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A derivation is presented which gives both the nonlinear dynamic inflow model and the perturbation dynamic inflow model in a general coordinate system. The perturbation model includes perturbations in hub motions, in skew angle, and in yaw angle. The governing equations may be switched to their dimensional forms prior to application.
Optical nonlinearities and transient dynamics of Fe doped GaN (GaN:Fe) were studied by Z-scan and pump-probe with phase object techniques under picosecond and nanosecond at 532 nm. From the pump-probe results, an additional decay pathway subsequent to two photon excitation was observed due to the carrier trapping of Fe{sup 3+}/Fe{sup 2+} deep acceptors. The trapping state in the band gap results in a pronounced modulation to nonlinear responses of GaN:Fe compared to that of undoped GaN. With an effective three-level model as well as carrier trapping effect we described the photo-physical dynamics in GaN:Fe unambiguously.
Presented in this paper are the results of three nonlinear computer programs, KRASH, ACTION and DYCAST used to analyze the dynamic response of a twin-engine, low-wing airplane section subjected to a 8.38 m/s (27.5 ft/s) vertical impact velocity crash condition. This impact condition simulates the vertical sink rate in a shallow aircraft landing or takeoff accident. The three distinct analysis techniques for nonlinear dynamic response of aircraft structures are briefly examined and compared versus each other and the experimental data. The report contains brief descriptions of the three computer programs, the respective aircraft section mathematical models, pertinent data from the experimental test performed at NASA Langley, and a comparison of the analyses versus test results. Cost and accuracy comparisons between the three analyses are made to illustrate the possible uses of the different nonlinear programs and their future potential.
The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.
Bifurcation theory is used to analyze the nonlinear dynamic stability characteristics of an aircraft subject to single-degree-of-freedom. The requisite moment of the aerodynamic forces in the equations of motion is shown to be representable in a form equivalent to the response to finite amplitude oscillations. It is shown how this information can be deduced from the case of infinitesimal-amplitude oscillations. The bifurcation theory analysis reveals that when the bifurcation parameter is increased beyond a critical value at which the aerodynamic damping vanishes, new solutions representing finite amplitude periodic motions bifurcate from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solutions are stable or unstable. For the pitching motion of flat-plate airfoils flying at supersonic/hypersonic speed and for oscillation of flaps at transonic speed, the bifurcation is subcritical, implying either the exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop.
The dynamic stability of formation geometry is vital to the design of large scale multiagent systems. In this paper, we probe into the structure of the formation system matrix using the Laplacian of a digraph to develop several fundamental theoretical results on the stability of formation geometry. Our key-results include the integration of the graph Laplacian into linear and weak-nonlinear relative dynamics, the development of several new coordinate transformations that expose the influence of the graph Laplacian matrix on the control laws of the agents, and the use of direct adaptive control as stability restoring devices. We also develop two fundamental results that provide upper bounds for stable formation evolution under nonlinear perturbations of agent dynamics. Finally, we use an illustrative example to demonstrate our theoretical findings.
A method of discrete modeling is presented that effectively isolates steady state model accuracy from dynamic model accuracy. The steady state model may be generated from the engine design equations with any desired degree of accuracy. The dynamic model is generated by applying a step disturbance of a manipulated variable to an open loop engine simulation. The sampled response of the variable is combined with the steady state model's response to form a set of weighting factors. These weighting factors are then used to weight past values of the manipulated variable, thus forming the dynamic model. The method is used to estimate various TF30-P-3 engine variables. A dynamic trim function is developed to compensate for the dynamic nonlinearities of the variables as well as for inaccuracies in dynamic definition. The trim function is shown to be realted to the square root of the sum of the squares of the weighting factors obtained at various engine operating conditions. Finally, the estimation of variables without dynamic modeling is discussed.
A methodology is described for the development of flight test trajectory control laws based on singular perturbation methodology and nonlinear dynamic modeling. The control design methodology is applied to a detailed nonlinear six degree-of-freedom simulation of the F-15 and results for a level accelerations, pushover/pullup maneuver, zoom and pushover maneuver, excess thrust windup turn, constant thrust windup turn, and a constant dynamic pressure/constant load factor trajectory are presented.
