An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints [Continuum modeling of elasto-plastic media with multiple embedded nonlinearly-compliant joints

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

Hurley, R. C.; Vorobiev, O. Y.; Ezzedine, S. M.

Here, we present a numerical method for modeling the mechanical effects of nonlinearly-compliant joints in elasto-plastic media. The method uses a series of strain-rate and stress update algorithms to determine joint closure, slip, and solid stress within computational cells containing multiple “embedded” joints. This work facilitates efficient modeling of nonlinear wave propagation in large spatial domains containing a large number of joints that affect bulk mechanical properties. We implement the method within the massively parallel Lagrangian code GEODYN-L and provide verification and examples. We highlight the ability of our algorithms to capture joint interactions and multiple weakness planes within individualmore » computational cells, as well as its computational efficiency. We also discuss the motivation for developing the proposed technique: to simulate large-scale wave propagation during the Source Physics Experiments (SPE), a series of underground explosions conducted at the Nevada National Security Site (NNSS).« less

An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints [Continuum modeling of elasto-plastic media with multiple embedded nonlinearly-compliant joints

DOE PAGES

Hurley, R. C.; Vorobiev, O. Y.; Ezzedine, S. M.

2017-04-06

Here, we present a numerical method for modeling the mechanical effects of nonlinearly-compliant joints in elasto-plastic media. The method uses a series of strain-rate and stress update algorithms to determine joint closure, slip, and solid stress within computational cells containing multiple “embedded” joints. This work facilitates efficient modeling of nonlinear wave propagation in large spatial domains containing a large number of joints that affect bulk mechanical properties. We implement the method within the massively parallel Lagrangian code GEODYN-L and provide verification and examples. We highlight the ability of our algorithms to capture joint interactions and multiple weakness planes within individualmore » computational cells, as well as its computational efficiency. We also discuss the motivation for developing the proposed technique: to simulate large-scale wave propagation during the Source Physics Experiments (SPE), a series of underground explosions conducted at the Nevada National Security Site (NNSS).« less

Extension of a nonlinear systems theory to general-frequency unsteady transonic aerodynamic responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1993-01-01

A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.

Computational models for the nonlinear analysis of reinforced concrete plates

NASA Technical Reports Server (NTRS)

Hinton, E.; Rahman, H. H. A.; Huq, M. M.

1980-01-01

A finite element computational model for the nonlinear analysis of reinforced concrete solid, stiffened and cellular plates is briefly outlined. Typically, Mindlin elements are used to model the plates whereas eccentric Timoshenko elements are adopted to represent the beams. The layering technique, common in the analysis of reinforced concrete flexural systems, is incorporated in the model. The proposed model provides an inexpensive and reasonably accurate approach which can be extended for use with voided plates.

Inferring Nonlinear Neuronal Computation Based on Physiologically Plausible Inputs

PubMed Central

McFarland, James M.; Cui, Yuwei; Butts, Daniel A.

2013-01-01

The computation represented by a sensory neuron's response to stimuli is constructed from an array of physiological processes both belonging to that neuron and inherited from its inputs. Although many of these physiological processes are known to be nonlinear, linear approximations are commonly used to describe the stimulus selectivity of sensory neurons (i.e., linear receptive fields). Here we present an approach for modeling sensory processing, termed the Nonlinear Input Model (NIM), which is based on the hypothesis that the dominant nonlinearities imposed by physiological mechanisms arise from rectification of a neuron's inputs. Incorporating such ‘upstream nonlinearities’ within the standard linear-nonlinear (LN) cascade modeling structure implicitly allows for the identification of multiple stimulus features driving a neuron's response, which become directly interpretable as either excitatory or inhibitory. Because its form is analogous to an integrate-and-fire neuron receiving excitatory and inhibitory inputs, model fitting can be guided by prior knowledge about the inputs to a given neuron, and elements of the resulting model can often result in specific physiological predictions. Furthermore, by providing an explicit probabilistic model with a relatively simple nonlinear structure, its parameters can be efficiently optimized and appropriately regularized. Parameter estimation is robust and efficient even with large numbers of model components and in the context of high-dimensional stimuli with complex statistical structure (e.g. natural stimuli). We describe detailed methods for estimating the model parameters, and illustrate the advantages of the NIM using a range of example sensory neurons in the visual and auditory systems. We thus present a modeling framework that can capture a broad range of nonlinear response functions while providing physiologically interpretable descriptions of neural computation. PMID:23874185

Optimization-Based Inverse Identification of the Parameters of a Concrete Cap Material Model

NASA Astrophysics Data System (ADS)

Král, Petr; Hokeš, Filip; Hušek, Martin; Kala, Jiří; Hradil, Petr

2017-10-01

Issues concerning the advanced numerical analysis of concrete building structures in sophisticated computing systems currently require the involvement of nonlinear mechanics tools. The efforts to design safer, more durable and mainly more economically efficient concrete structures are supported via the use of advanced nonlinear concrete material models and the geometrically nonlinear approach. The application of nonlinear mechanics tools undoubtedly presents another step towards the approximation of the real behaviour of concrete building structures within the framework of computer numerical simulations. However, the success rate of this application depends on having a perfect understanding of the behaviour of the concrete material models used and having a perfect understanding of the used material model parameters meaning. The effective application of nonlinear concrete material models within computer simulations often becomes very problematic because these material models very often contain parameters (material constants) whose values are difficult to obtain. However, getting of the correct values of material parameters is very important to ensure proper function of a concrete material model used. Today, one possibility, which permits successful solution of the mentioned problem, is the use of optimization algorithms for the purpose of the optimization-based inverse material parameter identification. Parameter identification goes hand in hand with experimental investigation while it trying to find parameter values of the used material model so that the resulting data obtained from the computer simulation will best approximate the experimental data. This paper is focused on the optimization-based inverse identification of the parameters of a concrete cap material model which is known under the name the Continuous Surface Cap Model. Within this paper, material parameters of the model are identified on the basis of interaction between nonlinear computer simulations, gradient based and nature inspired optimization algorithms and experimental data, the latter of which take the form of a load-extension curve obtained from the evaluation of uniaxial tensile test results. The aim of this research was to obtain material model parameters corresponding to the quasi-static tensile loading which may be further used for the research involving dynamic and high-speed tensile loading. Based on the obtained results it can be concluded that the set goal has been reached.

Efficient computational nonlinear dynamic analysis using modal modification response technique

NASA Astrophysics Data System (ADS)

Marinone, Timothy; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2012-08-01

Generally, structural systems contain nonlinear characteristics in many cases. These nonlinear systems require significant computational resources for solution of the equations of motion. Much of the model, however, is linear where the nonlinearity results from discrete local elements connecting different components together. Using a component mode synthesis approach, a nonlinear model can be developed by interconnecting these linear components with highly nonlinear connection elements. The approach presented in this paper, the Modal Modification Response Technique (MMRT), is a very efficient technique that has been created to address this specific class of nonlinear problem. By utilizing a Structural Dynamics Modification (SDM) approach in conjunction with mode superposition, a significantly smaller set of matrices are required for use in the direct integration of the equations of motion. The approach will be compared to traditional analytical approaches to make evident the usefulness of the technique for a variety of test cases.

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.

Method of performing computational aeroelastic analyses

NASA Technical Reports Server (NTRS)

Silva, Walter A. (Inventor)

2011-01-01

Computational aeroelastic analyses typically use a mathematical model for the structural modes of a flexible structure and a nonlinear aerodynamic model that can generate a plurality of unsteady aerodynamic responses based on the structural modes for conditions defining an aerodynamic condition of the flexible structure. In the present invention, a linear state-space model is generated using a single execution of the nonlinear aerodynamic model for all of the structural modes where a family of orthogonal functions is used as the inputs. Then, static and dynamic aeroelastic solutions are generated using computational interaction between the mathematical model and the linear state-space model for a plurality of periodic points in time.

Noise Estimation in Electroencephalogram Signal by Using Volterra Series Coefficients

PubMed Central

Hassani, Malihe; Karami, Mohammad Reza

2015-01-01

The Volterra model is widely used for nonlinearity identification in practical applications. In this paper, we employed Volterra model to find the nonlinearity relation between electroencephalogram (EEG) signal and the noise that is a novel approach to estimate noise in EEG signal. We show that by employing this method. We can considerably improve the signal to noise ratio by the ratio of at least 1.54. An important issue in implementing Volterra model is its computation complexity, especially when the degree of nonlinearity is increased. Hence, in many applications it is urgent to reduce the complexity of computation. In this paper, we use the property of EEG signal and propose a new and good approximation of delayed input signal to its adjacent samples in order to reduce the computation of finding Volterra series coefficients. The computation complexity is reduced by the ratio of at least 1/3 when the filter memory is 3. PMID:26284176

Minimum time acceleration of aircraft turbofan engines by using an algorithm based on nonlinear programming

NASA Technical Reports Server (NTRS)

Teren, F.

1977-01-01

Minimum time accelerations of aircraft turbofan engines are presented. The calculation of these accelerations was made by using a piecewise linear engine model, and an algorithm based on nonlinear programming. Use of this model and algorithm allows such trajectories to be readily calculated on a digital computer with a minimal expenditure of computer time.

Phenomenological modeling of nonlinear holograms based on metallic geometric metasurfaces.

PubMed

Ye, Weimin; Li, Xin; Liu, Juan; Zhang, Shuang

2016-10-31

Benefiting from efficient local phase and amplitude control at the subwavelength scale, metasurfaces offer a new platform for computer generated holography with high spatial resolution. Three-dimensional and high efficient holograms have been realized by metasurfaces constituted by subwavelength meta-atoms with spatially varying geometries or orientations. Metasurfaces have been recently extended to the nonlinear optical regime to generate holographic images in harmonic generation waves. Thus far, there has been no vector field simulation of nonlinear metasurface holograms because of the tremendous computational challenge in numerically calculating the collective nonlinear responses of the large number of different subwavelength meta-atoms in a hologram. Here, we propose a general phenomenological method to model nonlinear metasurface holograms based on the assumption that every meta-atom could be described by a localized nonlinear polarizability tensor. Applied to geometric nonlinear metasurfaces, we numerically model the holographic images formed by the second-harmonic waves of different spins. We show that, in contrast to the metasurface holograms operating in the linear optical regime, the wavelength of incident fundamental light should be slightly detuned from the fundamental resonant wavelength to optimize the efficiency and quality of nonlinear holographic images. The proposed modeling provides a general method to simulate nonlinear optical devices based on metallic metasurfaces.

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

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

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

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

DOE PAGES

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

2017-03-29

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

An Integrated Crustal Dynamics Simulator

NASA Astrophysics Data System (ADS)

Xing, H. L.; Mora, P.

2007-12-01

Numerical modelling offers an outstanding opportunity to gain an understanding of the crustal dynamics and complex crustal system behaviour. This presentation provides our long-term and ongoing effort on finite element based computational model and software development to simulate the interacting fault system for earthquake forecasting. A R-minimum strategy based finite-element computational model and software tool, PANDAS, for modelling 3-dimensional nonlinear frictional contact behaviour between multiple deformable bodies with the arbitrarily-shaped contact element strategy has been developed by the authors, which builds up a virtual laboratory to simulate interacting fault systems including crustal boundary conditions and various nonlinearities (e.g. from frictional contact, materials, geometry and thermal coupling). It has been successfully applied to large scale computing of the complex nonlinear phenomena in the non-continuum media involving the nonlinear frictional instability, multiple material properties and complex geometries on supercomputers, such as the South Australia (SA) interacting fault system, South California fault model and Sumatra subduction model. It has been also extended and to simulate the hot fractured rock (HFR) geothermal reservoir system in collaboration of Geodynamics Ltd which is constructing the first geothermal reservoir system in Australia and to model the tsunami generation induced by earthquakes. Both are supported by Australian Research Council.

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

Nonlinear Large Deflection Theory with Modified Aeroelastic Lifting Line Aerodynamics for a High Aspect Ratio Flexible Wing

NASA Technical Reports Server (NTRS)

Nguyen, Nhan; Ting, Eric; Chaparro, Daniel

2017-01-01

This paper investigates the effect of nonlinear large deflection bending on the aerodynamic performance of a high aspect ratio flexible wing. A set of nonlinear static aeroelastic equations are derived for the large bending deflection of a high aspect ratio wing structure. An analysis is conducted to compare the nonlinear bending theory with the linear bending theory. The results show that the nonlinear bending theory is length-preserving whereas the linear bending theory causes a non-physical effect of lengthening the wing structure under the no axial load condition. A modified lifting line theory is developed to compute the lift and drag coefficients of a wing structure undergoing a large bending deflection. The lift and drag coefficients are more accurately estimated by the nonlinear bending theory due to its length-preserving property. The nonlinear bending theory yields lower lift and span efficiency than the linear bending theory. A coupled aerodynamic-nonlinear finite element model is developed to implement the nonlinear bending theory for a Common Research Model (CRM) flexible wing wind tunnel model to be tested in the University of Washington Aeronautical Laboratory (UWAL). The structural stiffness of the model is designed to give about 10% wing tip deflection which is large enough that could cause the nonlinear deflection effect to become significant. The computational results show that the nonlinear bending theory yields slightly less lift than the linear bending theory for this wind tunnel model. As a result, the linear bending theory is deemed adequate for the CRM wind tunnel model.

Brain shift computation using a fully nonlinear biomechanical model.

PubMed

Wittek, Adam; Kikinis, Ron; Warfield, Simon K; Miller, Karol

2005-01-01

In the present study, fully nonlinear (i.e. accounting for both geometric and material nonlinearities) patient specific finite element brain model was applied to predict deformation field within the brain during the craniotomy-induced brain shift. Deformation of brain surface was used as displacement boundary conditions. Application of the computed deformation field to align (i.e. register) the preoperative images with the intraoperative ones indicated that the model very accurately predicts the displacements of gravity centers of the lateral ventricles and tumor even for very limited information about the brain surface deformation. These results are sufficient to suggest that nonlinear biomechanical models can be regarded as one possible way of complementing medical image processing techniques when conducting nonrigid registration. Important advantage of such models over the linear ones is that they do not require unrealistic assumptions that brain deformations are infinitesimally small and brain tissue stress-strain relationship is linear.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations.

PubMed

Hu, Eric Y; Bouteiller, Jean-Marie C; Song, Dong; Baudry, Michel; Berger, Theodore W

2015-01-01

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations

PubMed Central

Hu, Eric Y.; Bouteiller, Jean-Marie C.; Song, Dong; Baudry, Michel; Berger, Theodore W.

2015-01-01

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations. PMID:26441622

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2002-01-01

This talk describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations. Chapter 2

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2001-01-01

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

The development and validation of a numerical integration method for non-linear viscoelastic modeling

PubMed Central

Ramo, Nicole L.; Puttlitz, Christian M.

2018-01-01

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558

Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method.

PubMed

Treeby, Bradley E; Jaros, Jiri; Rendell, Alistair P; Cox, B T

2012-06-01

The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe.

Reduced-Order Models Based on Linear and Nonlinear Aerodynamic Impulse Responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

This paper discusses a method for the identification and application of reduced-order models based on linear and nonlinear aerodynamic impulse responses. The Volterra theory of nonlinear systems and an appropriate kernel identification technique are described. Insight into the nature of kernels is provided by applying the method to the nonlinear Riccati equation in a non-aerodynamic application. The method is then applied to a nonlinear aerodynamic model of RAE 2822 supercritical airfoil undergoing plunge motions using the CFL3D Navier-Stokes flow solver with the Spalart-Allmaras turbulence model. Results demonstrate the computational efficiency of the technique.

Reduced Order Models Based on Linear and Nonlinear Aerodynamic Impulse Responses

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

This paper discusses a method for the identification and application of reduced-order models based on linear and nonlinear aerodynamic impulse responses. The Volterra theory of nonlinear systems and an appropriate kernel identification technique are described. Insight into the nature of kernels is provided by applying the method to the nonlinear Riccati equation in a non-aerodynamic application. The method is then applied to a nonlinear aerodynamic model of an RAE 2822 supercritical airfoil undergoing plunge motions using the CFL3D Navier-Stokes flow solver with the Spalart-Allmaras turbulence model. Results demonstrate the computational efficiency of the technique.

