASA Astrophysics Data System (ADS)

Mukhin, D.; Gavrilov, A.; Loskutov, E. M.; Feigin, A. M.; Kurths, J.

2017-12-01

Data-driven modeling of climate requires adequate principal variables extracted from observed high-dimensional data. For constructing such variables it is needed to find spatial-temporal patterns explaining a substantial part of the variability and comprising all dynamically related time series from the data. The difficulties of this task rise from the nonlinearity and non-stationarity of the climate dynamical system. The nonlinearity leads to insufficiency of linear methods of data decomposition for separating different processes entangled in the observed time series. On the other hand, various forcings, both anthropogenic and natural, make the dynamics non-stationary, and we should be able to describe the response of the system to such forcings in order to separate the modes explaining the internal variability. The method we present is aimed to overcome both these problems. The method is based on the Nonlinear Dynamical Mode (NDM) decomposition [1,2], but takes into account external forcing signals. An each mode depends on hidden, unknown a priori, time series which, together with external forcing time series, are mapped onto data space. Finding both the hidden signals and the mapping allows us to study the evolution of the modes' structure in changing external conditions and to compare the roles of the internal variability and forcing in the observed behavior. The method is used for extracting of the principal modes of SST variability on inter-annual and multidecadal time scales accounting the external forcings such as CO2, variations of the solar activity and volcanic activity. The structure of the revealed teleconnection patterns as well as their forecast under different CO2 emission scenarios are discussed.[1] Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J. (2016). Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101.

Loss terms in free-piston Stirling engine models

NASA Technical Reports Server (NTRS)

Gordon, Lloyd B.

1992-01-01

Various models for free piston Stirling engines are reviewed. Initial models were developed primarily for design purposes and to predict operating parameters, especially efficiency. More recently, however, such models have been used to predict engine stability. Free piston Stirling engines have no kinematic constraints and stability may not only be sensitive to the load, but also to various nonlinear loss and spring constraints. The present understanding is reviewed of various loss mechanisms for free piston Stirling engines and how they have been incorporated into engine models is discussed.

Optimality and inference in hydrology from entropy production considerations: synthetic hillslope numerical experiments

NASA Astrophysics Data System (ADS)

Kollet, S. J.

2015-05-01

In this study, entropy production optimization and inference principles are applied to a synthetic semi-arid hillslope in high-resolution, physics-based simulations. The results suggest that entropy or power is indeed maximized, because of the strong nonlinearity of variably saturated flow and competing processes related to soil moisture fluxes, the depletion of gradients, and the movement of a free water table. Thus, it appears that the maximum entropy production (MEP) principle may indeed be applicable to hydrologic systems. In the application to hydrologic system, the free water table constitutes an important degree of freedom in the optimization of entropy production and may also relate the theory to actual observations. In an ensuing analysis, an attempt is made to transfer the complex, "microscopic" hillslope model into a macroscopic model of reduced complexity using the MEP principle as an interference tool to obtain effective conductance coefficients and forces/gradients. The results demonstrate a new approach for the application of MEP to hydrologic systems and may form the basis for fruitful discussions and research in future.

Nonlinear structures: Cnoidal, soliton, and periodical waves in quantum semiconductor plasma

NASA Astrophysics Data System (ADS)

Tolba, R. E.; El-Bedwehy, N. A.; Moslem, W. M.; El-Labany, S. K.; Yahia, M. E.

2016-01-01

Properties and emerging conditions of various nonlinear acoustic waves in a three dimensional quantum semiconductor plasma are explored. A plasma fluid model characterized by degenerate pressures, exchange correlation, and quantum recoil forces is established and solved. Our analysis approach is based on the reductive perturbation theory for deriving the Kadomtsev-Petviashvili equation from the fluid model and solving it by using Painlevé analysis to come up with different nonlinear solutions that describe different pulse profiles such as cnoidal, soliton, and periodical pulses. The model is then employed to recognize the possible perturbations in GaN semiconductor.

Nonlinear structures: Cnoidal, soliton, and periodical waves in quantum semiconductor plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tolba, R. E., E-mail: tolba-math@yahoo.com; El-Bedwehy, N. A., E-mail: nab-elbedwehy@yahoo.com; Moslem, W. M., E-mail: wmmoslem@hotmail.com

2016-01-15

Properties and emerging conditions of various nonlinear acoustic waves in a three dimensional quantum semiconductor plasma are explored. A plasma fluid model characterized by degenerate pressures, exchange correlation, and quantum recoil forces is established and solved. Our analysis approach is based on the reductive perturbation theory for deriving the Kadomtsev-Petviashvili equation from the fluid model and solving it by using Painlevé analysis to come up with different nonlinear solutions that describe different pulse profiles such as cnoidal, soliton, and periodical pulses. The model is then employed to recognize the possible perturbations in GaN semiconductor.

Electrostatic forces in the Poisson-Boltzmann systems

NASA Astrophysics Data System (ADS)

Xiao, Li; Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2013-09-01

Continuum modeling of electrostatic interactions based upon numerical solutions of the Poisson-Boltzmann equation has been widely used in structural and functional analyses of biomolecules. A limitation of the numerical strategies is that it is conceptually difficult to incorporate these types of models into molecular mechanics simulations, mainly because of the issue in assigning atomic forces. In this theoretical study, we first derived the Maxwell stress tensor for molecular systems obeying the full nonlinear Poisson-Boltzmann equation. We further derived formulations of analytical electrostatic forces given the Maxwell stress tensor and discussed the relations of the formulations with those published in the literature. We showed that the formulations derived from the Maxwell stress tensor require a weaker condition for its validity, applicable to nonlinear Poisson-Boltzmann systems with a finite number of singularities such as atomic point charges and the existence of discontinuous dielectric as in the widely used classical piece-wise constant dielectric models.

Phase relations in a forced turbulent boundary layer: implications for modelling of high Reynolds number wall turbulence

PubMed Central

2017-01-01

Phase relations between specific scales in a turbulent boundary layer are studied here by highlighting the associated nonlinear scale interactions in the flow. This is achieved through an experimental technique that allows for targeted forcing of the flow through the use of a dynamic wall perturbation. Two distinct large-scale modes with well-defined spatial and temporal wavenumbers were simultaneously forced in the boundary layer, and the resulting nonlinear response from their direct interactions was isolated from the turbulence signal for the study. This approach advances the traditional studies of large- and small-scale interactions in wall turbulence by focusing on the direct interactions between scales with triadic wavenumber consistency. The results are discussed in the context of modelling high Reynolds number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’. PMID:28167576

Model Development and Model-Based Control Design for High Performance Nonlinear Smart Systems

DTIC Science & Technology

2007-11-20

potentially impact a broad range of flow control problems of interest to the Air Force and Boeing. Point of contact: James Mabe , Boeing Phantom Works...rotorcraft blades. In both cases, models and control designs will be validated using data from Boeing experiments and flight tests. Point of contact: James ... Mabe , Boeing Phantom Works, Seattle, WA, 206-655-0091. 3. PZT Unimorphs – Boeing: Nonlinear structural models developed through AFOSR support are being

Optimizing Force Deployment and Force Structure for the Rapid Deployment Force

DTIC Science & Technology

1984-03-01

Analysis . . . . .. .. ... ... 97 Experimental Design . . . . . .. .. .. ... 99 IX. Use of a Flexible Response Surface ........ 10.2 Selection of a...setS . ere designe . arun, programming methodology , where the require: s.stem re..r is input and the model optimizes the num=er. :::pe, cargo. an...to obtain new computer outputs" (Ref 38:23). The methodology can be used with any decision model, linear or nonlinear. Experimental Desion Since the

High-order accurate finite-volume formulations for the pressure gradient force in layered ocean models

NASA Astrophysics Data System (ADS)

Engwirda, Darren; Kelley, Maxwell; Marshall, John

2017-08-01

Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates and/or terrain-following representations.

Electrostatic interaction between stereocilia: II. Influence on the mechanical properties of the hair bundle.

PubMed

Dolgobrodov, S G; Lukashkin, A N; Russell, I J

2000-12-01

This paper is based on our model [Dolgobrodov et al., 2000. Hear. Res., submitted for publication] in which we examine the significance of the polyanionic surface layers of stereocilia for electrostatic interaction between them. We analyse how electrostatic forces modify the mechanical properties of the sensory hair bundle. Different charge distribution profiles within the glycocalyx are considered. When modelling a typical experiment on bundle stiffness measurements, applying an external force to the tallest row of stereocilia shows that the asymptotic stiffness of the hair bundle for negative displacements is always larger than the asymptotic stiffness for positive displacements. This increase in stiffness is monotonic for even charge distribution and shows local minima when the negative charge is concentrated in a thinner layer within the cell coat. The minima can also originate from the co-operative effect of electrostatic repulsion and inter-ciliary links with non-linear mechanical properties. Existing experimental observations are compared with the predictions of the model. We conclude that the forces of electrostatic interaction between stereocilia may influence the mechanical properties of the hair bundle and, being strongly non-linear, contribute to the non-linear phenomena, which have been recorded from the auditory periphery.

TEMPORAL AND SPATIAL RELATIONSHIP OF FLARE SIGNATURES AND THE FORCE-FREE CORONAL MAGNETIC FIELD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thalmann, J. K.; Veronig, A.; Su, Y., E-mail: julia.thalmann@uni-graz.at

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 photosphericmore » 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.« less

Many-body effects in nonlinear optical responses of 2D layered semiconductors

DOE PAGES

Aivazian, Grant; Yu, Hongyi; Wu, Sanfeng; ...

2017-01-05

We performed ultrafast degenerate pump-probe spectroscopy on monolayer WSe2 near its exciton resonance. The observed differential reflectance signals exhibit signatures of strong many-body interactions including the exciton-exciton interaction and free carrier induced band gap renormalization. The exciton-exciton interaction results in a resonance blue shift which lasts for the exciton lifetime (several ps), while the band gap renormalization manifests as a resonance red shift with several tens ps lifetime. Our model based on the many-body interactions for the nonlinear optical susceptibility ts well the experimental observations. The power dependence of the spectra shows that with the increase of pump power, themore » exciton population increases linearly and then saturates, while the free carrier density increases superlinearly, implying that exciton Auger recombination could be the origin of these free carriers. Our model demonstrates a simple but efficient method for quantitatively analyzing the spectra, and indicates the important role of Coulomb interactions in nonlinear optical responses of such 2D materials.« less

Many-body effects in nonlinear optical responses of 2D layered semiconductors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aivazian, Grant; Yu, Hongyi; Wu, Sanfeng

We performed ultrafast degenerate pump-probe spectroscopy on monolayer WSe2 near its exciton resonance. The observed differential reflectance signals exhibit signatures of strong many-body interactions including the exciton-exciton interaction and free carrier induced band gap renormalization. The exciton-exciton interaction results in a resonance blue shift which lasts for the exciton lifetime (several ps), while the band gap renormalization manifests as a resonance red shift with several tens ps lifetime. Our model based on the many-body interactions for the nonlinear optical susceptibility ts well the experimental observations. The power dependence of the spectra shows that with the increase of pump power, themore » exciton population increases linearly and then saturates, while the free carrier density increases superlinearly, implying that exciton Auger recombination could be the origin of these free carriers. Our model demonstrates a simple but efficient method for quantitatively analyzing the spectra, and indicates the important role of Coulomb interactions in nonlinear optical responses of such 2D materials.« less

Communication: modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G

2014-10-07

We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley "bracelet" and "rod" test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, "Charge asymmetries in hydration of polar solutes," J. Phys. Chem. B 112, 2405-2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.

Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

PubMed Central

Bardhan, Jaydeep P.; Knepley, Matthew G.

2014-01-01

We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys. Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry. PMID:25296776

Three-dimensional vortex-induced vibrations of supported pipes conveying fluid based on wake oscillator models

NASA Astrophysics Data System (ADS)

Wang, L.; Jiang, T. L.; Dai, H. L.; Ni, Q.

2018-05-01

The present study develops a new three-dimensional nonlinear model for investigating vortex-induced vibrations (VIV) of flexible pipes conveying internal fluid flow. The unsteady hydrodynamic forces associated with the wake dynamics are modeled by two distributed van der Pol wake oscillators. In particular, the nonlinear partial differential equations of motion of the pipe and the wake are derived, taking into account the coupling between the structure and the fluid. The nonlinear equations of motion for the coupled system are then discretized by means of the Galerkin technique, resulting in a high-dimensional reduced-order model of the system. It is shown that the natural frequencies for in-plane and out-of-plane motions of the pipe may be different at high internal flow velocities beyond the threshold of buckling instability. The orientation angle of the postbuckling configuration is time-varying due to the disturbance of hydrodynamic forces, thus yielding sometimes unexpected results. For a buckled pipe with relatively low cross-flow velocity, interestingly, examining the nonlinear dynamics of the pipe indicates that the combined effects of the cross-flow-induced resonance of the in-plane first mode and the internal-flow-induced buckling on the IL and CF oscillation amplitudes may be significant. For higher cross-flow velocities, however, the effect of internal fluid flow on the nonlinear VIV responses of the pipe is not pronounced.

Increased Order Modeling Approach to Unsteady Aerodynamics and Aeroelasticity

DTIC Science & Technology

2010-03-01

dynamic simulation of a maneuvering air vehicle with actuator free play , limit-cycle oscillations (LCO) of platetype fins with nonlinear plate-stiffness...6 2.3 Response to maneuver command with actuator free play ............................................................ 8...15 3.2 LCO Simulations with actuator free play .....................................................................................18

Comparison of Two Coronal Magnetic Field Models to Reconstruct a Sigmoidal Solar Active Region with Coronal Loops

NASA Astrophysics Data System (ADS)

Duan, Aiying; Jiang, Chaowei; Hu, Qiang; Zhang, Huai; Gary, G. Allen; Wu, S. T.; Cao, Jinbin

2017-06-01

Magnetic field extrapolation is an important tool to study the three-dimensional (3D) solar coronal magnetic field, which is difficult to directly measure. Various analytic models and numerical codes exist, but their results often drastically differ. Thus, a critical comparison of the modeled magnetic field lines with the observed coronal loops is strongly required to establish the credibility of the model. Here we compare two different non-potential extrapolation codes, a nonlinear force-free field code (CESE-MHD-NLFFF) and a non-force-free field (NFFF) code, in modeling a solar active region (AR) that has a sigmoidal configuration just before a major flare erupted from the region. A 2D coronal-loop tracing and fitting method is employed to study the 3D misalignment angles between the extrapolated magnetic field lines and the EUV loops as imaged by SDO/AIA. It is found that the CESE-MHD-NLFFF code with preprocessed magnetogram performs the best, outputting a field that matches the coronal loops in the AR core imaged in AIA 94 Å with a misalignment angle of ˜10°. This suggests that the CESE-MHD-NLFFF code, even without using the information of the coronal loops in constraining the magnetic field, performs as good as some coronal-loop forward-fitting models. For the loops as imaged by AIA 171 Å in the outskirts of the AR, all the codes including the potential field give comparable results of the mean misalignment angle (˜30°). Thus, further improvement of the codes is needed for a better reconstruction of the long loops enveloping the core region.

Comparison of Two Coronal Magnetic Field Models to Reconstruct a Sigmoidal Solar Active Region with Coronal Loops

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duan, Aiying; Zhang, Huai; Jiang, Chaowei

Magnetic field extrapolation is an important tool to study the three-dimensional (3D) solar coronal magnetic field, which is difficult to directly measure. Various analytic models and numerical codes exist, but their results often drastically differ. Thus, a critical comparison of the modeled magnetic field lines with the observed coronal loops is strongly required to establish the credibility of the model. Here we compare two different non-potential extrapolation codes, a nonlinear force-free field code (CESE–MHD–NLFFF) and a non-force-free field (NFFF) code, in modeling a solar active region (AR) that has a sigmoidal configuration just before a major flare erupted from themore » region. A 2D coronal-loop tracing and fitting method is employed to study the 3D misalignment angles between the extrapolated magnetic field lines and the EUV loops as imaged by SDO /AIA. It is found that the CESE–MHD–NLFFF code with preprocessed magnetogram performs the best, outputting a field that matches the coronal loops in the AR core imaged in AIA 94 Å with a misalignment angle of ∼10°. This suggests that the CESE–MHD–NLFFF code, even without using the information of the coronal loops in constraining the magnetic field, performs as good as some coronal-loop forward-fitting models. For the loops as imaged by AIA 171 Å in the outskirts of the AR, all the codes including the potential field give comparable results of the mean misalignment angle (∼30°). Thus, further improvement of the codes is needed for a better reconstruction of the long loops enveloping the core region.« less

Identifying trends in climate: an application to the cenozoic

NASA Astrophysics Data System (ADS)

Richards, Gordon R.

1998-05-01

The recent literature on trending in climate has raised several issues, whether trends should be modeled as deterministic or stochastic, whether trends are nonlinear, and the relative merits of statistical models versus models based on physics. This article models trending since the late Cretaceous. This 68 million-year interval is selected because the reliability of tests for trending is critically dependent on the length of time spanned by the data. Two main hypotheses are tested, that the trend has been caused primarily by CO2 forcing, and that it reflects a variety of forcing factors which can be approximated by statistical methods. The CO2 data is obtained from model simulations. Several widely-used statistical models are found to be inadequate. ARIMA methods parameterize too much of the short-term variation, and do not identify low frequency movements. Further, the unit root in the ARIMA process does not predict the long-term path of temperature. Spectral methods also have little ability to predict temperature at long horizons. Instead, the statistical trend is estimated using a nonlinear smoothing filter. Both of these paradigms make it possible to model climate as a cointegrated process, in which temperature can wander quite far from the trend path in the intermediate term, but converges back over longer horizons. Comparing the forecasting properties of the two trend models demonstrates that the optimal forecasting model includes CO2 forcing and a parametric representation of the nonlinear variability in climate.

On the structure of attractors for discrete, periodically forced systems with applications to population models

Treesearch

James F. Selgrade; James H. Roberds

2001-01-01

This work discusses the effects of periodic forcing on attracting cycles and more complicated attractors for autonomous systems of nonlinear difference equations. Results indicate that an attractor for a periodically forced dynamical system may inherit structure from an attractor of the autonomous (unforced) system and also from the periodicity of the forcing. In...

Efficiency of energy conversion in model biological pumps. Optimization by linear nonequilibrium thermodynamic relations.

PubMed

Stucki, J W; Compiani, M; Caplan, S R

1983-09-01

Experimental investigations showed linear relations between flows and forces in some biological energy converters operating far from equilibrium. This observation cannot be understood on the basis of conventional nonequilibrium thermodynamics. Therefore, the efficiencies of a linear and a nonlinear mode of operation of an energy converter (a hypothetical redox-driven H+ pump) were compared. This comparison revealed that at physiological values of the forces and degrees of coupling (1) the force ratio permitting optimal efficiency was much higher in the linear than in the nonlinear mode and (2) the linear mode of operation was at least 10(6)-times more efficient that the nonlinear one. These observations suggest that the experimentally observed linear relations between flows and forces, particularly in the case of oxidative phosphorylation, may be due to a feedback regulation maintaining linear thermodynamic relations far from equilibrium. This regulation may have come about as the consequence of an evolutionary drive towards higher efficiency.

A "Kane's Dynamics" Model for the Active Rack Isolation System. Part 3; Addition of Umbilicals to the Nonlinear Model

NASA Technical Reports Server (NTRS)

Rupert, J. K.; Hampton, R. D.; Beech, G. S.

2005-01-01

In the late 1980s, microgravity researchers began to voice their concern that umbilical-transmitted energy could significantly degrade the acceleration environment of microgravity space science experiments onboard manned spacecraft. Since umbilicals are necessary for many experiments, control designers began to seek ways to compensate for these "indirect" disturbances. Hampton, et al., used the Kane s method to develop a model of the active rack isolation system (ARIS) that includes (1) actuator control forces, (2) direct disturbance forces, and (3) indirect, actuator-transmitted disturbances. Their model does not, however, include the indirect, umbilical-transmitted disturbances. Since the umbilical stiffnesses are not negligible, these indirect disturbances must be included in the model. Until the umbilicals have been appropriately included, the model will be incomplete. This Technical Memorandum presents a nonlinear model of ARIS with umbilicals included. Model verification was achieved by utilizing two commercial-off-the-shelf software tools. Various forces and moments were applied to the model to yield simulated responses of the system. Plots of the simulation results show how various critical points on an ARIS-outfitted international standard payload rack behave under the application of direct disturbances, indirect disturbances, and control forces. Simulations also show system response to a variety of initial conditions.

A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics

NASA Technical Reports Server (NTRS)

Ozguven, H. Nevzat

1991-01-01

A six-degree-of-freedom nonlinear semi-definite model with time varying mesh stiffness has been developed for the dynamic analysis of spur gears. The model includes a spur gear pair, two shafts, two inertias representing load and prime mover, and bearings. As the shaft and bearing dynamics have also been considered in the model, the effect of lateral-torsional vibration coupling on the dynamics of gears can be studied. In the nonlinear model developed several factors such as time varying mesh stiffness and damping, separation of teeth, backlash, single- and double-sided impacts, various gear errors and profile modifications have been considered. The dynamic response to internal excitation has been calculated by using the 'static transmission error method' developed. The software prepared (DYTEM) employs the digital simulation technique for the solution, and is capable of calculating dynamic tooth and mesh forces, dynamic factors for pinion and gear, dynamic transmission error, dynamic bearing forces and torsions of shafts. Numerical examples are given in order to demonstrate the effect of shaft and bearing dynamics on gear dynamics.

Using waveform information in nonlinear data assimilation

NASA Astrophysics Data System (ADS)

Rey, Daniel; Eldridge, Michael; Morone, Uriel; Abarbanel, Henry D. I.; Parlitz, Ulrich; Schumann-Bischoff, Jan

2014-12-01

Information in measurements of a nonlinear dynamical system can be transferred to a quantitative model of the observed system to establish its fixed parameters and unobserved state variables. After this learning period is complete, one may predict the model response to new forces and, when successful, these predictions will match additional observations. This adjustment process encounters problems when the model is nonlinear and chaotic because dynamical instability impedes the transfer of information from the data to the model when the number of measurements at each observation time is insufficient. We discuss the use of information in the waveform of the data, realized through a time delayed collection of measurements, to provide additional stability and accuracy to this search procedure. Several examples are explored, including a few familiar nonlinear dynamical systems and small networks of Colpitts oscillators.

Nonlinear friction dynamics on polymer surface under accelerated movement

NASA Astrophysics Data System (ADS)

Aita, Yuuki; Asanuma, Natsumi; Takahashi, Akira; Mayama, Hiroyuki; Nonomura, Yoshimune

2017-04-01

Nonlinear phenomena on the soft material surface are one of the most exciting topics of chemical physics. However, only a few reports exist on the friction phenomena under accelerated movement, because friction between two solid surfaces is considered a linear phenomenon in many cases. We aim to investigate how nonlinear accelerated motion affects friction on solid surfaces. In the present study, we evaluate the frictional forces between two polytetrafluoroethylene (PTFE) resins using an advanced friction evaluation system. On PTFE surfaces, the normalized delay time δ, which is the time lag in the response of the friction force to the accelerated movement, is observed in the pre-sliding friction process. Under high-velocity conditions, kinetic friction increases with velocity. Based on these experimental results, we propose a two-phase nonlinear model including a pre-sliding process (from the beginning of sliding of a contact probe to the establishment of static friction) and a kinetic friction process. The present model consists of several factors including velocity, acceleration, stiffness, viscosity, and vertical force. The findings reflecting the viscoelastic properties of soft material is useful for various fields such as in the fabrication of clothes, cosmetics, automotive materials, and virtual reality systems as well as for understanding friction phenomena on soft material surfaces.

Development of a non-linear simulation for generic hypersonic vehicles - ASUHS1

NASA Technical Reports Server (NTRS)

Salas, Juan; Lovell, T. Alan; Schmidt, David K.

1993-01-01

A nonlinear simulation is developed to model the longitudinal motion of a vehicle in hypersonic flight. The equations of motion pertinent to this study are presented. Analytic expressions for the aerodynamic forces acting on a hypersonic vehicle which were obtained from Newtonian Impact Theory are further developed. The control surface forces are further examined to incorporate vehicle elastic motion. The purpose is to establish feasible equations of motion which combine rigid body, elastic, and aeropropulsive dynamics for use in nonlinear simulations. The software package SIMULINK is used to implement the simulation. Also discussed are issues needing additional attention and potential problems associated with the implementation (with proposed solutions).

Post-capture vibration suppression of spacecraft via a bio-inspired isolation system

NASA Astrophysics Data System (ADS)

Dai, Honghua; Jing, Xingjian; Wang, Yu; Yue, Xiaokui; Yuan, Jianping

2018-05-01

Inspired by the smooth motions of a running kangaroo, a bio-inspired quadrilateral shape (BIQS) structure is proposed to suppress the vibrations of a free-floating spacecraft subject to periodic or impulsive forces, which may be encountered during on-orbit servicing missions. In particular, the BIQS structure is installed between the satellite platform and the capture mechanism. The dynamical model of the BIQS isolation system, i.e. a BIQS structure connecting the platform and the capture mechanism at each side, is established by Lagrange's equations to simulate the post-capture dynamical responses. The BIQS system suffering an impulsive force is dealt with by means of a modified version of Lagrange's equations. Furthermore, the classical harmonic balance method is used to solve the nonlinear dynamical system subject to periodic forces, while for the case under impulsive forces the numerical integration method is adopted. Due to the weightless environment in space, the present BIQS system is essentially an under-constrained dynamical system with one of its natural frequencies being identical to zero. The effects of system parameters, such as the number of layers in BIQS, stiffness, assembly angle, rod length, damping coefficient, masses of satellite platform and capture mechanism, on the isolation performance of the present system are thoroughly investigated. In addition, comparisons between the isolation performances of the presently proposed BIQS isolator and the conventional spring-mass-damper (SMD) isolator are conducted to demonstrate the advantages of the present isolator. Numerical simulations show that the BIQS system has a much better performance than the SMD system under either periodic or impulsive forces. Overall, the present BIQS isolator offers a highly efficient passive way for vibration suppressions of free-floating spacecraft.

Similar solutions of double-diffusive dissipative layers along free surfaces

NASA Astrophysics Data System (ADS)

Napolitano, L. G.; Viviani, A.; Savino, R.

1990-10-01

Free convection due to buoyant forces (natural convection) and surface tension gradients (Marangoni convection) generated by temperature and concentration gradients is discussed together with the formation of double-diffusive boundary layers along liquid-gas interfaces. Similarity solutions for each class of free convection are derived and the resulting nonlinear two-point problems are solved numerically using the quasi-linearization method. Velocity, temperature, concentration profiles, interfacial velocity, heat and mass transfer bulk coefficients for various Prandtl and Schmidt numbers, and different values of the similarity parameters are determined. The convective flows are of particular interest because they are considered to influence the processes of crystal growth, both on earth and in a microgravity environment.

Component mode synthesis and large deflection vibrations of complex structures. [beams and trusses

NASA Technical Reports Server (NTRS)

Mei, C.