In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of nonlinear system identification techniques, namely SINDy, weak-SINDy, and the occupation kernel method. Under the assumption that the dynamics are a finite linear combination of a set of basis functions, these methods establish a linear system to recover coefficients. We illuminate the structural similarities between these techniques and establish a projection property for the weak-SINDy technique. Following the overview, we analyze the error of surrogate models generated by a simplified version of weak-SINDy. In particular, under the assumption of boundedness of a composition operator given by the solution, we show that (i) the surrogate dynamics converges towards the true dynamics and (ii) the solution of the surrogate model is reasonably close to the true solution. Finally, as an application, we discuss the use of a combination of weak-SINDy surrogate modeling and proper orthogonal decomposition (POD) to build a surrogate model for partial differential equations (PDEs).
Considering the increase of disruptive variable renewable energy penetration into the power grid, this article focuses on the investigation of a multiobjective and dynamic real-time optimization framework to address the cycling of large-scale power plants under renewable penetration. In this framework, a parallelized particle swarm optimization step is first performed to generate feasible initial points. Then, a multiobjective and dynamic real-time optimization formulation generates optimal trajectories. Further, the benefit of predictive capability is investigated for the dynamic component, which introduces the novel nonlinear multiobjective and dynamic real-time predictive optimization approach. Two multiobjective formulations to obtain Pareto front optimal in real time are explored: the modified Tchebycheff-based weighted metric and ϵ-constraint methods. Economic and environmental objectives are considered in this study. A novel topical discussion on the intersection of dynamic real-time optimization with model predictive control is also presented. The developed framework is successfully applied to a baseload coal-fired power plant with postcombustion CO 2 capture. Results indicate that the approach can be deployed for a large-scale system if automatic differentiation, model reduction, and parallelization are adopted to improve computational tractability, with computational improvement up to 120-folds after performing these steps. Finally, market and carbon policies showed an impact on the optimal compromise between the objectives with an additional 63 ton of CO 2 captured under favorable market conditions.
Significance Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity exponential in the evolution time, we give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to nonlinear and forcing terms and the solution does not decay too rapidly. We also establish a lower bound showing that differential equations with sufficiently weak dissipation have worst-case complexity exponential in time, giving an almost tight classification of the quantum complexity of simulating nonlinear dynamics. Furthermore, numerical results for the Burgers equation suggest that our algorithm may potentially address complex nonlinear phenomena even in regimes with weaker dissipation.
The nonlinear dynamics of intra- and inter-spine interaction models of alpha-helical proteins is investigated by proposing a Hamiltonian using the first quantized operators. Hamilton's equations of motion are derived, and the dynamics is studied by constructing the trajectories and phase space plots in both cases. The phase space plots display a chaotic behaviour in the dynamics, which opens questions about the relationship between the chaos and exciton-exciton and exciton-phonon interactions. This is verified by plotting the Lyapunov characteristic exponent curves.
The origin and influence of finite-size effects on the nonlinear dynamics of space charge stored by multilayer graphene on a ferroelectric and resistivity of graphene channel were analyzed. In this paper, we develop a self-consistent approach combining the solution of electrostatic problems with the nonlinear Landau-Khalatnikov equations for a ferroelectric. The size-dependent behaviors are governed by the relations between the thicknesses of multilayer graphene, ferroelectric film, and the dielectric layer. The appearance of charge and electroresistance hysteresis loops and their versatility stem from the interplay of polarization reversal dynamics and its incomplete screening in an alternating electric field. These features are mostly determined by the dielectric layer thickness. The derived analytical expressions for electric fields and space-charge-density distribution in a multilayer system enable knowledge-driven design of graphene-on-ferroelectric heterostructures with advanced performance. We further investigate the effects of spatially nonuniform ferroelectric domain structures on the graphene layers’ conductivity and predict its dramatic increase under the transition from multi- to single-domain state in a ferroelectric. Finally, this intriguing effect can open possibilities for the graphene-based sensors and explore the underlying physical mechanisms in the operation of graphene field-effect transistor with ferroelectric gating.