Modeling of an intelligent pressure sensor using functional link artificial neural networks.

PubMed

Patra, J C; van den Bos, A

2000-01-01

A capacitor pressure sensor (CPS) is modeled for accurate readout of applied pressure using a novel artificial neural network (ANN). The proposed functional link ANN (FLANN) is a computationally efficient nonlinear network and is capable of complex nonlinear mapping between its input and output pattern space. The nonlinearity is introduced into the FLANN by passing the input pattern through a functional expansion unit. Three different polynomials such as, Chebyschev, Legendre and power series have been employed in the FLANN. The FLANN offers computational advantage over a multilayer perceptron (MLP) for similar performance in modeling of the CPS. The prime aim of the present paper is to develop an intelligent model of the CPS involving less computational complexity, so that its implementation can be economical and robust. It is shown that, over a wide temperature variation ranging from -50 to 150 degrees C, the maximum error of estimation of pressure remains within +/- 3%. With the help of computer simulation, the performance of the three types of FLANN models has been compared to that of an MLP based model.

A new constitutive model for simulation of softening, plateau, and densification phenomena for trabecular bone under compression.

PubMed

Lee, Chi-Seung; Lee, Jae-Myung; Youn, BuHyun; Kim, Hyung-Sik; Shin, Jong Ki; Goh, Tae Sik; Lee, Jung Sub

2017-01-01

A new type of constitutive model and its computational implementation procedure for the simulation of a trabecular bone are proposed in the present study. A yield surface-independent Frank-Brockman elasto-viscoplastic model is introduced to express the nonlinear material behavior such as softening beyond yield point, plateau, and densification under compressive loads. In particular, the hardening- and softening-dominant material functions are introduced and adopted in the plastic multiplier to describe each nonlinear material behavior separately. In addition, the elasto-viscoplastic model is transformed into an implicit type discrete model, and is programmed as a user-defined material subroutine in commercial finite element analysis code. In particular, the consistent tangent modulus method is proposed to improve the computational convergence and to save computational time during finite element analysis. Through the developed material library, the nonlinear stress-strain relationship is analyzed qualitatively and quantitatively, and the simulation results are compared with the results of compression test on the trabecular bone to validate the proposed constitutive model, computational method, and material library. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

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.

Computational modes and the Machenauer N.L.N.M.I. of the GLAS 4th order model. [NonLinear Normal Mode Initialization in numerical weather forecasting

NASA Technical Reports Server (NTRS)

Navon, I. M.; Bloom, S.; Takacs, L. L.

1985-01-01

An attempt was made to use the GLAS global 4th order shallow water equations to perform a Machenhauer nonlinear normal mode initialization (NLNMI) for the external vertical mode. A new algorithm was defined for identifying and filtering out computational modes which affect the convergence of the Machenhauer iterative procedure. The computational modes and zonal waves were linearly initialized and gravitational modes were nonlinearly initialized. The Machenhauer NLNMI was insensitive to the absence of high zonal wave numbers. The effects of the Machenhauer scheme were evaluated by performing 24 hr integrations with nondissipative and dissipative explicit time integration models. The NLNMI was found to be inferior to the Rasch (1984) pseudo-secant technique for obtaining convergence when the time scales of nonlinear forcing were much smaller than the time scales expected from the natural frequency of the mode.

Nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation

NASA Astrophysics Data System (ADS)

Li, Guang

2017-01-01

This paper presents a fast constrained optimization approach, which is tailored for nonlinear model predictive control of wave energy converters (WEC). The advantage of this approach relies on its exploitation of the differential flatness of the WEC model. This can reduce the dimension of the resulting nonlinear programming problem (NLP) derived from the continuous constrained optimal control of WEC using pseudospectral method. The alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for WEC control problems. The method is applicable to nonlinear WEC models, nonconvex objective functions and nonlinear constraints, which are commonly encountered in WEC control problems. Numerical simulations demonstrate the efficacy of this approach.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

PubMed

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models

PubMed Central

Xing, W. W.; Triantafyllidis, V.

2017-01-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach. PMID:28484327

GPU-based acceleration of computations in nonlinear finite element deformation analysis.

PubMed

Mafi, Ramin; Sirouspour, Shahin

2014-03-01

The physics of deformation for biological soft-tissue is best described by nonlinear continuum mechanics-based models, which then can be discretized by the FEM for a numerical solution. However, computational complexity of such models have limited their use in applications requiring real-time or fast response. In this work, we propose a graphic processing unit-based implementation of the FEM using implicit time integration for dynamic nonlinear deformation analysis. This is the most general formulation of the deformation analysis. It is valid for large deformations and strains and can account for material nonlinearities. The data-parallel nature and the intense arithmetic computations of nonlinear FEM equations make it particularly suitable for implementation on a parallel computing platform such as graphic processing unit. In this work, we present and compare two different designs based on the matrix-free and conventional preconditioned conjugate gradients algorithms for solving the FEM equations arising in deformation analysis. The speedup achieved with the proposed parallel implementations of the algorithms will be instrumental in the development of advanced surgical simulators and medical image registration methods involving soft-tissue deformation. Copyright © 2013 John Wiley & Sons, Ltd.

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

DOE PAGES

Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart

2015-02-14

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equationsmore » at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.« less

Computational study of nonlinear plasma waves. [plasma simulation model applied to electrostatic waves in collisionless plasma

NASA Technical Reports Server (NTRS)

Matsuda, Y.

1974-01-01

A low-noise plasma simulation model is developed and applied to a series of linear and nonlinear problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. It is demonstrated that use of the hybrid simulation model allows economical studies to be carried out in both the linear and nonlinear regimes with better quantitative results, for comparable computing time, than can be obtained by conventional particle simulation models, or direct solution of the Vlasov equation. The characteristics of the hybrid simulation model itself are first investigated, and it is shown to be capable of verifying the theoretical linear dispersion relation at wave energy levels as low as .000001 of the plasma thermal energy. Having established the validity of the hybrid simulation model, it is then used to study the nonlinear dynamics of monochromatic wave, sideband instability due to trapped particles, and satellite growth.

On discrete control of nonlinear systems with applications to robotics

NASA Technical Reports Server (NTRS)

Eslami, Mansour

1989-01-01

Much progress has been reported in the areas of modeling and control of nonlinear dynamic systems in a continuous-time framework. From implementation point of view, however, it is essential to study these nonlinear systems directly in a discrete setting that is amenable for interfacing with digital computers. But to develop discrete models and discrete controllers for a nonlinear system such as robot is a nontrivial task. Robot is also inherently a variable-inertia dynamic system involving additional complications. Not only the computer-oriented models of these systems must satisfy the usual requirements for such models, but these must also be compatible with the inherent capabilities of computers and must preserve the fundamental physical characteristics of continuous-time systems such as the conservation of energy and/or momentum. Preliminary issues regarding discrete systems in general and discrete models of a typical industrial robot that is developed with full consideration of the principle of conservation of energy are presented. Some research on the pertinent tactile information processing is reviewed. Finally, system control methods and how to integrate these issues in order to complete the task of discrete control of a robot manipulator are also reviewed.

Computation of Static Shapes and Voltages for Micromachined Deformable Mirrors with Nonlinear Electrostatic Actuators

NASA Technical Reports Server (NTRS)

Wang, P. K. C.; Hadaegh, F. Y.

1996-01-01

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics. Numerical methods for computing the mirror deformation due to given actuator voltages and the actuator voltages required for producing the desired deformations at the actuator locations are presented. The application of the proposed methods to circular deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical circular micromachined mirror with electrostatic actuators.

A novel track-before-detect algorithm based on optimal nonlinear filtering for detecting and tracking infrared dim target

NASA Astrophysics Data System (ADS)

Tian, Yuexin; Gao, Kun; Liu, Ying; Han, Lu

2015-08-01

Aiming at the nonlinear and non-Gaussian features of the real infrared scenes, an optimal nonlinear filtering based algorithm for the infrared dim target tracking-before-detecting application is proposed. It uses the nonlinear theory to construct the state and observation models and uses the spectral separation scheme based Wiener chaos expansion method to resolve the stochastic differential equation of the constructed models. In order to improve computation efficiency, the most time-consuming operations independent of observation data are processed on the fore observation stage. The other observation data related rapid computations are implemented subsequently. Simulation results show that the algorithm possesses excellent detection performance and is more suitable for real-time processing.

Direct biomechanical modeling of trabecular bone using a nonlinear manifold-based volumetric representation

NASA Astrophysics Data System (ADS)

Jin, Dakai; Lu, Jia; Zhang, Xiaoliu; Chen, Cheng; Bai, ErWei; Saha, Punam K.

2017-03-01

Osteoporosis is associated with increased fracture risk. Recent advancement in the area of in vivo imaging allows segmentation of trabecular bone (TB) microstructures, which is a known key determinant of bone strength and fracture risk. An accurate biomechanical modelling of TB micro-architecture provides a comprehensive summary measure of bone strength and fracture risk. In this paper, a new direct TB biomechanical modelling method using nonlinear manifold-based volumetric reconstruction of trabecular network is presented. It is accomplished in two sequential modules. The first module reconstructs a nonlinear manifold-based volumetric representation of TB networks from three-dimensional digital images. Specifically, it starts with the fuzzy digital segmentation of a TB network, and computes its surface and curve skeletons. An individual trabecula is identified as a topological segment in the curve skeleton. Using geometric analysis, smoothing and optimization techniques, the algorithm generates smooth, curved, and continuous representations of individual trabeculae glued at their junctions. Also, the method generates a geometrically consistent TB volume at junctions. In the second module, a direct computational biomechanical stress-strain analysis is applied on the reconstructed TB volume to predict mechanical measures. The accuracy of the method was examined using micro-CT imaging of cadaveric distal tibia specimens (N = 12). A high linear correlation (r = 0.95) between TB volume computed using the new manifold-modelling algorithm and that directly derived from the voxel-based micro-CT images was observed. Young's modulus (YM) was computed using direct mechanical analysis on the TB manifold-model over a cubical volume of interest (VOI), and its correlation with the YM, computed using micro-CT based conventional finite-element analysis over the same VOI, was examined. A moderate linear correlation (r = 0.77) was observed between the two YM measures. This preliminary results show the accuracy of the new nonlinear manifold modelling algorithm for TB, and demonstrate the feasibility of a new direct mechanical strain-strain analysis on a nonlinear manifold model of a highly complex biological structure.

A Lattice-Boltzmann model to simulate diffractive nonlinear ultrasound beam propagation in a dissipative fluid medium

NASA Astrophysics Data System (ADS)

Abdi, Mohamad; Hajihasani, Mojtaba; Gharibzadeh, Shahriar; Tavakkoli, Jahan

2012-12-01

Ultrasound waves have been widely used in diagnostic and therapeutic medical applications. Accurate and effective simulation of ultrasound beam propagation and its interaction with tissue has been proved to be important. The nonlinear nature of the ultrasound beam propagation, especially in the therapeutic regime, plays an important role in the mechanisms of interaction with tissue. There are three main approaches in current computational fluid dynamics (CFD) methods to model and simulate nonlinear ultrasound beams: macroscopic, mesoscopic and microscopic approaches. In this work, a mesoscopic CFD method based on the Lattice-Boltzmann model (LBM) was investigated. In the developed method, the Boltzmann equation is evolved to simulate the flow of a Newtonian fluid with the collision model instead of solving the Navier-Stokes, continuity and state equations which are used in conventional CFD methods. The LBM has some prominent advantages over conventional CFD methods, including: (1) its parallel computational nature; (2) taking microscopic boundaries into account; and (3) capability of simulating in porous and inhomogeneous media. In our proposed method, the propagating medium is discretized with a square grid in 2 dimensions with 9 velocity vectors for each node. Using the developed model, the nonlinear distortion and shock front development of a finiteamplitude diffractive ultrasonic beam in a dissipative fluid medium was computed and validated against the published data. The results confirm that the LBM is an accurate and effective approach to model and simulate nonlinearity in finite-amplitude ultrasound beams with Mach numbers of up to 0.01 which, among others, falls within the range of therapeutic ultrasound regime such as high intensity focused ultrasound (HIFU) beams. A comparison between the HIFU nonlinear beam simulations using the proposed model and pseudospectral methods in a 2D geometry is 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.

Nonlinear flutter analysis of composite panels

NASA Astrophysics Data System (ADS)

An, Xiaomin; Wang, Yan

2018-05-01

Nonlinear panel flutter is an interesting subject of fluid-structure interaction. In this paper, nonlinear flutter characteristics of curved composite panels are studied in very low supersonic flow. The composite panel with geometric nonlinearity is modeled by a nonlinear finite element method; and the responses are computed by the nonlinear Newmark algorithm. An unsteady aerodynamic solver, which contains a flux splitting scheme and dual time marching technology, is employed in calculating the unsteady pressure of the motion of the panel. Based on a half-step staggered coupled solution, the aeroelastic responses of two composite panels with different radius of R = 5 and R = 2.5 are computed and compared with each other at different dynamic pressure for Ma = 1.05. The nonlinear flutter characteristics comprising limited cycle oscillations and chaos are analyzed and discussed.

Laminar and orientation-dependent characteristics of spatial nonlinearities: implications for the computational architecture of visual cortex.

PubMed

Victor, Jonathan D; Mechler, Ferenc; Ohiorhenuan, Ifije; Schmid, Anita M; Purpura, Keith P

2009-12-01

A full understanding of the computations performed in primary visual cortex is an important yet elusive goal. Receptive field models consisting of cascades of linear filters and static nonlinearities may be adequate to account for responses to simple stimuli such as gratings and random checkerboards, but their predictions of responses to complex stimuli such as natural scenes are only approximately correct. It is unclear whether these discrepancies are limited to quantitative inaccuracies that reflect well-recognized mechanisms such as response normalization, gain controls, and cross-orientation suppression or, alternatively, imply additional qualitative features of the underlying computations. To address this question, we examined responses of V1 and V2 neurons in the monkey and area 17 neurons in the cat to two-dimensional Hermite functions (TDHs). TDHs are intermediate in complexity between traditional analytic stimuli and natural scenes and have mathematical properties that facilitate their use to test candidate models. By exploiting these properties, along with the laminar organization of V1, we identify qualitative aspects of neural computations beyond those anticipated from the above-cited model framework. Specifically, we find that V1 neurons receive signals from orientation-selective mechanisms that are highly nonlinear: they are sensitive to phase correlations, not just spatial frequency content. That is, the behavior of V1 neurons departs from that of linear-nonlinear cascades with standard modulatory mechanisms in a qualitative manner: even relatively simple stimuli evoke responses that imply complex spatial nonlinearities. The presence of these findings in the input layers suggests that these nonlinearities act in a feedback fashion.

Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1999-01-01

The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.

Intrinsic two-dimensional features as textons

NASA Technical Reports Server (NTRS)

Barth, E.; Zetzsche, C.; Rentschler, I.

1998-01-01

We suggest that intrinsic two-dimensional (i2D) features, computationally defined as the outputs of nonlinear operators that model the activity of end-stopped neurons, play a role in preattentive texture discrimination. We first show that for discriminable textures with identical power spectra the predictions of traditional models depend on the type of nonlinearity and fail for energy measures. We then argue that the concept of intrinsic dimensionality, and the existence of end-stopped neurons, can help us to understand the role of the nonlinearities. Furthermore, we show examples in which models without strong i2D selectivity fail to predict the correct ranking order of perceptual segregation. Our arguments regarding the importance of i2D features resemble the arguments of Julesz and co-workers regarding textons such as terminators and crossings. However, we provide a computational framework that identifies textons with the outputs of nonlinear operators that are selective to i2D features.

A Web Tool for Research in Nonlinear Optics

NASA Astrophysics Data System (ADS)

Prikhod'ko, Nikolay V.; Abramovsky, Viktor A.; Abramovskaya, Natalia V.; Demichev, Andrey P.; Kryukov, Alexandr P.; Polyakov, Stanislav P.