1984-01-01

The accuracy of the NASTRAN modal synthesis analysis was assessed by comparing it with full structure NASTRAN and nine other modal synthesis results using a nine-bay truss. A NASTRAN component mode transient response analysis was also performed on the free-free truss structure. A finite element method was developed for nonlinear vibration of beam structures subjected to harmonic excitation. Longitudinal deformation and inertia are both included in the formula. Tables show the finite element free vibration results with and without considering the effects of longitudinal deformation and inertia as well as the frequency ratios for a simply supported and a clamped beam subjected to a uniform harmonic force.

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2015-12-21

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Nonlinear saturation of the slab ITG instability and zonal flow generation with fully kinetic ions

NASA Astrophysics Data System (ADS)

Miecnikowski, Matthew T.; Sturdevant, Benjamin J.; Chen, Yang; Parker, Scott E.

2018-05-01

Fully kinetic turbulence models are of interest for their potential to validate or replace gyrokinetic models in plasma regimes where the gyrokinetic expansion parameters are marginal. Here, we demonstrate fully kinetic ion capability by simulating the growth and nonlinear saturation of the ion-temperature-gradient instability in shearless slab geometry assuming adiabatic electrons and including zonal flow dynamics. The ion trajectories are integrated using the Lorentz force, and the cyclotron motion is fully resolved. Linear growth and nonlinear saturation characteristics show excellent agreement with analogous gyrokinetic simulations across a wide range of parameters. The fully kinetic simulation accurately reproduces the nonlinearly generated zonal flow. This work demonstrates nonlinear capability, resolution of weak gradient drive, and zonal flow physics, which are critical aspects of modeling plasma turbulence with full ion dynamics.

The Generation of Harmonic Distortion and Distortion Products in a Computational Model of the Cochlea

NASA Astrophysics Data System (ADS)

Meaud, Julien; Li, Yizeng; Grosh, Karl

2011-11-01

It is generally agreed that the nonlinear response of the cochlea is due to the forward transduction of the outer hair cell (OHC) hair bundle (HB) and subsequent alteration of the active force applied to the cochlear structures, including the basilar membrane (BM). A mechanical-acoustical-electrical model of the cochlea with three-dimensional fluid representation, and feedback from OHC somatic motility coupled to nonlinear HB mechanotransduction is used to predict nonlinear distortion of the BM response to acoustic stimulus. An efficient alternating frequency time scheme is implemented to solve for the nonlinear stationary dynamics of the cochlea. The model is used to predict the location of maximum generation of nonlinear distortion during pure tone and two-tone stimulation as well as the propagation of the distortion components on the BM.

Sliding Mode Control of a Slewing Flexible Beam

NASA Technical Reports Server (NTRS)

Wilson, David G.; Parker, Gordon G.; Starr, Gregory P.; Robinett, Rush D., III

1997-01-01

An output feedback sliding mode controller (SMC) is proposed to minimize the effects of vibrations of slewing flexible manipulators. A spline trajectory is used to generate ideal position and velocity commands. Constrained nonlinear optimization techniques are used to both calibrate nonlinear models and determine optimized gains to produce a rest-to-rest, residual vibration-free maneuver. Vibration-free maneuvers are important for current and future NASA space missions. This study required the development of the nonlinear dynamic system equations of motion; robust control law design; numerical implementation; system identification; and verification using the Sandia National Laboratories flexible robot testbed. Results are shown for a slewing flexible beam.

A Modal Model to Simulate Typical Structural Dynamic Nonlinearity [PowerPoint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mayes, Randall L.; Pacini, Benjamin Robert; Roettgen, Dan

2016-01-01

Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combinationmore » with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.« less

A Modal Model to Simulate Typical Structural Dynamic Nonlinearity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pacini, Benjamin Robert; Mayes, Randall L.; Roettgen, Daniel R

2015-10-01

Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combinationmore » with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.« less

Flexible twist for pitch control in a high altitude long endurance aircraft with nonlinear response

NASA Astrophysics Data System (ADS)

Bond, Vanessa L.

Information dominance is the key motivator for employing high-altitude long-endurance (HALE) aircraft to provide continuous coverage in the theaters of operation. A joined-wing configuration of such a craft gives the advantage of a platform for higher resolution sensors. Design challenges emerge with structural flexibility that arise from a long-endurance aircraft design. The goal of this research was to demonstrate that scaling the nonlinear response of a full-scale finite element model was possible if the model was aeroelastically and "nonlinearly" scaled. The research within this dissertation showed that using the first three modes and the first bucking modes was not sufficient for proper scaling. In addition to analytical scaling several experiments were accomplished to understand and overcome design challenges of HALE aircraft. One such challenge is combated by eliminating pitch control surfaces and replacing them with an aft-wing twist concept. This design option was physically realized through wind tunnel measurement of forces, moments and pressures on a subscale experimental model. This design and experiment demonstrated that pitch control with aft-wing twist is feasible. Another challenge is predicting the nonlinear response of long-endurance aircraft. This was addressed by experimental validation of modeling nonlinear response on a subscale experimental model. It is important to be able to scale nonlinear behavior in this type of craft due to its highly flexible nature. The validation accomplished during this experiment on a subscale model will reduce technical risk for full-scale development of such pioneering craft. It is also important to experimentally reproduce the air loads following the wing as it deforms. Nonlinearities can be attributed to these follower forces that might otherwise be overlooked. This was found to be a significant influence in HALE aircraft to include the case study of the FEM and experimental models herein.

Dual RBFNNs-Based Model-Free Adaptive Control With Aspen HYSYS Simulation.

PubMed

Zhu, Yuanming; Hou, Zhongsheng; Qian, Feng; Du, Wenli

2017-03-01

In this brief, we propose a new data-driven model-free adaptive control (MFAC) method with dual radial basis function neural networks (RBFNNs) for a class of discrete-time nonlinear systems. The main novelty lies in that it provides a systematic design method for controller structure by the direct usage of I/O data, rather than using the first-principle model or offline identified plant model. The controller structure is determined by equivalent-dynamic-linearization representation of the ideal nonlinear controller, and the controller parameters are tuned by the pseudogradient information extracted from the I/O data of the plant, which can deal with the unknown nonlinear system. The stability of the closed-loop control system and the stability of the training process for RBFNNs are guaranteed by rigorous theoretical analysis. Meanwhile, the effectiveness and the applicability of the proposed method are further demonstrated by the numerical example and Aspen HYSYS simulation of distillation column in crude styrene produce process.

Imaging contrast and tip-sample interaction of non-contact amplitude modulation atomic force microscopy with Q-control

NASA Astrophysics Data System (ADS)

Shi, Shuai; Guo, Dan; Luo, Jianbin

2017-10-01

Active quality factor (Q) exhibits many promising properties in dynamic atomic force microscopy. Energy dissipation and image contrasts are investigated in the non-contact amplitude modulation atomic force microscopy (AM-AFM) with an active Q-control circuit in the ambient air environment. Dissipated power and virial were calculated to compare the highly nonlinear interaction of tip-sample and image contrasts with different Q gain values. Greater free amplitudes and lower effective Q values show better contrasts for the same setpoint ratio. Active quality factor also can be employed to change tip-sample interaction force in non-contact regime. It is meaningful that non-destructive and better contrast images can be realized in non-contact AM-AFM by applying an active Q-control to the dynamic system.

Equivalent model construction for a non-linear dynamic system based on an element-wise stiffness evaluation procedure and reduced analysis of the equivalent system

NASA Astrophysics Data System (ADS)

Kim, Euiyoung; Cho, Maenghyo

2017-11-01

In most non-linear analyses, the construction of a system matrix uses a large amount of computation time, comparable to the computation time required by the solving process. If the process for computing non-linear internal force matrices is substituted with an effective equivalent model that enables the bypass of numerical integrations and assembly processes used in matrix construction, efficiency can be greatly enhanced. A stiffness evaluation procedure (STEP) establishes non-linear internal force models using polynomial formulations of displacements. To efficiently identify an equivalent model, the method has evolved such that it is based on a reduced-order system. The reduction process, however, makes the equivalent model difficult to parameterize, which significantly affects the efficiency of the optimization process. In this paper, therefore, a new STEP, E-STEP, is proposed. Based on the element-wise nature of the finite element model, the stiffness evaluation is carried out element-by-element in the full domain. Since the unit of computation for the stiffness evaluation is restricted by element size, and since the computation is independent, the equivalent model can be constructed efficiently in parallel, even in the full domain. Due to the element-wise nature of the construction procedure, the equivalent E-STEP model is easily characterized by design parameters. Various reduced-order modeling techniques can be applied to the equivalent system in a manner similar to how they are applied in the original system. The reduced-order model based on E-STEP is successfully demonstrated for the dynamic analyses of non-linear structural finite element systems under varying design parameters.

The coupled dynamics of fluids and spacecraft in low gravity and low gravity fluid measurement

NASA Technical Reports Server (NTRS)

Hansman, R. John; Peterson, Lee D.; Crawley, Edward F.

1987-01-01

The very large mass fraction of liquids stored on broad current and future generation spacecraft has made critical the technologies of describing the fluid-spacecraft dynamics and measuring or gauging the fluid. Combined efforts in these areas are described, and preliminary results are presented. The coupled dynamics of fluids and spacecraft in low gravity study is characterizing the parametric behavior of fluid-spacecraft systems in which interaction between the fluid and spacecraft dynamics is encountered. Particular emphasis is given to the importance of nonlinear fluid free surface phenomena to the coupled dynamics. An experimental apparatus has been developed for demonstrating a coupled fluid-spacecraft system. In these experiments, slosh force signals are fed back to a model tank actuator through a tunable analog second order integration circuit. In this manner, the tank motion is coupled to the resulting slosh force. Results are being obtained in 1-g and in low-g (on the NASA KC-135) using dynamic systems nondimensionally identical except for the Bond numbers.

New nonlinear control algorithms for multiple robot arms

NASA Technical Reports Server (NTRS)

Tarn, T. J.; Bejczy, A. K.; Yun, X.

1988-01-01

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space.

Mechanics of the acoustic radiation force in tissue-like solids

NASA Astrophysics Data System (ADS)

Dontsov, Egor V.

The acoustic radiation force (ARF) is a phenomenon affiliated with the nonlinear effects of high-intensity wave propagation. It represents the mean momentum transfer from the sound wave to the medium, and allows for an effective computation of the mean motion (e.g. acoustic streaming in fluids) induced by a high-intensity sound wave. Nowadays, the high-intensity focused ultrasound is frequently used in medical diagnosis applications due to its ability to "push" inside the tissue with the radiation body force and facilitate the local quantification of tissue's viscoelastic properties. The main objectives of this study include: i) the theoretical investigation of the ARF in fluids and tissue-like solids generated respectively by the amplitude modulated plane wave and focused ultrasound; ii) computation of the nonlinear acoustic wave propagation when the amplitude of the focused ultrasound field is modulated by a low-frequency signal, and iii) modeling of the ARF-induced motion in tissue-like solids for the purpose of quantifying their nonlinear elasticity via the magnitude of the ARF. Regarding the first part, a comparison with the existing theory of the ARF reveals a number of key features that are brought to light by the new formulation, including the contributions to the ARF of ultrasound modulation and thermal expansion, as well as the precise role of constitutive nonlinearities in generating the sustained body force in tissue-like solids by a focused ultrasound beam. In the second part, the hybrid time-frequency domain algorithm for the numerical analysis of the nonlinear wave equation is proposed. The approach is validated by comparing the results to the finite-difference modeling in time domain. Regarding the third objective, the Fourier transform approach is used to compute the ARF-induced shear wave motion in tissue-mimicking phantoms. A comparison between the experiment (tests performed at the Mayo Clinic) and model permitted the estimation of a particular coefficient of nonlinear tissue elasticity from the amplitude of the ARF-generated shear waves. For completeness, the ARF estimates of this coefficient are verified via an established technique known as acoustoelasticity.

Optimizing separate phase light hydrocarbon recovery from contaminated unconfined aquifers

NASA Astrophysics Data System (ADS)

Cooper, Grant S.; Peralta, Richard C.; Kaluarachchi, Jagath J.

A modeling approach is presented that optimizes separate phase recovery of light non-aqueous phase liquids (LNAPL) for a single dual-extraction well in a homogeneous, isotropic unconfined aquifer. A simulation/regression/optimization (S/R/O) model is developed to predict, analyze, and optimize the oil recovery process. The approach combines detailed simulation, nonlinear regression, and optimization. The S/R/O model utilizes nonlinear regression equations describing system response to time-varying water pumping and oil skimming. Regression equations are developed for residual oil volume and free oil volume. The S/R/O model determines optimized time-varying (stepwise) pumping rates which minimize residual oil volume and maximize free oil recovery while causing free oil volume to decrease a specified amount. This S/R/O modeling approach implicitly immobilizes the free product plume by reversing the water table gradient while achieving containment. Application to a simple representative problem illustrates the S/R/O model utility for problem analysis and remediation design. When compared with the best steady pumping strategies, the optimal stepwise pumping strategy improves free oil recovery by 11.5% and reduces the amount of residual oil left in the system due to pumping by 15%. The S/R/O model approach offers promise for enhancing the design of free phase LNAPL recovery systems and to help in making cost-effective operation and management decisions for hydrogeologists, engineers, and regulators.

DAISY: a new software tool to test global identifiability of biological and physiological systems

PubMed Central

Bellu, Giuseppina; Saccomani, Maria Pia; Audoly, Stefania; D’Angiò, Leontina

2009-01-01

A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/. PMID:17707944

Thrust generation by a heaving flexible foil: Resonance, nonlinearities, and optimality

NASA Astrophysics Data System (ADS)

Paraz, Florine; Schouveiler, Lionel; Eloy, Christophe

2016-01-01

Flexibility of marine animal fins has been thought to enhance swimming performance. However, despite numerous experimental and numerical studies on flapping flexible foils, there is still no clear understanding of the effect of flexibility and flapping amplitude on thrust generation and swimming efficiency. Here, to address this question, we combine experiments on a model system and a weakly nonlinear analysis. Experiments consist in immersing a flexible rectangular plate in a uniform flow and forcing this plate into a heaving motion at its leading edge. A complementary theoretical model is developed assuming a two-dimensional inviscid problem. In this model, nonlinear effects are taken into account by considering a transverse resistive drag. Under these hypotheses, a modal decomposition of the system motion allows us to predict the plate response amplitude and the generated thrust, as a function of the forcing amplitude and frequency. We show that this model can correctly predict the experimental data on plate kinematic response and thrust generation, as well as other data found in the literature. We also discuss the question of efficiency in the context of bio-inspired propulsion. Using the proposed model, we show that the optimal propeller for a given thrust and a given swimming speed is achieved when the actuating frequency is tuned to a resonance of the system, and when the optimal forcing amplitude scales as the square root of the required thrust.

Nonlinear dynamic behaviors of permanent magnet synchronous motors in electric vehicles caused by unbalanced magnetic pull

NASA Astrophysics Data System (ADS)

Xiang, Changle; Liu, Feng; Liu, Hui; Han, Lijin; Zhang, Xun

2016-06-01

Unbalanced magnetic pull (UMP) plays a key role in nonlinear dynamic behaviors of permanent magnet synchronous motors (PMSM) in electric vehicles. Based on Jeffcott rotor model, the stiffness characteristics of the rotor system of the PMSM are analyzed and the nonlinear dynamic behaviors influenced by UMP are investigated. In free vibration study, eigenvalue-based stability analysis for multiple equilibrium points is performed which offers an insight in system stiffness. Amplitude modulation effects are discovered of which the mechanism is explained and the period of modulating signal is carried out by phase analysis and averaging method. The analysis indicates that the effects are caused by the interaction of the initial phases of forward and backward whirling motions. In forced vibration study, considering dynamic eccentricity, frequency characteristics revealing softening type are obtained by harmonic balance method, and the stability of periodic solution is investigated by Routh-Hurwitz criterion. The frequency characteristics analysis indicates that the response amplitude is limited in the range between the amplitudes of the two kinds of equilibrium points. In the vicinity of the continuum of equilibrium points, the system hardly provides resistance to bending, and hence external disturbances easily cause loss of stability. It is useful for the design of the PMSM with high stability and low vibration and acoustic noise.

An approach to simultaneous control of trajectory and interaction forces in dual-arm configurations

NASA Technical Reports Server (NTRS)

Yun, Xiaoping; Kumar, Vijay R.

1991-01-01

An approach to the control of constrained dynamic systems such as multiple arm systems, multifingered grippers, and walking vehicles is described. The basic philosophy is to utilize a minimal set of inputs to control the trajectory and the surplus input to control the constraint or interaction forces and moments in the closed chain. A dynamic control model for the closed chain is derived that is suitable for designing a controller in which the trajectory and the interaction forces and moments are explicitly controlled. Nonlinear feedback techniques derived from differential geometry are then applied to linearize and decouple the nonlinear model. These ideas are illustrated through a planar example in which two arms are used for cooperative manipulation. Results from a simulation are used to illustrate the efficacy of the method.

Model updating strategy for structures with localised nonlinearities using frequency response measurements

NASA Astrophysics Data System (ADS)

Wang, Xing; Hill, Thomas L.; Neild, Simon A.; Shaw, Alexander D.; Haddad Khodaparast, Hamed; Friswell, Michael I.

2018-02-01

This paper proposes a model updating strategy for localised nonlinear structures. It utilises an initial finite-element (FE) model of the structure and primary harmonic response data taken from low and high amplitude excitations. The underlying linear part of the FE model is first updated using low-amplitude test data with established techniques. Then, using this linear FE model, the nonlinear elements are localised, characterised, and quantified with primary harmonic response data measured under stepped-sine or swept-sine excitations. Finally, the resulting model is validated by comparing the analytical predictions with both the measured responses used in the updating and with additional test data. The proposed strategy is applied to a clamped beam with a nonlinear mechanism and good agreements between the analytical predictions and measured responses are achieved. Discussions on issues of damping estimation and dealing with data from amplitude-varying force input in the updating process are also provided.

The Bayesian Decoding of Force Stimuli from Slowly Adapting Type I Fibers in Humans.

PubMed

Kasi, Patrick; Wright, James; Khamis, Heba; Birznieks, Ingvars; van Schaik, André

2016-01-01

It is well known that signals encoded by mechanoreceptors facilitate precise object manipulation in humans. It is therefore of interest to study signals encoded by the mechanoreceptors because this will contribute further towards the understanding of fundamental sensory mechanisms that are responsible for coordinating force components during object manipulation. From a practical point of view, this may suggest strategies for designing sensory-controlled biomedical devices and robotic manipulators. We use a two-stage nonlinear decoding paradigm to reconstruct the force stimulus given signals from slowly adapting type one (SA-I) tactile afferents. First, we describe a nonhomogeneous Poisson encoding model which is a function of the force stimulus and the force's rate of change. In the decoding phase, we use a recursive nonlinear Bayesian filter to reconstruct the force profile, given the SA-I spike patterns and parameters described by the encoding model. Under the current encoding model, the mode ratio of force to its derivative is: 1.26 to 1.02. This indicates that the force derivative contributes significantly to the rate of change to the SA-I afferent spike modulation. Furthermore, using recursive Bayesian decoding algorithms is advantageous because it can incorporate past and current information in order to make predictions--consistent with neural systems--with little computational resources. This makes it suitable for interfacing with prostheses.

Nonlinear model for thermal effects in free-electron lasers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peter, E., E-mail: peterpeter@uol.com.br; Endler, A., E-mail: aendler@if.ufrgs.br; Rizzato, F. B., E-mail: rizzato@if.ufrgs.br

2014-11-15

In the present work, we extend results of a previous paper [Peter et al., Phys. Plasmas 20, 12 3104 (2013)] and develop a semi-analytical model to account for thermal effects on the nonlinear dynamics of the electron beam in free-electron lasers. We relax the condition of a cold electron beam but still use the concept of compressibility, now associated with a warm beam model, to evaluate the time scale for saturation and the peak laser intensity in high-gain regimes. Although vanishing compressibilites and the associated divergent densities are absent in warm models, a series of discontinuities in the electron density precedemore » the saturation process. We show that full wave-particle simulations agree well with the predictions of the model.« less

Non-compact nonlinear sigma models

NASA Astrophysics Data System (ADS)

de Rham, Claudia; Tolley, Andrew J.; Zhou, Shuang-Yong

2016-09-01

The target space of a nonlinear sigma model is usually required to be positive definite to avoid ghosts. We introduce a unique class of nonlinear sigma models where the target space metric has a Lorentzian signature, thus the associated group being non-compact. We show that the would-be ghost associated with the negative direction is fully projected out by 2 second-class constraints, and there exist stable solutions in this class of models. This result also has important implications for Lorentz-invariant massive gravity: There exist stable nontrivial vacua in massive gravity that are free from any linear vDVZ-discontinuity and a Λ2 decoupling limit can be defined on these vacua.

Chaos as an intermittently forced linear system.

PubMed

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

2017-05-30

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

Attractors for non-dissipative irrotational von Karman plates with boundary damping

NASA Astrophysics Data System (ADS)

Bociu, Lorena; Toundykov, Daniel

Long-time behavior of solutions to a von Karman plate equation is considered. The system has an unrestricted first-order perturbation and a nonlinear damping acting through free boundary conditions only. This model differs from those previously considered (e.g. in the extensive treatise (Chueshov and Lasiecka, 2010 [11])) because the semi-flow may be of a non-gradient type: the unique continuation property is not known to hold, and there is no strict Lyapunov function on the natural finite-energy space. Consequently, global bounds on the energy, let alone the existence of an absorbing ball, cannot be a priori inferred. Moreover, the free boundary conditions are not recognized by weak solutions and some helpful estimates available for clamped, hinged or simply-supported plates cannot be invoked. It is shown that this non-monotone flow can converge to a global compact attractor with the help of viscous boundary damping and appropriately structured restoring forces acting only on the boundary or its collar.

Investigation of broadband terahertz generation from metasurface

NASA Astrophysics Data System (ADS)

Fang, Ming; Niu, Kaikun; Huang, Zhiaxiang; Sha, Wei E. I.; Wu, Xianliang; Koschny, Thomas; Soukoulis, Costas M.

2018-05-01

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designing nonlinear plasmonic metamaterials.

Investigation of broadband terahertz generation from metasurface.

PubMed

Fang, Ming; Niu, Kaikun; Huang, Zhiaxiang; Sha, Wei E I; Wu, Xianliang; Koschny, Thomas; Soukoulis, Costas M

2018-05-28

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designing nonlinear plasmonic metamaterials.

Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit

NASA Astrophysics Data System (ADS)

Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie

2015-09-01

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Sequential reconstruction of driving-forces from nonlinear nonstationary dynamics

NASA Astrophysics Data System (ADS)

Güntürkün, Ulaş

2010-07-01

This paper describes a functional analysis-based method for the estimation of driving-forces from nonlinear dynamic systems. The driving-forces account for the perturbation inputs induced by the external environment or the secular variations in the internal variables of the system. The proposed algorithm is applicable to the problems for which there is too little or no prior knowledge to build a rigorous mathematical model of the unknown dynamics. We derive the estimator conditioned on the differentiability of the unknown system’s mapping, and smoothness of the driving-force. The proposed algorithm is an adaptive sequential realization of the blind prediction error method, where the basic idea is to predict the observables, and retrieve the driving-force from the prediction error. Our realization of this idea is embodied by predicting the observables one-step into the future using a bank of echo state networks (ESN) in an online fashion, and then extracting the raw estimates from the prediction error and smoothing these estimates in two adaptive filtering stages. The adaptive nature of the algorithm enables to retrieve both slowly and rapidly varying driving-forces accurately, which are illustrated by simulations. Logistic and Moran-Ricker maps are studied in controlled experiments, exemplifying chaotic state and stochastic measurement models. The algorithm is also applied to the estimation of a driving-force from another nonlinear dynamic system that is stochastic in both state and measurement equations. The results are judged by the posterior Cramer-Rao lower bounds. The method is finally put into test on a real-world application; extracting sun’s magnetic flux from the sunspot time series.

The Numerical Studies Program for the Atmospheric General Circulation Experiment (AGCE) for Spacelab Flights

NASA Technical Reports Server (NTRS)

Fowlis, W. W. (Editor); Davis, M. H. (Editor)

1981-01-01

The atmospheric general circulation experiment (AGCE) numerical design for Spacelab flights was studied. A spherical baroclinic flow experiment which models the large scale circulations of the Earth's atmosphere was proposed. Gravity is simulated by a radial dielectric body force. The major objective of the AGCE is to study nonlinear baroclinic wave flows in spherical geometry. Numerical models must be developed which accurately predict the basic axisymmetric states and the stability of nonlinear baroclinic wave flows. A three dimensional, fully nonlinear, numerical model and the AGCE based on the complete set of equations is required. Progress in the AGCE numerical design studies program is reported.

The Eruption of a Small-scale Emerging Flux Rope as the Driver of an M-class Flare and of a Coronal Mass Ejection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yan, X. L.; Xue, Z. K.; Wang, J. C.

Solar flares and coronal mass ejections are the most powerful explosions in the Sun. They are major sources of potentially destructive space weather conditions. However, the possible causes of their initiation remain controversial. Using high-resolution data observed by the New Solar Telescope of Big Bear Solar Observatory, supplemented by Solar Dynamics Observatory observations, we present unusual observations of a small-scale emerging flux rope near a large sunspot, whose eruption produced an M-class flare and a coronal mass ejection. The presence of the small-scale flux rope was indicated by static nonlinear force-free field extrapolation as well as data-driven magnetohydrodynamics modeling ofmore » the dynamic evolution of the coronal three-dimensional magnetic field. During the emergence of the flux rope, rotation of satellite sunspots at the footpoints of the flux rope was observed. Meanwhile, the Lorentz force, magnetic energy, vertical current, and transverse fields were increasing during this phase. The free energy from the magnetic flux emergence and twisting magnetic fields is sufficient to power the M-class flare. These observations present, for the first time, the complete process, from the emergence of the small-scale flux rope, to the production of solar eruptions.« less

Studying Climate Response to Forcing by the Nonlinear Dynamical Mode Decomposition

NASA Astrophysics Data System (ADS)

Mukhin, Dmitry; Gavrilov, Andrey; Loskutov, Evgeny; Feigin, Alexander

2017-04-01

An analysis of global climate response to external forcing, both anthropogenic (mainly, CO2 and aerosol) and natural (solar and volcanic), is needed for adequate predictions of global climate change. Being complex dynamical system, the climate reacts to external perturbations exciting feedbacks (both positive and negative) making the response non-trivial and poorly predictable. Thus an extraction of internal modes of climate system, investigation of their interaction with external forcings and further modeling and forecast of their dynamics, are all the problems providing the success of climate modeling. In the report the new method for principal mode extraction from climate data is presented. The method is based on the Nonlinear Dynamical Mode (NDM) expansion [1,2], but takes into account a number of external forcings applied to the system. Each NDM is represented by hidden time series governing the observed variability, which, together with external forcing time series, are mapped onto data space. While forcing time series are considered to be known, the hidden unknown signals underlying the internal climate dynamics are extracted from observed data by the suggested method. In particular, it gives us an opportunity to study the evolution of principal system's mode structure in changing external conditions and separate the internal climate variability from trends forced by external perturbations. Furthermore, the modes so obtained can be extrapolated beyond the observational time series, and long-term prognosis of modes' structure including characteristics of interconnections and responses to external perturbations, can be carried out. In this work the method is used for reconstructing and studying the principal modes of climate variability on inter-annual and decadal time scales accounting the external forcings such as anthropogenic emissions, variations of the solar activity and volcanic activity. The structure of the obtained modes as well as their response to external factors, e.g. forecast their change in 21 century under different CO2 emission scenarios, are discussed. [1] Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical modes of climate variability. Scientific Reports, 5, 15510. http://doi.org/10.1038/srep15510 [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J. (2016). Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101. http://doi.org/10.1063/1.4968852

Nonlinear Insolation Forcing: A Physical Mechanism for Climate Change

NASA Technical Reports Server (NTRS)

Liu, H. S.