Abstract Extreme El Niño events have outsized global impacts and control the El Niño Southern Oscillation (ENSO) warm/cold phases asymmetries. Yet, a consensus regarding the relative contributions of atmospheric and oceanic nonlinearities to their genesis remains elusive. Here, we isolate the contribution of oceanic nonlinearities by conducting paired experiments forced with opposite wind stress anomalies in an oceanic general circulation model, which realistically simulates extreme El Niño events and oceanic nonlinearities thought to contribute to ENSO skewness (Tropical Instability Waves (TIWs), Nonlinear Dynamical Heating (NDH)). Our findings indicate a weak contribution of oceanic nonlinearities to extreme El Niño events in the eastern Pacific, owing to compensatory effects between lateral (NDH and TIWs) and vertical processes. These results hold across different vertical mixing schemes and modifications of the upper‐ocean heat budget mixed layer criterion. Our study reinforces previous research underscoring the pivotal role of atmospheric nonlinearities in shaping extreme El Niño events.
Collective excitations presenting nonlinear dynamics are fundamental phenomena with broad applications. A prime example is nonlinear optics, where diverse frequency mixing processes are central to communication, sensing, wavelength conversion, and attosecond physics. Leveraging recent progress in van der Waals magnetic semiconductors, we demonstrate nonlinear opto-magnonic coupling by presenting exciton states dressed by up to 20 harmonics of magnons, resulting from their nonlinearities, in the layered antiferromagnetic semiconductor CrSBr. We also create tunable optical side bands from sum- and difference-frequency generation between two optically bright magnon modes under symmetry breaking magnetic fields. Moreover, the observed difference-frequency generation mode can be continuously tuned into resonance with one of the fundamental magnons, resulting in parametric amplification of magnons. These findings realize the modulation of the optical frequency exciton with the extreme nonlinearity of magnons at microwave frequencies, which could find applications in magnonics and hybrid quantum systems, and provide new avenues for implementing opto-magnonic devices.
A symposium honoring Mark Cane and his role in the advancement of climate science was held at the Lamont-Doherty Earth Observatory of Columbia University in October 2014. Over 150 climate scientists from the United States and abroad participated in the program. First day of the symposium began with a retrospective session on the development of tropical ocean?atmosphere interactions, equatorial wave dynamics, and a theory for ENSO. Steve Zebiak, David Halpern and Ed Sarachik, each provided historical context on the advances during the 1960s to 1980s that led to ENSO prediction. The first session of the second day was devoted to outstanding issues in paleoclimate dynamics. David Battisti. He revisited the question of why the ocean overturning circulation was situated in the Atlantic and not the Pacific, reviewing various hypotheses for why the Atlantic is the saltier ocean. The final session of the symposium highlighted the perspectives of climate dynamics from some key contributors to the field. Tim Palmer discussed nonlinear dynamics and regime shifts as a paradigm for understanding climate changes.
NASA Langley Research Center is engaged in an extensive research and development task aimed at providing the general aviation industry with reliable crashworthy airframe design technology. This paper describes the full-scale crash tests of general aviation airplanes being conducted to generate data on simulated crashes and to study the nonlinear dynamic behavior of aircraft structures. Analytical techniques under development for predicting nonlinear behavior of general airframe structures under crash-loading conditions are also described. Data are presented from the full-scale crash tests as well as comparison of analytical predictions with experimental results on some simplified structures.
The stability characteristics of dynamic dissipative compensators are investigated for multibody flexible space structures having nonlinear dynamics. The problem addressed is that of proving asymptotic stability of dynamic dissipative compensators. The stability proof uses the Liapunov approach and exploits the inherent passivity of such systems. For such systems these compensators are shown to be robust to parametric uncertainties and unmodeled dynamics. The results are applicable to a large class of structures such as flexible space structures with articulated flexible appendages.