2016-02-01

This paper presents a project of developing the web platform called WebNLO for computer modeling of nonlinear optics phenomena. We discuss a general scheme of the platform and a model for interaction between the platform modules. The platform is built as a set of interacting RESTful web services (SaaS approach). Users can interact with the platform through a web browser or command line interface. Such a resource has no analogues in the field of nonlinear optics and will be created for the first time therefore allowing researchers to access high-performance computing resources that will significantly reduce the cost of the research and development process.

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.

Prediction of High-Lift Flows using Turbulent Closure Models

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Gatski, Thomas B.; Ying, Susan X.; Bertelrud, Arild

1997-01-01

The flow over two different multi-element airfoil configurations is computed using linear eddy viscosity turbulence models and a nonlinear explicit algebraic stress model. A subset of recently-measured transition locations using hot film on a McDonnell Douglas configuration is presented, and the effect of transition location on the computed solutions is explored. Deficiencies in wake profile computations are found to be attributable in large part to poor boundary layer prediction on the generating element, and not necessarily inadequate turbulence modeling in the wake. Using measured transition locations for the main element improves the prediction of its boundary layer thickness, skin friction, and wake profile shape. However, using measured transition locations on the slat still yields poor slat wake predictions. The computation of the slat flow field represents a key roadblock to successful predictions of multi-element flows. In general, the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models.

A hierarchy for modeling high speed propulsion systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Deabreu, Alex

1991-01-01

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery such as inlets, ramjets, and scramjets. The discussion is separated into four sections: (1) computational fluid dynamics model for the entire nonlinear system or high order nonlinear models; (2) high order linearized model derived from fundamental physics; (3) low order linear models obtained from other high order models; and (4) low order nonlinear models. Included are special considerations on any relevant control system designs. The methods discussed are for the quasi-one dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, moving normal shocks, hammershocks, subsonic combustion via heat addition, temperature dependent gases, detonation, and thermal choking.

Modeling of fatigue crack induced nonlinear ultrasonics using a highly parallelized explicit local interaction simulation approach

NASA Astrophysics Data System (ADS)

Shen, Yanfeng; Cesnik, Carlos E. S.

2016-04-01

This paper presents a parallelized modeling technique for the efficient simulation of nonlinear ultrasonics introduced by the wave interaction with fatigue cracks. The elastodynamic wave equations with contact effects are formulated using an explicit Local Interaction Simulation Approach (LISA). The LISA formulation is extended to capture the contact-impact phenomena during the wave damage interaction based on the penalty method. A Coulomb friction model is integrated into the computation procedure to capture the stick-slip contact shear motion. The LISA procedure is coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized supercomputing on powerful graphic cards. Both the explicit contact formulation and the parallel feature facilitates LISA's superb computational efficiency over the conventional finite element method (FEM). The theoretical formulations based on the penalty method is introduced and a guideline for the proper choice of the contact stiffness is given. The convergence behavior of the solution under various contact stiffness values is examined. A numerical benchmark problem is used to investigate the new LISA formulation and results are compared with a conventional contact finite element solution. Various nonlinear ultrasonic phenomena are successfully captured using this contact LISA formulation, including the generation of nonlinear higher harmonic responses. Nonlinear mode conversion of guided waves at fatigue cracks is also studied.

Impact of isotropic constitutive descriptions on the predicted peak wall stress in abdominal aortic aneurysms.

PubMed

Man, V; Polzer, S; Gasser, T C; Novotny, T; Bursa, J

2018-03-01

Biomechanics-based assessment of Abdominal Aortic Aneurysm (AAA) rupture risk has gained considerable scientific and clinical momentum. However, computation of peak wall stress (PWS) using state-of-the-art finite element models is time demanding. This study investigates which features of the constitutive description of AAA wall are decisive for achieving acceptable stress predictions in it. Influence of five different isotropic constitutive descriptions of AAA wall is tested; models reflect realistic non-linear, artificially stiff non-linear, or artificially stiff pseudo-linear constitutive descriptions of AAA wall. Influence of the AAA wall model is tested on idealized (n=4) and patient-specific (n=16) AAA geometries. Wall stress computations consider a (hypothetical) load-free configuration and include residual stresses homogenizing the stresses across the wall. Wall stress differences amongst the different descriptions were statistically analyzed. When the qualitatively similar non-linear response of the AAA wall with low initial stiffness and subsequent strain stiffening was taken into consideration, wall stress (and PWS) predictions did not change significantly. Keeping this non-linear feature when using an artificially stiff wall can save up to 30% of the computational time, without significant change in PWS. In contrast, a stiff pseudo-linear elastic model may underestimate the PWS and is not reliable for AAA wall stress computations. Copyright © 2018 IPEM. Published by Elsevier Ltd. All rights reserved.

Hysteresis in the trade cycle

NASA Astrophysics Data System (ADS)

Mc Namara, Hugh A.; Pokrovskii, Alexei V.

2006-02-01

The Kaldor model-one of the first nonlinear models of macroeconomics-is modified to incorporate a Preisach nonlinearity. The new dynamical system thus created shows highly complicated behaviour. This paper presents a rigorous (computer aided) proof of chaos in this new model, and of the existence of unstable periodic orbits of all minimal periods p>57.

Reservoir Computing Beyond Memory-Nonlinearity Trade-off.

PubMed

Inubushi, Masanobu; Yoshimura, Kazuyuki

2017-08-31

Reservoir computing is a brain-inspired machine learning framework that employs a signal-driven dynamical system, in particular harnessing common-signal-induced synchronization which is a widely observed nonlinear phenomenon. Basic understanding of a working principle in reservoir computing can be expected to shed light on how information is stored and processed in nonlinear dynamical systems, potentially leading to progress in a broad range of nonlinear sciences. As a first step toward this goal, from the viewpoint of nonlinear physics and information theory, we study the memory-nonlinearity trade-off uncovered by Dambre et al. (2012). Focusing on a variational equation, we clarify a dynamical mechanism behind the trade-off, which illustrates why nonlinear dynamics degrades memory stored in dynamical system in general. Moreover, based on the trade-off, we propose a mixture reservoir endowed with both linear and nonlinear dynamics and show that it improves the performance of information processing. Interestingly, for some tasks, significant improvements are observed by adding a few linear dynamics to the nonlinear dynamical system. By employing the echo state network model, the effect of the mixture reservoir is numerically verified for a simple function approximation task and for more complex tasks.

Investigations into the triggered lightning response of the F106B thunderstorm research aircraft

NASA Technical Reports Server (NTRS)

Rudolph, Terence H.; Perala, Rodney A.; Mckenna, Paul M.; Parker, Steven L.

1985-01-01

An investigation has been conducted into the lightning characteristics of the NASA F106B thunderstorm research aircraft. The investigation includes analysis of measured data from the aircraft in the time and frequency domains. Linear and nonlinear computer modelling has also been performed. In addition, new computer tools have been developed, including a new enhanced nonlinear air breakdown model, and a subgrid model useful for analyzing fine details of the aircraft's geometry. Comparison of measured and calculated electromagnetic responses of the aircraft to a triggered lightning environment are presented.

Development of a computational model on the neural activity patterns of a visual working memory in a hierarchical feedforward Network

NASA Astrophysics Data System (ADS)

An, Soyoung; Choi, Woochul; Paik, Se-Bum

2015-11-01

Understanding the mechanism of information processing in the human brain remains a unique challenge because the nonlinear interactions between the neurons in the network are extremely complex and because controlling every relevant parameter during an experiment is difficult. Therefore, a simulation using simplified computational models may be an effective approach. In the present study, we developed a general model of neural networks that can simulate nonlinear activity patterns in the hierarchical structure of a neural network system. To test our model, we first examined whether our simulation could match the previously-observed nonlinear features of neural activity patterns. Next, we performed a psychophysics experiment for a simple visual working memory task to evaluate whether the model could predict the performance of human subjects. Our studies show that the model is capable of reproducing the relationship between memory load and performance and may contribute, in part, to our understanding of how the structure of neural circuits can determine the nonlinear neural activity patterns in the human brain.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Spectral decontamination of a real-time helicopter simulation

NASA Technical Reports Server (NTRS)

Mcfarland, R. E.

1983-01-01

Nonlinear mathematical models of a rotor system, referred to as rotating blade-element models, produce steady-state, high-frequency harmonics of significant magnitude. In a discrete simulation model, certain of these harmonics may be incompatible with realistic real-time computational constraints because of their aliasing into the operational low-pass region. However, the energy is an aliased harmonic may be suppressed by increasing the computation rate of an isolated, causal nonlinearity and using an appropriate filter. This decontamination technique is applied to Sikorsky's real-time model of the Black Hawk helicopter, as supplied to NASA for handling-qualities investigations.

Structure Computation of Quiet Spike[Trademark] Flight-Test Data During Envelope Expansion

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2008-01-01

System identification or mathematical modeling is used in the aerospace community for development of simulation models for robust control law design. These models are often described as linear time-invariant processes. Nevertheless, it is well known that the underlying process is often nonlinear. The reason for using a linear approach has been due to the lack of a proper set of tools for the identification of nonlinear systems. Over the past several decades, the controls and biomedical communities have made great advances in developing tools for the identification of nonlinear systems. These approaches are robust and readily applicable to aerospace systems. In this paper, we show the application of one such nonlinear system identification technique, structure detection, for the analysis of F-15B Quiet Spike(TradeMark) aeroservoelastic flight-test data. Structure detection is concerned with the selection of a subset of candidate terms that best describe the observed output. This is a necessary procedure to compute an efficient system description that may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modeling may be of critical importance for the development of robust parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion, which may save significant development time and costs. The objectives of this study are to demonstrate via analysis of F-15B Quiet Spike aeroservoelastic flight-test data for several flight conditions that 1) linear models are inefficient for modeling aeroservoelastic data, 2) nonlinear identification provides a parsimonious model description while providing a high percent fit for cross-validated data, and 3) the model structure and parameters vary as the flight condition is altered.

Mixed Models and Reduction Techniques for Large-Rotation, Nonlinear Analysis of Shells of Revolution with Application to Tires

NASA Technical Reports Server (NTRS)

Noor, A. K.; Andersen, C. M.; Tanner, J. A.

1984-01-01

An effective computational strategy is presented for the large-rotation, nonlinear axisymmetric analysis of shells of revolution. The three key elements of the computational strategy are: (1) use of mixed finite-element models with discontinuous stress resultants at the element interfaces; (2) substantial reduction in the total number of degrees of freedom through the use of a multiple-parameter reduction technique; and (3) reduction in the size of the analysis model through the decomposition of asymmetric loads into symmetric and antisymmetric components coupled with the use of the multiple-parameter reduction technique. The potential of the proposed computational strategy is discussed. Numerical results are presented to demonstrate the high accuracy of the mixed models developed and to show the potential of using the proposed computational strategy for the analysis of tires.

Kerr nonlinearity and nonlinear absorption coefficient in a four-level M-model cylindrical quantum dot under the phenomenon of electromagnetically induced transparency

NASA Astrophysics Data System (ADS)

Behroozian, B.; Askari, H. R.

2018-07-01

The Kerr nonlinearity and the nonlinear absorption coefficient in a four-level M-model of a GaAs cylindrical quantum dot (QD) with parabolic potential under electromagnetically induced transparency are investigated. By solving the density matrix equations in the steady-state, the third order susceptibility is obtained. Then, by using the real and imaginary parts of third order susceptibility, the Kerr nonlinearity and the nonlinear absorption coefficient, respectively, for this system are computed. The effects of the radius and height of the cylindrical QD are then investigated. In addition, the effects of the control laser fields on the Kerr nonlinearity and the nonlinear absorption coefficient are investigated.

Nonlinear system guidance in the presence of transmission zero dynamics

NASA Technical Reports Server (NTRS)

Meyer, G.; Hunt, L. R.; Su, R.

1995-01-01

An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.

Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling.

PubMed

Perdikaris, P; Raissi, M; Damianou, A; Lawrence, N D; Karniadakis, G E

2017-02-01

Multi-fidelity modelling enables accurate inference of quantities of interest by synergistically combining realizations of low-cost/low-fidelity models with a small set of high-fidelity observations. This is particularly effective when the low- and high-fidelity models exhibit strong correlations, and can lead to significant computational gains over approaches that solely rely on high-fidelity models. However, in many cases of practical interest, low-fidelity models can only be well correlated to their high-fidelity counterparts for a specific range of input parameters, and potentially return wrong trends and erroneous predictions if probed outside of their validity regime. Here we put forth a probabilistic framework based on Gaussian process regression and nonlinear autoregressive schemes that is capable of learning complex nonlinear and space-dependent cross-correlations between models of variable fidelity, and can effectively safeguard against low-fidelity models that provide wrong trends. This introduces a new class of multi-fidelity information fusion algorithms that provide a fundamental extension to the existing linear autoregressive methodologies, while still maintaining the same algorithmic complexity and overall computational cost. The performance of the proposed methods is tested in several benchmark problems involving both synthetic and real multi-fidelity datasets from computational fluid dynamics simulations.

Research on an augmented Lagrangian penalty function algorithm for nonlinear programming

NASA Technical Reports Server (NTRS)

Frair, L.

1978-01-01

The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.

Patient-specific non-linear finite element modelling for predicting soft organ deformation in real-time: application to non-rigid neuroimage registration.

PubMed

Wittek, Adam; Joldes, Grand; Couton, Mathieu; Warfield, Simon K; Miller, Karol

2010-12-01

Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear finite element procedures implemented on a graphics processing unit (GPU). In contrast to commercial finite element codes that rely on an updated Lagrangian formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total Lagrangian formulation with explicit time stepping and dynamic relaxation. We used patient-specific finite element meshes consisting of hexahedral and non-locking tetrahedral elements, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial finite element solver executed on a personal computer. Copyright © 2010 Elsevier Ltd. All rights reserved.

The role of finite displacements in vocal fold modeling.

PubMed

Chang, Siyuan; Tian, Fang-Bao; Luo, Haoxiang; Doyle, James F; Rousseau, Bernard

2013-11-01

Human vocal folds experience flow-induced vibrations during phonation. In previous computational models, the vocal fold dynamics has been treated with linear elasticity theory in which both the strain and the displacement of the tissue are assumed to be infinitesimal (referred to as model I). The effect of the nonlinear strain, or geometric nonlinearity, caused by finite displacements is yet not clear. In this work, a two-dimensional model is used to study the effect of geometric nonlinearity (referred to as model II) on the vocal fold and the airflow. The result shows that even though the deformation is under 1 mm, i.e., less than 10% of the size of the vocal fold, the geometric nonlinear effect is still significant. Specifically, model I underpredicts the gap width, the flow rate, and the impact stress on the medial surfaces as compared to model II. The study further shows that the differences are caused by the contact mechanics and, more importantly, the fluid-structure interaction that magnifies the error from the small-displacement assumption. The results suggest that using the large-displacement formulation in a computational model would be more appropriate for accurate simulations of the vocal fold dynamics.

Novel procedure for characterizing nonlinear systems with memory: 2017 update

NASA Astrophysics Data System (ADS)

Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.

2017-05-01

The present article discusses novel improvements in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra or 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] . The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order and alleviate the Curse of Dimensionality (COD) in order to realize practical nonlinear solutions of scientific and engineering interest.

Optimal clinical trial design based on a dichotomous Markov-chain mixed-effect sleep model.