1998-01-01

This paper focuses on recent advances in the understanding of nonlinear insolation forcing for climate change. The amplitude-frequency resonances in the insolation variations induced by the Earth's changing obliquity are emergent and may provide a physical mechanism to drive the glaciation cycles. To establish the criterion that nonlinear insolation forcing is responsible for major climate changes, the cooperative phenomena between the frequency and amplitude of the insolation are defined as insolation pulsation. Coupling of the insolation frequency and amplitude variations has established an especially new and interesting series of insolation pulses. These pulses would modulate the insolation in such a way that the mode of insolation variations could be locked to generate the 100-kyr ice age cycle which is a long-time geophysical puzzle. The nonlinear behavior of insolation forcing is tested by energy balance and ice sheet climate models and the physical mechanism behind this forcing is explained in terms of pulse duration in the incoming solar radiation. Calculations of the solar energy flux at the top of the atmosphere show that the duration of the negative and positive insolation pulses is about 2 thousand years which is long enough to prolong glaciation into deep ice ages and cause rapid melting of large ice sheets in the high latitudes of the northern hemisphere. We have performed numerical simulations of climate response to nonlinear insolation forcing for the past 2 million years. Our calculated results of temperature fluctuations are in good agreement with the climate cycles as seen in the terrestrial biogenic silica (BDP-96-2) data as well as in the marine oxygen isotope (delta(sup 18)O) records.

Model-free inference of direct network interactions from nonlinear collective dynamics.

PubMed

Casadiego, Jose; Nitzan, Mor; Hallerberg, Sarah; Timme, Marc

2017-12-19

The topology of interactions in network dynamical systems fundamentally underlies their function. Accelerating technological progress creates massively available data about collective nonlinear dynamics in physical, biological, and technological systems. Detecting direct interaction patterns from those dynamics still constitutes a major open problem. In particular, current nonlinear dynamics approaches mostly require to know a priori a model of the (often high dimensional) system dynamics. Here we develop a model-independent framework for inferring direct interactions solely from recording the nonlinear collective dynamics generated. Introducing an explicit dependency matrix in combination with a block-orthogonal regression algorithm, the approach works reliably across many dynamical regimes, including transient dynamics toward steady states, periodic and non-periodic dynamics, and chaos. Together with its capabilities to reveal network (two point) as well as hypernetwork (e.g., three point) interactions, this framework may thus open up nonlinear dynamics options of inferring direct interaction patterns across systems where no model is known.

Transverse thermal depinning and nonlinear sliding friction of an adsorbed monolayer.

PubMed

Granato, E; Ying, S C

2000-12-18

We study the response of an adsorbed monolayer under a driving force as a model of sliding friction phenomena between two crystalline surfaces with a boundary lubrication layer. Using Langevin-dynamics simulation, we determine the nonlinear response in the direction transverse to a high symmetry direction along which the layer is already sliding. We find that below a finite transition temperature there exist a critical depinning force and hysteresis effects in the transverse response in the dynamical state when the adlayer is sliding smoothly along the longitudinal direction.

Chaotic non-planar vibrations of the thin elastica. Part I: Experimental observation of planar instability

NASA Astrophysics Data System (ADS)

Cusumano, J. P.; Moon, F. C.

1995-01-01

In this two-part paper, the results of an investigation into the non-linear dynamics of a flexible cantilevered rod (the elastica) with a thin rectangular cross-section are presented. An experimental examination of the dynamics of the elastica over a broad parameter range forms the core of Part I. In Part II, the experimental work is related to a theoretical study of the mechanics of the elastica, and the study of a two-degree-of-freedom model obtained by modal projection. The experimental system used in this investigation is a rod with clamped-free boundary conditions, forced by sinusoidally displacing the clamped end. Planar periodic motions of the driven elastica are shown to lose stability at distinct resonant wedges, and the resulting motions are shown in general to be non-planar, chaotic, bending-torsion oscillations. Non-planar motions in all resonances exhibit energy cascading and dynamic two-well phenomena, and a family of asymmetric, bending-torsion non-linear modes is discovered. Correlation dimension calculations are used to estimate the number of active degrees of freedom in the system.

Mechanical nonlinearity elimination with a micromechanical clamped-free semicircular beams resonator

NASA Astrophysics Data System (ADS)

Chen, Dongyang; Chen, Xuying; Wang, Yong; Liu, Xinxin; Guan, Yangyang; Xie, Jin

2018-04-01

This paper reports a micro-machined clamped-free semicircular beam resonator aiming to eliminate the nonlinearity that widely exists in traditional mechanical resonators. Cubic coefficients over vibration displacement due to axial extension of the beams are analyzed through theoretical modelling, and the corresponding frequency effect is demonstrated. With the device working in the elastic vibration mode, the cubic coefficients are eliminated by using a free end to release the nonlinear extension of beams and thus the inside axial stress. The amplitude-frequency (A-f) effect is overcome in a large region of source power, and the coefficient of frequency softening is linearized in a large region of polarization voltage. As a result, the resonator can be driven at larger vibration amplitude to achieve a high signal to noise ratio and power handling performance.

Impact of mechanism vibration characteristics by joint clearance and optimization design of its multi-objective robustness

NASA Astrophysics Data System (ADS)

Zeng, Baoping; Wang, Chao; Zhang, Yu; Gong, Yajun; Hu, Sanbao

2017-12-01

Joint clearances and friction characteristics significantly influence the mechanism vibration characteristics; for example: as for joint clearances, the shaft and bearing of its clearance joint collide to bring about the dynamic normal contact force and tangential coulomb friction force while the mechanism works; thus, the whole system may vibrate; moreover, the mechanism is under contact-impact with impact force constraint from free movement under action of the above dynamic forces; in addition, the mechanism topology structure also changes. The constraint relationship between joints may be established by a repeated complex nonlinear dynamic process (idle stroke - contact-impact - elastic compression - rebound - impact relief - idle stroke movement - contact-impact). Analysis of vibration characteristics of joint parts is still a challenging open task by far. The dynamic equations for any mechanism with clearance is often a set of strong coupling, high-dimensional and complex time-varying nonlinear differential equations which are solved very difficultly. Moreover, complicated chaotic motions very sensitive to initial values in impact and vibration due to clearance let high-precision simulation and prediction of their dynamic behaviors be more difficult; on the other hand, their subsequent wearing necessarily leads to some certain fluctuation of structure clearance parameters, which acts as one primary factor for vibration of the mechanical system. A dynamic model was established to the device for opening the deepwater robot cabin door with joint clearance by utilizing the finite element method and analysis was carried out to its vibration characteristics in this study. Moreover, its response model was carried out by utilizing the DOE method and then the robust optimization design was performed to sizes of the joint clearance and the friction coefficient change range so that the optimization design results may be regarded as reference data for selecting bearings and controlling manufacturing process parameters for the opening mechanism. Several optimization objectives such as x/y/z accelerations for various measuring points and dynamic reaction forces of mounting brackets, and a few constraints including manufacturing process were taken into account in the optimization models, which were solved by utilizing the multi-objective genetic algorithm (NSGA-II). The vibration characteristics of the optimized opening mechanism are superior to those of the original design. In addition, the numerical forecast results are in good agreement with the test results of the prototype.

The ins and outs of modelling vertical displacement events

NASA Astrophysics Data System (ADS)

Pfefferle, David

2017-10-01

Of the many reasons a plasma discharge disrupts, Vertical Displacement Events (VDEs) lead to the most severe forces and stresses on the vacuum vessel and Plasma Facing Components (PFCs). After loss of positional control, the plasma column drifts across the vacuum vessel and comes in contact with the first wall, at which point the stored magnetic and thermal energy is abruptly released. The vessel forces have been extensively modelled in 2D but, with the constraint of axisymmetry, the fundamental 3D effects that lead to toroidal peaking, sideways forces, field-line stochastisation and halo current rotation have been vastly overlooked. In this work, we present the main results of an intense VDE modelling activity using the implicit 3D extended MHD code M3D-C1 and share our experience with the multi-domain and highly non-linear physics encountered. At the culmination of code development by the M3D-C1 group over the last decade, highlighted by the inclusion of a finite-thickness resistive vacuum vessel within the computational domain, a series of fully 3D non-linear simulations are performed using realistic transport coefficients based on the reconstruction of so-called NSTX frozen VDEs, where the feedback control was purposely switched off to trigger a vertical instability. The vertical drift phase, the evolution of the current quench and the onset of 3D halo/eddy currents are diagnosed and investigated in detail. The sensitivity of the current quench to parameter changes is assessed via 2D non-linear runs. The growth of individual toroidal modes is monitored via linear-complex runs. The intricate evolution of the plasma, which is decaying to large extent in force-balance with induced halo/wall currents, is carefully resolved via 3D non-linear runs. The location, amplitude and rotation of normal currents and wall forces are analysed and compared with experimental traces.

Energy harvesting from controlled buckling of piezoelectric beams

NASA Astrophysics Data System (ADS)

Ansari, M. H.; Karami, M. Amin

2015-11-01

A piezoelectric vibration energy harvester is presented that can generate electricity from the weight of passing cars or crowds. The energy harvester consists of a piezoelectric beam, which buckles when the device is stepped on. The energy harvester can have a horizontal or vertical configuration. In the vertical (direct) configuration, the piezoelectric beam is vertical and directly sustains the weight of the vehicles or people. In the horizontal (indirect) configuration, the vertical weight is transferred to a horizontal axial force through a scissor-like mechanism. Buckling of the beam results in significant stresses and, thus, large power production. However, if the beam’s buckling is not controlled, the beam will fracture. To prevent this, the axial deformation is constrained to limit the deformations of the beam. In this paper, the energy harvester is analytically modeled. The considered piezoelectric beam is a general non-uniform beam. The natural frequencies, mode shapes, and the critical buckling force corresponding to each mode shape are calculated. The electro-mechanical coupling and the geometric nonlinearities are included in the model. The design criteria for the device are discussed. It is demonstrated that a device, realized with commonly used piezoelectric patches, can generate tens of milliwatts of power from passing car traffic. The proposed device could also be implemented in the sidewalks or integrated in shoe soles for energy generation. One of the key features of the device is its frequency up-conversion characteristics. The piezoelectric beam undergoes free vibrations each time the weight is applied to or removed from the energy harvester. The frequency of the free vibrations is orders of magnitude larger than the frequency of the load. The device is, thus, both efficient and insensitive to the frequency of the force excitations.

A nonlinear beam model to describe the postbuckling of wide neo-Hookean beams

NASA Astrophysics Data System (ADS)

Lubbers, Luuk A.; van Hecke, Martin; Coulais, Corentin

2017-09-01

Wide beams can exhibit subcritical buckling, i.e. the slope of the force-displacement curve can become negative in the postbuckling regime. In this paper, we capture this intriguing behaviour by constructing a 1D nonlinear beam model, where the central ingredient is the nonlinearity in the stress-strain relation of the beams constitutive material. First, we present experimental and numerical evidence of a transition to subcritical buckling for wide neo-Hookean hyperelastic beams, when their width-to-length ratio exceeds a critical value of 12%. Second, we construct an effective 1D energy density by combining the Mindlin-Reissner kinematics with a nonlinearity in the stress-strain relation. Finally, we establish and solve the governing beam equations to analytically determine the slope of the force-displacement curve in the postbuckling regime. We find, without any adjustable parameters, excellent agreement between the 1D theory, experiments and simulations. Our work extends the understanding of the postbuckling of structures made of wide elastic beams and opens up avenues for the reverse-engineering of instabilities in soft and metamaterials.

Drag reduction in channel flow using nonlinear control

NASA Technical Reports Server (NTRS)

Keefe, Laurence R.

1993-01-01

Two nonlinear control schemes have been applied to the problem of drag reduction in channel flow. Both schemes have been tested using numerical simulations at a mass flux Reynolds numbers of 4408, utilizing 2D nonlinear neutral modes for goal dynamics. The OGY-method, which requires feedback, reduces drag to 60-80 percent of the turbulent value at the same Reynolds number, and employs forcing only within a thin region near the wall. The H-method, or model-based control, fails to achieve any drag reduction when starting from a fully turbulent initial condition, but shows potential for suppressing or retarding laminar-to-turbulent transition by imposing instead a transition to a low drag, nonlinear traveling wave solution to the Navier-Stokes equation. The drag in this state corresponds to that achieved by the OGY-method. Model-based control requires no feedback, but in experiments to date has required the forcing be imposed within a thicker layer than the OGY-method. Control energy expenditures in both methods are small, representing less than 0.1 percent of the uncontrolled flow's energy.

Cosmological N -body simulations with generic hot dark matter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brandbyge, Jacob; Hannestad, Steen, E-mail: jacobb@phys.au.dk, E-mail: sth@phys.au.dk

2017-10-01

We have calculated the non-linear effects of generic fermionic and bosonic hot dark matter components in cosmological N -body simulations. For sub-eV masses, the non-linear power spectrum suppression caused by thermal free-streaming resembles the one seen for massive neutrinos, whereas for masses larger than 1 eV, the non-linear relative suppression of power is smaller than in linear theory. We furthermore find that in the non-linear regime, one can map fermionic to bosonic models by performing a simple transformation.

Cosmological N-body simulations with generic hot dark matter

NASA Astrophysics Data System (ADS)

Brandbyge, Jacob; Hannestad, Steen

2017-10-01

We have calculated the non-linear effects of generic fermionic and bosonic hot dark matter components in cosmological N-body simulations. For sub-eV masses, the non-linear power spectrum suppression caused by thermal free-streaming resembles the one seen for massive neutrinos, whereas for masses larger than 1 eV, the non-linear relative suppression of power is smaller than in linear theory. We furthermore find that in the non-linear regime, one can map fermionic to bosonic models by performing a simple transformation.

Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

PubMed

Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan

2018-05-30

Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.

A modified variational method for nonlinear vibration analysis of rotating beams including Coriolis effects

NASA Astrophysics Data System (ADS)

Tian, Jiajin; Su, Jinpeng; Zhou, Kai; Hua, Hongxing

2018-07-01

This paper presents a general formulation for nonlinear vibration analysis of rotating beams. A modified variational method combined with a multi-segment partitioning technique is employed to derive the free and transient vibration behaviors of the rotating beams. The strain energy and kinetic energy functional are formulated based on the order truncation principle of the fully geometrically nonlinear beam theory. The Coriolis effects as well as nonlinear effects due to the coupling of bending-stretching, bending-twist and twist-stretching are taken into account. The present method relaxes the need to explicitly meet the requirements of the boundary conditions for the admissible functions, and allows the use of any linearly independent, complete basis functions as admissible functions for rotating beams. Moreover, the method is readily used to deal with the nonlinear transient vibration problems for rotating beams subjected to dynamic loads. The accuracy, convergence and efficiency of the proposed method are examined by numerical examples. The influences of Coriolis and centrifugal forces on the vibration behaviors of the beams with various hub radiuses and slenderness ratios and rotating at different angular velocities are also investigated.

Nonlinear evolution of magnetic flux ropes. I - Low-beta limit

NASA Technical Reports Server (NTRS)

Osherovich, V. A.; Farrugia, C. J.; Burlaga, L. F.

1993-01-01

We study the nonlinear self-similar evolution of a cylindrical magnetic flux tube with two components of the magnetic field, axial and azimuthal. We restrict ourselves to the case of a plasma of low beta. Introducing a special class of configurations we call 'separable fields', we reduce the problem to an ordinary differential equation. Two cases are to be distinguished: (1) when the total field minimizes on the symmetry axis, the magnetic configuration inexorably collapses, and (2) when, on the other hand, the total field maximizes on the symmetry axis, the magnetic configuration behaves analogously to a nonlinear oscillator. Here we focus on the latter case. The effective potential of the motion contains two terms: a strong repulsive term and a weak restoring term associated with the pinch. We solve the nonlinear differential equation of motion numerically and find that the period of oscillations grows exponentially with the energy of the oscillator. Our treatment emphasizes the role of the force-free configuration as the lowest potential energy state about which the system oscillates.

On the analytical modeling of the nonlinear vibrations of pretensioned space structures

NASA Technical Reports Server (NTRS)

Housner, J. M.; Belvin, W. K.

1983-01-01

Pretensioned structures are receiving considerable attention as candidate large space structures. A typical example is a hoop-column antenna. The large number of preloaded members requires efficient analytical methods for concept validation and design. Validation through analyses is especially important since ground testing may be limited due to gravity effects and structural size. The present investigation has the objective to present an examination of the analytical modeling of pretensioned members undergoing nonlinear vibrations. Two approximate nonlinear analysis are developed to model general structural arrangements which include beam-columns and pretensioned cables attached to a common nucleus, such as may occur at a joint of a pretensioned structure. Attention is given to structures undergoing nonlinear steady-state oscillations due to sinusoidal excitation forces. Three analyses, linear, quasi-linear, and nonlinear are conducted and applied to study the response of a relatively simple cable stiffened structure.

Rayleigh-type parametric chemical oscillation.

PubMed

Ghosh, Shyamolina; Ray, Deb Shankar

2015-09-28

We consider a nonlinear chemical dynamical system of two phase space variables in a stable steady state. When the system is driven by a time-dependent sinusoidal forcing of a suitable scaling parameter at a frequency twice the output frequency and the strength of perturbation exceeds a threshold, the system undergoes sustained Rayleigh-type periodic oscillation, wellknown for parametric oscillation in pipe organs and distinct from the usual forced quasiperiodic oscillation of a damped nonlinear system where the system is oscillatory even in absence of any external forcing. Our theoretical analysis of the parametric chemical oscillation is corroborated by full numerical simulation of two well known models of chemical dynamics, chlorite-iodine-malonic acid and iodine-clock reactions.

On the origin of amplitude reduction mechanism in tapping mode atomic force microscopy

NASA Astrophysics Data System (ADS)

Keyvani, Aliasghar; Sadeghian, Hamed; Goosen, Hans; van Keulen, Fred

2018-04-01

The origin of amplitude reduction in Tapping Mode Atomic Force Microscopy (TM-AFM) is typically attributed to the shift in resonance frequency of the cantilever due to the nonlinear tip-sample interactions. In this paper, we present a different insight into the same problem which, besides explaining the amplitude reduction mechanism, provides a simple reasoning for the relationship between tip-sample interactions and operation parameters (amplitude and frequency). The proposed formulation, which attributes the amplitude reduction to an interference between the tip-sample and dither force, only deals with the linear part of the system; however, it fully agrees with experimental results and numerical solutions of the full nonlinear model of TM-AFM.

Force-Induced Unravelling of DNA Origami.

PubMed

Engel, Megan C; Smith, David M; Jobst, Markus A; Sajfutdinow, Martin; Liedl, Tim; Romano, Flavio; Rovigatti, Lorenzo; Louis, Ard A; Doye, Jonathan P K

2018-05-31

The mechanical properties of DNA nanostructures are of widespread interest as applications that exploit their stability under constant or intermittent external forces become increasingly common. We explore the force response of DNA origami in comprehensive detail by combining AFM single molecule force spectroscopy experiments with simulations using oxDNA, a coarse-grained model of DNA at the nucleotide level, to study the unravelling of an iconic origami system: the Rothemund tile. We contrast the force-induced melting of the tile with simulations of an origami 10-helix bundle. Finally, we simulate a recently-proposed origami biosensor, whose function takes advantage of origami behaviour under tension. We observe characteristic stick-slip unfolding dynamics in our force-extension curves for both the Rothemund tile and the helix bundle and reasonable agreement with experimentally observed rupture forces for these systems. Our results highlight the effect of design on force response: we observe regular, modular unfolding for the Rothemund tile that contrasts with strain-softening of the 10-helix bundle which leads to catastropic failure under monotonically increasing force. Further, unravelling occurs straightforwardly from the scaffold ends inwards for the Rothemund tile, while the helix bundle unfolds more nonlinearly. The detailed visualization of the yielding events provided by simulation allows preferred pathways through the complex unfolding free-energy landscape to be mapped, as a key factor in determining relative barrier heights is the extensional release per base pair broken. We shed light on two important questions: how stable DNA nanostructures are under external forces; and what design principles can be applied to enhance stability.

Simulating Thin Sheets: Buckling, Wrinkling, Folding and Growth

NASA Astrophysics Data System (ADS)

Vetter, Roman; Stoop, Norbert; Wittel, Falk K.; Herrmann, Hans J.

2014-03-01

Numerical simulations of thin sheets undergoing large deformations are computationally challenging. Depending on the scenario, they may spontaneously buckle, wrinkle, fold, or crumple. Nature's thin tissues often experience significant anisotropic growth, which can act as the driving force for such instabilities. We use a recently developed finite element model to simulate the rich variety of nonlinear responses of Kirchhoff-Love sheets. The model uses subdivision surface shape functions in order to guarantee convergence of the method, and to allow a finite element description of anisotropically growing sheets in the classical Rayleigh-Ritz formalism. We illustrate the great potential in this approach by simulating the inflation of airbags, the buckling of a stretched cylinder, as well as the formation and scaling of wrinkles at free boundaries of growing sheets. Finally, we compare the folding of spatially confined sheets subject to growth and shrinking confinement to find that the two processes are equivalent.

Time-Dependent Testing Evaluation and Modeling for Rubber Stopper Seal Performance.

PubMed

Zeng, Qingyu; Zhao, Xia

2018-01-01

Sufficient rubber stopper sealing performance throughout the entire sealed product life cycle is essential for maintaining container closure integrity in the parenteral packaging industry. However, prior publications have lacked systematic considerations for the time-dependent influence on sealing performance that results from the viscoelastic characteristics of the rubber stoppers. In this paper, we report results of an effort to study these effects by applying both compression stress relaxation testing and residual seal force testing for time-dependent experimental data collection. These experiments were followed by modeling fit calculations based on the Maxwell-Wiechert theory modified with the Kohlrausch-Williams-Watts stretched exponential function, resulting in a nonlinear, time-dependent sealing force model. By employing both testing evaluations and modeling calculations, an in-depth understanding of the time-dependent effects on rubber stopper sealing force was developed. Both testing and modeling data show good consistency, demonstrating that the sealing force decays exponentially over time and eventually levels off because of the viscoelastic nature of the rubber stoppers. The nonlinearity of stress relaxation derives from the viscoelastic characteristics of the rubber stoppers coupled with the large stopper compression deformation into restrained geometry conditions. The modeling fit with capability to handle actual testing data can be employed as a tool to calculate the compression stress relaxation and residual seal force throughout the entire sealed product life cycle. In addition to being time-dependent, stress relaxation is also experimentally shown to be temperature-dependent. The present work provides a new, integrated methodology framework and some fresh insights to the parenteral packaging industry for practically and proactively considering, designing, setting up, controlling, and managing stopper sealing performance throughout the entire sealed product life cycle. LAY ABSTRACT: Historical publications in the parenteral packaging industry have lacked systematic considerations for the time-dependent influence on the sealing performance that results from effects of viscoelastic characteristic of the rubber stoppers. This study applied compression stress relaxation testing and residual seal force testing for time-dependent experimental data collection. These experiments were followed by modeling fit calculations based on the Maxwell-Wiechert theory modified with the Kohlrausch-Williams-Watts stretched exponential function, resulting in a nonlinear, time-dependent sealing force model. Experimental and modeling data show good consistency, demonstrating that sealing force decays exponentially over time and eventually levels off. The nonlinearity of stress relaxation derives from the viscoelastic characteristics of the rubber stoppers coupled with the large stopper compression deformation into restrained geometry conditions. In addition to being time-dependent stress relaxation, it is also experimentally shown to be temperature-dependent. The present work provides a new, integrated methodology framework and some fresh insights to the industry for practically and proactively considering, designing, setting up, controlling, and managing of the stopper sealing performance throughout the entire sealed product life cycle. © PDA, Inc. 2018.

Analytical and Computational Modeling of Mechanical Waves in Microscale Granular Crystals: Nonlinearity and Rotational Dynamics

NASA Astrophysics Data System (ADS)

Wallen, Samuel P.

Granular media are one of the most common, yet least understood forms of matter on earth. The difficulties in understanding the physics of granular media stem from the fact that they are typically heterogeneous and highly disordered, and the grains interact via nonlinear contact forces. Historically, one approach to reducing these complexities and gaining new insight has been the study of granular crystals, which are ordered arrays of similarly-shaped particles (typically spheres) in Hertzian contact. Using this setting, past works explored the rich nonlinear dynamics stemming from contact forces, and proposed avenues where such granular crystals could form designer, dynamically responsive materials, which yield beneficial functionality in dynamic regimes. In recent years, the combination of self-assembly fabrication methods and laser ultrasonic experimental characterization have enabled the study of granular crystals at microscale. While our intuition may suggest that these microscale granular crystals are simply scaled-down versions of their macroscale counterparts, in fact, the relevant physics change drastically; for example, short-range adhesive forces between particles, which are negligible at macroscale, are several orders of magnitude stronger than gravity at microscale. In this thesis, we present recent advances in analytical and computational modeling of microscale granular crystals, in particular concerning the interplay of nonlinearity, shear interactions, and particle rotations, which have previously been either absent, or included separately at macroscale. Drawing inspiration from past works on phononic crystals and nonlinear lattices, we explore problems involving locally-resonant metamaterials, nonlinear localized modes, amplitude-dependent energy partition, and other rich dynamical phenomena. This work enhances our understanding of microscale granular media, which may find applicability in fields such as ultrasonic wave tailoring, signal processing, shock and vibration mitigation, and powder processing.

Unstable flow structures in the Blasius boundary layer.

PubMed

Wedin, H; Bottaro, A; Hanifi, A; Zampogna, G

2014-04-01

Finite amplitude coherent structures with a reflection symmetry in the spanwise direction of a parallel boundary layer flow are reported together with a preliminary analysis of their stability. The search for the solutions is based on the self-sustaining process originally described by Waleffe (Phys. Fluids 9, 883 (1997)). This requires adding a body force to the Navier-Stokes equations; to locate a relevant nonlinear solution it is necessary to perform a continuation in the nonlinear regime and parameter space in order to render the body force of vanishing amplitude. Some states computed display a spanwise spacing between streaks of the same length scale as turbulence flow structures observed in experiments (S.K. Robinson, Ann. Rev. Fluid Mech. 23, 601 (1991)), and are found to be situated within the buffer layer. The exact coherent structures are unstable to small amplitude perturbations and thus may be part of a set of unstable nonlinear states of possible use to describe the turbulent transition. The nonlinear solutions survive down to a displacement thickness Reynolds number Re * = 496 , displaying a 4-vortex structure and an amplitude of the streamwise root-mean-square velocity of 6% scaled with the free-stream velocity. At this Re* the exact coherent structure bifurcates supercritically and this is the point where the laminar Blasius flow starts to cohabit the phase space with alternative simple exact solutions of the Navier-Stokes equations.

Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force

NASA Astrophysics Data System (ADS)

Lu, S. F.; Zhang, W.; Song, X. J.

2017-09-01

Using Reddy's high-order shear theory for laminated plates and Hamilton's principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom (DOF) nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics, including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.

Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration.

PubMed

Chen, Yunjin; Pock, Thomas

2017-06-01

Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image restoration problems. By embodying recent improvements in nonlinear diffusion models, we propose a dynamic nonlinear reaction diffusion model with time-dependent parameters (i.e., linear filters and influence functions). In contrast to previous nonlinear diffusion models, all the parameters, including the filters and the influence functions, are simultaneously learned from training data through a loss based approach. We call this approach TNRD-Trainable Nonlinear Reaction Diffusion. The TNRD approach is applicable for a variety of image restoration tasks by incorporating appropriate reaction force. We demonstrate its capabilities with three representative applications, Gaussian image denoising, single image super resolution and JPEG deblocking. Experiments show that our trained nonlinear diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for the tested applications. Our trained models preserve the structural simplicity of diffusion models and take only a small number of diffusion steps, thus are highly efficient. Moreover, they are also well-suited for parallel computation on GPUs, which makes the inference procedure extremely fast.

Nonparametric Model of Smooth Muscle Force Production During Electrical Stimulation.

PubMed

Cole, Marc; Eikenberry, Steffen; Kato, Takahide; Sandler, Roman A; Yamashiro, Stanley M; Marmarelis, Vasilis Z

2017-03-01

A nonparametric model of smooth muscle tension response to electrical stimulation was estimated using the Laguerre expansion technique of nonlinear system kernel estimation. The experimental data consisted of force responses of smooth muscle to energy-matched alternating single pulse and burst current stimuli. The burst stimuli led to at least a 10-fold increase in peak force in smooth muscle from Mytilus edulis, despite the constant energy constraint. A linear model did not fit the data. However, a second-order model fit the data accurately, so the higher-order models were not required to fit the data. Results showed that smooth muscle force response is not linearly related to the stimulation power.

A Bayesian approach to identifying structural nonlinearity using free-decay response: Application to damage detection in composites

USGS Publications Warehouse

Nichols, J.M.; Link, W.A.; Murphy, K.D.; Olson, C.C.

2010-01-01

This work discusses a Bayesian approach to approximating the distribution of parameters governing nonlinear structural systems. Specifically, we use a Markov Chain Monte Carlo method for sampling the posterior parameter distributions thus producing both point and interval estimates for parameters. The method is first used to identify both linear and nonlinear parameters in a multiple degree-of-freedom structural systems using free-decay vibrations. The approach is then applied to the problem of identifying the location, size, and depth of delamination in a model composite beam. The influence of additive Gaussian noise on the response data is explored with respect to the quality of the resulting parameter estimates.

Solar Magnetic Carpet III: Coronal Modelling of Synthetic Magnetograms

NASA Astrophysics Data System (ADS)

Meyer, K. A.; Mackay, D. H.; van Ballegooijen, A. A.; Parnell, C. E.

2013-09-01

This article is the third in a series working towards the construction of a realistic, evolving, non-linear force-free coronal-field model for the solar magnetic carpet. Here, we present preliminary results of 3D time-dependent simulations of the small-scale coronal field of the magnetic carpet. Four simulations are considered, each with the same evolving photospheric boundary condition: a 48-hour time series of synthetic magnetograms produced from the model of Meyer et al. ( Solar Phys. 272, 29, 2011). Three simulations include a uniform, overlying coronal magnetic field of differing strength, the fourth simulation includes no overlying field. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. In particular, we study their dependence upon the evolution of the photospheric magnetic field and the strength of the overlying coronal field. We also consider where energy is stored and dissipated within the coronal field. The free magnetic energy built up is found to be more than sufficient to power small-scale, transient phenomena such as nanoflares and X-ray bright points, with the bulk of the free energy found to be stored low down, between 0.5 - 0.8 Mm. The energy dissipated is currently found to be too small to account for the heating of the entire quiet-Sun corona. However, the form and location of energy-dissipation regions qualitatively agree with what is observed on small scales on the Sun. Future MHD modelling using the same synthetic magnetograms may lead to a higher energy release.

Deflection and Supporting Force Analysis of a Slender Beam under Combined Transverse and Tensile Axial Loads

DTIC Science & Technology

2016-05-01

force T > 0 case (this study) ............................................. 3 3.3 Nonlinear FEA solution for tension force T ≥ 0 case...6 3.4 Computed analytical and nonlinear FEA results...4.1 Analytical modal solution for tension force T = 0 case (textbook) ................................... 8 4.2 Computed nonlinear FEA results for

Application of nonlinear models to estimate the gain of one-dimensional free-electron lasers

NASA Astrophysics Data System (ADS)

Peter, E.; Rizzato, F. B.; Endler, A.

2017-06-01

In the present work, we make use of simplified nonlinear models based on the compressibility factor (Peter et al., Phys. Plasmas, vol. 20 (12), 2013, 123104) to predict the gain of one-dimensional (1-D) free-electron lasers (FELs), considering space-charge and thermal effects. These models proved to be reasonable to estimate some aspects of 1-D FEL theory, such as the position of the onset of mixing, in the case of a initially cold electron beam, and the position of the breakdown of the laminar regime, in the case of an initially warm beam (Peter et al., Phys. Plasmas, vol. 21 (11), 2014, 113104). The results given by the models are compared to wave-particle simulations showing a reasonable agreement.

Integration of system identification and finite element modelling of nonlinear vibrating structures

NASA Astrophysics Data System (ADS)

Cooper, Samson B.; DiMaio, Dario; Ewins, David J.

2018-03-01

The Finite Element Method (FEM), Experimental modal analysis (EMA) and other linear analysis techniques have been established as reliable tools for the dynamic analysis of engineering structures. They are often used to provide solutions to small and large structures and other variety of cases in structural dynamics, even those exhibiting a certain degree of nonlinearity. Unfortunately, when the nonlinear effects are substantial or the accuracy of the predicted response is of vital importance, a linear finite element model will generally prove to be unsatisfactory. As a result, the validated linear FE model requires further enhancement so that it can represent and predict the nonlinear behaviour exhibited by the structure. In this paper, a pragmatic approach to integrating test-based system identification and FE modelling of a nonlinear structure is presented. This integration is based on three different phases: the first phase involves the derivation of an Underlying Linear Model (ULM) of the structure, the second phase includes experiment-based nonlinear identification using measured time series and the third phase covers augmenting the linear FE model and experimental validation of the nonlinear FE model. The proposed case study is demonstrated on a twin cantilever beam assembly coupled with a flexible arch shaped beam. In this case, polynomial-type nonlinearities are identified and validated with force-controlled stepped-sine test data at several excitation levels.

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

The Bayesian Decoding of Force Stimuli from Slowly Adapting Type I Fibers in Humans

PubMed Central

Wright, James; Khamis, Heba; Birznieks, Ingvars; van Schaik, André

2016-01-01

It is well known that signals encoded by mechanoreceptors facilitate precise object manipulation in humans. It is therefore of interest to study signals encoded by the mechanoreceptors because this will contribute further towards the understanding of fundamental sensory mechanisms that are responsible for coordinating force components during object manipulation. From a practical point of view, this may suggest strategies for designing sensory-controlled biomedical devices and robotic manipulators. We use a two-stage nonlinear decoding paradigm to reconstruct the force stimulus given signals from slowly adapting type one (SA-I) tactile afferents. First, we describe a nonhomogeneous Poisson encoding model which is a function of the force stimulus and the force’s rate of change. In the decoding phase, we use a recursive nonlinear Bayesian filter to reconstruct the force profile, given the SA-I spike patterns and parameters described by the encoding model. Under the current encoding model, the mode ratio of force to its derivative is: 1.26 to 1.02. This indicates that the force derivative contributes significantly to the rate of change to the SA-I afferent spike modulation. Furthermore, using recursive Bayesian decoding algorithms is advantageous because it can incorporate past and current information in order to make predictions—consistent with neural systems—with little computational resources. This makes it suitable for interfacing with prostheses. PMID:27077750

Seasonally forced disease dynamics explored as switching between attractors

NASA Astrophysics Data System (ADS)

Keeling, Matt J.; Rohani, Pejman; Grenfell, Bryan T.

2001-01-01

Biological phenomena offer a rich diversity of problems that can be understood using mathematical techniques. Three key features common to many biological systems are temporal forcing, stochasticity and nonlinearity. Here, using simple disease models compared to data, we examine how these three factors interact to produce a range of complicated dynamics. The study of disease dynamics has been amongst the most theoretically developed areas of mathematical biology; simple models have been highly successful in explaining the dynamics of a wide variety of diseases. Models of childhood diseases incorporate seasonal variation in contact rates due to the increased mixing during school terms compared to school holidays. This ‘binary’ nature of the seasonal forcing results in dynamics that can be explained as switching between two nonlinear spiral sinks. Finally, we consider the stability of the attractors to understand the interaction between the deterministic dynamics and demographic and environmental stochasticity. Throughout attention is focused on the behaviour of measles, whooping cough and rubella.

Phase relations in a forced turbulent boundary layer: implications for modelling of high Reynolds number wall turbulence.

PubMed

Duvvuri, Subrahmanyam; McKeon, Beverley

2017-03-13

Phase relations between specific scales in a turbulent boundary layer are studied here by highlighting the associated nonlinear scale interactions in the flow. This is achieved through an experimental technique that allows for targeted forcing of the flow through the use of a dynamic wall perturbation. Two distinct large-scale modes with well-defined spatial and temporal wavenumbers were simultaneously forced in the boundary layer, and the resulting nonlinear response from their direct interactions was isolated from the turbulence signal for the study. This approach advances the traditional studies of large- and small-scale interactions in wall turbulence by focusing on the direct interactions between scales with triadic wavenumber consistency. The results are discussed in the context of modelling high Reynolds number wall turbulence.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

Roll Damping Derivatives from Generalized Lifting-Surface Theory and Wind Tunnel Forced-Oscillation Tests

NASA Technical Reports Server (NTRS)

Pototzky, Anthony S; Murphy, Patrick C.

2014-01-01

Improving aerodynamic models for adverse loss-of-control conditions in flight is an area being researched under the NASA Aviation Safety Program. Aerodynamic models appropriate for loss of control conditions require a more general mathematical representation to predict nonlinear unsteady behaviors. As more general aerodynamic models are studied that include nonlinear higher order effects, the possibility of measurements that confound aerodynamic and structural responses are probable. In this study an initial step is taken to look at including structural flexibility in analysis of rigid-body forced-oscillation testing that accounts for dynamic rig, sting and balance flexibility. Because of the significant testing required and associated costs in a general study, it makes sense to capitalize on low cost analytical methods where possible, especially where structural flexibility can be accounted for by a low cost method. This paper provides an initial look at using linear lifting surface theory applied to rigid-body aircraft roll forced-oscillation tests.

Anharmonic longitudinal motion of bases and dynamics of nonlinear excitation in DNA.

PubMed

Di Garbo, Angelo

2016-01-01

The dynamics of the transcription bubble in DNA is studied by using a nonlinear model in which torsional and longitudinal conformations of the biomolecule are coupled. In the absence of forcing and dissipation the torsional dynamics is described by a perturbed kink of the Sine-Gordon DNA model, while the longitudinal conformational energy propagate as phonons. It was found that for random initial conditions of the longitudinal conformational field the presence of the kink promotes the creation of phonons propagating along the chain axis. Moreover, the presence of forcing, describing the active role of RNA polymerase, determines in agreement to the experimental data a modulation of the velocity of the transcription bubble. Lastly, it was shown that the presence of dissipation impacts the dynamic of the phonon by reducing the amplitude of the corresponding conformational field. On the contrary, dissipation and forcing modulate the velocity of the transcription bubble alone.

On the nonlinear dynamics of trolling-mode AFM: Analytical solution using multiple time scales method

NASA Astrophysics Data System (ADS)

Sajjadi, Mohammadreza; Pishkenari, Hossein Nejat; Vossoughi, Gholamreza

2018-06-01

Trolling mode atomic force microscopy (TR-AFM) has resolved many imaging problems by a considerable reduction of the liquid-resonator interaction forces in liquid environments. The present study develops a nonlinear model of the meniscus force exerted to the nanoneedle of TR-AFM and presents an analytical solution to the distributed-parameter model of TR-AFM resonator utilizing multiple time scales (MTS) method. Based on the developed analytical solution, the frequency-response curves of the resonator operation in air and liquid (for different penetration length of the nanoneedle) are obtained. The closed-form analytical solution and the frequency-response curves are validated by the comparison with both the finite element solution of the main partial differential equations and the experimental observations. The effect of excitation angle of the resonator on horizontal oscillation of the probe tip and the effect of different parameters on the frequency-response of the system are investigated.

A Novel Nonlinear Piezoelectric Energy Harvesting System Based on Linear-Element Coupling: Design, Modeling and Dynamic Analysis.

PubMed

Zhou, Shengxi; Yan, Bo; Inman, Daniel J

2018-05-09

This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting efficiency where magnets are forbidden. The linear spring inevitably produces the nonlinear spring force on the connected harvesters, because of the geometrical relationship and the time-varying relative displacement between two adjacent harvesters. Therefore, the presented nonlinear system has strong nonlinear characteristics. A theoretical model of the presented nonlinear system is deduced, based on Euler-Bernoulli beam theory, Kirchhoff’s law, piezoelectric theory and the relevant geometrical relationship. The energy harvesting enhancement of the presented nonlinear system (when n = 2, 3) is numerically verified by comparing with its linear counterparts. In the case study, the output power area of the presented nonlinear system with two and three energy harvesters is 268.8% and 339.8% of their linear counterparts, respectively. In addition, the nonlinear dynamic response characteristics are analyzed via bifurcation diagrams, Poincare maps of the phase trajectory, and the spectrum of the output voltage.

Determination of forces in a magnetic bearing actuator - Numerical computation with comparison to experiment

NASA Technical Reports Server (NTRS)

Knight, J. D.; Xia, Z.; Mccaul, E.; Hacker, H., Jr.

1992-01-01

Calculations of the forces exerted on a journal by a magnetic bearing actuator are presented, along with comparisons to experimentally measured forces. The calculations are based on two-dimensional solutions for the flux distribution in the metal parts and free space, using finite but constant permeability in the metals. Above a relative permeability of 10,000 the effects of changes in permeability are negligible, but below 10,000 decreases in permeability cause significant decreases in the force. The calculated forces are shown to depend on the metal permeability more strongly when the journal is displaced from its centered position. The predicted forces in the principal attractive direction are in good agreement with experiment when a relatively low value of permeability is chosen. The forces measured normal to the axis of symmetry when the journal is displaced from that axis, however, are significantly higher than predicted by theory, even with a value of relative permeability larger than 5000. These results indicate a need for further work including nonlinear permeability distributions.

ON ESTIMATING FORCE-FREENESS BASED ON OBSERVED MAGNETOGRAMS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, X. M.; Zhang, M.; Su, J. T., E-mail: xmzhang@nao.cas.cn

It is a common practice in the solar physics community to test whether or not measured photospheric or chromospheric vector magnetograms are force-free, using the Maxwell stress as a measure. Some previous studies have suggested that magnetic fields of active regions in the solar chromosphere are close to being force-free whereas there is no consistency among previous studies on whether magnetic fields of active regions in the solar photosphere are force-free or not. Here we use three kinds of representative magnetic fields (analytical force-free solutions, modeled solar-like force-free fields, and observed non-force-free fields) to discuss how measurement issues such asmore » limited field of view (FOV), instrument sensitivity, and measurement error could affect the estimation of force-freeness based on observed magnetograms. Unlike previous studies that focus on discussing the effect of limited FOV or instrument sensitivity, our calculation shows that just measurement error alone can significantly influence the results of estimates of force-freeness, due to the fact that measurement errors in horizontal magnetic fields are usually ten times larger than those in vertical fields. This property of measurement errors, interacting with the particular form of a formula for estimating force-freeness, would result in wrong judgments of the force-freeness: a truly force-free field may be mistakenly estimated as being non-force-free and a truly non-force-free field may be estimated as being force-free. Our analysis calls for caution when interpreting estimates of force-freeness based on measured magnetograms, and also suggests that the true photospheric magnetic field may be further away from being force-free than it currently appears to be.« less

Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bardhan, Jaydeep P.; Knepley, Matthew G.

2014-10-07

We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory after replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single multiplicative scaling factor to determine atomic radii from molecular dynamics Lennard-Jones parameters, the new model accurately reproduces MD free-energy calculations of hydration asymmetries for: (i) monatomic ions, (ii) titratable amino acids in both their protonated and unprotonated states, and (iii) the Mobley “bracelet” and “rod” test problems [D. L. Mobley, A. E. Barber II, C. J. Fennell, and K. A. Dill, “Charge asymmetries in hydration of polar solutes,” J. Phys.more » Chem. B 112, 2405–2414 (2008)]. Remarkably, the model also justifies the use of linear response expressions for charging free energies. Our boundary-element method implementation demonstrates the ease with which other continuum-electrostatic solvers can be extended to include asymmetry.« less

Modelled non-linear response to climate of Hardangerjøkulen ice cap, southern Norway, since the mid-Holocene

NASA Astrophysics Data System (ADS)

Åkesson, Henning; Nisancioglu, Kerim H.; Giesen, Rianne H.; Morlighem, Mathieu

2016-04-01

Glacier and ice cap volume changes currently amount to half of the total cryospheric contribution to sea-level rise and are projected to remain substantial throughout the 21st century. To simulate glacier behavior on centennial and longer time scales, models rely on simplified dynamics and tunable parameters for processes not well understood. Model calibration is often done using present-day observations, even though the relationship between parameters and parametrized processes may be altered for significantly different glacier states. In this study, we simulate the Hardangerjøkulen ice cap in southern Norway since the mid-Holocene, through the Little Ice Age (LIA) and into the future. We run an ensemble for both calibration and transient experiments, using a two-dimensional ice flow model with mesh refinement. For the Holocene, we apply a simple mass balance forcing based on climate reconstructions. For the LIA until 1962, we use geomorphological evidence and measured outlet glacier positions to find a mass balance history, while we use direct mass balance measurements from 1963 until today. Given a linear climate forcing, we show that Hardangerøkulen grew from ice-free conditions in the mid-Holocene, to its maximum LIA extent in a highly non-linear fashion. We relate this to local bed topography and demonstrate that volume and area of some but not all outlet glaciers, as well as the entire ice cap, become decoupled for several centuries during our simulation of the late Holocene, before co-varying approaching the LIA. Our model is able to simulate most recorded ice cap and outlet glacier changes from the LIA until today. We show that present-day Hardangerøkulen is highly sensitive to mass balance changes, and estimate that the ice cap will melt completely by the year 2100.

Amplitude and phase fluctuations of Van der Pol oscillator under external random forcing

NASA Astrophysics Data System (ADS)

Singh, Aman K.; Yadava, R. D. S.

2018-05-01

The paper presents an analytical study of noise in Van der Pol oscillator output subjected to an external force noise assumed to be characterized by delta function (white noise). The external fluctuations are assumed to be small in comparison to the average response of the noise free system. The autocorrelation function and power spectrum are calculated under the condition of weak nonlinearity. The latter ensures limit cycle oscillations. The total spectral power density is dominated by the contributions from the phase fluctuations. The amplitude fluctuations are at least two orders of magnitude smaller. The analysis is shown to be useful to interpretation microcantilever based biosensing data.

Numerical simulations of an elastica pendulum

NASA Astrophysics Data System (ADS)

Sinclair, R.

Folklore would have it that a massless clamped-free elastica undergoing planar motion with a point end mass possesses periodic solutions corresponding to a single mode of oscillation. We present a battery of numerical simulations leading to the single conclusion that these supposed periodic solutions do not exist, due to a strong nonlinear coupling of two modes, the frequency of one of which is apparently inversely proportional to the magnitude of the force acting on the elastica.

Investigation of broadband terahertz generation from metasurface

DOE PAGES

Fang, Ming; Niu, Kaikun; Huang, ZHixiang; ...

2018-01-01

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designingmore » nonlinear plasmonic metamaterials.« less

Investigation of broadband terahertz generation from metasurface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fang, Ming; Niu, Kaikun; Huang, ZHixiang

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designingmore » nonlinear plasmonic metamaterials.« less

Investigation of broadband terahertz generation from metasurface

DOE PAGES

Fang, Ming; Niu, Kaikun; Huang, ZHixiang; ...

2018-05-21

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designingmore » nonlinear plasmonic metamaterials.« less

Analysis of 20 magnetic clouds at 1 AU during a solar minimum

NASA Astrophysics Data System (ADS)

Gulisano, A. M.; Dasso, S.; Mandrini, C. H.; Démoulin, P.

We study 20 magnetic clouds, observed in situ by the spacecraft Wind, at the Lagrangian point L1, from 22 August, 1995, to 7 November, 1997. In previous works, assuming a cylindrical symmetry for the local magnetic configuration and a satellite trajectory crossing the axis of the cloud, we obtained their orientations using a minimum variance analysis. In this work we compute the orientations and magnetic configurations using a non-linear simultaneous fit of the geometric and physical parameters for a linear force-free model, including the possibility of a not null impact parameter. We quantify global magnitudes such as the relative magnetic helicity per unit length and compare the values found with both methods (minimum variance and the simultaneous fit). FULL TEXT IN SPANISH

Self-assembly of skyrmion-dressed chiral nematic colloids with tangential anchoring.

PubMed

Pandey, M B; Porenta, T; Brewer, J; Burkart, A; Copar, S; Zumer, S; Smalyukh, Ivan I

2014-06-01

We describe dipolar nematic colloids comprising mutually bound solid microspheres, three-dimensional skyrmions, and point defects in a molecular alignment field of chiral nematic liquid crystals. Nonlinear optical imaging and numerical modeling based on minimization of Landau-de Gennes free energy reveal that the particle-induced skyrmions resemble torons and hopfions, while matching surface boundary conditions at the interfaces of liquid crystal and colloidal spheres. Laser tweezers and videomicroscopy reveal that the skyrmion-colloidal hybrids exhibit purely repulsive elastic pair interactions in the case of parallel dipoles and an unexpected reversal of interaction forces from repulsive to attractive as the center-to-center distance decreases for antiparallel dipoles. The ensuing elastic self-assembly gives rise to colloidal chains of antiparallel dipoles with particles entangled by skyrmions.

I-Wire Heart-on-a-Chip II: Biomechanical analysis of contractile, three-dimensional cardiomyocyte tissue constructs.

PubMed

Schroer, Alison K; Shotwell, Matthew S; Sidorov, Veniamin Y; Wikswo, John P; Merryman, W David

2017-01-15

This companion study presents the biomechanical analysis of the "I-Wire" platform using a modified Hill model of muscle mechanics that allows for further characterization of construct function and response to perturbation. The I-Wire engineered cardiac tissue construct (ECTC) is a novel experimental platform to investigate cardiac cell mechanics during auxotonic contraction. Whereas passive biomaterials often exhibit nonlinear and dissipative behavior, active tissue equivalents, such as ECTCs, also expend metabolic energy to perform mechanical work that presents additional challenges in quantifying their properties. The I-Wire model uses the passive mechanical response to increasing applied tension to measure the inherent stress and resistance to stretch of the construct before, during, and after treatments. Both blebbistatin and isoproterenol reduced prestress and construct stiffness; however, blebbistatin treatment abolished subsequent force-generating potential while isoproterenol enhanced this property. We demonstrate that the described model can replicate the response of these constructs to intrinsic changes in force-generating potential in response to both increasing frequency of stimulation and decreasing starting length. This analysis provides a useful mathematical model of the I-Wire platform, increases the number of parameters that can be derived from the device, and serves as a demonstration of quantitative characterization of nonlinear, active biomaterials. We anticipate that this quantitative analysis of I-Wire constructs will prove useful for qualifying patient-specific cardiomyocytes and fibroblasts prior to their utilization for cardiac regenerative medicine. Passive biomaterials may have non-linear elasticity and losses, but engineered muscle tissue also exhibits time- and force-dependent contractions. Historically, mathematical muscle models include series-elastic, parallel-elastic, contractile, and viscous elements. While hearts-on-a-chip can demonstrate in vitro the contractile properties of engineered cardiac constructs and their response to drugs, most of these use cellular monolayers that cannot be readily probed with controlled forces. The I-Wire platform described in the preceding paper by Sidorov et al. addresses these limitations with three-dimensional tissue constructs to which controlled forces can be applied. In this companion paper, we show how to characterize I-Wire constructs using a non-linear, active Hill model, which should be useful for qualifying cells prior to their use in cardiac regenerative medicine. Copyright © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Hybrid fusion of linear, non-linear and spectral models for the dynamic modeling of sEMG and skeletal muscle force: an application to upper extremity amputation.

PubMed

Potluri, Chandrasekhar; Anugolu, Madhavi; Schoen, Marco P; Subbaram Naidu, D; Urfer, Alex; Chiu, Steve

2013-11-01

Estimating skeletal muscle (finger) forces using surface Electromyography (sEMG) signals poses many challenges. In general, the sEMG measurements are based on single sensor data. In this paper, two novel hybrid fusion techniques for estimating the skeletal muscle force from the sEMG array sensors are proposed. The sEMG signals are pre-processed using five different filters: Butterworth, Chebychev Type II, Exponential, Half-Gaussian and Wavelet transforms. Dynamic models are extracted from the acquired data using Nonlinear Wiener Hammerstein (NLWH) models and Spectral Analysis Frequency Dependent Resolution (SPAFDR) models based system identification techniques. A detailed comparison is provided for the proposed filters and models using 18 healthy subjects. Wavelet transforms give higher mean correlation of 72.6 ± 1.7 (mean ± SD) and 70.4 ± 1.5 (mean ± SD) for NLWH and SPAFDR models, respectively, when compared to the other filters used in this work. Experimental verification of the fusion based hybrid models with wavelet transform shows a 96% mean correlation and 3.9% mean relative error with a standard deviation of ± 1.3 and ± 0.9 respectively between the overall hybrid fusion algorithm estimated and the actual force for 18 test subjects' k-fold cross validation data. © 2013 Elsevier Ltd. All rights reserved.