PubMed

Steven Ernest, C; Nyberg, Joakim; Karlsson, Mats O; Hooker, Andrew C

2014-12-01

D-optimal designs for discrete-type responses have been derived using generalized linear mixed models, simulation based methods and analytical approximations for computing the fisher information matrix (FIM) of non-linear mixed effect models with homogeneous probabilities over time. In this work, D-optimal designs using an analytical approximation of the FIM for a dichotomous, non-homogeneous, Markov-chain phase advanced sleep non-linear mixed effect model was investigated. The non-linear mixed effect model consisted of transition probabilities of dichotomous sleep data estimated as logistic functions using piecewise linear functions. Theoretical linear and nonlinear dose effects were added to the transition probabilities to modify the probability of being in either sleep stage. D-optimal designs were computed by determining an analytical approximation the FIM for each Markov component (one where the previous state was awake and another where the previous state was asleep). Each Markov component FIM was weighted either equally or by the average probability of response being awake or asleep over the night and summed to derive the total FIM (FIM(total)). The reference designs were placebo, 0.1, 1-, 6-, 10- and 20-mg dosing for a 2- to 6-way crossover study in six dosing groups. Optimized design variables were dose and number of subjects in each dose group. The designs were validated using stochastic simulation/re-estimation (SSE). Contrary to expectations, the predicted parameter uncertainty obtained via FIM(total) was larger than the uncertainty in parameter estimates computed by SSE. Nevertheless, the D-optimal designs decreased the uncertainty of parameter estimates relative to the reference designs. Additionally, the improvement for the D-optimal designs were more pronounced using SSE than predicted via FIM(total). Through the use of an approximate analytic solution and weighting schemes, the FIM(total) for a non-homogeneous, dichotomous Markov-chain phase advanced sleep model was computed and provided more efficient trial designs and increased nonlinear mixed-effects modeling parameter precision.

Nonlinear spectral mixture effects for photosynthetic/non-photosynthetic vegetation cover estimates of typical desert vegetation in western China.

PubMed

Ji, Cuicui; Jia, Yonghong; Gao, Zhihai; Wei, Huaidong; Li, Xiaosong

2017-01-01

Desert vegetation plays significant roles in securing the ecological integrity of oasis ecosystems in western China. Timely monitoring of photosynthetic/non-photosynthetic desert vegetation cover is necessary to guide management practices on land desertification and research into the mechanisms driving vegetation recession. In this study, nonlinear spectral mixture effects for photosynthetic/non-photosynthetic vegetation cover estimates are investigated through comparing the performance of linear and nonlinear spectral mixture models with different endmembers applied to field spectral measurements of two types of typical desert vegetation, namely, Nitraria shrubs and Haloxylon. The main results were as follows. (1) The correct selection of endmembers is important for improving the accuracy of vegetation cover estimates, and in particular, shadow endmembers cannot be neglected. (2) For both the Nitraria shrubs and Haloxylon, the Kernel-based Nonlinear Spectral Mixture Model (KNSMM) with nonlinear parameters was the best unmixing model. In consideration of the computational complexity and accuracy requirements, the Linear Spectral Mixture Model (LSMM) could be adopted for Nitraria shrubs plots, but this will result in significant errors for the Haloxylon plots since the nonlinear spectral mixture effects were more obvious for this vegetation type. (3) The vegetation canopy structure (planophile or erectophile) determines the strength of the nonlinear spectral mixture effects. Therefore, no matter for Nitraria shrubs or Haloxylon, the non-linear spectral mixing effects between the photosynthetic / non-photosynthetic vegetation and the bare soil do exist, and its strength is dependent on the three-dimensional structure of the vegetation canopy. The choice of linear or nonlinear spectral mixture models is up to the consideration of computational complexity and the accuracy requirement.

Nonlinear spectral mixture effects for photosynthetic/non-photosynthetic vegetation cover estimates of typical desert vegetation in western China

PubMed Central

Jia, Yonghong; Gao, Zhihai; Wei, Huaidong

2017-01-01

Desert vegetation plays significant roles in securing the ecological integrity of oasis ecosystems in western China. Timely monitoring of photosynthetic/non-photosynthetic desert vegetation cover is necessary to guide management practices on land desertification and research into the mechanisms driving vegetation recession. In this study, nonlinear spectral mixture effects for photosynthetic/non-photosynthetic vegetation cover estimates are investigated through comparing the performance of linear and nonlinear spectral mixture models with different endmembers applied to field spectral measurements of two types of typical desert vegetation, namely, Nitraria shrubs and Haloxylon. The main results were as follows. (1) The correct selection of endmembers is important for improving the accuracy of vegetation cover estimates, and in particular, shadow endmembers cannot be neglected. (2) For both the Nitraria shrubs and Haloxylon, the Kernel-based Nonlinear Spectral Mixture Model (KNSMM) with nonlinear parameters was the best unmixing model. In consideration of the computational complexity and accuracy requirements, the Linear Spectral Mixture Model (LSMM) could be adopted for Nitraria shrubs plots, but this will result in significant errors for the Haloxylon plots since the nonlinear spectral mixture effects were more obvious for this vegetation type. (3) The vegetation canopy structure (planophile or erectophile) determines the strength of the nonlinear spectral mixture effects. Therefore, no matter for Nitraria shrubs or Haloxylon, the non-linear spectral mixing effects between the photosynthetic / non-photosynthetic vegetation and the bare soil do exist, and its strength is dependent on the three-dimensional structure of the vegetation canopy. The choice of linear or nonlinear spectral mixture models is up to the consideration of computational complexity and the accuracy requirement. PMID:29240777

Development of Advanced Computational Aeroelasticity Tools at NASA Langley Research Center

NASA Technical Reports Server (NTRS)

Bartels, R. E.

2008-01-01

NASA Langley Research Center has continued to develop its long standing computational tools to address new challenges in aircraft and launch vehicle design. This paper discusses the application and development of those computational aeroelastic tools. Four topic areas will be discussed: 1) Modeling structural and flow field nonlinearities; 2) Integrated and modular approaches to nonlinear multidisciplinary analysis; 3) Simulating flight dynamics of flexible vehicles; and 4) Applications that support both aeronautics and space exploration.

Maximum Likelihood Estimation of Nonlinear Structural Equation Models with Ignorable Missing Data

ERIC Educational Resources Information Center

Lee, Sik-Yum; Song, Xin-Yuan; Lee, John C. K.

2003-01-01

The existing maximum likelihood theory and its computer software in structural equation modeling are established on the basis of linear relationships among latent variables with fully observed data. However, in social and behavioral sciences, nonlinear relationships among the latent variables are important for establishing more meaningful models…

Skeletal muscle tensile strain dependence: hyperviscoelastic nonlinearity

PubMed Central

Wheatley, Benjamin B; Morrow, Duane A; Odegard, Gregory M; Kaufman, Kenton R; Donahue, Tammy L Haut

2015-01-01

Introduction Computational modeling of skeletal muscle requires characterization at the tissue level. While most skeletal muscle studies focus on hyperelasticity, the goal of this study was to examine and model the nonlinear behavior of both time-independent and time-dependent properties of skeletal muscle as a function of strain. Materials and Methods Nine tibialis anterior muscles from New Zealand White rabbits were subject to five consecutive stress relaxation cycles of roughly 3% strain. Individual relaxation steps were fit with a three-term linear Prony series. Prony series coefficients and relaxation ratio were assessed for strain dependence using a general linear statistical model. A fully nonlinear constitutive model was employed to capture the strain dependence of both the viscoelastic and instantaneous components. Results Instantaneous modulus (p<0.0005) and mid-range relaxation (p<0.0005) increased significantly with strain level, while relaxation at longer time periods decreased with strain (p<0.0005). Time constants and overall relaxation ratio did not change with strain level (p>0.1). Additionally, the fully nonlinear hyperviscoelastic constitutive model provided an excellent fit to experimental data, while other models which included linear components failed to capture muscle function as accurately. Conclusions Material properties of skeletal muscle are strain-dependent at the tissue level. This strain dependence can be included in computational models of skeletal muscle performance with a fully nonlinear hyperviscoelastic model. PMID:26409235

Simulations of nonlinear continuous wave pressure fields in FOCUS

NASA Astrophysics Data System (ADS)

Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.

2017-03-01

The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.

Multilayer Perceptron for Robust Nonlinear Interval Regression Analysis Using Genetic Algorithms

PubMed Central

2014-01-01

On the basis of fuzzy regression, computational models in intelligence such as neural networks have the capability to be applied to nonlinear interval regression analysis for dealing with uncertain and imprecise data. When training data are not contaminated by outliers, computational models perform well by including almost all given training data in the data interval. Nevertheless, since training data are often corrupted by outliers, robust learning algorithms employed to resist outliers for interval regression analysis have been an interesting area of research. Several approaches involving computational intelligence are effective for resisting outliers, but the required parameters for these approaches are related to whether the collected data contain outliers or not. Since it seems difficult to prespecify the degree of contamination beforehand, this paper uses multilayer perceptron to construct the robust nonlinear interval regression model using the genetic algorithm. Outliers beyond or beneath the data interval will impose slight effect on the determination of data interval. Simulation results demonstrate that the proposed method performs well for contaminated datasets. PMID:25110755

Multilayer perceptron for robust nonlinear interval regression analysis using genetic algorithms.

PubMed

Hu, Yi-Chung

2014-01-01

On the basis of fuzzy regression, computational models in intelligence such as neural networks have the capability to be applied to nonlinear interval regression analysis for dealing with uncertain and imprecise data. When training data are not contaminated by outliers, computational models perform well by including almost all given training data in the data interval. Nevertheless, since training data are often corrupted by outliers, robust learning algorithms employed to resist outliers for interval regression analysis have been an interesting area of research. Several approaches involving computational intelligence are effective for resisting outliers, but the required parameters for these approaches are related to whether the collected data contain outliers or not. Since it seems difficult to prespecify the degree of contamination beforehand, this paper uses multilayer perceptron to construct the robust nonlinear interval regression model using the genetic algorithm. Outliers beyond or beneath the data interval will impose slight effect on the determination of data interval. Simulation results demonstrate that the proposed method performs well for contaminated datasets.

PRECONDITIONED CONJUGATE-GRADIENT 2 (PCG2), a computer program for solving ground-water flow equations

USGS Publications Warehouse

Hill, Mary C.

1990-01-01

This report documents PCG2 : a numerical code to be used with the U.S. Geological Survey modular three-dimensional, finite-difference, ground-water flow model . PCG2 uses the preconditioned conjugate-gradient method to solve the equations produced by the model for hydraulic head. Linear or nonlinear flow conditions may be simulated. PCG2 includes two reconditioning options : modified incomplete Cholesky preconditioning, which is efficient on scalar computers; and polynomial preconditioning, which requires less computer storage and, with modifications that depend on the computer used, is most efficient on vector computers . Convergence of the solver is determined using both head-change and residual criteria. Nonlinear problems are solved using Picard iterations. This documentation provides a description of the preconditioned conjugate gradient method and the two preconditioners, detailed instructions for linking PCG2 to the modular model, sample data inputs, a brief description of PCG2, and a FORTRAN listing.

Application of nonlinear transformations to automatic flight control

NASA Technical Reports Server (NTRS)

Meyer, G.; Su, R.; Hunt, L. R.

1984-01-01

The theory of transformations of nonlinear systems to linear ones is applied to the design of an automatic flight controller for the UH-1H helicopter. The helicopter mathematical model is described and it is shown to satisfy the necessary and sufficient conditions for transformability. The mapping is constructed, taking the nonlinear model to canonical form. The performance of the automatic control system in a detailed simulation on the flight computer is summarized.

Solution of nonlinear multivariable constrained systems using a gradient projection digital algorithm that is insensitive to the initial state

NASA Technical Reports Server (NTRS)

Hargrove, A.

1982-01-01

Optimal digital control of nonlinear multivariable constrained systems was studied. The optimal controller in the form of an algorithm was improved and refined by reducing running time and storage requirements. A particularly difficult system of nine nonlinear state variable equations was chosen as a test problem for analyzing and improving the controller. Lengthy analysis, modeling, computing and optimization were accomplished. A remote interactive teletype terminal was installed. Analysis requiring computer usage of short duration was accomplished using Tuskegee's VAX 11/750 system.

Nonlinear Model Predictive Control for Cooperative Control and Estimation

NASA Astrophysics Data System (ADS)

Ru, Pengkai

Recent advances in computational power have made it possible to do expensive online computations for control systems. It is becoming more realistic to perform computationally intensive optimization schemes online on systems that are not intrinsically stable and/or have very small time constants. Being one of the most important optimization based control approaches, model predictive control (MPC) has attracted a lot of interest from the research community due to its natural ability to incorporate constraints into its control formulation. Linear MPC has been well researched and its stability can be guaranteed in the majority of its application scenarios. However, one issue that still remains with linear MPC is that it completely ignores the system's inherent nonlinearities thus giving a sub-optimal solution. On the other hand, if achievable, nonlinear MPC, would naturally yield a globally optimal solution and take into account all the innate nonlinear characteristics. While an exact solution to a nonlinear MPC problem remains extremely computationally intensive, if not impossible, one might wonder if there is a middle ground between the two. We tried to strike a balance in this dissertation by employing a state representation technique, namely, the state dependent coefficient (SDC) representation. This new technique would render an improved performance in terms of optimality compared to linear MPC while still keeping the problem tractable. In fact, the computational power required is bounded only by a constant factor of the completely linearized MPC. The purpose of this research is to provide a theoretical framework for the design of a specific kind of nonlinear MPC controller and its extension into a general cooperative scheme. The controller is designed and implemented on quadcopter systems.

Extended MHD modeling of nonlinear instabilities in fusion and space plasmas

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

Germaschewski, Kai

A number of different sub-projects where pursued within this DOE early career project. The primary focus was on using fully nonlinear, curvilinear, extended MHD simulations of instabilities with applications to fusion and space plasmas. In particular, we performed comprehensive studies of the dynamics of the double tearing mode in different regimes and confi gurations, using Cartesian and cyclindrical geometry and investigating both linear and non-linear dynamics. In addition to traditional extended MHD involving Hall term and electron pressure gradient, we also employed a new multi-fluid moment model, which shows great promise to incorporate kinetic effects, in particular off-diagonal elements ofmore » the pressure tensor, in a fluid model, which is naturally computationally much cheaper than fully kinetic particle or Vlasov simulations. We used our Vlasov code for detailed studies of how weak collisions effect plasma echos. In addition, we have played an important supporting role working with the PPPL theory group around Will Fox and Amitava Bhattacharjee on providing simulation support for HED plasma experiments performed at high-powered laser facilities like OMEGA-EP in Rochester, NY. This project has support a great number of computational advances in our fluid and kinetic plasma models, and has been crucial to winning multiple INCITE computer time awards that supported our computational modeling.« less

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.

Effect of nonlinearity on lesion formation for high-intensity focused ultrasound (HIFU) exposures

NASA Astrophysics Data System (ADS)

Lee, Paul; Lizzi, Frederic L.; Ketterling, Jeffrey A.; Vecchio, Christopher J.

2004-05-01

This study examined the effects of nonlinear propagation phenomena on two types of HIFU transducers (5 MHz) being used for thermal treatments of disease. The first transducer is a 5-element annular array. The second is a transducer with a 5-strip electrode; its multilobed focused beam is designed to efficiently produce broad, paddle-shaped lesions. The beam patterns of these transducers were computed using a variety of excitation patterns for electronic focusing of the annular array and variation of lesion size for the strip-electrode transducer. A range of intensities was studied to determine how nonlinear propagation affects the beam shape, constituent frequency content, grating lobes, etc. These 3D computations used a finite-amplitude beam propagation model that combined the angular spectrum method and Burger's equation to compute the diffraction and nonlinear effects, respectively. Computed beam patterns were compared with hydrophone measurements for each transducer. The linear and nonlinear beam patterns were used to compute the absorbed thermal dose, and the bioheat equation was evaluated to calculate 3D temperature rises and geometry of induced lesions. Computed lesion sizes and shapes were compared to in vitro lesions created by each HIFU transducer. [Work supported by NCI and NHLBI Grant 5R01 CA84588.

Research study on stabilization and control: Modern sampled-data control theory. Continuous and discrete describing function analysis of the LST system. [with emphasis on the control moment gyroscope control loop

NASA Technical Reports Server (NTRS)

Kuo, B. C.; Singh, G.

1974-01-01

The dynamics of the Large Space Telescope (LST) control system were studied in order to arrive at a simplified model for computer simulation without loss of accuracy. The frictional nonlinearity of the Control Moment Gyroscope (CMG) Control Loop was analyzed in a model to obtain data for the following: (1) a continuous describing function for the gimbal friction nonlinearity; (2) a describing function of the CMG nonlinearity using an analytical torque equation; and (3) the discrete describing function and function plots for CMG functional linearity. Preliminary computer simulations are shown for the simplified LST system, first without, and then with analytical torque expressions. Transfer functions of the sampled-data LST system are also described. A final computer simulation is presented which uses elements of the simplified sampled-data LST system with analytical CMG frictional torque expressions.

Evaluation of Inelastic Constitutive Models for Nonlinear Structural Analysis

NASA Technical Reports Server (NTRS)

Kaufman, A.

1983-01-01

The influence of inelastic material models on computed stress-strain states, and therefore predicted lives, was studied for thermomechanically loaded structures. Nonlinear structural analyses were performed on a fatigue specimen which was subjected to thermal cycling in fluidized beds and on a mechanically load cycled benchmark notch specimen. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic-kinematic, combined plus transient creep) were exercised. Of the plasticity models, kinematic hardening gave results most consistent with experimental observations. Life predictions using the computed strain histories at the critical location with a Strainrange Partitioning approach considerably overpredicted the crack initiation life of the thermal fatigue specimen.

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.

On the numerical treatment of nonlinear source terms in reaction-convection equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1992-01-01

The objectives of this paper are to investigate how various numerical treatments of the nonlinear source term in a model reaction-convection equation can affect the stability of steady-state numerical solutions and to show under what conditions the conventional linearized analysis breaks down. The underlying goal is to provide part of the basic building blocks toward the ultimate goal of constructing suitable numerical schemes for hypersonic reacting flows, combustions and certain turbulence models in compressible Navier-Stokes computations. It can be shown that nonlinear analysis uncovers much of the nonlinear phenomena which linearized analysis is not capable of predicting in a model reaction-convection equation.

Employment of CB models for non-linear dynamic analysis

NASA Technical Reports Server (NTRS)

Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.

1990-01-01

The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.

Quasi-Maximum Likelihood Estimation of Structural Equation Models with Multiple Interaction and Quadratic Effects

ERIC Educational Resources Information Center

Klein, Andreas G.; Muthen, Bengt O.

2007-01-01

In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly…

Nonlinear stability in reaction-diffusion systems via optimal Lyapunov functions

NASA Astrophysics Data System (ADS)

Lombardo, S.; Mulone, G.; Trovato, M.

2008-06-01

We define optimal Lyapunov functions to study nonlinear stability of constant solutions to reaction-diffusion systems. A computable and finite radius of attraction for the initial data is obtained. Applications are given to the well-known Brusselator model and a three-species model for the spatial spread of rabies among foxes.

A LEAST ABSOLUTE SHRINKAGE AND SELECTION OPERATOR (LASSO) FOR NONLINEAR SYSTEM IDENTIFICATION

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Lofberg, Johan; Brenner, Martin J.

2006-01-01

Identification of parametric nonlinear models involves estimating unknown parameters and detecting its underlying structure. Structure computation is concerned with selecting a subset of parameters to give a parsimonious description of the system which may afford greater insight into the functionality of the system or a simpler controller design. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear systems. The LASSO minimises the residual sum of squares by the addition of a 1 penalty term on the parameter vector of the traditional 2 minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. The performance of this LASSO structure detection method was evaluated by using it to estimate the structure of a nonlinear polynomial model. Applicability of the method to more complex systems such as those encountered in aerospace applications was shown by identifying a parsimonious system description of the F/A-18 Active Aeroelastic Wing using flight test data.

PROGRAM VSAERO: A computer program for calculating the non-linear aerodynamic characteristics of arbitrary configurations: User's manual

NASA Technical Reports Server (NTRS)

Maskew, B.

1982-01-01

VSAERO is a computer program used to predict the nonlinear aerodynamic characteristics of arbitrary three-dimensional configurations in subsonic flow. Nonlinear effects of vortex separation and vortex surface interaction are treated in an iterative wake-shape calculation procedure, while the effects of viscosity are treated in an iterative loop coupling potential-flow and integral boundary-layer calculations. The program employs a surface singularity panel method using quadrilateral panels on which doublet and source singularities are distributed in a piecewise constant form. This user's manual provides a brief overview of the mathematical model, instructions for configuration modeling and a description of the input and output data. A listing of a sample case is included.

Photonic single nonlinear-delay dynamical node for information processing

NASA Astrophysics Data System (ADS)

Ortín, Silvia; San-Martín, Daniel; Pesquera, Luis; Gutiérrez, José Manuel

2012-06-01

An electro-optical system with a delay loop based on semiconductor lasers is investigated for information processing by performing numerical simulations. This system can replace a complex network of many nonlinear elements for the implementation of Reservoir Computing. We show that a single nonlinear-delay dynamical system has the basic properties to perform as reservoir: short-term memory and separation property. The computing performance of this system is evaluated for two prediction tasks: Lorenz chaotic time series and nonlinear auto-regressive moving average (NARMA) model. We sweep the parameters of the system to find the best performance. The results achieved for the Lorenz and the NARMA-10 tasks are comparable to those obtained by other machine learning methods.

Virtual-pulse time integral methodology: A new explicit approach for computational dynamics - Theoretical developments for general nonlinear structural dynamics

NASA Technical Reports Server (NTRS)

Chen, Xiaoqin; Tamma, Kumar K.; Sha, Desong

1993-01-01

The present paper describes a new explicit virtual-pulse time integral methodology for nonlinear structural dynamics problems. The purpose of the paper is to provide the theoretical basis of the methodology and to demonstrate applicability of the proposed formulations to nonlinear dynamic structures. Different from the existing numerical methods such as direct time integrations or mode superposition techniques, the proposed methodology offers new perspectives and methodology of development, and possesses several unique and attractive computational characteristics. The methodology is tested and compared with the implicit Newmark method (trapezoidal rule) through a nonlinear softening and hardening spring dynamic models. The numerical results indicate that the proposed explicit virtual-pulse time integral methodology is an excellent alternative for solving general nonlinear dynamic problems.

Regression modeling of ground-water flow

USGS Publications Warehouse

Cooley, R.L.; Naff, R.L.

1985-01-01

Nonlinear multiple regression methods are developed to model and analyze groundwater flow systems. Complete descriptions of regression methodology as applied to groundwater flow models allow scientists and engineers engaged in flow modeling to apply the methods to a wide range of problems. Organization of the text proceeds from an introduction that discusses the general topic of groundwater flow modeling, to a review of basic statistics necessary to properly apply regression techniques, and then to the main topic: exposition and use of linear and nonlinear regression to model groundwater flow. Statistical procedures are given to analyze and use the regression models. A number of exercises and answers are included to exercise the student on nearly all the methods that are presented for modeling and statistical analysis. Three computer programs implement the more complex methods. These three are a general two-dimensional, steady-state regression model for flow in an anisotropic, heterogeneous porous medium, a program to calculate a measure of model nonlinearity with respect to the regression parameters, and a program to analyze model errors in computed dependent variables such as hydraulic head. (USGS)

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

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

Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Errormore » analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.« less

Numerical solution methods for viscoelastic orthotropic materials

NASA Technical Reports Server (NTRS)

Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

1988-01-01

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Equivalent reduced model technique development for nonlinear system dynamic response

NASA Astrophysics Data System (ADS)

Thibault, Louis; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2013-04-01

The dynamic response of structural systems commonly involves nonlinear effects. Often times, structural systems are made up of several components, whose individual behavior is essentially linear compared to the total assembled system. However, the assembly of linear components using highly nonlinear connection elements or contact regions causes the entire system to become nonlinear. Conventional transient nonlinear integration of the equations of motion can be extremely computationally intensive, especially when the finite element models describing the components are very large and detailed. In this work, the equivalent reduced model technique (ERMT) is developed to address complicated nonlinear contact problems. ERMT utilizes a highly accurate model reduction scheme, the System equivalent reduction expansion process (SEREP). Extremely reduced order models that provide dynamic characteristics of linear components, which are interconnected with highly nonlinear connection elements, are formulated with SEREP for the dynamic response evaluation using direct integration techniques. The full-space solution will be compared to the response obtained using drastically reduced models to make evident the usefulness of the technique for a variety of analytical cases.

A numerical study of different projection-based model reduction techniques applied to computational homogenisation

NASA Astrophysics Data System (ADS)

Soldner, Dominic; Brands, Benjamin; Zabihyan, Reza; Steinmann, Paul; Mergheim, Julia

2017-10-01

Computing the macroscopic material response of a continuum body commonly involves the formulation of a phenomenological constitutive model. However, the response is mainly influenced by the heterogeneous microstructure. Computational homogenisation can be used to determine the constitutive behaviour on the macro-scale by solving a boundary value problem at the micro-scale for every so-called macroscopic material point within a nested solution scheme. Hence, this procedure requires the repeated solution of similar microscopic boundary value problems. To reduce the computational cost, model order reduction techniques can be applied. An important aspect thereby is the robustness of the obtained reduced model. Within this study reduced-order modelling (ROM) for the geometrically nonlinear case using hyperelastic materials is applied for the boundary value problem on the micro-scale. This involves the Proper Orthogonal Decomposition (POD) for the primary unknown and hyper-reduction methods for the arising nonlinearity. Therein three methods for hyper-reduction, differing in how the nonlinearity is approximated and the subsequent projection, are compared in terms of accuracy and robustness. Introducing interpolation or Gappy-POD based approximations may not preserve the symmetry of the system tangent, rendering the widely used Galerkin projection sub-optimal. Hence, a different projection related to a Gauss-Newton scheme (Gauss-Newton with Approximated Tensors- GNAT) is favoured to obtain an optimal projection and a robust reduced model.

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems

PubMed Central

Rodriguez-Fernandez, Maria; Egea, Jose A; Banga, Julio R

2006-01-01

Background We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness. Results We have developed a new procedure based on the scatter search methodology for nonlinear optimization of dynamic models of arbitrary (or even unknown) structure (i.e. black-box models). In this contribution, we describe and apply this novel metaheuristic, inspired by recent developments in the field of operations research, to a set of complex identification problems and we make a critical comparison with respect to the previous (above mentioned) successful methods. Conclusion Robust and efficient methods for parameter estimation are of key importance in systems biology and related areas. The new metaheuristic presented in this paper aims to ensure the proper solution of these problems by adopting a global optimization approach, while keeping the computational effort under reasonable values. This new metaheuristic was applied to a set of three challenging parameter estimation problems of nonlinear dynamic biological systems, outperforming very significantly all the methods previously used for these benchmark problems. PMID:17081289

Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems.

PubMed

Rodriguez-Fernandez, Maria; Egea, Jose A; Banga, Julio R

2006-11-02

We consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness. We have developed a new procedure based on the scatter search methodology for nonlinear optimization of dynamic models of arbitrary (or even unknown) structure (i.e. black-box models). In this contribution, we describe and apply this novel metaheuristic, inspired by recent developments in the field of operations research, to a set of complex identification problems and we make a critical comparison with respect to the previous (above mentioned) successful methods. Robust and efficient methods for parameter estimation are of key importance in systems biology and related areas. The new metaheuristic presented in this paper aims to ensure the proper solution of these problems by adopting a global optimization approach, while keeping the computational effort under reasonable values. This new metaheuristic was applied to a set of three challenging parameter estimation problems of nonlinear dynamic biological systems, outperforming very significantly all the methods previously used for these benchmark problems.

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.

Nonlinear Visco-Elastic Response of Composites via Micro-Mechanical Models

NASA Technical Reports Server (NTRS)

Gates, Thomas S.; Sridharan, Srinivasan

2005-01-01

Micro-mechanical models for a study of nonlinear visco-elastic response of composite laminae are developed and their performance compared. A single integral constitutive law proposed by Schapery and subsequently generalized to multi-axial states of stress is utilized in the study for the matrix material. This is used in conjunction with a computationally facile scheme in which hereditary strains are computed using a recursive relation suggested by Henriksen. Composite response is studied using two competing micro-models, viz. a simplified Square Cell Model (SSCM) and a Finite Element based self-consistent Cylindrical Model (FECM). The algorithm is developed assuming that the material response computations are carried out in a module attached to a general purpose finite element program used for composite structural analysis. It is shown that the SSCM as used in investigations of material nonlinearity can involve significant errors in the prediction of transverse Young's modulus and shear modulus. The errors in the elastic strains thus predicted are of the same order of magnitude as the creep strains accruing due to visco-elasticity. The FECM on the other hand does appear to perform better both in the prediction of elastic constants and the study of creep response.

A hierarchy for modeling high speed propulsion systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Deabreu, Alex

1991-01-01

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery, such as inlets, ramjets, and scramjets. The discussion is separated into four areas: (1) computational fluid dynamics models for the entire nonlinear system or high order nonlinear models; (2) high order linearized models derived from fundamental physics; (3) low order linear models obtained from the other high order models; and (4) low order nonlinear models (order here refers to the number of dynamic states). Included in the discussion are any special considerations based on the relevant control system designs. The methods discussed are for the quasi-one-dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, including moving normal shocks, hammershocks, simple subsonic combustion via heat addition, temperature dependent gases, detonations, and thermal choking. The report also contains a comprehensive list of papers and theses generated by this grant.

Modern meta-heuristics based on nonlinear physics processes: A review of models and design procedures

NASA Astrophysics Data System (ADS)

Salcedo-Sanz, S.

2016-10-01

Meta-heuristic algorithms are problem-solving methods which try to find good-enough solutions to very hard optimization problems, at a reasonable computation time, where classical approaches fail, or cannot even been applied. Many existing meta-heuristics approaches are nature-inspired techniques, which work by simulating or modeling different natural processes in a computer. Historically, many of the most successful meta-heuristic approaches have had a biological inspiration, such as evolutionary computation or swarm intelligence paradigms, but in the last few years new approaches based on nonlinear physics processes modeling have been proposed and applied with success. Non-linear physics processes, modeled as optimization algorithms, are able to produce completely new search procedures, with extremely effective exploration capabilities in many cases, which are able to outperform existing optimization approaches. In this paper we review the most important optimization algorithms based on nonlinear physics, how they have been constructed from specific modeling of a real phenomena, and also their novelty in terms of comparison with alternative existing algorithms for optimization. We first review important concepts on optimization problems, search spaces and problems' difficulty. Then, the usefulness of heuristics and meta-heuristics approaches to face hard optimization problems is introduced, and some of the main existing classical versions of these algorithms are reviewed. The mathematical framework of different nonlinear physics processes is then introduced as a preparatory step to review in detail the most important meta-heuristics based on them. A discussion on the novelty of these approaches, their main computational implementation and design issues, and the evaluation of a novel meta-heuristic based on Strange Attractors mutation will be carried out to complete the review of these techniques. We also describe some of the most important application areas, in broad sense, of meta-heuristics, and describe free-accessible software frameworks which can be used to make easier the implementation of these algorithms.

A Physics-driven Neural Networks-based Simulation System (PhyNNeSS) for multimodal interactive virtual environments involving nonlinear deformable objects

PubMed Central

De, Suvranu; Deo, Dhannanjay; Sankaranarayanan, Ganesh; Arikatla, Venkata S.