Non-compact nonlinear sigma models

DOE PAGES

de Rham, Claudia; Tolley, Andrew J.; Zhou, Shuang-Yong

2016-07-19

The target space of a nonlinear sigma model is usually required to be positive definite to avoid ghosts. We introduce a unique class of nonlinear sigma models where the target space metric has a Lorentzian signature, thus the associated group being non-compact. We show that the would-be ghost associated with the negative direction is fully projected out by 2 second-class constraints, and there exist stable solutions in this class of models. This result also has important implications for Lorentz–invariant massive gravity: There exist stable nontrivial vacua in massive gravity that are free from any linear vDVZ-discontinuity and a decoupling limitmore » can be defined on these vacua.« less

Non-compact nonlinear sigma models

DOE Office of Scientific and Technical Information (OSTI.GOV)

de Rham, Claudia; Tolley, Andrew J.; Zhou, Shuang-Yong

The target space of a nonlinear sigma model is usually required to be positive definite to avoid ghosts. We introduce a unique class of nonlinear sigma models where the target space metric has a Lorentzian signature, thus the associated group being non-compact. We show that the would-be ghost associated with the negative direction is fully projected out by 2 second-class constraints, and there exist stable solutions in this class of models. This result also has important implications for Lorentz–invariant massive gravity: There exist stable nontrivial vacua in massive gravity that are free from any linear vDVZ-discontinuity and a decoupling limitmore » can be defined on these vacua.« less

A novel free floating accelerometer force balance system for shock tunnel applications

NASA Astrophysics Data System (ADS)

Joarder, R.; Mahaptra, D. R.; Jagadeesh, G.

In order to overcome the interference of the model mounting system with the external aerodynamics of the body during shock tunnel testing, a new free floating internally mountable balance system that ensures unrestrained model motion during testing has been designed, fabricated and tested. Minimal friction ball bearings are used for ensuring the free floating condition of the model during tunnel testing. The drag force acting on a blunt leading edge flat plate at hypersonic Mach number has been measured using the new balance system. Finite element model (FEM) and CFD are exhaustively used in the design as well as for calibrating the new balance system. The experimentally measured drag force on the blunt leading edge flat plate at stagnation enthalpy of 0.7 and 1.2 MJ/kg and nominal Mach number of 5.75 matches well with FEM results. The concept can also be extended for measuring all the three fundamental aerodynamic forces in short duration test facilities like free piston driven shock tunnels.

Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter.

PubMed

Song, Xuegang; Zhang, Yuexin; Liang, Dakai

2017-10-10

This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF) was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Agarwal, S.; Wettlaufer, J. S.

2014-12-01

We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.

Thermal effects on nonlinear vibration of a carbon nanotube-based mass sensor using finite element analysis

NASA Astrophysics Data System (ADS)

Kang, Dong-Keun; Kim, Chang-Wan; Yang, Hyun-Ik

2017-01-01

In the present study we carried out a dynamic analysis of a CNT-based mass sensor by using a finite element method (FEM)-based nonlinear analysis model of the CNT resonator to elucidate the combined effects of thermal effects and nonlinear oscillation behavior upon the overall mass detection sensitivity. Mass sensors using carbon nanotube (CNT) resonators provide very high sensing performance. Because CNT-based resonators can have high aspect ratios, they can easily exhibit nonlinear oscillation behavior due to large displacements. Also, CNT-based devices may experience high temperatures during their manufacture and operation. These geometrical nonlinearities and temperature changes affect the sensing performance of CNT-based mass sensors. However, it is very hard to find previous literature addressing the detection sensitivity of CNT-based mass sensors including considerations of both these nonlinear behaviors and thermal effects. We modeled the nonlinear equation of motion by using the von Karman nonlinear strain-displacement relation, taking into account the additional axial force associated with the thermal effect. The FEM was employed to solve the nonlinear equation of motion because it can effortlessly handle the more complex geometries and boundary conditions. A doubly clamped CNT resonator actuated by distributed electrostatic force was the configuration subjected to the numerical experiments. Thermal effects upon the fundamental resonance behavior and the shift of resonance frequency due to attached mass, i.e., the mass detection sensitivity, were examined in environments of both high and low (or room) temperature. The fundamental resonance frequency increased with decreasing temperature in the high temperature environment, and increased with increasing temperature in the low temperature environment. The magnitude of the shift in resonance frequency caused by an attached mass represents the sensing performance of a mass sensor, i.e., its mass detection sensitivity, and it can be seen that this shift is affected by the temperature change and the amount of electrostatic force. The thermal effects on the mass detection sensitivity are intensified in the linear oscillation regime and increase with increasing CNT length; this intensification can either improve or worsen the detection sensitivity.

A reduced-order nonlinear sliding mode observer for vehicle slip angle and tyre forces

NASA Astrophysics Data System (ADS)

Chen, Yuhang; Ji, Yunfeng; Guo, Konghui

2014-12-01

In this paper, a reduced-order sliding mode observer (RO-SMO) is developed for vehicle state estimation. Several improvements are achieved in this paper. First, the reference model accuracy is improved by considering vehicle load transfers and using a precise nonlinear tyre model 'UniTire'. Second, without the reference model accuracy degraded, the computing burden of the state observer is decreased by a reduced-order approach. Third, nonlinear system damping is integrated into the SMO to speed convergence and reduce chattering. The proposed RO-SMO is evaluated through simulation and experiments based on an in-wheel motor electric vehicle. The results show that the proposed observer accurately predicts the vehicle states.

Nonlinear analysis for dual-frequency concurrent energy harvesting

NASA Astrophysics Data System (ADS)

Yan, Zhimiao; Lei, Hong; Tan, Ting; Sun, Weipeng; Huang, Wenhu

2018-05-01

The dual-frequency responses of the hybrid energy harvester undergoing the base excitation and galloping were analyzed numerically. In this work, an approximate dual-frequency analytical method is proposed for the nonlinear analysis of such a system. To obtain the approximate analytical solutions of the full coupled distributed-parameter model, the forcing interactions is first neglected. Then, the electromechanical decoupled governing equation is developed using the equivalent structure method. The hybrid mechanical response is finally separated to be the self-excited and forced responses for deriving the analytical solutions, which are confirmed by the numerical simulations of the full coupled model. The forced response has great impacts on the self-excited response. The boundary of Hopf bifurcation is analytically determined by the onset wind speed to galloping, which is linearly increased by the electrical damping. Quenching phenomenon appears when the increasing base excitation suppresses the galloping. The theoretical quenching boundary depends on the forced mode velocity. The quenching region increases with the base acceleration and electrical damping, but decreases with the wind speed. Superior to the base-excitation-alone case, the existence of the aerodynamic force protects the hybrid energy harvester at resonance from damages caused by the excessive large displacement. From the view of the harvested power, the hybrid system surpasses the base-excitation-alone system or the galloping-alone system. This study advances our knowledge on intrinsic nonlinear dynamics of the dual-frequency energy harvesting system by taking advantage of the analytical solutions.

Assessing the utility of frequency dependent nudging for reducing biases in biogeochemical models

NASA Astrophysics Data System (ADS)

Lagman, Karl B.; Fennel, Katja; Thompson, Keith R.; Bianucci, Laura

2014-09-01

Bias errors, resulting from inaccurate boundary and forcing conditions, incorrect model parameterization, etc. are a common problem in environmental models including biogeochemical ocean models. While it is important to correct bias errors wherever possible, it is unlikely that any environmental model will ever be entirely free of such errors. Hence, methods for bias reduction are necessary. A widely used technique for online bias reduction is nudging, where simulated fields are continuously forced toward observations or a climatology. Nudging is robust and easy to implement, but suppresses high-frequency variability and introduces artificial phase shifts. As a solution to this problem Thompson et al. (2006) introduced frequency dependent nudging where nudging occurs only in prescribed frequency bands, typically centered on the mean and the annual cycle. They showed this method to be effective for eddy resolving ocean circulation models. Here we add a stability term to the previous form of frequency dependent nudging which makes the method more robust for non-linear biological models. Then we assess the utility of frequency dependent nudging for biological models by first applying the method to a simple predator-prey model and then to a 1D ocean biogeochemical model. In both cases we only nudge in two frequency bands centered on the mean and the annual cycle, and then assess how well the variability in higher frequency bands is recovered. We evaluate the effectiveness of frequency dependent nudging in comparison to conventional nudging and find significant improvements with the former.

Structural design models for tunnels in soft soil

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duddeck, H.; Erdmann, J.

In 1982 the ITA (International Tunnelling Association) working group on structural design models for tunnelling published the answers to a questionnaire in the form of a synopsis. As a continuation of that work, results of an investigation on design models for soft ground tunnels are presented and a comparative review of the progress to date in this field is given. The main differences in the assumptions entering the different models are stated. Diagrams for the hoop forces, bending moments and radial displacements shows the differences in the design values evaluated for three different models: (1) the continuum models; (2) themore » design model by Muir Wood; and (3) the bedded beam model without bedding at the crown region. Because a comparison with free parameters necessitates analytical solutions, only circular cross-sections were investigated. Nevertheless the results of the investigation also may be valid to a great extent for noncircular cross-sections and a more refined numerical analyses. It can be shown that there is a trend toward agreement on the proper assumptions and on the design models applied either for shallow or for deep tunnels. As should be expected, the bending moments are sensitive with regard to the model chosen, whereas the hoop forces in the tunnel ring are rather unaffected by the change of ground and lining properties. The significance of the nonlinearity due to geometrical deformations or to plastic behavior is demonstrated from specific examples.« less

Stochastic Ocean Predictions with Dynamically-Orthogonal Primitive Equations

NASA Astrophysics Data System (ADS)

Subramani, D. N.; Haley, P., Jr.; Lermusiaux, P. F. J.

2017-12-01

The coastal ocean is a prime example of multiscale nonlinear fluid dynamics. Ocean fields in such regions are complex and intermittent with unstationary heterogeneous statistics. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters, and even the model parameterizations and equations themselves. For efficient and rigorous quantification and prediction of these uncertainities, the stochastic Dynamically Orthogonal (DO) PDEs for a primitive equation ocean modeling system with a nonlinear free-surface are derived and numerical schemes for their space-time integration are obtained. Detailed numerical studies with idealized-to-realistic regional ocean dynamics are completed. These include consistency checks for the numerical schemes and comparisons with ensemble realizations. As an illustrative example, we simulate the 4-d multiscale uncertainty in the Middle Atlantic/New York Bight region during the months of Jan to Mar 2017. To provide intitial conditions for the uncertainty subspace, uncertainties in the region were objectively analyzed using historical data. The DO primitive equations were subsequently integrated in space and time. The probability distribution function (pdf) of the ocean fields is compared to in-situ, remote sensing, and opportunity data collected during the coincident POSYDON experiment. Results show that our probabilistic predictions had skill and are 3- to 4- orders of magnitude faster than classic ensemble schemes.

Nonlinear oscillations of gas in an open tube near the resonance frequency in the shock-free mode

NASA Astrophysics Data System (ADS)

Tkachenko, L. A.; Sergienko, M. V.

2014-11-01

The forced oscillations of gas in an open tube, excited by harmonical oscillations of piston in the shock-free mode were investigated near the first first eigenfrequencies. An expression for the pressure oscillations of gas was obtained for the tube with unrounded end without flange. The amplitude impact of piston displacement on the oscillations of pressure and velocity of the secondary flow of gas was investigated. The comparison of theoretical calculations with experimental data was executed. The effect of secondary flow on the particle drift along the tube axis with acoustic oscillations of gas was shown.

Free Language Selection in the Bilingual Brain: An Event-Related fMRI Study

PubMed Central

Zhang, Yong; Wang, Tao; Huang, Peiyu; Li, Dan; Qiu, Jiang; Shen, Tong; Xie, Peng

2015-01-01

Bilingual speakers may select between two languages either on demand (forced language selection) or on their own volition (free language selection). However, the neural substrates underlying free and forced language selection may differ. While the neural substrates underlying forced language selection have been well-explored with language switching paradigms, those underlying free language selection have remained unclear. Using a modified digit-naming switching paradigm, we addressed the neural substrates underlying free language selection by contrasting free language switching with forced language switching. For a digit-pair trial, Chinese-English bilinguals named each digit in Chinese or English either on demand under forced language selection condition or on their own volition under free language selection condition. The results revealed activation in the frontoparietal regions that mediate volition of language selection. Furthermore, a comparison of free and forced language switching demonstrated differences in the patterns of brain activation. Additionally, free language switching showed reduced switching costs as compared to forced language switching. These findings suggest differences between the mechanism(s) underlying free and forced language switching. As such, the current study suggests interactivity between control of volition and control of language switching in free language selection, providing insights into a model of bilingual language control. PMID:26177885

Coupled oscillators in identification of nonlinear damping of a real parametric pendulum

NASA Astrophysics Data System (ADS)

Olejnik, Paweł; Awrejcewicz, Jan

2018-01-01

A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.

Microstructural Characterization of Vocal Folds toward a Strain-Energy Model of Collagen Remodeling

PubMed Central

Miri, Amir K.; Heris, Hossein K.; Tripathy, Umakanta; Wiseman, Paul W.; Mongeau, Luc

2013-01-01

Collagen fibrils are believed to control the immediate deformation of soft tissues under biomechanical load. Most extracellular matrix proteins remain intact during frozen sectioning, which allows them to be scanned using atomic force microscopy (AFM). Collagen fibrils are distinguishable because of their helical shape. In the present study, the shape and organization of collagen fibrils in dissected porcine vocal folds were quantified using nonlinear laser scanning microscopy data at the micrometer scale and AFM data at the nanometer scale. Rope-shape collagen fibrils were observed. Geometric characteristics for the fibrils were fed to a hyperelastic model to predict the biomechanical response of the tissue. The model simulates the micrometer-scale unlocking behavior of collagen bundles when extended from their unloaded configuration. Force spectroscopy using AFM was used to estimate the stiffness of collagen fibrils (1 ± 0.5 MPa). The presence of rope-shape fibrils is postulated to change the slope of the force-deflection response near the onset of nonlinearity. The proposed model could ultimately be used to evaluate changes in elasticity of soft tissues that result from the collagen remodeling. PMID:23643604

Modeling, Dynamics, Bifurcation Behavior and Stability Analysis of a DC-DC Boost Converter in Photovoltaic Systems

NASA Astrophysics Data System (ADS)

Zhioua, M.; El Aroudi, A.; Belghith, S.; Bosque-Moncusí, J. M.; Giral, R.; Al Hosani, K.; Al-Numay, M.

A study of a DC-DC boost converter fed by a photovoltaic (PV) generator and supplying a constant voltage load is presented. The input port of the converter is controlled using fixed frequency pulse width modulation (PWM) based on the loss-free resistor (LFR) concept whose parameter is selected with the aim to force the PV generator to work at its maximum power point. Under this control strategy, it is shown that the system can exhibit complex nonlinear behaviors for certain ranges of parameter values. First, using the nonlinear models of the converter and the PV source, the dynamics of the system are explored in terms of some of its parameters such as the proportional gain of the controller and the output DC bus voltage. To present a comprehensive approach to the overall system behavior under parameter changes, a series of bifurcation diagrams are computed from the circuit-level switched model and from a simplified model both implemented in PSIM© software showing a remarkable agreement. These diagrams show that the first instability that takes place in the system period-1 orbit when a primary parameter is varied is a smooth period-doubling bifurcation and that the nonlinearity of the PV generator is irrelevant for predicting this phenomenon. Different bifurcation scenarios can take place for the resulting period-2 subharmonic regime depending on a secondary bifurcation parameter. The boundary between the desired period-1 orbit and subharmonic oscillation resulting from period-doubling in the parameter space is obtained by calculating the eigenvalues of the monodromy matrix of the simplified model. The results from this model have been validated with time-domain numerical simulation using the circuit-level switched model and also experimentally from a laboratory prototype. This study can help in selecting the parameter values of the circuit in order to delimit the region of period-1 operation of the converter which is of practical interest in PV systems.

Finite element for rotor/stator interactive forces in general engine dynamic simulation. Part 1: Development of bearing damper element

NASA Technical Reports Server (NTRS)

Adams, M. L.; Padovan, J.; Fertis, D. G.

1980-01-01

A general purpose squeeze-film damper interactive force element was developed, coded into a software package (module) and debugged. This software package was applied to nonliner dynamic analyses of some simple rotor systems. Results for pressure distributions show that the long bearing (end sealed) is a stronger bearing as compared to the short bearing as expected. Results of the nonlinear dynamic analysis, using a four degree of freedom simulation model, showed that the orbit of the rotating shaft increases nonlinearity to fill the bearing clearance as the unbalanced weight increases.

Continuous theory of active matter systems with metric-free interactions.

PubMed

Peshkov, Anton; Ngo, Sandrine; Bertin, Eric; Chaté, Hugues; Ginelli, Francesco

2012-08-31

We derive a hydrodynamic description of metric-free active matter: starting from self-propelled particles aligning with neighbors defined by "topological" rules, not metric zones-a situation advocated recently to be relevant for bird flocks, fish schools, and crowds-we use a kinetic approach to obtain well-controlled nonlinear field equations. We show that the density-independent collision rate per particle characteristic of topological interactions suppresses the linear instability of the homogeneous ordered phase and the nonlinear density segregation generically present near threshold in metric models, in agreement with microscopic simulations.

Nonlinear refraction at the absorption edge in InAs.

PubMed

Poole, C D; Garmire, E

1984-08-01

The results of measurements of nonlinear refraction at the absorption edge in InAs between 68 and 90 K taken with an HF laser are compared with those of a band-gap resonant model in which the contribution of the light-hole band is included and found to account for more than 40% of the observed nonlinear refraction. A generalized expression for the nonlinear index is derived by using the complete Fermi-Dirac distribution function. Good agreement between theory and experiment is obtained, with no free parameters.

Traveling wave solution of driven nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-09-01

The traveling solitary and cnoidal wave solutions of the one dimensional driven nonlinear Schrödinger equation with a generalized form of nonlinearity are presented in this paper. We examine the modulation of nonlinear solitary excitations in two known weakly nonlinear models of classic oscillators, namely, the Helmholtz and Duffing oscillators and envelope structure formations for different oscillator and driver parameters. It is shown that two distinct regimes of subcritical and supercritical modulations may occur for nonlinear excitations with propagation speeds v <√{4 F0 } and v >√{4 F0 } , respectively, in which F0 is the driver force strength. The envelope soliton and cnoidal waves in these regimes are observed to be fundamentally different. The effect of pseudoenergy on the structure of the modulated envelope excitations is studied in detail for both sub- and supercritical modulation types. The current model for traveling envelope excitations may be easily extended to pseudopotentials with full nonlinearity relevant to more realistic gases, fluids, and plasmas.

Subgrid-scale models for large-eddy simulation of rotating turbulent channel flows

NASA Astrophysics Data System (ADS)

Silvis, Maurits H.; Bae, Hyunji Jane; Trias, F. Xavier; Abkar, Mahdi; Moin, Parviz; Verstappen, Roel

2017-11-01

We aim to design subgrid-scale models for large-eddy simulation of rotating turbulent flows. Rotating turbulent flows form a challenging test case for large-eddy simulation due to the presence of the Coriolis force. The Coriolis force conserves the total kinetic energy while transporting it from small to large scales of motion, leading to the formation of large-scale anisotropic flow structures. The Coriolis force may also cause partial flow laminarization and the occurrence of turbulent bursts. Many subgrid-scale models for large-eddy simulation are, however, primarily designed to parametrize the dissipative nature of turbulent flows, ignoring the specific characteristics of transport processes. We, therefore, propose a new subgrid-scale model that, in addition to the usual dissipative eddy viscosity term, contains a nondissipative nonlinear model term designed to capture transport processes, such as those due to rotation. We show that the addition of this nonlinear model term leads to improved predictions of the energy spectra of rotating homogeneous isotropic turbulence as well as of the Reynolds stress anisotropy in spanwise-rotating plane-channel flows. This work is financed by the Netherlands Organisation for Scientific Research (NWO) under Project Number 613.001.212.

Period of vibration of axially vibrating truly nonlinear rod

NASA Astrophysics Data System (ADS)

Cveticanin, L.

2016-07-01

In this paper the axial vibration of a muscle whose fibers are parallel to the direction of muscle compression is investigated. The model is a clamped-free rod with a strongly nonlinear elastic property. Axial vibration is described by a nonlinear partial differential equation. A solution of the equation is constructed for special initial conditions by using the method of separation of variables. The partial differential equation is separated into two uncoupled strongly nonlinear second order differential equations. Both equations, with displacement function and with time function are exactly determined. Exact solutions are given in the form of inverse incomplete and inverse complete Beta function. Using boundary and initial conditions, the frequency of vibration is obtained. It has to be mentioned that the determined frequency represents the exact analytic description for the axially vibrating truly nonlinear clamped-free rod. The procedure suggested in this paper is applied for calculation of the frequency of the longissimus dorsi muscle of a cow. The influence of elasticity order and elasticity coefficient on the frequency property is tested.

User-defined Material Model for Thermo-mechanical Progressive Failure Analysis

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.

2008-01-01

Previously a user-defined material model for orthotropic bimodulus materials was developed for linear and nonlinear stress analysis of composite structures using either shell or solid finite elements within a nonlinear finite element analysis tool. Extensions of this user-defined material model to thermo-mechanical progressive failure analysis are described, and the required input data are documented. The extensions include providing for temperature-dependent material properties, archival of the elastic strains, and a thermal strain calculation for materials exhibiting a stress-free temperature.

Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system

NASA Astrophysics Data System (ADS)

Kurt, Mehmet; Moore, Keegan J.; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.

2017-05-01

We consider the application of a new nonlinear model updating strategy to a computational benchmark system. The approach relies on analyzing system response time series in the frequency-energy domain by constructing both Hamiltonian and forced and damped frequency-energy plots (FEPs). The system parameters are then characterized and updated by matching the backbone branches of the FEPs with the frequency-energy wavelet transforms of experimental and/or computational time series. The main advantage of this method is that no nonlinearity model is assumed a priori, and the system model is updated solely based on simulation and/or experimental measured time series. By matching the frequency-energy plots of the benchmark system and its reduced-order model, we show that we are able to retrieve the global strongly nonlinear dynamics in the frequency and energy ranges of interest, identify bifurcations, characterize local nonlinearities, and accurately reconstruct time series. We apply the proposed methodology to a benchmark problem, which was posed to the system identification community prior to the IMAC XXXII (2014) and XXXIII (2015) Conferences as a "Round Robin Exercise on Nonlinear System Identification". We show that we are able to identify the parameters of the non-linear element in the problem with a priori knowledge about its position.

Zero Forcing Conditions for Nonlinear channel Equalisation using a pre-coding scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arfa, Hichem; Belghith, Safya; El Asmi, Sadok

2009-03-05

This paper shows how we can present a zero forcing conditions for a nonlinear channel equalisation. These zero forcing conditions based on the rank of nonlinear system are issued from an algebraic approach based on the module theoretical approach, in which the rank of nonlinear channel is clearly defined. In order to improve the performance of equalisation and reduce the complexity of used nonlinear systems, we will apply a pre-coding scheme. Theoretical results are given and computer simulation is used to corroborate the theory.

A novel constant-force scanning probe incorporating mechanical-magnetic coupled structures.

PubMed

Wang, Hongxi; Zhao, Jian; Gao, Renjing; Yang, Yintang

2011-07-01

A one-dimensional scanning probe with constant measuring force is designed and fabricated by utilizing the negative stiffness of the magnetic coupled structure, which mainly consists of the magnetic structure, the parallel guidance mechanism, and the pre-stressed spring. Based on the theory of material mechanics and the equivalent surface current model for computing the magnetic force, the analytical model of the scanning probe subjected to multi-forces is established, and the nonlinear relationship between the measuring force and the probe displacement is obtained. The practicability of introducing magnetic coupled structure in the constant-force probe is validated by the consistency of the results in numerical simulation and experiments.

The effectiveness of adhesives on the retention of mandibular free end saddle partial dentures: An in vitro study.

PubMed

Quiney, Daniel; Nishio Ayre, Wayne; Milward, Paul

2017-07-01

Existing in vitro methods for testing denture adhesives do not fully replicate the complex oral geometries and environment; and in vivo methods are qualitative, prone to bias and not easily reproducible. The purpose of this study was to develop a novel, quantitative and more accurate model to test the effect of adhesives on the retentive force of mandibular free end saddle partial dentures. An in vitro model was developed based on an anatomically accurate cast of a clinical case. Experimentally, the amount of adhesive was varied (0.2g-1g) and the tensile force required for displacement was measured. Different commercially available adhesives were then tested at the optimum volume using the in vitro model. A 3D finite element model of the denture was used to assess how the forces to induce denture displacement varied according to the position of the force along the saddle length. The mass of adhesive was found to significantly alter retention forces, with 0.4-0.7g being the optimum range for this particular scenario. Use of adhesives significantly improved mandibular free end saddle partial denture retention with the worst performing adhesive increasing retention nine-fold whilst the best performing adhesive increased retention twenty three-fold. The finite element model revealed that 77% more force was required to displace the denture by positioning forces towards the mesial end of the saddle compared to the distal end. An in vitro denture adhesive model was developed, which demonstrated that mass of adhesive plays a significant role in enhancing denture retention and supported the design principle of placing as few teeth as clinically necessary on the distal end of the free end saddles. Limiting the position of teeth on free end saddles to the mesial and mid portion of the saddle will reduce displacements caused by mastication. The movement of mandibular free end saddle partial dentures can be restricted with the use of denture adhesives. Altering the mass of adhesive used can further improve the retention of mandibular free end saddle partial dentures for patients. Copyright © 2017 Elsevier Ltd. All rights reserved.

Optimizing Cubature for Efficient Integration of Subspace Deformations

PubMed Central

An, Steven S.; Kim, Theodore; James, Doug L.

2009-01-01

We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integrate functions that lie in particular polynomial subspaces, we propose cubature schemes (multi-dimensional quadrature) optimized for efficient integration of force densities associated with particular subspace deformations, particular materials, and particular geometric domains. We support generic subspace deformation kinematics, and nonlinear hyperelastic materials. For an r-dimensional deformation subspace with O(r) cubature points, our method is able to evaluate subspace forces at O(r2) cost. We also describe composite cubature rules for runtime error estimation. Results are provided for various subspace deformation models, several hyperelastic materials (St.Venant-Kirchhoff, Mooney-Rivlin, Arruda-Boyce), and multimodal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration. CR Categories: I.6.8 [Simulation and Modeling]: Types of Simulation—Animation, I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Physically based modeling G.1.4 [Mathematics of Computing]: Numerical Analysis—Quadrature and Numerical Differentiation PMID:19956777

Generation of stable subfemtosecond hard x-ray pulses with optimized nonlinear bunch compression

DOE PAGES

Huang, Senlin; Ding, Yuantao; Huang, Zhirong; ...

2014-12-15

In this paper, we propose a simple scheme that leverages existing x-ray free-electron laser hardware to produce stable single-spike, subfemtosecond x-ray pulses. By optimizing a high-harmonic radio-frequency linearizer to achieve nonlinear compression of a low-charge (20 pC) electron beam, we obtain a sharp current profile possessing a few-femtosecond full width at half maximum temporal duration. A reverse undulator taper is applied to enable lasing only within the current spike, where longitudinal space charge forces induce an electron beam time-energy chirp. Simulations based on the Linac Coherent Light Source parameters show that stable single-spike x-ray pulses with a duration less thanmore » 200 attoseconds can be obtained.« less

Stability diagram for the forced Kuramoto model.