2012-01-01

Background While an update rate of 30 Hz is considered adequate for real time graphics, a much higher update rate of about 1 kHz is necessary for haptics. Physics-based modeling of deformable objects, especially when large nonlinear deformations and complex nonlinear material properties are involved, at these very high rates is one of the most challenging tasks in the development of real time simulation systems. While some specialized solutions exist, there is no general solution for arbitrary nonlinearities. Methods In this work we present PhyNNeSS - a Physics-driven Neural Networks-based Simulation System - to address this long-standing technical challenge. The first step is an off-line pre-computation step in which a database is generated by applying carefully prescribed displacements to each node of the finite element models of the deformable objects. In the next step, the data is condensed into a set of coefficients describing neurons of a Radial Basis Function network (RBFN). During real-time computation, these neural networks are used to reconstruct the deformation fields as well as the interaction forces. Results We present realistic simulation examples from interactive surgical simulation with real time force feedback. As an example, we have developed a deformable human stomach model and a Penrose-drain model used in the Fundamentals of Laparoscopic Surgery (FLS) training tool box. Conclusions A unique computational modeling system has been developed that is capable of simulating the response of nonlinear deformable objects in real time. The method distinguishes itself from previous efforts in that a systematic physics-based pre-computational step allows training of neural networks which may be used in real time simulations. We show, through careful error analysis, that the scheme is scalable, with the accuracy being controlled by the number of neurons used in the simulation. PhyNNeSS has been integrated into SoFMIS (Software Framework for Multimodal Interactive Simulation) for general use. PMID:22629108

Center for Extended Magnetohydrodynamic Modeling Cooperative Agreement

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

Carl R. Sovinec

The Center for Extended Magnetohydrodynamic Modeling (CEMM) is developing computer simulation models for predicting the behavior of magnetically confined plasmas. Over the first phase of support from the Department of Energy’s Scientific Discovery through Advanced Computing (SciDAC) initiative, the focus has been on macroscopic dynamics that alter the confinement properties of magnetic field configurations. The ultimate objective is to provide computational capabilities to predict plasma behavior—not unlike computational weather prediction—to optimize performance and to increase the reliability of magnetic confinement for fusion energy. Numerical modeling aids theoretical research by solving complicated mathematical models of plasma behavior including strong nonlinear effectsmore » and the influences of geometrical shaping of actual experiments. The numerical modeling itself remains an area of active research, due to challenges associated with simulating multiple temporal and spatial scales. The research summarized in this report spans computational and physical topics associated with state of the art simulation of magnetized plasmas. The tasks performed for this grant are categorized according to whether they are primarily computational, algorithmic, or application-oriented in nature. All involve the development and use of the Non-Ideal Magnetohydrodynamics with Rotation, Open Discussion (NIMROD) code, which is described at http://nimrodteam.org. With respect to computation, we have tested and refined methods for solving the large algebraic systems of equations that result from our numerical approximations of the physical model. Collaboration with the Terascale Optimal PDE Solvers (TOPS) SciDAC center led us to the SuperLU_DIST software library [http://crd.lbl.gov/~xiaoye/SuperLU/] for solving large sparse matrices using direct methods on parallel computers. Switching to this solver library boosted NIMROD’s performance by a factor of five in typical large nonlinear simulations, which has been publicized as a success story of SciDAC-fostered collaboration. Furthermore, the SuperLU software does not assume any mathematical symmetry, and its generality provides an important capability for extending the physical model beyond magnetohydrodynamics (MHD). With respect to algorithmic and model development, our most significant accomplishment is the development of a new method for solving plasma models that treat electrons as an independent plasma component. These ‘two-fluid’ models encompass MHD and add temporal and spatial scales that are beyond the response of the ion species. Implementation and testing of a previously published algorithm did not prove successful for NIMROD, and the new algorithm has since been devised, analyzed, and implemented. Two-fluid modeling, an important objective of the original NIMROD project, is now routine in 2D applications. Algorithmic components for 3D modeling are in place and tested; though, further computational work is still needed for efficiency. Other algorithmic work extends the ion-fluid stress tensor to include models for parallel and gyroviscous stresses. In addition, our hot-particle simulation capability received important refinements that permitted completion of a benchmark with the M3D code. A highlight of our applications work is the edge-localized mode (ELM) modeling, which was part of the first-ever computational Performance Target for the DOE Office of Fusion Energy Science, see http://www.science.doe.gov/ofes/performancetargets.shtml. Our efforts allowed MHD simulations to progress late into the nonlinear stage, where energy is conducted to the wall location. They also produced a two-fluid ELM simulation starting from experimental information and demonstrating critical drift effects that are characteristic of two-fluid physics. Another important application is the internal kink mode in a tokamak. Here, the primary purpose of the study has been to benchmark the two main code development lines of CEMM, NIMROD and M3D, on a relevant nonlinear problem. Results from the two codes show repeating nonlinear relaxation events driven by the kink mode over quantitatively comparable timescales. The work has launched a more comprehensive nonlinear benchmarking exercise, where realistic transport effects have an important role.« less

A unified model for transfer alignment at random misalignment angles based on second-order EKF

NASA Astrophysics Data System (ADS)

Cui, Xiao; Mei, Chunbo; Qin, Yongyuan; Yan, Gongmin; Liu, Zhenbo

2017-04-01

In the transfer alignment process of inertial navigation systems (INSs), the conventional linear error model based on the small misalignment angle assumption cannot be applied to large misalignment situations. Furthermore, the nonlinear model based on the large misalignment angle suffers from redundant computation with nonlinear filters. This paper presents a unified model for transfer alignment suitable for arbitrary misalignment angles. The alignment problem is transformed into an estimation of the relative attitude between the master INS (MINS) and the slave INS (SINS), by decomposing the attitude matrix of the latter. Based on the Rodriguez parameters, a unified alignment model in the inertial frame with the linear state-space equation and a second order nonlinear measurement equation are established, without making any assumptions about the misalignment angles. Furthermore, we employ the Taylor series expansions on the second-order nonlinear measurement equation to implement the second-order extended Kalman filter (EKF2). Monte-Carlo simulations demonstrate that the initial alignment can be fulfilled within 10 s, with higher accuracy and much smaller computational cost compared with the traditional unscented Kalman filter (UKF) at large misalignment angles.

Numerical modeling of the atmosphere with an isentropic vertical coordinate

NASA Technical Reports Server (NTRS)

Hsu, Yueh-Jiuan G.; Arakawa, Akio

1990-01-01

A theta-coordinate model simulating the nonlinear evolution of a baroclinic wave is presented. In the model, vertical discretization maintains important integral constraints such as conservation of the angular momentum and total energy. A massless-layer approach is used in the treatment of the intersections of coordinate surfaces with the lower boundary. This formally eliminates the intersection problem, but raises other computational problems. Horizontal discretization of the continuity and momentum equations in the model are designed to overcome these problems. Selected results from a 10-day integration with the 25-layer, beta-plane version of the model are presented. It is concluded that the model can simulate the nonlinear evolution of a baroclinic wave and associated dynamical processes without major computational difficulties.

Bio-inspired computational heuristics to study Lane-Emden systems arising in astrophysics model.

PubMed

Ahmad, Iftikhar; Raja, Muhammad Asif Zahoor; Bilal, Muhammad; Ashraf, Farooq

2016-01-01

This study reports novel hybrid computational methods for the solutions of nonlinear singular Lane-Emden type differential equation arising in astrophysics models by exploiting the strength of unsupervised neural network models and stochastic optimization techniques. In the scheme the neural network, sub-part of large field called soft computing, is exploited for modelling of the equation in an unsupervised manner. The proposed approximated solutions of higher order ordinary differential equation are calculated with the weights of neural networks trained with genetic algorithm, and pattern search hybrid with sequential quadratic programming for rapid local convergence. The results of proposed solvers for solving the nonlinear singular systems are in good agreements with the standard solutions. Accuracy and convergence the design schemes are demonstrated by the results of statistical performance measures based on the sufficient large number of independent runs.

Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models.

PubMed

Raja, Muhammad Asif Zahoor; Kiani, Adiqa Kausar; Shehzad, Azam; Zameer, Aneela

2016-01-01

In this study, bio-inspired computing is exploited for solving system of nonlinear equations using variants of genetic algorithms (GAs) as a tool for global search method hybrid with sequential quadratic programming (SQP) for efficient local search. The fitness function is constructed by defining the error function for systems of nonlinear equations in mean square sense. The design parameters of mathematical models are trained by exploiting the competency of GAs and refinement are carried out by viable SQP algorithm. Twelve versions of the memetic approach GA-SQP are designed by taking a different set of reproduction routines in the optimization process. Performance of proposed variants is evaluated on six numerical problems comprising of system of nonlinear equations arising in the interval arithmetic benchmark model, kinematics, neurophysiology, combustion and chemical equilibrium. Comparative studies of the proposed results in terms of accuracy, convergence and complexity are performed with the help of statistical performance indices to establish the worth of the schemes. Accuracy and convergence of the memetic computing GA-SQP is found better in each case of the simulation study and effectiveness of the scheme is further established through results of statistics based on different performance indices for accuracy and complexity.

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

Non-linear shipboard shock analysis of the Tomahawk missile shock isolation system

NASA Technical Reports Server (NTRS)

Leifer, Joel; Gross, Michael

1987-01-01

The identification, quantification, computer modeling and verification of the Tomahawk nonlinear liquid spring shock isolation system in a surface ship Vertical Launch System (VLS) are discussed. The isolation system hardware and mode of operation is detailed in an effort to understand the nonlinearities. These nonlinearities are then quantified and modeled using the MSC/NASTRAN finite element code. The model was verified using experimental data from the Navel Ordnance Systems Center MIL-S-901 medium weight shock tests of August 1986. The model was then used to predict the Tomahawk response to the CG-53 USS Mobile Bay shock trials of May-June 1987. Results indicate that the model is an accurate mathematical representation of the physical system either functioning as designed or in an impaired condition due to spring failure.

Galerkin finite element scheme for magnetostrictive structures and composites

NASA Astrophysics Data System (ADS)

Kannan, Kidambi Srinivasan

The ever increasing-role of magnetostrictives in actuation and sensing applications is an indication of their importance in the emerging field of smart structures technology. As newer, and more complex, applications are developed, there is a growing need for a reliable computational tool that can effectively address the magneto-mechanical interactions and other nonlinearities in these materials and in structures incorporating them. This thesis presents a continuum level quasi-static, three-dimensional finite element computational scheme for modeling the nonlinear behavior of bulk magnetostrictive materials and particulate magnetostrictive composites. Models for magnetostriction must deal with two sources of nonlinearities-nonlinear body forces/moments in equilibrium equations governing magneto-mechanical interactions in deformable and magnetized bodies; and nonlinear coupled magneto-mechanical constitutive models for the material of interest. In the present work, classical differential formulations for nonlinear magneto-mechanical interactions are recast in integral form using the weighted-residual method. A discretized finite element form is obtained by applying the Galerkin technique. The finite element formulation is based upon three dimensional eight-noded (isoparametric) brick element interpolation functions and magnetostatic infinite elements at the boundary. Two alternative possibilities are explored for establishing the nonlinear incremental constitutive model-characterization in terms of magnetic field or in terms of magnetization. The former methodology is the one most commonly used in the literature. In this work, a detailed comparative study of both methodologies is carried out. The computational scheme is validated, qualitatively and quantitatively, against experimental measurements published in the literature on structures incorporating the magnetostrictive material Terfenol-D. The influence of nonlinear body forces and body moments of magnetic origin, on the response of magnetostrictive structures to complex mechanical and magnetic loading conditions, is carefully examined. While monolithic magnetostrictive materials have been commercially-available since the late eighties, attention in the smart structures research community has recently focussed upon building and using magnetostrictive particulate composite structures for conventional actuation applications and novel sensing methodologies in structural health monitoring. A particulate magnetostrictive composite element has been developed in the present work to model such structures. This composite element incorporates interactions between magnetostrictive particles by combining a numerical micromechanical analysis based on magneto-mechanical Green's functions, with a homogenization scheme based upon the Mori-Tanaka approach. This element has been applied to the simulation of particulate actuators and sensors reported in the literature. Simulation results are compared to experimental data for validation purposes. The computational schemes developed, for bulk materials and for composites, are expected to be of great value to researchers and designers of novel applications based on magnetostrictives.

Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

NASA Astrophysics Data System (ADS)

Boudineau, Mégane; Carfantan, Hervé; Bourguignon, Sébastien; Bazot, Michael

2016-06-01

We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.

Modeling Elastic Wave Propagation from an Underground Chemical Explosion Using Higher Order Finite Difference Approximation: Theory, Validation and Application to SPE

NASA Astrophysics Data System (ADS)

Hirakawa, E. T.; Ezzedine, S. M.; Petersson, A.; Sjogreen, B.; Vorobiev, O.; Pitarka, A.; Antoun, T.; Walter, W. R.

2016-12-01

Motions from underground explosions are governed by non-linear hydrodynamic response of material. However, the numerical calculation of this non-linear constitutive behavior is computationally intensive in contrast to the elastic and acoustic linear wave propagation solvers. Here, we develop a hybrid modeling approach with one-way hydrodynamic-to-elastic coupling in three dimensions in order to propagate explosion generated ground motions from the non-linear near-source region to the far-field. Near source motions are computed using GEODYN-L, a Lagrangian hydrodynamics code for high-energy loading of earth materials. Motions on a dense grid of points sampled on two nested shells located beyond the non-linear damaged zone are saved, and then passed to SW4, an anelastic anisotropic fourth order finite difference code for seismic wave modeling. Our coupling strategy is based on the decomposition and uniqueness theorems where motions are introduced into SW4 as a boundary source and continue to propagate as elastic waves at a much lower computational cost than by using GEODYN-L to cover the entire near- and the far-field domain. The accuracy of the numerical calculations and the coupling strategy is demonstrated in cases with a purely elastic medium as well as non-linear medium. Our hybrid modeling approach is applied to SPE-4' and SPE-5 which are the most recent underground chemical explosions conducted at the Nevada National Security Site (NNSS) where the Source Physics Experiments (SPE) are performed. Our strategy by design is capable of incorporating complex non-linear effects near the source as well as volumetric and topographic material heterogeneity along the propagation path to receiver, and provides new prospects for modeling and understanding explosion generated seismic waveforms. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-698608.

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

Frequency-domain full-waveform inversion with non-linear descent directions

NASA Astrophysics Data System (ADS)

Geng, Yu; Pan, Wenyong; Innanen, Kristopher A.

2018-05-01

Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. We examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss-Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s0 is, in our scheme, proportional to at most (Δs/s0)3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss-Newton FWI update is proportional to (Δs/s0)2. For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. The inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a benchmark FWI approach involving the standard gradient.

Updated Lagrangian finite element formulations of various biological soft tissue non-linear material models: a comprehensive procedure and review.

PubMed

Townsend, Molly T; Sarigul-Klijn, Nesrin

2016-01-01

Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.

Ranking Support Vector Machine with Kernel Approximation

PubMed Central

Dou, Yong

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms. PMID:28293256

Ranking Support Vector Machine with Kernel Approximation.

PubMed

Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2016-02-03

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

Human systems dynamics: Toward a computational model

NASA Astrophysics Data System (ADS)

Eoyang, Glenda H.

2012-09-01

A robust and reliable computational model of complex human systems dynamics could support advancements in theory and practice for social systems at all levels, from intrapersonal experience to global politics and economics. Models of human interactions have evolved from traditional, Newtonian systems assumptions, which served a variety of practical and theoretical needs of the past. Another class of models has been inspired and informed by models and methods from nonlinear dynamics, chaos, and complexity science. None of the existing models, however, is able to represent the open, high dimension, and nonlinear self-organizing dynamics of social systems. An effective model will represent interactions at multiple levels to generate emergent patterns of social and political life of individuals and groups. Existing models and modeling methods are considered and assessed against characteristic pattern-forming processes in observed and experienced phenomena of human systems. A conceptual model, CDE Model, based on the conditions for self-organizing in human systems, is explored as an alternative to existing models and methods. While the new model overcomes the limitations of previous models, it also provides an explanatory base and foundation for prospective analysis to inform real-time meaning making and action taking in response to complex conditions in the real world. An invitation is extended to readers to engage in developing a computational model that incorporates the assumptions, meta-variables, and relationships of this open, high dimension, and nonlinear conceptual model of the complex dynamics of human systems.

Spurious Numerical Solutions Of Differential Equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1995-01-01

Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

Nonlinear Unsteady Aerodynamic Modeling Using Wind Tunnel and Computational Data

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.; Klein, Vladislav; Frink, Neal T.

2016-01-01

Extensions to conventional aircraft aerodynamic models are required to adequately predict responses when nonlinear unsteady flight regimes are encountered, especially at high incidence angles and under maneuvering conditions. For a number of reasons, such as loss of control, both military and civilian aircraft may extend beyond normal and benign aerodynamic flight conditions. In addition, military applications may require controlled flight beyond the normal envelope, and civilian flight may require adequate recovery or prevention methods from these adverse conditions. These requirements have led to the development of more general aerodynamic modeling methods and provided impetus for researchers to improve both techniques and the degree of collaboration between analytical and experimental research efforts. In addition to more general mathematical model structures, dynamic test methods have been designed to provide sufficient information to allow model identification. This paper summarizes research to develop a modeling methodology appropriate for modeling aircraft aerodynamics that include nonlinear unsteady behaviors using both experimental and computational test methods. This work was done at Langley Research Center, primarily under the NASA Aviation Safety Program, to address aircraft loss of control, prevention, and recovery aerodynamics.