PubMed

Childs, Lauren M; Strogatz, Steven H

2008-12-01

We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an idealization of many phenomena in physics, chemistry, and biology in which mutual synchronization competes with forced synchronization. In other words, the oscillators in the population try to synchronize with one another while also trying to lock onto an external drive. Previous work on the forced Kuramoto model uncovered two main types of attractors, called forced entrainment and mutual entrainment, but the details of the bifurcations between them were unclear. Here we present a complete bifurcation analysis of the model for a special case in which the infinite-dimensional dynamics collapse to a two-dimensional system. Exact results are obtained for the locations of Hopf, saddle-node, and Takens-Bogdanov bifurcations. The resulting stability diagram bears a striking resemblance to that for the weakly nonlinear forced van der Pol oscillator.

Pattern Formation in Complex Fluids

NASA Astrophysics Data System (ADS)

Shelley, Michael

2000-03-01

Classical fluid instabilities -- such as the Saffman-Taylor instability in a Hele-Shaw cell -- are dramatically modified by using complex fluids. For example, polymeric liquids driven in a Hele-Shaw cell yield "dendritic" patterns with an apparent directional anisotropy. The dynamics of complex liquids can also lead to new instabilities and patterns, such as space-filling patterns formed by successive bucklings of growing "elastica" seen in the phase transition of a liquid crystalline material. Understanding such problems requires an interplay between physical modeling, mathematical analysis, and sophisticated nonlinear simulation. For the first problem, I will discuss a non-Newtonian version of Darcy's law for Hele-Shaw flow. This yields a free-boundary problem for the pattern formation, and requires the solution of a nonlinear elliptic equation in a time-dependent domain. This is pushing the development of adaptive grid methods that represent the geometry accurately and efficiently. Our simulations yield insight into how shear-thinning, as is evinced by polymeric liquids, can produce patterns reminiscent of experiment, with "dendritic fingers", side-branching, and reduced tip-splitting. In the second problem, a long filament in a smectic-A phase grows within an isotropic fluid. The splay deformation of the material gives this filament an elastic response. The macroscopic model describes the dynamics of a growing, elastic filament immersed in a Stokesian fluid. The model marries filament elasticity and tensile forces with a numerically tractable nonlocal slender-body theory. Analysis shows that growth of the filament, despite fluid drag, produces a buckling instability. When coupled to a nonlocal hydrodynamic self-interaction, our fully nonlinear simulations show that such instabilities iterate along the filament, and give "space-filling" patterns.

Automated reverse engineering of nonlinear dynamical systems

PubMed Central

Bongard, Josh; Lipson, Hod

2007-01-01

Complex nonlinear dynamics arise in many fields of science and engineering, but uncovering the underlying differential equations directly from observations poses a challenging task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate symbolic equations for a nonlinear coupled dynamical system directly from time series data. This method is applicable to any system that can be described using sets of ordinary nonlinear differential equations, and assumes that the (possibly noisy) time series of all variables are observable. Previous automated symbolic modeling approaches of coupled physical systems produced linear models or required a nonlinear model to be provided manually. The advance presented here is made possible by allowing the method to model each (possibly coupled) variable separately, intelligently perturbing and destabilizing the system to extract its less observable characteristics, and automatically simplifying the equations during modeling. We demonstrate this method on four simulated and two real systems spanning mechanics, ecology, and systems biology. Unlike numerical models, symbolic models have explanatory value, suggesting that automated “reverse engineering” approaches for model-free symbolic nonlinear system identification may play an increasing role in our ability to understand progressively more complex systems in the future. PMID:17553966

Automated reverse engineering of nonlinear dynamical systems.

PubMed

Bongard, Josh; Lipson, Hod

2007-06-12

Complex nonlinear dynamics arise in many fields of science and engineering, but uncovering the underlying differential equations directly from observations poses a challenging task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate symbolic equations for a nonlinear coupled dynamical system directly from time series data. This method is applicable to any system that can be described using sets of ordinary nonlinear differential equations, and assumes that the (possibly noisy) time series of all variables are observable. Previous automated symbolic modeling approaches of coupled physical systems produced linear models or required a nonlinear model to be provided manually. The advance presented here is made possible by allowing the method to model each (possibly coupled) variable separately, intelligently perturbing and destabilizing the system to extract its less observable characteristics, and automatically simplifying the equations during modeling. We demonstrate this method on four simulated and two real systems spanning mechanics, ecology, and systems biology. Unlike numerical models, symbolic models have explanatory value, suggesting that automated "reverse engineering" approaches for model-free symbolic nonlinear system identification may play an increasing role in our ability to understand progressively more complex systems in the future.

Inertial Force Coupling to Nonlinear Aeroelasticity of Flexible Wing Aircraft

NASA Technical Reports Server (NTRS)

Nguyen, Nhan T.; Ting, Eric

2016-01-01

This paper investigates the inertial force effect on nonlinear aeroelasticity of flexible wing aircraft. The geometric are nonlinearity due to rotational and tension stiffening. The effect of large bending deflection will also be investigated. Flutter analysis will be conducted for a truss-braced wing aircraft concept with tension stiffening and inertial force coupling.

Nonlinear Dynamics and Control of Flexible Structures

DTIC Science & Technology

1991-03-01

of which might be used for space applications. This project was a collaborative one involving structural, electrical and mechanical engineers and...methods for vibration analysis and new models to analyze chaotic dynamics in nonlinear structures with large deformations and friction forces. Finally... electrical and mechanical engineers and resulted in nine doctoral dissertations and two masters theses wholly or partially supported by this grant

Investigating the interaction between the homeostatic and circadian processes of sleep-wake regulation for the prediction of waking neurobehavioural performance

NASA Technical Reports Server (NTRS)

Van Dongen, Hans P A.; Dinges, David F.

2003-01-01

The two-process model of sleep regulation has been applied successfully to describe, predict, and understand sleep-wake regulation in a variety of experimental protocols such as sleep deprivation and forced desynchrony. A non-linear interaction between the homeostatic and circadian processes was reported when the model was applied to describe alertness and performance data obtained during forced desynchrony. This non-linear interaction could also be due to intrinsic non-linearity in the metrics used to measure alertness and performance, however. Distinguishing these possibilities would be of theoretical interest, but could also have important implications for the design and interpretation of experiments placing sleep at different circadian phases or varying the duration of sleep and/or wakefulness. Although to date no resolution to this controversy has been found, here we show that the issue can be addressed with existing data sets. The interaction between the homeostatic and circadian processes of sleep-wake regulation was investigated using neurobehavioural performance data from a laboratory experiment involving total sleep deprivation. The results provided evidence of an actual non-linear interaction between the homeostatic and circadian processes of sleep-wake regulation for the prediction of waking neurobehavioural performance.

Do Responses to Different Anthropogenic Forcings Add Linearly in Climate Models?

NASA Technical Reports Server (NTRS)

Marvel, Kate; Schmidt, Gavin A.; Shindell, Drew; Bonfils, Celine; LeGrande, Allegra N.; Nazarenko, Larissa; Tsigaridis, Kostas

2015-01-01

Many detection and attribution and pattern scaling studies assume that the global climate response to multiple forcings is additive: that the response over the historical period is statistically indistinguishable from the sum of the responses to individual forcings. Here, we use the NASA Goddard Institute for Space Studies (GISS) and National Center for Atmospheric Research Community Climate System Model (CCSM) simulations from the CMIP5 archive to test this assumption for multi-year trends in global-average, annual-average temperature and precipitation at multiple timescales. We find that responses in models forced by pre-computed aerosol and ozone concentrations are generally additive across forcings; however, we demonstrate that there are significant nonlinearities in precipitation responses to di?erent forcings in a configuration of the GISS model that interactively computes these concentrations from precursor emissions. We attribute these to di?erences in ozone forcing arising from interactions between forcing agents. Our results suggest that attribution to specific forcings may be complicated in a model with fully interactive chemistry and may provide motivation for other modeling groups to conduct further single-forcing experiments.

Do responses to different anthropogenic forcings add linearly in climate models?

DOE PAGES

Marvel, Kate; Schmidt, Gavin A.; Shindell, Drew; ...

2015-10-14

Many detection and attribution and pattern scaling studies assume that the global climate response to multiple forcings is additive: that the response over the historical period is statistically indistinguishable from the sum of the responses to individual forcings. Here, we use the NASA Goddard Institute for Space Studies (GISS) and National Center for Atmospheric Research Community Climate System Model (CCSM4) simulations from the CMIP5 archive to test this assumption for multi-year trends in global-average, annual-average temperature and precipitation at multiple timescales. We find that responses in models forced by pre-computed aerosol and ozone concentrations are generally additive across forcings. However,more » we demonstrate that there are significant nonlinearities in precipitation responses to different forcings in a configuration of the GISS model that interactively computes these concentrations from precursor emissions. We attribute these to differences in ozone forcing arising from interactions between forcing agents. Lastly, our results suggest that attribution to specific forcings may be complicated in a model with fully interactive chemistry and may provide motivation for other modeling groups to conduct further single-forcing experiments.« less

Computation of Nonlinear Hydrodynamic Loads on Floating Wind Turbines Using Fluid-Impulse Theory: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kok Yan Chan, G.; Sclavounos, P. D.; Jonkman, J.

2015-04-02

A hydrodynamics computer module was developed for the evaluation of the linear and nonlinear loads on floating wind turbines using a new fluid-impulse formulation for coupling with the FAST program. The recently developed formulation allows the computation of linear and nonlinear loads on floating bodies in the time domain and avoids the computationally intensive evaluation of temporal and nonlinear free-surface problems and efficient methods are derived for its computation. The body instantaneous wetted surface is approximated by a panel mesh and the discretization of the free surface is circumvented by using the Green function. The evaluation of the nonlinear loadsmore » is based on explicit expressions derived by the fluid-impulse theory, which can be computed efficiently. Computations are presented of the linear and nonlinear loads on the MIT/NREL tension-leg platform. Comparisons were carried out with frequency-domain linear and second-order methods. Emphasis was placed on modeling accuracy of the magnitude of nonlinear low- and high-frequency wave loads in a sea state. Although fluid-impulse theory is applied to floating wind turbines in this paper, the theory is applicable to other offshore platforms as well.« less

Comparison of free-piston Stirling engine model predictions with RE1000 engine test data

NASA Technical Reports Server (NTRS)

Tew, R. C., Jr.

1984-01-01

Predictions of a free-piston Stirling engine model are compared with RE1000 engine test data taken at NASA-Lewis Research Center. The model validation and the engine testing are being done under a joint interagency agreement between the Department of Energy's Oak Ridge National Laboratory and NASA-Lewis. A kinematic code developed at Lewis was upgraded to permit simulation of free-piston engine performance; it was further upgraded and modified at Lewis and is currently being validated. The model predicts engine performance by numerical integration of equations for each control volume in the working space. Piston motions are determined by numerical integration of the force balance on each piston or can be specified as Fourier series. In addition, the model Fourier analyzes the various piston forces to permit the construction of phasor force diagrams. The paper compares predicted and experimental values of power and efficiency and shows phasor force diagrams for the RE1000 engine displacer and piston. Further development plans for the model are also discussed.

A new energy transfer model for turbulent free shear flow

NASA Technical Reports Server (NTRS)

Liou, William W.-W.

1992-01-01

A new model for the energy transfer mechanism in the large-scale turbulent kinetic energy equation is proposed. An estimate of the characteristic length scale of the energy containing large structures is obtained from the wavelength associated with the structures predicted by a weakly nonlinear analysis for turbulent free shear flows. With the inclusion of the proposed energy transfer model, the weakly nonlinear wave models for the turbulent large-scale structures are self-contained and are likely to be independent flow geometries. The model is tested against a plane mixing layer. Reasonably good agreement is achieved. Finally, it is shown by using the Liapunov function method, the balance between the production and the drainage of the kinetic energy of the turbulent large-scale structures is asymptotically stable as their amplitude saturates. The saturation of the wave amplitude provides an alternative indicator for flow self-similarity.

A comparison between progressive extension method (PEM) and iterative method (IM) for magnetic field extrapolations in the solar atmosphere

NASA Technical Reports Server (NTRS)

Wu, S. T.; Sun, M. T.; Sakurai, Takashi

1990-01-01

This paper presents a comparison between two numerical methods for the extrapolation of nonlinear force-free magnetic fields, viz the Iterative Method (IM) and the Progressive Extension Method (PEM). The advantages and disadvantages of these two methods are summarized, and the accuracy and numerical instability are discussed. On the basis of this investigation, it is claimed that the two methods do resemble each other qualitatively.

Internal resonance of an elastic body levitated above high-Tc superconducting bulks

NASA Astrophysics Data System (ADS)

Kokuzawa, T.; Toshihiko, S.; Yoshizawa, M.

2010-06-01

In high-Tc superconducting magnetic levitation systems, levitated bodies can keep stable levitation with no contact and no control and thus their damping is very small. Thanks to these features, their applications to various apparatus are expected. However, on account of their small damping, the nonlinearity of electromagnetic levitation force can give notable effects upon motion of the levitated bodies. Therefore this nonlinearity must be taken into account to accurately analyze the dynamical behavior of the levitated bodies. Structures of such a levitated body can show elastic deformation if the large electromagnetic force acts on it. Therefore, we need to deal with the model as an elastic body. As mentioned above, nonlinear characteristics easily appear in this elastic vibration on account of the small damping. Especially when the ratio of the natural frequencies of the eigenmodes is integer, internal resonance can occur. This nonlinear resonance is derived from nonlinear interactions among the eigenmodes of the elastic levitated body. This kind of internal resonance of an elastic body appearing in high-Tc superconducting levitation systems has not been studied so far. This research especially deals with internal resonance of a beam supported at both its ends by electromagnetic forces acting on permanent magnets. The governing equation with the nonlinear boundary conditions for the dynamics of a levitated beam has been derived. Numerical results show internal resonance of the 1st mode and the 3rd mode. Experimental results are qualitatively in good agreement with numerical ones.

Generating Converged Accurate Free Energy Surfaces for Chemical Reactions with a Force-Matched Semiempirical Model.

PubMed

Kroonblawd, Matthew P; Pietrucci, Fabio; Saitta, Antonino Marco; Goldman, Nir

2018-04-10

We demonstrate the capability of creating robust density functional tight binding (DFTB) models for chemical reactivity in prebiotic mixtures through force matching to short time scale quantum free energy estimates. Molecular dynamics using density functional theory (DFT) is a highly accurate approach to generate free energy surfaces for chemical reactions, but the extreme computational cost often limits the time scales and range of thermodynamic states that can feasibly be studied. In contrast, DFTB is a semiempirical quantum method that affords up to a thousandfold reduction in cost and can recover DFT-level accuracy. Here, we show that a force-matched DFTB model for aqueous glycine condensation reactions yields free energy surfaces that are consistent with experimental observations of reaction energetics. Convergence analysis reveals that multiple nanoseconds of combined trajectory are needed to reach a steady-fluctuating free energy estimate for glycine condensation. Predictive accuracy of force-matched DFTB is demonstrated by direct comparison to DFT, with the two approaches yielding surfaces with large regions that differ by only a few kcal mol -1 .

Generating Converged Accurate Free Energy Surfaces for Chemical Reactions with a Force-Matched Semiempirical Model

DOE PAGES

Kroonblawd, Matthew P.; Pietrucci, Fabio; Saitta, Antonino Marco; ...

2018-03-15

Here, we demonstrate the capability of creating robust density functional tight binding (DFTB) models for chemical reactivity in prebiotic mixtures through force matching to short time scale quantum free energy estimates. Molecular dynamics using density functional theory (DFT) is a highly accurate approach to generate free energy surfaces for chemical reactions, but the extreme computational cost often limits the time scales and range of thermodynamic states that can feasibly be studied. In contrast, DFTB is a semiempirical quantum method that affords up to a thousandfold reduction in cost and can recover DFT-level accuracy. Here, we show that a force-matched DFTBmore » model for aqueous glycine condensation reactions yields free energy surfaces that are consistent with experimental observations of reaction energetics. Convergence analysis reveals that multiple nanoseconds of combined trajectory are needed to reach a steady-fluctuating free energy estimate for glycine condensation. Predictive accuracy of force-matched DFTB is demonstrated by direct comparison to DFT, with the two approaches yielding surfaces with large regions that differ by only a few kcal mol –1.« less

Generating Converged Accurate Free Energy Surfaces for Chemical Reactions with a Force-Matched Semiempirical Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kroonblawd, Matthew P.; Pietrucci, Fabio; Saitta, Antonino Marco

Here, we demonstrate the capability of creating robust density functional tight binding (DFTB) models for chemical reactivity in prebiotic mixtures through force matching to short time scale quantum free energy estimates. Molecular dynamics using density functional theory (DFT) is a highly accurate approach to generate free energy surfaces for chemical reactions, but the extreme computational cost often limits the time scales and range of thermodynamic states that can feasibly be studied. In contrast, DFTB is a semiempirical quantum method that affords up to a thousandfold reduction in cost and can recover DFT-level accuracy. Here, we show that a force-matched DFTBmore » model for aqueous glycine condensation reactions yields free energy surfaces that are consistent with experimental observations of reaction energetics. Convergence analysis reveals that multiple nanoseconds of combined trajectory are needed to reach a steady-fluctuating free energy estimate for glycine condensation. Predictive accuracy of force-matched DFTB is demonstrated by direct comparison to DFT, with the two approaches yielding surfaces with large regions that differ by only a few kcal mol –1.« less

Nonlinear problems in flight dynamics

NASA Technical Reports Server (NTRS)

Chapman, G. T.; Tobak, M.

1984-01-01

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

Dynamics of Oscillating and Rotating Liquid Drop using Electrostatic Levitator

NASA Astrophysics Data System (ADS)

Matsumoto, Satoshi; Awazu, Shigeru; Abe, Yutaka; Watanabe, Tadashi; Nishinari, Katsuhiro; Yoda, Shinichi

2006-11-01

In order to understand the nonlinear behavior of liquid drop with oscillatory and/or rotational motions, an experimental study was performed. The electrostatic levitator was employed to achieve liquid drop formation on ground. A liquid drop with about 3 mm in diameter was levitated. The oscillation of mode n=2 along the vertical axis was induced by an external electrostatic force. The oscillatory motions were observed to clarify the nonlinearities of oscillatory behavior. A relationship between amplitude and frequency shift was made clear and the effect of frequency shift on amplitude agreed well with the theory. The frequency shift became larger with increasing the amplitude of oscillation. To confirm the nonlinear effects, we modeled the oscillation by employing the mass-spring-damper system included the nonlinear term. The result indicates that the large-amplitude oscillation includes the effect of nonlinear oscillation. The sound pressure was imposed to rotate the liquid drop along a vertical axis by using a pair of acoustic transducers. The drop transited to the two lobed shape due to centrifugal force when nondimensional angular velocity exceeded to 0.58.

Hyperextended Cosmological Perturbation Theory: Predicting Nonlinear Clustering Amplitudes

NASA Astrophysics Data System (ADS)

Scoccimarro, Román; Frieman, Joshua A.

1999-07-01

We consider the long-standing problem of predicting the hierarchical clustering amplitudes Sp in the strongly nonlinear regime of gravitational evolution. N-body results for the nonlinear evolution of the bispectrum (the Fourier transform of the three-point density correlation function) suggest a physically motivated Ansatz that yields the strongly nonlinear behavior of the skewness, S3, starting from leading-order perturbation theory. When generalized to higher order (p>3) polyspectra or correlation functions, this Ansatz leads to a good description of nonlinear amplitudes in the strongly nonlinear regime for both scale-free and cold dark matter models. Furthermore, these results allow us to provide a general fitting formula for the nonlinear evolution of the bispectrum that interpolates between the weakly and strongly nonlinear regimes, analogous to previous expressions for the power spectrum.

Modeling and boundary force control of microcantilevers utilized in atomic force microscopy for cellular imaging and characterization

NASA Astrophysics Data System (ADS)

Eslami, Sohrab

This dissertation undertakes the theoretical and experimental developments microcantilevers utilized in Atomic Force Microscopy (AFM) with applications to cellular imaging and characterization. The capability of revealing the inhomogeneties or interior of ultra-small materials has been of most interest to many researchers. However, the fundamental concept of signal and image formation remains unexplored and not fully understood. For his, a semi-empirical nonlinear force model is proposed to show that virtual frequency generation, regarded as the simplest synthesized subsurface probe, occurs optimally when the force is tuned to the van der Waals form. This is the first-time observation of a novel theoretical dynamic multi-frequency force microscopy that has not been already reported. Owing to the broad applications of microcantilevers in the nanoscale imaging and microscopic techniques, there is an essential feeling to study and propose a comprehensive model of such systems. Therefore, in the theoretical part of this dissertation, a distributed-parameters representation modeling of the microcantilever along with a general interaction force comprising of two attractive and repulsive components with general amplitude and power terms is studied. This model is investigated in a general 2D Cartesian coordinate to consider the motions of the probe with a tip mass. There is an excitation at the microcantilever's base such that the end of the beam is subject to the proposed general force. These forces are very sensitive to the amplitude and power terms of these parts; on the other hand, atomic intermolecular force is a function of the distance such that this distance itself is also a function of the interaction force that will result in a nonlinear implicit equation. From a parametric study in the probe-sample excitation, it is shown that the predicted behavior of the generated difference-frequency oscillation amplitude agrees well with experimental measurements. Following the proposed Euler-Bernoulli model, a more comprehensive model is developed by modeling the probe dynamics and including the effects of the rotary inertia and shear deformation under the same proposed tip-sample interaction force. An extensive comparative study between the Euler-Bernoulli and Timoshenko beam assumptions is conducted for different conditions including different base-excitation amplitudes and higher modes. The results underline that the comprehensive Timoshenko model unveils the effects of the nonlinear interaction force better than the Euler-Bernoulli beam model. In addition to extensive modeling efforts on the microcantilever and its interaction with sample, an adaptive control framework is developed in order to make the microcantilever's tip follow a desired trajectory. This trajectory can further be considered as an important path acquired by the path planning techniques to manipulate the nanoparticles. There is a base excitation considered for this model and can be considered as an input force control to excite the probe by taking advantage of flexibility of the cantilever despite its complexity and under existence of the external nonlinear interaction forces between the tip and sample's surface. When building such complicated controller on top of the proposed comprehensive model, the results could be extended to study a macro-micro hybrid rigid-flexible model of a microrobot to mimic the realistic behavior of the MM3ARTM microrobot. The MM3ARTM microrobot is equipped with a piezoresistive layer which functions as a force sensor and is capable of measuring very slight forces as small as micro to nano-Newton. Two types of controllers are investigated for the case of the tip force control. Lyapunov-based PD and robust adaptive controllers are developed for this purpose and their performances and stabilities are compared. In the experimental part, a platform for performing the automated nanomanipulation and real-time cellular imaging is developed by integrating a microrobot, digital signal processor platform (dSPACERTM), computer, and a state-of-the-art light microscope. The closed-loop boundary force control framework is additionally developed for the autonomous in-situ applications. Since the incoming and outgoing signals of the piezoresistive microrobot are in the form of the electrical voltage and the string commands (ASCII code), respectively, an intuitive programming code for interfacing the MATLAB and dSPACE RTM has been written for the online quasi-data acquisition. As a result, the height of the corneal cell has been obtained and additionally, the microcantilever's tip force has been automatically controlled by taking advantage of the proposed control framework.

Effect of nonlinear electrostatic forces on the dynamic behaviour of a capacitive ring-based Coriolis Vibrating Gyroscope under severe shock

NASA Astrophysics Data System (ADS)

Chouvion, B.; McWilliam, S.; Popov, A. A.

2018-06-01

This paper investigates the dynamic behaviour of capacitive ring-based Coriolis Vibrating Gyroscopes (CVGs) under severe shock conditions. A general analytical model is developed for a multi-supported ring resonator by describing the in-plane ring response as a finite sum of modes of a perfect ring and the electrostatic force as a Taylor series expansion. It is shown that the supports can induce mode coupling and that mode coupling occurs when the shock is severe and the electrostatic forces are nonlinear. The influence of electrostatic nonlinearity is investigated by numerically simulating the governing equations of motion. For the severe shock cases investigated, when the electrode gap reduces by ∼ 60 % , it is found that three ring modes of vibration (1 θ, 2 θ and 3 θ) and a 9th order force expansion are needed to obtain converged results for the global shock behaviour. Numerical results when the 2 θ mode is driven at resonance indicate that electrostatic nonlinearity introduces mode coupling which has potential to reduce sensor performance under operating conditions. Under some circumstances it is also found that severe shocks can cause the vibrating response to jump to another stable state with much lower vibration amplitude. This behaviour is mainly a function of shock amplitude and rigid-body motion damping.

Closed-form solution for static pull-in voltage of electrostatically actuated clamped-clamped micro/nano beams under the effect of fringing field and van der Waals force

NASA Astrophysics Data System (ADS)

Bhojawala, V. M.; Vakharia, D. P.

2017-12-01

This investigation provides an accurate prediction of static pull-in voltage for clamped-clamped micro/nano beams based on distributed model. The Euler-Bernoulli beam theory is used adapting geometric non-linearity of beam, internal (residual) stress, van der Waals force, distributed electrostatic force and fringing field effects for deriving governing differential equation. The Galerkin discretisation method is used to make reduced-order model of the governing differential equation. A regime plot is presented in the current work for determining the number of modes required in reduced-order model to obtain completely converged pull-in voltage for micro/nano beams. A closed-form relation is developed based on the relationship obtained from curve fitting of pull-in instability plots and subsequent non-linear regression for the proposed relation. The output of regression analysis provides Chi-square (χ 2) tolerance value equals to 1  ×  10-9, adjusted R-square value equals to 0.999 29 and P-value equals to zero, these statistical parameters indicate the convergence of non-linear fit, accuracy of fitted data and significance of the proposed model respectively. The closed-form equation is validated using available data of experimental and numerical results. The relative maximum error of 4.08% in comparison to several available experimental and numerical data proves the reliability of the proposed closed-form equation.

Numerical assessment of factors affecting nonlinear internal waves in the South China Sea

NASA Astrophysics Data System (ADS)

Li, Qiang

2014-02-01

Nonlinear internal waves in the South China Sea exhibit diverse characteristics, which are associated with the complex conditions in Luzon Strait, such as the double ridge topography, the Earth’s rotation, variations in stratification and the background current induced by the Kuroshio. These effects are individually assessed using the MITgcm. The performance of the model is first validated through comparison with field observations. Because of in-phased ray interaction, the western ridge in Luzon Strait intensifies the semidiurnal internal tides generated from the eastern ridge, thus reinforcing the formation of nonlinear internal waves. However, the ray interaction for K1 forcing becomes anti-phased so that the K1 internal tide generation is reduced by the western ridge. Not only does the rotational dispersion suppress internal tide generation, it also inhibits nonlinear steepening and consequent internal solitary wave formation. As a joint effect, the double ridges and the rotational dispersion result in a paradoxical phenomenon: diurnal barotropic tidal forcing is dominant in Luzon Strait, but semidiurnal internal tides prevail in the deep basin of the South China Sea. The seasonal variation of the Kuroshio is consistent with the seasonal appearance of nonlinear internal waves in the South China Sea. The model results show that the westward inflow due to the Kuroshio intrusion reduces the amplitude of internal tides in the South China Sea, causing the weakening or absence of internal solitary waves. Winter stratification cannot account for the significant reduction of nonlinear internal waves, because the amplitude growth of internal tides due to increased thermocline tilting counteracts the reduced nonlinearity caused by thermocline deepening.

Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles

PubMed Central

Kononova, Olga; Snijder, Joost; Kholodov, Yaroslav; Marx, Kenneth A.; Wuite, Gijs J. L.; Roos, Wouter H.; Barsegov, Valeri

2016-01-01

The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams) modeling the particle structure. The beams’ deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F)-deformation (X) spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young’s moduli for Hertzian and bending deformations, and the structural damage dependent beams’ survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications. PMID:26821264

Recent advances in understanding secondary organic aerosol: Implications for global climate forcing

NASA Astrophysics Data System (ADS)

Shrivastava, Manish; Cappa, Christopher D.; Fan, Jiwen; Goldstein, Allen H.; Guenther, Alex B.; Jimenez, Jose L.; Kuang, Chongai; Laskin, Alexander; Martin, Scot T.; Ng, Nga Lee; Petaja, Tuukka; Pierce, Jeffrey R.; Rasch, Philip J.; Roldin, Pontus; Seinfeld, John H.; Shilling, John; Smith, James N.; Thornton, Joel A.; Volkamer, Rainer; Wang, Jian; Worsnop, Douglas R.; Zaveri, Rahul A.; Zelenyuk, Alla; Zhang, Qi

2017-06-01

Anthropogenic emissions and land use changes have modified atmospheric aerosol concentrations and size distributions over time. Understanding preindustrial conditions and changes in organic aerosol due to anthropogenic activities is important because these features (1) influence estimates of aerosol radiative forcing and (2) can confound estimates of the historical response of climate to increases in greenhouse gases. Secondary organic aerosol (SOA), formed in the atmosphere by oxidation of organic gases, represents a major fraction of global submicron-sized atmospheric organic aerosol. Over the past decade, significant advances in understanding SOA properties and formation mechanisms have occurred through measurements, yet current climate models typically do not comprehensively include all important processes. This review summarizes some of the important developments during the past decade in understanding SOA formation. We highlight the importance of some processes that influence the growth of SOA particles to sizes relevant for clouds and radiative forcing, including formation of extremely low volatility organics in the gas phase, acid-catalyzed multiphase chemistry of isoprene epoxydiols, particle-phase oligomerization, and physical properties such as volatility and viscosity. Several SOA processes highlighted in this review are complex and interdependent and have nonlinear effects on the properties, formation, and evolution of SOA. Current global models neglect this complexity and nonlinearity and thus are less likely to accurately predict the climate forcing of SOA and project future climate sensitivity to greenhouse gases. Efforts are also needed to rank the most influential processes and nonlinear process-related interactions, so that these processes can be accurately represented in atmospheric chemistry-climate models.

On the coupling of nonlinear macro-fiber composite piezoelectric cantilever dynamics with hydrodynamic loads

NASA Astrophysics Data System (ADS)

Tan, D.; Erturk, A.

2018-03-01

For bio-inspired, fish-like robotic propulsion, the Macro-Fiber Composite (MFC) piezoelectric technology offers noiseless actuation with a balance between actuation force and velocity response. However, internal nonlinear- ities within the MFCs, such as piezoelectric softening, geometric hardening, inertial softening, and nonlinear dissipation, couple with the hydrodynamic loading on the structure from the surrounding fluid. In the present work, we explore nonlinear actuation of MFC cantilevers underwater and develop a mathematical framework for modeling and analysis. In vacuo resonant actuation experiments are conducted for a set of MFC cantilevers of varying length to width aspect ratios to validate the structural model in the absence of fluid loading. These MFC cantilevers are then subjected to underwater resonant actuation experiments, and model simulations are compared with nonlinear experimental frequency response functions. It is observed that semi-empirical hydro- dynamic loads obtained from quasilinear experiments have to be modified to account for amplitude dependent added mass, and additional nonlinear hydrodynamic effects might be present, yielding qualitative differences in the resulting underwater frequency respones curves with increased excitation amplitude.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Rumeng; Wang, Lifeng, E-mail: walfe@nuaa.edu.cn

The nonlinear thermal vibration behavior of a single-walled carbon nanotube (SWCNT) is investigated by molecular dynamics simulation and a nonlinear, nonplanar beam model. Whirling motion with energy transfer between flexural motions is found in the free vibration of the SWCNT excited by the thermal motion of atoms where the geometric nonlinearity is significant. A nonlinear, nonplanar beam model considering the coupling in two vertical vibrational directions is presented to explain the whirling motion of the SWCNT. Energy in different vibrational modes is not equal even over a time scale of tens of nanoseconds, which is much larger than the periodmore » of fundamental natural vibration of the SWCNT at equilibrium state. The energy of different modes becomes equal when the time scale increases to the microsecond range.« less

Non-linear scale interactions in a forced turbulent boundary layer

NASA Astrophysics Data System (ADS)

Duvvuri, Subrahmanyam; McKeon, Beverley

2015-11-01

A strong phase-organizing influence exerted by a single synthetic large-scale spatio-temporal mode on directly-coupled (through triadic interactions) small scales in a turbulent boundary layer forced by a spatially-impulsive dynamic wall-roughness patch was previously demonstrated by the authors (J. Fluid Mech. 2015, vol. 767, R4). The experimental set-up was later enhanced to allow for simultaneous forcing of multiple scales in the flow. Results and analysis are presented from a new set of novel experiments where two distinct large scales are forced in the flow by a dynamic wall-roughness patch. The internal non-linear forcing of two other scales with triadic consistency to the artificially forced large scales, corresponding to sum and difference in wavenumbers, is dominated by the latter. This allows for a forcing-response (input-output) type analysis of the two triadic scales, and naturally lends itself to a resolvent operator based model (e.g. McKeon & Sharma, J. Fluid Mech. 2010, vol. 658, pp. 336-382) of the governing Navier-Stokes equations. The support of AFOSR (grant #FA 9550-12-1-0469, program manager D. Smith) is gratefully acknowledged.

Free energy landscapes of small peptides in an implicit solvent model determined by force-biased multicanonical molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Watanabe, Yukihisa S.; Kim, Jae Gil; Fukunishi, Yoshifumi; Nakamura, Haruki

2004-12-01

In order to investigate whether the implicit solvent (GB/SA) model could reproduce the free energy landscapes of peptides, the potential of mean forces (PMFs) of eight tripeptides was examined and compared with the PMFs of the explicit water model. The force-biased multicanonical molecular dynamics method was used for the enhanced conformational sampling. Consequently, the GB/SA model reproduced almost all the global and local minima in the PMFs observed with the explicit water model. However, the GB/SA model overestimated frequencies of the structures that are stabilized by intra-peptide hydrogen bonds.

Computational Methods for Nonlinear Dynamic Problems in Solid and Structural Mechanics: Progress in the Theory and Modeling of Friction and in the Control of Dynamical Systems with Frictional Forces

DTIC Science & Technology

1989-03-31

present several numerical studies designed to reveal the effect that some of the governing parameters have on the behavior of the system and, whenever...Friction and in the Control of Dynamical Systems with Frictional Forces FINAL TECHNICAL REPORT March 31, 1989 _ -- I -.7: .-.- - : AFOSR Contract F49620...SOLID AND STRUCTURAL MECHANICS: Progress in the Theory and Modeling of Friction and in the Control of Dynamical Systems with Frictional Forces I I * FINAL

Nonlinear focal shift beyond the geometrical focus in moderately focused acoustic beams.

PubMed

Camarena, Francisco; Adrián-Martínez, Silvia; Jiménez, Noé; Sánchez-Morcillo, Víctor

2013-08-01

The phenomenon of the displacement of the position along the axis of the pressure, intensity, and radiation force maxima of focused acoustic beams under increasing driving voltages (nonlinear focal shift) is studied for the case of a moderately focused beam. The theoretical and experimental results show the existence of this shift along the axis when the initial pressure in the transducer increases until the acoustic field reaches the fully developed nonlinear regime of propagation. Experimental data show that at high amplitudes and for moderate focusing, the position of the on-axis pressure maximum and radiation force maximum can surpass the geometrical focal length. On the contrary, the on-axis pressure minimum approaches the transducer under increasing driving voltages, increasing the distance between the positive and negative peak pressure in the beam. These results are in agreement with numerical KZK model predictions and the existed data of other authors and can be explained according to the effect of self-refraction characteristic of the nonlinear regime of propagation.

A nonlinear and fractional derivative viscoelastic model for rail pads in the dynamic analysis of coupled vehicle-slab track systems

NASA Astrophysics Data System (ADS)

Zhu, Shengyang; Cai, Chengbiao; Spanos, Pol D.

2015-01-01

A nonlinear and fractional derivative viscoelastic (FDV) model is used to capture the complex behavior of rail pads. It is implemented into the dynamic analysis of coupled vehicle-slab track (CVST) systems. The vehicle is treated as a multi-body system with 10 degrees of freedom, and the slab track is represented by a three layer Bernoulli-Euler beam model. The model for the rail pads is one dimensional, and the force-displacement relation is based on a superposition of elastic, friction, and FDV forces. This model takes into account the influences of the excitation frequency and of the displacement amplitude through a fractional derivative element, and a nonlinear friction element, respectively. The Grünwald representation of the fractional derivatives is employed to numerically solve the fractional and nonlinear equations of motion of the CVST system by means of an explicit integration algorithm. A dynamic analysis of the CVST system exposed to excitations of rail harmonic irregularities is carried out, pointing out the stiffness and damping dependence on the excitation frequency and the displacement amplitude. The analysis indicates that the dynamic stiffness and damping of the rail pads increase with the excitation frequency while they decrease with the displacement amplitude. Furthermore, comparisons between the proposed model and ordinary Kelvin model adopted for the CVST system, under excitations of welded rail joint irregularities and of random track irregularities, are conducted in the time domain as well as in the frequency domain. The proposed model is shown to possess several modeling advantages over the ordinary Kelvin element which overestimates both the stiffness and damping features at high frequencies.

Force and Moment Approach for Achievable Dynamics Using Nonlinear Dynamic Inversion

NASA Technical Reports Server (NTRS)

Ostroff, Aaron J.; Bacon, Barton J.

1999-01-01

This paper describes a general form of nonlinear dynamic inversion control for use in a generic nonlinear simulation to evaluate candidate augmented aircraft dynamics. The implementation is specifically tailored to the task of quickly assessing an aircraft's control power requirements and defining the achievable dynamic set. The achievable set is evaluated while undergoing complex mission maneuvers, and perfect tracking will be accomplished when the desired dynamics are achievable. Variables are extracted directly from the simulation model each iteration, so robustness is not an issue. Included in this paper is a description of the implementation of the forces and moments from simulation variables, the calculation of control effectiveness coefficients, methods for implementing different types of aerodynamic and thrust vectoring controls, adjustments for control effector failures, and the allocation approach used. A few examples illustrate the perfect tracking results obtained.

Bifurcation, chaos, and scan instability in dynamic atomic force microscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cantrell, John H., E-mail: john.h.cantrell@nasa.gov; Cantrell, Sean A., E-mail: scantrell@nlsanalytics.com

The dynamical motion at any point on the cantilever of an atomic force microscope can be expressed quite generally as a superposition of simple harmonic oscillators corresponding to the vibrational modes allowed by the cantilever shape. Central to the dynamical equations is the representation of the cantilever-sample interaction force as a polynomial expansion with coefficients that account for the interaction force “stiffness,” the cantilever-to-sample energy transfer, and the displacement amplitude of cantilever oscillation. Renormalization of the cantilever beam model shows that for a given cantilever drive frequency cantilever dynamics can be accurately represented by a single nonlinear mass-spring model withmore » frequency-dependent stiffness and damping coefficients [S. A. Cantrell and J. H. Cantrell, J. Appl. Phys. 110, 094314 (2011)]. Application of the Melnikov method to the renormalized dynamical equation is shown to predict a cascade of period doubling bifurcations with increasing cantilever drive force that terminates in chaos. The threshold value of the drive force necessary to initiate bifurcation is shown to depend strongly on the cantilever setpoint and drive frequency, effective damping coefficient, nonlinearity of the cantilever-sample interaction force, and the displacement amplitude of cantilever oscillation. The model predicts the experimentally observed interruptions of the bifurcation cascade for cantilevers of sufficiently large stiffness. Operational factors leading to the loss of image quality in dynamic atomic force microscopy are addressed, and guidelines for optimizing scan stability are proposed using a quantitative analysis based on system dynamical parameters and choice of feedback loop parameter.« less

Counterbalance of cutting force for advanced milling operations

NASA Astrophysics Data System (ADS)

Tsai, Nan-Chyuan; Shih, Li-Wen; Lee, Rong-Mao

2010-05-01

The goal of this work is to concurrently counterbalance the dynamic cutting force and regulate the spindle position deviation under various milling conditions by integrating active magnetic bearing (AMB) technique, fuzzy logic algorithm and an adaptive self-tuning feedback loop. Since the dynamics of milling system is highly determined by a few operation conditions, such as speed of spindle, cut depth and feedrate, therefore the dynamic model for cutting process is more appropriate to be constructed by experiments, instead of using theoretical approach. The experimental data, either for idle or cutting, are utilized to establish the database of milling dynamics so that the system parameters can be on-line estimated by employing the proposed fuzzy logic algorithm as the cutting mission is engaged. Based on the estimated milling system model and preset operation conditions, i.e., spindle speed, cut depth and feedrate, the current cutting force can be numerically estimated. Once the current cutting force can be real-time estimated, the corresponding compensation force can be exerted by the equipped AMB to counterbalance the cutting force, in addition to the spindle position regulation by feedback of spindle position. On the other hand, for the magnetic force is nonlinear with respect to the applied electric current and air gap, the characteristics of the employed AMB is investigated also by experiments and a nonlinear mathematic model, in terms of air gap between spindle and electromagnetic pole and coil current, is developed. At the end, the experimental simulations on realistic milling are presented to verify the efficacy of the fuzzy controller for spindle position regulation and the capability of the dynamic cutting force counterbalance.

Nonlinear quasi-static analysis of ultra-deep-water top-tension riser

NASA Astrophysics Data System (ADS)

Gao, Guanghai; Qiu, Xingqi; Wang, Ke; Liu, Jianjun

2017-09-01

In order to analyse the ultra-deep-water top-tension riser deformation in drilling conditions, a nonlinear quasi-static analysis model and equation are established. The riser in this model is regarded as a simply supported beam located in the vertical plane and is subjected to non-uniform axial and lateral forces. The model and the equation are solved by the finite element method. The effects of riser outside diameter, top tension ratio, sea surface current velocity, drag force coefficient, floating system drift distance and water depth on the riser lateral displacement are discussed. Results show that the riser lateral displacement increase with the increase in the sea surface current velocity, drag force coefficient and water depth, whereas decrease with the increase in the riser outside diameter, top tension ratio. The top tension ratio has an important influence on the riser deformation and it should be set reasonably under different circumstances. The drift of the floating system has a complicated influence on the riser deformation and it should avoid a large drift distance in the proceedings of drilling and production.

Relationships between nonlinear normal modes and response to random inputs

NASA Astrophysics Data System (ADS)

Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

2017-02-01

The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). This work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.

Statistical Neurodynamics.

NASA Astrophysics Data System (ADS)

Paine, Gregory Harold

1982-03-01

The primary objective of the thesis is to explore the dynamical properties of small nerve networks by means of the methods of statistical mechanics. To this end, a general formalism is developed and applied to elementary groupings of model neurons which are driven by either constant (steady state) or nonconstant (nonsteady state) forces. Neuronal models described by a system of coupled, nonlinear, first-order, ordinary differential equations are considered. A linearized form of the neuronal equations is studied in detail. A Lagrange function corresponding to the linear neural network is constructed which, through a Legendre transformation, provides a constant of motion. By invoking the Maximum-Entropy Principle with the single integral of motion as a constraint, a probability distribution function for the network in a steady state can be obtained. The formalism is implemented for some simple networks driven by a constant force; accordingly, the analysis focuses on a study of fluctuations about the steady state. In particular, a network composed of N noninteracting neurons, termed Free Thinkers, is considered in detail, with a view to interpretation and numerical estimation of the Lagrange multiplier corresponding to the constant of motion. As an archetypical example of a net of interacting neurons, the classical neural oscillator, consisting of two mutually inhibitory neurons, is investigated. It is further shown that in the case of a network driven by a nonconstant force, the Maximum-Entropy Principle can be applied to determine a probability distribution functional describing the network in a nonsteady state. The above examples are reconsidered with nonconstant driving forces which produce small deviations from the steady state. Numerical studies are performed on simplified models of two physical systems: the starfish central nervous system and the mammalian olfactory bulb. Discussions are given as to how statistical neurodynamics can be used to gain a better understanding of the behavior of these systems.

A free energy-based surface tension force model for simulation of multiphase flows by level-set method

NASA Astrophysics Data System (ADS)

Yuan, H. Z.; Chen, Z.; Shu, C.; Wang, Y.; Niu, X. D.; Shu, S.

2017-09-01

In this paper, a free energy-based surface tension force (FESF) model is presented for accurately resolving the surface tension force in numerical simulation of multiphase flows by the level set method. By using the analytical form of order parameter along the normal direction to the interface in the phase-field method and the free energy principle, FESF model offers an explicit and analytical formulation for the surface tension force. The only variable in this formulation is the normal distance to the interface, which can be substituted by the distance function solved by the level set method. On one hand, as compared to conventional continuum surface force (CSF) model in the level set method, FESF model introduces no regularized delta function, due to which it suffers less from numerical diffusions and performs better in mass conservation. On the other hand, as compared to the phase field surface tension force (PFSF) model, the evaluation of surface tension force in FESF model is based on an analytical approach rather than numerical approximations of spatial derivatives. Therefore, better numerical stability and higher accuracy can be expected. Various numerical examples are tested to validate the robustness of the proposed FESF model. It turns out that FESF model performs better than CSF model and PFSF model in terms of accuracy, stability, convergence speed and mass conservation. It is also shown in numerical tests that FESF model can effectively simulate problems with high density/viscosity ratio, high Reynolds number and severe topological interfacial changes.

On the Boltzmann relation in a cold magnetized plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nasi, L.; Raimbault, J.-L.

A systematic and exact comparison between the forces acting on magnetized electrons in a current-free plasma is considered within a fluid model. We show that the Boltzmann relation is fulfilled in the drift-diffusion approximation when (h{sub i}/h{sub e})(1+h{sub e}{sup 2})/(1+h{sub i}{sup 2})<<1 where h{sub e} (or h{sub i}) is the ratio of the electron (or ion) cyclotron to the collision frequency. When the nonlinear inertia terms are taken into account, the previous criterion is too rough and must be modified. In particular it is proved that the Boltzmann relation is not uniformly valid in the plasma. The case of boundedmore » plasmas where the electron temperature must be determined self-consistently is discussed in detail.« less

Enhanced model of gear transmission dynamics for condition monitoring applications: Effects of torque, friction and bearing clearance

NASA Astrophysics Data System (ADS)

Fernandez-del-Rincon, A.; Garcia, P.; Diez-Ibarbia, A.; de-Juan, A.; Iglesias, M.; Viadero, F.

2017-02-01

Gear transmissions remain as one of the most complex mechanical systems from the point of view of noise and vibration behavior. Research on gear modeling leading to the obtaining of models capable of accurately reproduce the dynamic behavior of real gear transmissions has spread out the last decades. Most of these models, although useful for design stages, often include simplifications that impede their application for condition monitoring purposes. Trying to filling this gap, the model presented in this paper allows us to simulate gear transmission dynamics including most of these features usually neglected by the state of the art models. This work presents a model capable of considering simultaneously the internal excitations due to the variable meshing stiffness (including the coupling among successive tooth pairs in contact, the non-linearity linked with the contacts between surfaces and the dissipative effects), and those excitations consequence of the bearing variable compliance (including clearances or pre-loads). The model can also simulate gear dynamics in a realistic torque dependent scenario. The proposed model combines a hybrid formulation for calculation of meshing forces with a non-linear variable compliance approach for bearings. Meshing forces are obtained by means of a double approach which combines numerical and analytical aspects. The methodology used provides a detailed description of the meshing forces, allowing their calculation even when gear center distance is modified due to shaft and bearing flexibilities, which are unavoidable in real transmissions. On the other hand, forces at bearing level were obtained considering a variable number of supporting rolling elements, depending on the applied load and clearances. Both formulations have been developed and applied to the simulation of the vibration of a sample transmission, focusing the attention on the transmitted load, friction meshing forces and bearing preloads.

Impact of implant support on mandibular free-end base removable partial denture: theoretical study.

PubMed

Oh, Won-suk; Oh, Tae-Ju; Park, Ju-mi

2016-02-01

This study investigated the impact of implant support on the development of shear force and bending moment in mandibular free-end base removable partial dentures (RPDs). Three theoretical test models of unilateral mandibular free-end base RPDs were constructed to represent the base of tooth replacement, as follows: Model 1: first and second molars (M1 and M2); Model 2: second premolar (P2), M1, and M2; and Model 3: first premolar (P1), P2, M1, and M2. The implant support located either at M1 or M2 sites. The occlusal loading was concentrated at each replacement tooth to calculate the stress resultants developed in the RPD models using the free-body diagrams of shear force and bending moment. There was a trend of reduction in the peak shear force and bending moment when the base was supported by implant. However, the degree of reduction varied with the location of implant support. The moment reduced by 76% in Model 1, 58% in Model 2, and 42% in Model 3, when the implant location shifted from M1 to M2 sites. The shear forces and bending moments subjected to mandibular free-end base RPDs were found to decrease with the addition of implant support. However, the impact of implant support varied with the location of implant in this theoretical study. © 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

NASA Technical Reports Server (NTRS)

Murthy, V. R.; Shultz, Louis A.

1994-01-01

The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.

The nonlinear response in a baroclinic model to stationary forcings

NASA Technical Reports Server (NTRS)

Roads, J. O.

1982-01-01

Wave-zonal-flow interaction studies demonstrated that stratospheric warnings and blocking may be described by the same basic mechanisms although different results occurred for different horizontal scales.

FLARE ENERGY BUILD-UP IN A DECAYING ACTIVE REGION NEAR A CORONAL HOLE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Su Yingna; Van Ballegooijen, Adriaan; Golub, Leon

2009-10-10

A B1.7 two-ribbon flare occurred in a highly non-potential decaying active region near a coronal hole at 10:00 UT on 2008 May 17. This flare is 'large' in the sense that it involves the entire region, and it is associated with both a filament eruption and a coronal mass ejection. We present multi-wavelength observations from EUV (TRACE, STEREO/EUVI), X-rays (Hinode/XRT), and Halpha (THEMIS, BBSO) prior to, during and after the flare. Prior to the flare, the region contained two filaments. The long J-shaped sheared loops corresponding to the southern filament were evolved from two short loop systems, which happened aroundmore » 22:00 UT after a filament eruption on May 16. Formation of highly sheared loops in the southeastern part of the region was observed by STEREO 8 hr before the flare. We also perform nonlinear force-free field (NLFFF) modeling for the region at two times prior to the flare, using the flux rope insertion method. The models include the non-force-free effect of magnetic buoyancy in the photosphere. The best-fit NLFFF models show good fit to observations both in the corona (X-ray and EUV loops) and chromosphere (Halpha filament). We find that the horizontal fields in the photosphere are relatively insensitive to the present of flux ropes in the corona. The axial flux of the flux rope in the NLFFF model on May 17 is twice that on May 16, and the model on May 17 is only marginally stable. We also find that the quasi-circular flare ribbons are associated with the separatrix between open and closed fields. This observation and NLFFF modeling suggest that this flare may be triggered by the reconnection at the null point on the separatrix surface.« less

Time-Accurate Simulations and Acoustic Analysis of Slat Free-Shear-Layer. Part 2

NASA Technical Reports Server (NTRS)

Khorrami, Mehdi R.; Singer, Bart A.; Lockard, David P.

2002-01-01

Unsteady computational simulations of a multi-element, high-lift configuration are performed. Emphasis is placed on accurate spatiotemporal resolution of the free shear layer in the slat-cove region. The excessive dissipative effects of the turbulence model, so prevalent in previous simulations, are circumvented by switching off the turbulence-production term in the slat cove region. The justifications and physical arguments for taking such a step are explained in detail. The removal of this excess damping allows the shear layer to amplify large-scale structures, to achieve a proper non-linear saturation state, and to permit vortex merging. The large-scale disturbances are self-excited, and unlike our prior fully turbulent simulations, no external forcing of the shear layer is required. To obtain the farfield acoustics, the Ffowcs Williams and Hawkings equation is evaluated numerically using the simulated time-accurate flow data. The present comparison between the computed and measured farfield acoustic spectra shows much better agreement for the amplitude and frequency content than past calculations. The effect of the angle-of-attack on the slat's flow features radiated acoustic field are also simulated presented.

Adaptive regularization network based neural modeling paradigm for nonlinear adaptive estimation of cerebral evoked potentials.

PubMed

Zhang, Jian-Hua; Böhme, Johann F

2007-11-01

In this paper we report an adaptive regularization network (ARN) approach to realizing fast blind separation of cerebral evoked potentials (EPs) from background electroencephalogram (EEG) activity with no need to make any explicit assumption on the statistical (or deterministic) signal model. The ARNs are proposed to construct nonlinear EEG and EP signal models. A novel adaptive regularization training (ART) algorithm is proposed to improve the generalization performance of the ARN. Two adaptive neural modeling methods based on the ARN are developed and their implementation and performance analysis are also presented. The computer experiments using simulated and measured visual evoked potential (VEP) data have shown that the proposed ARN modeling paradigm yields computationally efficient and more accurate VEP signal estimation owing to its intrinsic model-free and nonlinear processing characteristics.

A Nonlinear Interactions Approximation Model for Large-Eddy Simulation

NASA Astrophysics Data System (ADS)

Haliloglu, Mehmet U.; Akhavan, Rayhaneh

2003-11-01

A new approach to LES modelling is proposed based on direct approximation of the nonlinear terms \\overlineu_iuj in the filtered Navier-Stokes equations, instead of the subgrid-scale stress, τ_ij. The proposed model, which we call the Nonlinear Interactions Approximation (NIA) model, uses graded filters and deconvolution to parameterize the local interactions across the LES cutoff, and a Smagorinsky eddy viscosity term to parameterize the distant interactions. A dynamic procedure is used to determine the unknown eddy viscosity coefficient, rendering the model free of adjustable parameters. The proposed NIA model has been applied to LES of turbulent channel flows at Re_τ ≈ 210 and Re_τ ≈ 570. The results show good agreement with DNS not only for the mean and resolved second-order turbulence statistics but also for the full (resolved plus subgrid) Reynolds stress and turbulence intensities.

On framing potential features of SWCNTs and MWCNTs in mixed convective flow

NASA Astrophysics Data System (ADS)

Hayat, T.; Ullah, Siraj; Khan, M. Ijaz; Alsaedi, A.