Nonlinear hybrid modal synthesis based on branch modes for dynamic analysis of assembled structure

NASA Astrophysics Data System (ADS)

Huang, Xing-Rong; Jézéquel, Louis; Besset, Sébastien; Li, Lin; Sauvage, Olivier

2018-01-01

This paper describes a simple and fast numerical procedure to study the steady state responses of assembled structures with nonlinearities along continuous interfaces. The proposed strategy is based on a generalized nonlinear modal superposition approach supplemented by a double modal synthesis strategy. The reduced nonlinear modes are derived by combining a single nonlinear mode method with reduction techniques relying on branch modes. The modal parameters containing essential nonlinear information are determined and then employed to calculate the stationary responses of the nonlinear system subjected to various types of excitation. The advantages of the proposed nonlinear modal synthesis are mainly derived in three ways: (1) computational costs are considerably reduced, when analyzing large assembled systems with weak nonlinearities, through the use of reduced nonlinear modes; (2) based on the interpolation models of nonlinear modal parameters, the nonlinear modes introduced during the first step can be employed to analyze the same system under various external loads without having to reanalyze the entire system; and (3) the nonlinear effects can be investigated from a modal point of view by analyzing these nonlinear modal parameters. The proposed strategy is applied to an assembled system composed of plates and nonlinear rubber interfaces. Simulation results have proven the efficiency of this hybrid nonlinear modal synthesis, and the computation time has also been significantly reduced.

Localization of Non-Linearly Modeled Autonomous Mobile Robots Using Out-of-Sequence Measurements

PubMed Central

Besada-Portas, Eva; Lopez-Orozco, Jose A.; Lanillos, Pablo; de la Cruz, Jesus M.

2012-01-01

This paper presents a state of the art of the estimation algorithms dealing with Out-of-Sequence (OOS) measurements for non-linearly modeled systems. The state of the art includes a critical analysis of the algorithm properties that takes into account the applicability of these techniques to autonomous mobile robot navigation based on the fusion of the measurements provided, delayed and OOS, by multiple sensors. Besides, it shows a representative example of the use of one of the most computationally efficient approaches in the localization module of the control software of a real robot (which has non-linear dynamics, and linear and non-linear sensors) and compares its performance against other approaches. The simulated results obtained with the selected OOS algorithm shows the computational requirements that each sensor of the robot imposes to it. The real experiments show how the inclusion of the selected OOS algorithm in the control software lets the robot successfully navigate in spite of receiving many OOS measurements. Finally, the comparison highlights that not only is the selected OOS algorithm among the best performing ones of the comparison, but it also has the lowest computational and memory cost. PMID:22736962

Localization of non-linearly modeled autonomous mobile robots using out-of-sequence measurements.

PubMed

Besada-Portas, Eva; Lopez-Orozco, Jose A; Lanillos, Pablo; de la Cruz, Jesus M

2012-01-01

This paper presents a state of the art of the estimation algorithms dealing with Out-of-Sequence (OOS) measurements for non-linearly modeled systems. The state of the art includes a critical analysis of the algorithm properties that takes into account the applicability of these techniques to autonomous mobile robot navigation based on the fusion of the measurements provided, delayed and OOS, by multiple sensors. Besides, it shows a representative example of the use of one of the most computationally efficient approaches in the localization module of the control software of a real robot (which has non-linear dynamics, and linear and non-linear sensors) and compares its performance against other approaches. The simulated results obtained with the selected OOS algorithm shows the computational requirements that each sensor of the robot imposes to it. The real experiments show how the inclusion of the selected OOS algorithm in the control software lets the robot successfully navigate in spite of receiving many OOS measurements. Finally, the comparison highlights that not only is the selected OOS algorithm among the best performing ones of the comparison, but it also has the lowest computational and memory cost.

Bandlimited computerized improvements in characterization of nonlinear systems with memory

NASA Astrophysics Data System (ADS)

Nuttall, Albert H.; Katz, Richard A.; Hughes, Derke R.; Koch, Robert M.

2016-05-01

The present article discusses some inroads in nonlinear signal processing made by the prime algorithm developer, Dr. Albert H. Nuttall and co-authors, a consortium of research scientists from the Naval Undersea Warfare Center Division, Newport, RI. The algorithm, called the Nuttall-Wiener-Volterra 'NWV' algorithm is named for its principal contributors [1], [2],[ 3] over many years of developmental research. The NWV algorithm significantly reduces the computational workload for characterizing nonlinear systems with memory. Following this formulation, two measurement waveforms on the system are required in order to characterize a specified nonlinear system under consideration: (1) an excitation input waveform, x(t) (the transmitted signal); and, (2) a response output waveform, z(t) (the received signal). Given these two measurement waveforms for a given propagation channel, a 'kernel' or 'channel response', h= [h0,h1,h2,h3] between the two measurement points, is computed via a least squares approach that optimizes modeled kernel values by performing a best fit between measured response z(t) and a modeled response y(t). New techniques significantly diminish the exponential growth of the number of computed kernel coefficients at second and third order in order to combat and reasonably alleviate the curse of dimensionality.

On the dimension of complex responses in nonlinear structural vibrations

NASA Astrophysics Data System (ADS)

Wiebe, R.; Spottswood, S. M.

2016-07-01

The ability to accurately model engineering systems under extreme dynamic loads would prove a major breakthrough in many aspects of aerospace, mechanical, and civil engineering. Extreme loads frequently induce both nonlinearities and coupling which increase the complexity of the response and the computational cost of finite element models. Dimension reduction has recently gained traction and promises the ability to distill dynamic responses down to a minimal dimension without sacrificing accuracy. In this context, the dimensionality of a response is related to the number of modes needed in a reduced order model to accurately simulate the response. Thus, an important step is characterizing the dimensionality of complex nonlinear responses of structures. In this work, the dimensionality of the nonlinear response of a post-buckled beam is investigated. Significant detail is dedicated to carefully introducing the experiment, the verification of a finite element model, and the dimensionality estimation algorithm as it is hoped that this system may help serve as a benchmark test case. It is shown that with minor modifications, the method of false nearest neighbors can quantitatively distinguish between the response dimension of various snap-through, non-snap-through, random, and deterministic loads. The state-space dimension of the nonlinear system in question increased from 2-to-10 as the system response moved from simple, low-level harmonic to chaotic snap-through. Beyond the problem studied herein, the techniques developed will serve as a prescriptive guide in developing fast and accurate dimensionally reduced models of nonlinear systems, and eventually as a tool for adaptive dimension-reduction in numerical modeling. The results are especially relevant in the aerospace industry for the design of thin structures such as beams, panels, and shells, which are all capable of spatio-temporally complex dynamic responses that are difficult and computationally expensive to model.

Identification of nonlinear normal modes of engineering structures under broadband forcing

NASA Astrophysics Data System (ADS)

Noël, Jean-Philippe; Renson, L.; Grappasonni, C.; Kerschen, G.

2016-06-01

The objective of the present paper is to develop a two-step methodology integrating system identification and numerical continuation for the experimental extraction of nonlinear normal modes (NNMs) under broadband forcing. The first step processes acquired input and output data to derive an experimental state-space model of the structure. The second step converts this state-space model into a model in modal space from which NNMs are computed using shooting and pseudo-arclength continuation. The method is demonstrated using noisy synthetic data simulated on a cantilever beam with a hardening-softening nonlinearity at its free end.

Does Nonlinear Modeling Play a Role in Plasmid Bioprocess Monitoring Using Fourier Transform Infrared Spectra?

PubMed

Lopes, Marta B; Calado, Cecília R C; Figueiredo, Mário A T; Bioucas-Dias, José M

2017-06-01

The monitoring of biopharmaceutical products using Fourier transform infrared (FT-IR) spectroscopy relies on calibration techniques involving the acquisition of spectra of bioprocess samples along the process. The most commonly used method for that purpose is partial least squares (PLS) regression, under the assumption that a linear model is valid. Despite being successful in the presence of small nonlinearities, linear methods may fail in the presence of strong nonlinearities. This paper studies the potential usefulness of nonlinear regression methods for predicting, from in situ near-infrared (NIR) and mid-infrared (MIR) spectra acquired in high-throughput mode, biomass and plasmid concentrations in Escherichia coli DH5-α cultures producing the plasmid model pVAX-LacZ. The linear methods PLS and ridge regression (RR) are compared with their kernel (nonlinear) versions, kPLS and kRR, as well as with the (also nonlinear) relevance vector machine (RVM) and Gaussian process regression (GPR). For the systems studied, RR provided better predictive performances compared to the remaining methods. Moreover, the results point to further investigation based on larger data sets whenever differences in predictive accuracy between a linear method and its kernelized version could not be found. The use of nonlinear methods, however, shall be judged regarding the additional computational cost required to tune their additional parameters, especially when the less computationally demanding linear methods herein studied are able to successfully monitor the variables under study.

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes.

PubMed

Cheviakov, A F; Ganghoffer, J-F

2016-05-01

The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures. Copyright © 2015 Elsevier Ltd. All rights reserved.

DAKOTA Design Analysis Kit for Optimization and Terascale

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

Adams, Brian M.; Dalbey, Keith R.; Eldred, Michael S.

2010-02-24

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes (computational models) and iterative analysis methods. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and analysis of computational models on high performance computers.A user provides a set of DAKOTA commands in an input file and launches DAKOTA. DAKOTA invokes instances of the computational models, collects their results, and performs systems analyses. DAKOTA contains algorithms for optimization with gradient and nongradient-basedmore » methods; uncertainty quantification with sampling, reliability, polynomial chaos, stochastic collocation, and epistemic methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as hybrid optimization, surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. Services for parallel computing, simulation interfacing, approximation modeling, fault tolerance, restart, and graphics are also included.« less

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

A Computational and Experimental Study of Nonlinear Aspects of Induced Drag

NASA Technical Reports Server (NTRS)

Smith, Stephen C.

1996-01-01

Despite the 80-year history of classical wing theory, considerable research has recently been directed toward planform and wake effects on induced drag. Nonlinear interactions between the trailing wake and the wing offer the possibility of reducing drag. The nonlinear effect of compressibility on induced drag characteristics may also influence wing design. This thesis deals with the prediction of these nonlinear aspects of induced drag and ways to exploit them. A potential benefit of only a few percent of the drag represents a large fuel savings for the world's commercial transport fleet. Computational methods must be applied carefully to obtain accurate induced drag predictions. Trefftz-plane drag integration is far more reliable than surface pressure integration, but is very sensitive to the accuracy of the force-free wake model. The practical use of Trefftz plane drag integration was extended to transonic flow with the Tranair full-potential code. The induced drag characteristics of a typical transport wing were studied with Tranair, a full-potential method, and A502, a high-order linear panel method to investigate changes in lift distribution and span efficiency due to compressibility. Modeling the force-free wake is a nonlinear problem, even when the flow governing equation is linear. A novel method was developed for computing the force-free wake shape. This hybrid wake-relaxation scheme couples the well-behaved nature of the discrete vortex wake with viscous-core modeling and the high-accuracy velocity prediction of the high-order panel method. The hybrid scheme produced converged wake shapes that allowed accurate Trefftz-plane integration. An unusual split-tip wing concept was studied for exploiting nonlinear wake interaction to reduced induced drag. This design exhibits significant nonlinear interactions between the wing and wake that produced a 12% reduction in induced drag compared to an equivalent elliptical wing at a lift coefficient of 0.7. The performance of the split-tip wing was also investigated by wing tunnel experiments. Induced drag was determined from force measurements by subtracting the estimated viscous drag, and from an analytical drag-decomposition method using a wake survey. The experimental results confirm the computational prediction.

Space-time least-squares Petrov-Galerkin projection in nonlinear model reduction.

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

Choi, Youngsoo; Carlberg, Kevin Thomas

Our work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply Petrov-Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed method applies projection in space and time simultaneously. To accomplish this, the method first introduces a low-dimensional space-time trial subspace, which can be obtained by computing tensor decompositions of state-snapshot data. The method then computes discrete-optimal approximations in this space-time trial subspace by minimizing the residual arising after time discretization over allmore » space and time in a weighted ℓ 2-norm. This norm can be de ned to enable complexity reduction (i.e., hyper-reduction) in time, which leads to space-time collocation and space-time GNAT variants of the ST-LSPG method. Advantages of the approach relative to typical spatial-projection-based nonlinear model reduction methods such as Galerkin projection and least-squares Petrov-Galerkin projection include: (1) a reduction of both the spatial and temporal dimensions of the dynamical system, (2) the removal of spurious temporal modes (e.g., unstable growth) from the state space, and (3) error bounds that exhibit slower growth in time. Numerical examples performed on model problems in fluid dynamics demonstrate the ability of the method to generate orders-of-magnitude computational savings relative to spatial-projection-based reduced-order models without sacrificing accuracy.« less

Robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks.

PubMed

Yan, Zheng; Wang, Jun

2014-03-01

This paper presents a neural network approach to robust model predictive control (MPC) for constrained discrete-time nonlinear systems with unmodeled dynamics affected by bounded uncertainties. The exact nonlinear model of underlying process is not precisely known, but a partially known nominal model is available. This partially known nonlinear model is first decomposed to an affine term plus an unknown high-order term via Jacobian linearization. The linearization residue combined with unmodeled dynamics is then modeled using an extreme learning machine via supervised learning. The minimax methodology is exploited to deal with bounded uncertainties. The minimax optimization problem is reformulated as a convex minimization problem and is iteratively solved by a two-layer recurrent neural network. The proposed neurodynamic approach to nonlinear MPC improves the computational efficiency and sheds a light for real-time implementability of MPC technology. Simulation results are provided to substantiate the effectiveness and characteristics of the proposed approach.

Nonlinear, discrete flood event models, 1. Bayesian estimation of parameters

NASA Astrophysics Data System (ADS)

Bates, Bryson C.; Townley, Lloyd R.

1988-05-01

In this paper (Part 1), a Bayesian procedure for parameter estimation is applied to discrete flood event models. The essence of the procedure is the minimisation of a sum of squares function for models in which the computed peak discharge is nonlinear in terms of the parameters. This objective function is dependent on the observed and computed peak discharges for several storms on the catchment, information on the structure of observation error, and prior information on parameter values. The posterior covariance matrix gives a measure of the precision of the estimated parameters. The procedure is demonstrated using rainfall and runoff data from seven Australian catchments. It is concluded that the procedure is a powerful alternative to conventional parameter estimation techniques in situations where a number of floods are available for parameter estimation. Parts 2 and 3 will discuss the application of statistical nonlinearity measures and prediction uncertainty analysis to calibrated flood models. Bates (this volume) and Bates and Townley (this volume).

Mapping nonlinear receptive field structure in primate retina at single cone resolution

PubMed Central

Li, Peter H; Greschner, Martin; Gunning, Deborah E; Mathieson, Keith; Sher, Alexander; Litke, Alan M; Paninski, Liam

2015-01-01

The function of a neural circuit is shaped by the computations performed by its interneurons, which in many cases are not easily accessible to experimental investigation. Here, we elucidate the transformation of visual signals flowing from the input to the output of the primate retina, using a combination of large-scale multi-electrode recordings from an identified ganglion cell type, visual stimulation targeted at individual cone photoreceptors, and a hierarchical computational model. The results reveal nonlinear subunits in the circuity of OFF midget ganglion cells, which subserve high-resolution vision. The model explains light responses to a variety of stimuli more accurately than a linear model, including stimuli targeted to cones within and across subunits. The recovered model components are consistent with known anatomical organization of midget bipolar interneurons. These results reveal the spatial structure of linear and nonlinear encoding, at the resolution of single cells and at the scale of complete circuits. DOI: http://dx.doi.org/10.7554/eLife.05241.001 PMID:26517879

Computational analysis of nonlinearities within dynamics of cable-based driving systems

NASA Astrophysics Data System (ADS)

Anghelache, G. D.; Nastac, S.