2018-03-01

Our target in this research article is to elaborate the characteristics of Darcy-Forchheimer relation in carbon-water nanoliquid flow induced by impermeable stretched cylinder. Energy expression is modeled through viscous dissipation and nonlinear thermal radiation. Application of appropriate transformations yields nonlinear ODEs through nonlinear PDEs. Shooting technique is adopted for the computations of nonlinear ODEs. Importance of influential variables for velocity and thermal fields is elaborated graphically. Moreover rate of heat transfer and drag force are calculated and demonstrated through Tables. Our analysis reports that velocity is higher for ratio of rate constant and buoyancy factor when compared with porosity and volume fraction.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krasnobaeva, L. A., E-mail: kla1983@mail.ru; Siberian State Medical University Moscowski Trakt 2, Tomsk, 634050; Shapovalov, A. V.

Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on dynamics local conformational perturbations (kink) propagating along the DNA molecule is investigated. Such waves have an important role in the regulation of important biological processes in living systems at the molecular level. As a dynamic model of DNA was used a modified sine-Gordon equation, simulating the rotational oscillations of bases in one of the chains DNA. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the frameworkmore » of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker– Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum. Within the formalism of the Fokker–Planck equation, the influence of nonstationary external force, random force, and dissipation effects on the kink dynamics is investigated in the sine–Gordon model. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the framework of the well-known McLaughlin and Scott energy approach. The corresponding Fokker–Planck equation for the momentum distribution function coincides with the equation describing the Ornstein–Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker–Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum.« less

Nonlinear analysis of a rotor-bearing system using describing functions

NASA Astrophysics Data System (ADS)

Maraini, Daniel; Nataraj, C.

2018-04-01

This paper presents a technique for modelling the nonlinear behavior of a rotor-bearing system with Hertzian contact, clearance, and rotating unbalance. The rotor-bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain. The describing function captures the relationship between the amplitude of the fundamental input to the nonlinearity and the fundamental output. The frequency response is constructed for various values of the clearance parameter, and the results show the presence of a jump resonance in bearings with both clearance and preload. Nonlinear hardening type behavior is observed in the case with clearance and softening behavior is observed for the case with preload. Numerical integration is also carried out on the nonlinear equations of motion showing strong agreement with the approximate solution. This work could easily be extended to include additional nonlinearities that arise from defects, providing a powerful diagnostic tool.

Quantum and semiclassical physics behind ultrafast optical nonlinearity in the midinfrared: the role of ionization dynamics within the field half cycle.

PubMed

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.

Accurate Characterization of Free Carrier Refraction in InP (Postprint)

DTIC Science & Technology

2010-02-01

COMMAND UNITED STATES AIR FORCE i REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 The public reporting burden for this collection of...amplitude, A(x, y, t), through a third order nonlinear medium along the z direction using only the slowly varying amplitude approximation. ∂A ∂z = i 2k0... I , is given as γ. While included for completeness, since the pulse duration studied here is on the order of nanoseconds, NLR due to γ is much weaker

Effects of the horizontal component of the Earth's rotation on wave propagation on an f-plane

NASA Astrophysics Data System (ADS)

Beckmann, Aike; Diebels, Stefan

Scaling arguments are used to show that effects due to the horizontal component of the Coriolis force should be taken into account as a first correction to the traditional hydrostatic theory, before frequency dispersion due to vertical acceleration and nonlinearity are included. It is shown analytically that wave propagation of the f--plane becomes anisotropic and that amphidromic systems do not exist in their usual definition. Another important consequence is the existence of free wave solutions at subinertial frequencies.

Swinging atwood machine. Far- and near-resonance region

NASA Astrophysics Data System (ADS)

Roy Chowdhury, A.; Debnath, M.

1988-11-01

The swinging Atwood machine, a prototype nonlinear dynamical system, is analyzed following an idea of Bogoliubov and Mitropolsky. A series solution is found for the radial and angular displacement as functions of time. The analysis is repeated in the resonance case, when the frequency of the driving force maintains a fixed ratio to that of the free motion. The condition of resonance requires the mass ratio μ to be equal to 2 j 2-1, where j is an integer not equal to one.

Modeling dynamic interactions and coherence between marine zooplankton and fishes linked to environmental variability

NASA Astrophysics Data System (ADS)

Liu, Hui; Fogarty, Michael J.; Hare, Jonathan A.; Hsieh, Chih-hao; Glaser, Sarah M.; Ye, Hao; Deyle, Ethan; Sugihara, George

2014-03-01

The dynamics of marine fishes are closely related to lower trophic levels and the environment. Quantitatively understanding ecosystem dynamics linking environmental variability and prey resources to exploited fishes is crucial for ecosystem-based management of marine living resources. However, standard statistical models typically grounded in the concept of linear system may fail to capture the complexity of ecological processes. We have attempted to model ecosystem dynamics using a flexible, nonparametric class of nonlinear forecasting models. We analyzed annual time series of four environmental indices, 22 marine copepod taxa, and four ecologically and commercially important fish species during 1977 to 2009 on Georges Bank, a highly productive and intensively studied area of the northeast U.S. continental shelf ecosystem. We examined the underlying dynamic features of environmental indices and copepods, quantified the dynamic interactions and coherence with fishes, and explored the potential control mechanisms of ecosystem dynamics from a nonlinear perspective. We found: (1) the dynamics of marine copepods and environmental indices exhibiting clear nonlinearity; (2) little evidence of complex dynamics across taxonomic levels of copepods; (3) strong dynamic interactions and coherence between copepods and fishes; and (4) the bottom-up forcing of fishes and top-down control of copepods coexisting as target trophic levels vary. These findings highlight the nonlinear interactions among ecosystem components and the importance of marine zooplankton to fish populations which point to two forcing mechanisms likely interactively regulating the ecosystem dynamics on Georges Bank under a changing environment.

Observation of soliton compression in silicon photonic crystals

PubMed Central

Blanco-Redondo, A.; Husko, C.; Eades, D.; Zhang, Y.; Li, J.; Krauss, T.F.; Eggleton, B.J.

2014-01-01

Solitons are nonlinear waves present in diverse physical systems including plasmas, water surfaces and optics. In silicon, the presence of two photon absorption and accompanying free carriers strongly perturb the canonical dynamics of optical solitons. Here we report the first experimental demonstration of soliton-effect pulse compression of picosecond pulses in silicon, despite two photon absorption and free carriers. Here we achieve compression of 3.7 ps pulses to 1.6 ps with <10 pJ energy. We demonstrate a ~1-ps free-carrier-induced pulse acceleration and show that picosecond input pulses are critical to these observations. These experiments are enabled by a dispersion-engineered slow-light photonic crystal waveguide and an ultra-sensitive frequency-resolved electrical gating technique to detect the ultralow energies in the nanostructured device. Strong agreement with a nonlinear Schrödinger model confirms the measurements. These results further our understanding of nonlinear waves in silicon and open the way to soliton-based functionalities in complementary metal-oxide-semiconductor-compatible platforms. PMID:24423977

Time-domain parameter identification of aeroelastic loads by forced-vibration method for response of flexible structures subject to transient wind

NASA Astrophysics Data System (ADS)

Cao, Bochao

Slender structures representing civil, mechanical and aerospace systems such as long-span bridges, high-rise buildings, stay cables, power-line cables, high light mast poles, crane-booms and aircraft wings could experience vortex-induced and buffeting excitations below their design wind speeds and divergent self-excited oscillations (flutter) beyond a critical wind speed because these are flexible. Traditional linear aerodynamic theories that are routinely applied for their response prediction are not valid in the galloping, or near-flutter regime, where large-amplitude vibrations could occur and during non-stationary and transient wind excitations that occur, for example, during hurricanes, thunderstorms and gust fronts. The linear aerodynamic load formulation for lift, drag and moment are expressed in terms of aerodynamic functions in frequency domain that are valid for straight-line winds which are stationary or weakly-stationary. Application of the frequency domain formulation is restricted from use in the nonlinear and transient domain because these are valid for linear models and stationary wind. The time-domain aerodynamic force formulations are suitable for finite element modeling, feedback-dependent structural control mechanism, fatigue-life prediction, and above all modeling of transient structural behavior during non-stationary wind phenomena. This has motivated the developing of time-domain models of aerodynamic loads that are in parallel to the existing frequency-dependent models. Parameters defining these time-domain models can be now extracted from wind tunnel tests, for example, the Rational Function Coefficients defining the self-excited wind loads can be extracted using section model tests using the free vibration technique. However, the free vibration method has some limitations because it is difficult to apply at high wind speeds, in turbulent wind environment, or on unstable cross sections with negative aerodynamic damping. In the current research, new algorithms were developed based on forced vibration technique for direct extraction of the Rational Functions. The first of the two algorithms developed uses the two angular phase lag values between the measured vertical or torsional displacement and the measured aerodynamic lift and moment produced on the section model subject to forced vibration to identify the Rational Functions. This algorithm uses two separate one-degree-of-freedom tests (vertical or torsional) to identify all the four Rational Functions or corresponding Rational Function Coefficients for a two degrees-of-freedom (DOF) vertical-torsional vibration model. It was applied to a streamlined section model and the results compared well with those obtained from earlier free vibration experiment. The second algorithm that was developed is based on direct least squares method. It uses all the data points of displacements and aerodynamic lift and moment instead of phase lag values for more accurate estimates. This algorithm can be used for one-, two- and three-degree-of-freedom motions. A two-degree-of-freedom forced vibration system was developed and the algorithm was shown to work well for both streamlined and bluff section models. The uniqueness of the second algorithms lies in the fact that it requires testing the model at only two wind speeds for extraction of all four Rational Functions. The Rational Function Coefficients that were extracted for a streamlined section model using the two-DOF Least Squares algorithm were validated in a separate wind tunnel by testing a larger scaled model subject to straight-line, gusty and boundary-layer wind.

A nonlinear cochlear model with the outer hair cell piezoelectric activity

NASA Astrophysics Data System (ADS)

Jiang, Xiaoai; Grosh, Karl

2003-10-01

In this paper we present a simple cochlear model which captures the most important aspect of nonlinearity in the cochlea-the nonlinearity caused by the piezoelectric-like activity of outer hair cells and the variable conductance of the outer hair cell stereocilia. A one-dimensional long-wave model is built to simulate the dynamic response of the fluid-loaded basilar membrane. The basilar membrane is simulated as isolated linear oscillators along the cochlear length, and its motion is coupled with the fluid pressure and the nonlinear force produced by the outer hair cells. As the basilar membrane moves, the fluid shears stereocilia, and the resulting ion flow changes the transmembrane potential of the outer hair cells and subsequently their length, leading to further movement of the basilar membrane. The piezoelectric-like activity of the outer hair cell is simulated by a current source, and stereocilia motion is modeled as a varying conductance that changes as the basilar membrane moves. A solution in the time domain will be presented. [Work supported by NIH.

Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

NASA Astrophysics Data System (ADS)

Mansoori Kermani, Maryam; Dehestani, Maryam

2018-06-01

We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell-Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.

Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

NASA Astrophysics Data System (ADS)

Mansoori Kermani, Maryam; Dehestani, Maryam

2018-03-01

We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell-Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.

Which way will the circulation shift in a changing climate? Possible nonlinearity of extratropical cloud feedbacks

NASA Astrophysics Data System (ADS)

Tandon, Neil F.; Cane, Mark A.

2017-06-01

In a suite of idealized experiments with the Community Atmospheric Model version 3 coupled to a slab ocean, we show that the atmospheric circulation response to CO2 increase is sensitive to extratropical cloud feedback that is potentially nonlinear. Doubling CO2 produces a poleward shift of the Southern Hemisphere (SH) midlatitude jet that is driven primarily by cloud shortwave feedback and modulated by ice albedo feedback, in agreement with earlier studies. More surprisingly, for CO2 increases smaller than 25 %, the SH jet shifts equatorward. Nonlinearities are also apparent in the Northern Hemisphere, but with less zonal symmetry. Baroclinic instability theory and climate feedback analysis suggest that as the CO2 forcing amplitude is reduced, there is a transition from a regime in which cloud and circulation changes are largely decoupled to a regime in which they are highly coupled. In the dynamically coupled regime, there is an apparent cancellation between cloud feedback due to warming and cloud feedback due to the shifting jet, and this allows the ice albedo feedback to dominate in the high latitudes. The extent to which dynamical coupling effects exceed thermodynamic forcing effects is strongly influenced by cloud microphysics: an alternate model configuration with slightly increased cloud liquid (LIQ) produces poleward jet shifts regardless of the amplitude of CO2 forcing. Altering the cloud microphysics also produces substantial spread in the circulation response to CO2 doubling: the LIQ configuration produces a poleward SH jet shift approximately twice that produced under the default configuration. Analysis of large ensembles of the Canadian Earth System Model version 2 demonstrates that nonlinear, cloud-coupled jet shifts are also possible in comprehensive models. We still expect a poleward trend in SH jet latitude for timescales on which CO2 increases by more than 25 %. But on shorter timescales, our results give good reason to expect significant equatorward deviations. We also discuss the implications for understanding the circulation response to small external forcings from other sources, such as the solar cycle.

[Forced Oscillations of DNA Bases].

PubMed

Yakushevich, L V; Krasnobaeva, L A

2016-01-01

This paper presents the results of the studying of forced angular oscillations of the DNA bases with the help of the mathematical model consisting of two coupled nonlinear differential equations that take into account the effects of dissipation and the influence of an external periodic field. The calculation results are illustrated for sequence of gene encoding interferon alpha 17 (IFNA 17).

FAST TRACK PAPER: Non-iterative multiple-attenuation methods: linear inverse solutions to non-linear inverse problems - II. BMG approximation

NASA Astrophysics Data System (ADS)

Ikelle, Luc T.; Osen, Are; Amundsen, Lasse; Shen, Yunqing

2004-12-01

The classical linear solutions to the problem of multiple attenuation, like predictive deconvolution, τ-p filtering, or F-K filtering, are generally fast, stable, and robust compared to non-linear solutions, which are generally either iterative or in the form of a series with an infinite number of terms. These qualities have made the linear solutions more attractive to seismic data-processing practitioners. However, most linear solutions, including predictive deconvolution or F-K filtering, contain severe assumptions about the model of the subsurface and the class of free-surface multiples they can attenuate. These assumptions limit their usefulness. In a recent paper, we described an exception to this assertion for OBS data. We showed in that paper that a linear and non-iterative solution to the problem of attenuating free-surface multiples which is as accurate as iterative non-linear solutions can be constructed for OBS data. We here present a similar linear and non-iterative solution for attenuating free-surface multiples in towed-streamer data. For most practical purposes, this linear solution is as accurate as the non-linear ones.

Predominant nonlinear atmospheric response to meridional shift of the Gulf Stream path from the WRF atmospheric model simulations

NASA Astrophysics Data System (ADS)

Seo, H.; Kwon, Y. O.; Joyce, T. M.

2016-02-01

A remarkably strong nonlinear behavior of the atmospheric circulation response to North Atlantic SST anomalies (SSTA) is revealed from a set of large-ensemble, high-resolution, and hemispheric-scale Weather Research and Forecasting (WRF) model simulations. The model is forced with the SSTA associated with meridional shift of the Gulf Stream (GS) path, constructed from a lag regression of the winter SST on a GS Index from observation. Analysis of the systematic set of experiments with SSTAs of varied amplitudes and switched signs representing various GS-shift scenarios provides unique insights into mechanism for emergence and evolution of transient and equilibrium response of atmospheric circulation to extratropical SSTA. Results show that, independent of sign of the SSTA, the equilibrium response is characterized by an anomalous trough over the North Atlantic Ocean and the Western Europe concurrent with enhanced storm track, increased rainfall, and reduced blocking days. To the north of the anomalous low, an anomalous ridge emerges over the Greenland, Iceland, and Norwegian Seas accompanied by weakened storm track, reduced rainfall and increased blocking days. This nonlinear component of the total response dominates the weak and oppositely signed linear response that is directly forced by the SSTA, yielding an anomalous ridge (trough) downstream of the warm (cold) SSTA. The amplitude of the linear response is proportional to that of the SSTA, but this is masked by the overwhelmingly strong nonlinear behavior showing no clear correspondence to the SSTA amplitude. The nonlinear pattern emerges 3-4 weeks after the model initialization in November and reaches its first peak amplitude in December/January. It appears that altered baroclinic wave activity due to the GS SSTA in November lead to low-frequency height responses in December/January through transient eddy vorticity flux convergence.

Analytical investigation of the faster-is-slower effect with a simplified phenomenological model

NASA Astrophysics Data System (ADS)

Suzuno, K.; Tomoeda, A.; Ueyama, D.

2013-11-01

We investigate the mechanism of the phenomenon called the “faster-is-slower”effect in pedestrian flow studies analytically with a simplified phenomenological model. It is well known that the flow rate is maximized at a certain strength of the driving force in simulations using the social force model when we consider the discharge of self-driven particles through a bottleneck. In this study, we propose a phenomenological and analytical model based on a mechanics-based modeling to reveal the mechanism of the phenomenon. We show that our reduced system, with only a few degrees of freedom, still has similar properties to the original many-particle system and that the effect comes from the competition between the driving force and the nonlinear friction from the model. Moreover, we predict the parameter dependences on the effect from our model qualitatively, and they are confirmed numerically by using the social force model.

Nonlinear system identification of smart structures under high impact loads

NASA Astrophysics Data System (ADS)

Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon

2013-05-01

The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure-MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure-MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes.

Flutter Sensitivity to Boundary Layer Thickness, Structural Damping, and Static Pressure Differential for a Shuttle Tile Overlay Repair Concept

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Bartels, Robert E.

2009-01-01

This paper examines the aeroelastic stability of an on-orbit installable Space Shuttle patch panel. CFD flutter solutions were obtained for thick and thin boundary layers at a free stream Mach number of 2.0 and several Mach numbers near sonic speed. The effect of structural damping on these flutter solutions was also examined, and the effect of structural nonlinearities associated with in-plane forces in the panel was considered on the worst case linear flutter solution. The results of the study indicated that adequate flutter margins exist for the panel at the Mach numbers examined. The addition of structural damping improved flutter margins as did the inclusion of nonlinear effects associated with a static pressure difference across the panel.

Rogue Wave Modes for the Long Wave-Short Wave Resonance and the Derivative Nonlinear Schrödinger Models

NASA Astrophysics Data System (ADS)

Chan, Hiu Ning; Chow, Kwok Wing; Kedziora, David Jacob; Grimshaw, Roger Hamilton James; Ding, Edwin

2014-11-01

Rogue waves are unexpectedly large displacements of the water surface and will obviously pose threat to maritime activities. Recently, the formation of rogue waves is correlated with the onset of modulation instabilities of plane waves of the system. The long wave-short wave resonance and the derivative nonlinear Schrödinger models are considered. They are relevant in a two-layer fluid and a fourth order perturbation expansion of free surface waves respectively. Analytical solutions of rogue wave modes for the two models are derived by the Hirota bilinear method. Properties and amplitudes of these rogue wave modes are investigated. Conditions for modulation instability of the plane waves are shown to be precisely the requirements for the occurrence of rogue waves. In contrast with the nonlinear Schrödinger equation, rogue wave modes for the derivative nonlinear Schrödinger model exist even if the dispersion and cubic nonlinearity are of the opposite signs, provided that a sufficiently strong self-steepening nonlinearity is present. Extensions to the coupled case (multiple waveguides) will be discussed. This work is partially supported by the Research Grants Council General Research Fund Contract HKU 711713E.

Simulation of noisy dynamical system by Deep Learning

NASA Astrophysics Data System (ADS)

Yeo, Kyongmin

2017-11-01

Deep learning has attracted huge attention due to its powerful representation capability. However, most of the studies on deep learning have been focused on visual analytics or language modeling and the capability of the deep learning in modeling dynamical systems is not well understood. In this study, we use a recurrent neural network to model noisy nonlinear dynamical systems. In particular, we use a long short-term memory (LSTM) network, which constructs internal nonlinear dynamics systems. We propose a cross-entropy loss with spatial ridge regularization to learn a non-stationary conditional probability distribution from a noisy nonlinear dynamical system. A Monte Carlo procedure to perform time-marching simulations by using the LSTM is presented. The behavior of the LSTM is studied by using noisy, forced Van der Pol oscillator and Ikeda equation.

Assessment of current state of the art in modeling techniques and analysis methods for large space structures

NASA Technical Reports Server (NTRS)

Noor, A. K.

1983-01-01

Advances in continuum modeling, progress in reduction methods, and analysis and modeling needs for large space structures are covered with specific attention given to repetitive lattice trusses. As far as continuum modeling is concerned, an effective and verified analysis capability exists for linear thermoelastic stress, birfurcation buckling, and free vibration problems of repetitive lattices. However, application of continuum modeling to nonlinear analysis needs more development. Reduction methods are very effective for bifurcation buckling and static (steady-state) nonlinear analysis. However, more work is needed to realize their full potential for nonlinear dynamic and time-dependent problems. As far as analysis and modeling needs are concerned, three areas are identified: loads determination, modeling and nonclassical behavior characteristics, and computational algorithms. The impact of new advances in computer hardware, software, integrated analysis, CAD/CAM stems, and materials technology is also discussed.

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

NASA Astrophysics Data System (ADS)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

Moving boundary problems for a rarefied gas: Spatially one-dimensional case

NASA Astrophysics Data System (ADS)

Tsuji, Tetsuro; Aoki, Kazuo

2013-10-01

Unsteady flows of a rarefied gas in a full space caused by an oscillation of an infinitely wide plate in its normal direction are investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation. The paper aims at showing properties and difficulties inherent to moving boundary problems in kinetic theory of gases using a simple one-dimensional setting. More specifically, the following two problems are considered: (Problem I) the plate starts a forced harmonic oscillation (forced motion); (Problem II) the plate, which is subject to an external restoring force obeying Hooke’s law, is displaced from its equilibrium position and released (free motion). The physical interest in Problem I lies in the propagation of nonlinear acoustic waves in a rarefied gas, whereas that in Problem II in the decay rate of the oscillation of the plate. An accurate numerical method, which is capable of describing singularities caused by the oscillating plate, is developed on the basis of the method of characteristics and is applied to the two problems mentioned above. As a result, the unsteady behavior of the solution, such as the propagation of discontinuities and some weaker singularities in the molecular velocity distribution function, are clarified. Some results are also compared with those based on the existing method.

Voluntary EMG-to-force estimation with a multi-scale physiological muscle model

PubMed Central

2013-01-01

Background EMG-to-force estimation based on muscle models, for voluntary contraction has many applications in human motion analysis. The so-called Hill model is recognized as a standard model for this practical use. However, it is a phenomenological model whereby muscle activation, force-length and force-velocity properties are considered independently. Perreault reported Hill modeling errors were large for different firing frequencies, level of activation and speed of contraction. It may be due to the lack of coupling between activation and force-velocity properties. In this paper, we discuss EMG-force estimation with a multi-scale physiology based model, which has a link to underlying crossbridge dynamics. Differently from the Hill model, the proposed method provides dual dynamics of recruitment and calcium activation. Methods The ankle torque was measured for the plantar flexion along with EMG measurements of the medial gastrocnemius (GAS) and soleus (SOL). In addition to Hill representation of the passive elements, three models of the contractile parts have been compared. Using common EMG signals during isometric contraction in four able-bodied subjects, torque was estimated by the linear Hill model, the nonlinear Hill model and the multi-scale physiological model that refers to Huxley theory. The comparison was made in normalized scale versus the case in maximum voluntary contraction. Results The estimation results obtained with the multi-scale model showed the best performances both in fast-short and slow-long term contraction in randomized tests for all the four subjects. The RMS errors were improved with the nonlinear Hill model compared to linear Hill, however it showed limitations to account for the different speed of contractions. Average error was 16.9% with the linear Hill model, 9.3% with the modified Hill model. In contrast, the error in the multi-scale model was 6.1% while maintaining a uniform estimation performance in both fast and slow contractions schemes. Conclusions We introduced a novel approach that allows EMG-force estimation based on a multi-scale physiology model integrating Hill approach for the passive elements and microscopic cross-bridge representations for the contractile element. The experimental evaluation highlights estimation improvements especially a larger range of contraction conditions with integration of the neural activation frequency property and force-velocity relationship through cross-bridge dynamics consideration. PMID:24007560

Evaluating the far-field sound of a turbulent jet with one-way Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Pickering, Ethan; Rigas, Georgios; Towne, Aaron; Colonius, Tim

2017-11-01

The one-way Navier-Stokes (OWNS) method has shown promising ability to predict both near field coherent structures (i.e. wave packets) and far field acoustics of turbulent jets while remaining computationally efficient through implementation of a spatial marching scheme. Considering the speed and relative accuracy of OWNS, a predictive model for various jet configurations may be conceived and applied for noise control. However, there still remain discrepancies between OWNS and large eddy simulation (LES) databases which may be linked to the previous neglect of nonlinear forcing. Therefore, to better predict wave packets and far field acoustics, this study investigates the effect of nonlinear forcing terms derived from high-fidelity LES databases. The results of the nonlinear forcings are evaluated for several azimuthal modes and frequencies, as well as compared to LES derived acoustics using spectral proper orthogonal decomposition (SPOD). This research was supported by the Department of Defense (DoD) through the Office of Naval Research (Grant No. N00014-16-1-2445) and the National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.

Nonlinear core deflection in injection molding

NASA Astrophysics Data System (ADS)

Poungthong, P.; Giacomin, A. J.; Saengow, C.; Kolitawong, C.; Liao, H.-C.; Tseng, S.-C.

2018-05-01

Injection molding of thin slender parts is often complicated by core deflection. This deflection is caused by molten plastics race tracking through the slit between the core and the rigid cavity wall. The pressure of this liquid exerts a lateral force of the slender core causing the core to bend, and this bending is governed by a nonlinear fifth order ordinary differential equation for the deflection that is not directly in the position along the core. Here we subject this differential equation to 6 sets of boundary conditions, corresponding to 6 commercial core constraints. For each such set of boundary conditions, we develop an explicit approximate analytical solution, including both a linear term and a nonlinear term. By comparison with finite difference solutions, we find our new analytical solutions to be accurate. We then use these solutions to derive explicit analytical approximations for maximum deflections and for the core position of these maximum deflections. Our experiments on the base-gated free-tip boundary condition agree closely with our new explicit approximate analytical solution.

Electrokinetic instability in microchannel ferrofluid/water co-flows

PubMed Central

Song, Le; Yu, Liandong; Zhou, Yilong; Antao, Asher Reginald; Prabhakaran, Rama Aravind; Xuan, Xiangchun

2017-01-01

Electrokinetic instability refers to unstable electric field-driven disturbance to fluid flows, which can be harnessed to promote mixing for various electrokinetic microfluidic applications. This work presents a combined numerical and experimental study of electrokinetic ferrofluid/water co-flows in microchannels of various depths. Instability waves are observed at the ferrofluid and water interface when the applied DC electric field is beyond a threshold value. They are generated by the electric body force that acts on the free charge induced by the mismatch of ferrofluid and water electric conductivities. A nonlinear depth-averaged numerical model is developed to understand and simulate the interfacial electrokinetic behaviors. It considers the top and bottom channel walls’ stabilizing effects on electrokinetic flow through the depth averaging of three-dimensional transport equations in a second-order asymptotic analysis. This model is found accurate to predict both the observed electrokinetic instability patterns and the measured threshold electric fields for ferrofluids of different concentrations in shallow microchannels. PMID:28406228