2017-08-01

This paper deals with computational nonlinear dynamics of mechanical systems containing some flexural parts within the actuating scheme, and, especially, the situations of the cable-based driving systems were treated. It was supposed both functional nonlinearities and the real characteristic of the power supply, in order to obtain a realistically computer simulation model being able to provide very feasible results regarding the system dynamics. It was taken into account the transitory and stable regimes during a regular exploitation cycle. The authors present a particular case of a lift system, supposed to be representatively for the objective of this study. The simulations were made based on the values of the essential parameters acquired from the experimental tests and/or the regular practice in the field. The results analysis and the final discussions reveal the correlated dynamic aspects within the mechanical parts, the driving system, and the power supply, whole of these supplying potential sources of particular resonances, within some transitory phases of the working cycle, and which can affect structural and functional dynamics. In addition, it was underlines the influences of computational hypotheses on the both quantitative and qualitative behaviour of the system. Obviously, the most significant consequence of this theoretical and computational research consist by developing an unitary and feasible model, useful to dignify the nonlinear dynamic effects into the systems with cable-based driving scheme, and hereby to help an optimization of the exploitation regime including a dynamics control measures.

A Computer Model of the Cardiovascular System for Effective Learning.

ERIC Educational Resources Information Center

Rothe, Carl F.

1979-01-01

Described is a physiological model which solves a set of interacting, possibly nonlinear, differential equations through numerical integration on a digital computer. Sample printouts are supplied and explained for effects on the components of a cardiovascular system when exercise, hemorrhage, and cardiac failure occur. (CS)

Nonlinear Dynamic Model-Based Multiobjective Sensor Network Design Algorithm for a Plant with an Estimator-Based Control System

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

Paul, Prokash; Bhattacharyya, Debangsu; Turton, Richard

Here, a novel sensor network design (SND) algorithm is developed for maximizing process efficiency while minimizing sensor network cost for a nonlinear dynamic process with an estimator-based control system. The multiobjective optimization problem is solved following a lexicographic approach where the process efficiency is maximized first followed by minimization of the sensor network cost. The partial net present value, which combines the capital cost due to the sensor network and the operating cost due to deviation from the optimal efficiency, is proposed as an alternative objective. The unscented Kalman filter is considered as the nonlinear estimator. The large-scale combinatorial optimizationmore » problem is solved using a genetic algorithm. The developed SND algorithm is applied to an acid gas removal (AGR) unit as part of an integrated gasification combined cycle (IGCC) power plant with CO 2 capture. Due to the computational expense, a reduced order nonlinear model of the AGR process is identified and parallel computation is performed during implementation.« less

Stabilization Approaches for Linear and Nonlinear Reduced Order Models

NASA Astrophysics Data System (ADS)

Rezaian, Elnaz; Wei, Mingjun

2017-11-01

It has been a major concern to establish reduced order models (ROMs) as reliable representatives of the dynamics inherent in high fidelity simulations, while fast computation is achieved. In practice it comes to stability and accuracy of ROMs. Given the inviscid nature of Euler equations it becomes more challenging to achieve stability, especially where moving discontinuities exist. Originally unstable linear and nonlinear ROMs are stabilized here by two approaches. First, a hybrid method is developed by integrating two different stabilization algorithms. At the same time, symmetry inner product is introduced in the generation of ROMs for its known robust behavior for compressible flows. Results have shown a notable improvement in computational efficiency and robustness compared to similar approaches. Second, a new stabilization algorithm is developed specifically for nonlinear ROMs. This method adopts Particle Swarm Optimization to enforce a bounded ROM response for minimum discrepancy between the high fidelity simulation and the ROM outputs. Promising results are obtained in its application on the nonlinear ROM of an inviscid fluid flow with discontinuities. Supported by ARL.

Nonlinear Dynamic Model-Based Multiobjective Sensor Network Design Algorithm for a Plant with an Estimator-Based Control System

DOE PAGES

Paul, Prokash; Bhattacharyya, Debangsu; Turton, Richard; ...

2017-06-06

Here, a novel sensor network design (SND) algorithm is developed for maximizing process efficiency while minimizing sensor network cost for a nonlinear dynamic process with an estimator-based control system. The multiobjective optimization problem is solved following a lexicographic approach where the process efficiency is maximized first followed by minimization of the sensor network cost. The partial net present value, which combines the capital cost due to the sensor network and the operating cost due to deviation from the optimal efficiency, is proposed as an alternative objective. The unscented Kalman filter is considered as the nonlinear estimator. The large-scale combinatorial optimizationmore » problem is solved using a genetic algorithm. The developed SND algorithm is applied to an acid gas removal (AGR) unit as part of an integrated gasification combined cycle (IGCC) power plant with CO 2 capture. Due to the computational expense, a reduced order nonlinear model of the AGR process is identified and parallel computation is performed during implementation.« less

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.

A dc model for power switching transistors suitable for computer-aided design and analysis

NASA Technical Reports Server (NTRS)

Wilson, P. M.; George, R. T., Jr.; Owen, H. A., Jr.; Wilson, T. G.

1979-01-01

The proposed dc model for bipolar junction power switching transistors is based on measurements which may be made with standard laboratory equipment. Those nonlinearities which are of importance to power electronics design are emphasized. Measurements procedures are discussed in detail. A model formulation adapted for use with a computer program is presented, and a comparison between actual and computer-generated results is made.

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

NASA Technical Reports Server (NTRS)

Saleeb, A. F.; Chang, T. Y. P.; Wilt, T.; Iskovitz, I.

1989-01-01

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

Construction of pore network models for Berea and Fontainebleau sandstones using non-linear programing and optimization techniques

NASA Astrophysics Data System (ADS)

Sharqawy, Mostafa H.

2016-12-01

Pore network models (PNM) of Berea and Fontainebleau sandstones were constructed using nonlinear programming (NLP) and optimization methods. The constructed PNMs are considered as a digital representation of the rock samples which were based on matching the macroscopic properties of the porous media and used to conduct fluid transport simulations including single and two-phase flow. The PNMs consisted of cubic networks of randomly distributed pores and throats sizes and with various connectivity levels. The networks were optimized such that the upper and lower bounds of the pore sizes are determined using the capillary tube bundle model and the Nelder-Mead method instead of guessing them, which reduces the optimization computational time significantly. An open-source PNM framework was employed to conduct transport and percolation simulations such as invasion percolation and Darcian flow. The PNM model was subsequently used to compute the macroscopic properties; porosity, absolute permeability, specific surface area, breakthrough capillary pressure, and primary drainage curve. The pore networks were optimized to allow for the simulation results of the macroscopic properties to be in excellent agreement with the experimental measurements. This study demonstrates that non-linear programming and optimization methods provide a promising method for pore network modeling when computed tomography imaging may not be readily available.

Numerical investigation of nonlinear interactions between multimodal guided waves and delamination in composite structures

NASA Astrophysics Data System (ADS)

Shen, Yanfeng

2017-04-01

This paper presents a numerical investigation of the nonlinear interactions between multimodal guided waves and delamination in composite structures. The elastodynamic wave equations for anisotropic composite laminate were formulated using an explicit Local Interaction Simulation Approach (LISA). The contact dynamics was modeled using the penalty method. In order to capture the stick-slip contact motion, a Coulomb friction law was integrated into the computation procedure. A random gap function was defined for the contact pairs to model distributed initial closures or openings to approximate the nature of rough delamination interfaces. The LISA procedure was coded using the Compute Unified Device Architecture (CUDA), which enables the highly parallelized computation on powerful graphic cards. Several guided wave modes centered at various frequencies were investigated as the incident wave. Numerical case studies of different delamination locations across the thickness were carried out. The capability of different wave modes at various frequencies to trigger the Contact Acoustic Nonlinearity (CAN) was studied. The correlation between the delamination size and the signal nonlinearity was also investigated. Furthermore, the influence from the roughness of the delamination interfaces was discussed as well. The numerical investigation shows that the nonlinear features of wave delamination interactions can enhance the evaluation capability of guided wave Structural Health Monitoring (SHM) system. This paper finishes with discussion, concluding remarks, and suggestions for future work.

The spectral cell method in nonlinear earthquake modeling

NASA Astrophysics Data System (ADS)

Giraldo, Daniel; Restrepo, Doriam

2017-12-01

This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.

Nonlinear grid error effects on numerical solution of partial differential equations

NASA Technical Reports Server (NTRS)

Dey, S. K.

1980-01-01

Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.

Computation of Nonlinear Backscattering Using a High-Order Numerical Method

NASA Technical Reports Server (NTRS)

Fibich, G.; Ilan, B.; Tsynkov, S.

2001-01-01

The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.

A method for nonlinear exponential regression analysis

NASA Technical Reports Server (NTRS)

Junkin, B. G.

1971-01-01

A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

Nonlinear Optics and Applications

NASA Technical Reports Server (NTRS)

Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)

2007-01-01

Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.

Robust and efficient pharmacokinetic parameter non-linear least squares estimation for dynamic contrast enhanced MRI of the prostate.

PubMed

Kargar, Soudabeh; Borisch, Eric A; Froemming, Adam T; Kawashima, Akira; Mynderse, Lance A; Stinson, Eric G; Trzasko, Joshua D; Riederer, Stephen J

2018-05-01

To describe an efficient numerical optimization technique using non-linear least squares to estimate perfusion parameters for the Tofts and extended Tofts models from dynamic contrast enhanced (DCE) MRI data and apply the technique to prostate cancer. Parameters were estimated by fitting the two Tofts-based perfusion models to the acquired data via non-linear least squares. We apply Variable Projection (VP) to convert the fitting problem from a multi-dimensional to a one-dimensional line search to improve computational efficiency and robustness. Using simulation and DCE-MRI studies in twenty patients with suspected prostate cancer, the VP-based solver was compared against the traditional Levenberg-Marquardt (LM) strategy for accuracy, noise amplification, robustness to converge, and computation time. The simulation demonstrated that VP and LM were both accurate in that the medians closely matched assumed values across typical signal to noise ratio (SNR) levels for both Tofts models. VP and LM showed similar noise sensitivity. Studies using the patient data showed that the VP method reliably converged and matched results from LM with approximate 3× and 2× reductions in computation time for the standard (two-parameter) and extended (three-parameter) Tofts models. While LM failed to converge in 14% of the patient data, VP converged in the ideal 100%. The VP-based method for non-linear least squares estimation of perfusion parameters for prostate MRI is equivalent in accuracy and robustness to noise, while being more reliably (100%) convergent and computationally about 3× (TM) and 2× (ETM) faster than the LM-based method. Copyright © 2017 Elsevier Inc. All rights reserved.

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.

NLSCIDNT user's guide maximum likehood parameter identification computer program with nonlinear rotorcraft model

NASA Technical Reports Server (NTRS)

1979-01-01

A nonlinear, maximum likelihood, parameter identification computer program (NLSCIDNT) is described which evaluates rotorcraft stability and control coefficients from flight test data. The optimal estimates of the parameters (stability and control coefficients) are determined (identified) by minimizing the negative log likelihood cost function. The minimization technique is the Levenberg-Marquardt method, which behaves like the steepest descent method when it is far from the minimum and behaves like the modified Newton-Raphson method when it is nearer the minimum. Twenty-one states and 40 measurement variables are modeled, and any subset may be selected. States which are not integrated may be fixed at an input value, or time history data may be substituted for the state in the equations of motion. Any aerodynamic coefficient may be expressed as a nonlinear polynomial function of selected 'expansion variables'.

Nonlinear and non-Gaussian Bayesian based handwriting beautification

NASA Astrophysics Data System (ADS)

Shi, Cao; Xiao, Jianguo; Xu, Canhui; Jia, Wenhua

2013-03-01

A framework is proposed in this paper to effectively and efficiently beautify handwriting by means of a novel nonlinear and non-Gaussian Bayesian algorithm. In the proposed framework, format and size of handwriting image are firstly normalized, and then typeface in computer system is applied to optimize vision effect of handwriting. The Bayesian statistics is exploited to characterize the handwriting beautification process as a Bayesian dynamic model. The model parameters to translate, rotate and scale typeface in computer system are controlled by state equation, and the matching optimization between handwriting and transformed typeface is employed by measurement equation. Finally, the new typeface, which is transformed from the original one and gains the best nonlinear and non-Gaussian optimization, is the beautification result of handwriting. Experimental results demonstrate the proposed framework provides a creative handwriting beautification methodology to improve visual acceptance.

Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model

NASA Astrophysics Data System (ADS)

Panajotov, Krassimir; Clerc, Marcel G.; Tlidi, Mustapha

2017-06-01

Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height. Contribution to the Topical Issue "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

Nonlinear channel equalization for QAM signal constellation using artificial neural networks.

PubMed

Patra, J C; Pal, R N; Baliarsingh, R; Panda, G

1999-01-01

Application of artificial neural networks (ANN's) to adaptive channel equalization in a digital communication system with 4-QAM signal constellation is reported in this paper. A novel computationally efficient single layer functional link ANN (FLANN) is proposed for this purpose. This network has a simple structure in which the nonlinearity is introduced by functional expansion of the input pattern by trigonometric polynomials. Because of input pattern enhancement, the FLANN is capable of forming arbitrarily nonlinear decision boundaries and can perform complex pattern classification tasks. Considering channel equalization as a nonlinear classification problem, the FLANN has been utilized for nonlinear channel equalization. The performance of the FLANN is compared with two other ANN structures [a multilayer perceptron (MLP) and a polynomial perceptron network (PPN)] along with a conventional linear LMS-based equalizer for different linear and nonlinear channel models. The effect of eigenvalue ratio (EVR) of input correlation matrix on the equalizer performance has been studied. The comparison of computational complexity involved for the three ANN structures is also provided.

Computer Facilitated Mathematical Methods in Chemical Engineering--Similarity Solution

ERIC Educational Resources Information Center

Subramanian, Venkat R.

2006-01-01

High-performance computers coupled with highly efficient numerical schemes and user-friendly software packages have helped instructors to teach numerical solutions and analysis of various nonlinear models more efficiently in the classroom. One of the main objectives of a model is to provide insight about the system of interest. Analytical…

Proceedings of the Annual Symposium on Frequency Control (45th) held in Los Angeles, California on May 29 -31, 1991

DTIC Science & Technology

1991-05-31

Corporation High Precision Nonlinear Computer Modelling Technique for Quartz Crystal Oscillators ............... 341 R. Brendel, F. Djian, CNRS & E. Robert...34) A.1.5% IV.1 Results of the computations for resonators having circular electrodes. The model was applied to compute the resonances 0f-.I frequencies...having circular electrodes. *- I The model was applied to compute the resonances frequencies of the fundamental mode and of its anharmonics ,odel and

Global identifiability of linear compartmental models--a computer algebra algorithm.

PubMed

Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C

1998-01-01

A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.

Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design

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

Marzouk, Youssef

Predictive simulation of complex physical systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, but at prohibitive computional expense. This project intends to make rigorous predictive modeling *feasible* in complex physical systems, via accelerated and scalable tools for uncertainty quantification, Bayesianmore » inference, and experimental design. Specific objectives are as follows: 1. Develop adaptive posterior approximations and dimensionality reduction approaches for Bayesian inference in high-dimensional nonlinear systems. 2. Extend accelerated Bayesian methodologies to large-scale {\\em sequential} data assimilation, fully treating nonlinear models and non-Gaussian state and parameter distributions. 3. Devise efficient surrogate-based methods for Bayesian model selection and the learning of model structure. 4. Develop scalable simulation/optimization approaches to nonlinear Bayesian experimental design, for both parameter inference and model selection. 5. Demonstrate these inferential tools on chemical kinetic models in reacting flow, constructing and refining thermochemical and electrochemical models from limited data. Demonstrate Bayesian filtering on canonical stochastic PDEs and in the dynamic estimation of inhomogeneous subsurface properties and flow fields.« less

An impulsive receptance technique for the time domain computation of the vibration of a whole aero-engine model with nonlinear bearings

NASA Astrophysics Data System (ADS)

Hai, Pham Minh; Bonello, Philip

2008-12-01

The direct study of the vibration of real engine structures with nonlinear bearings, particularly aero-engines, has been severely limited by the fact that current nonlinear computational techniques are not well-suited for complex large-order systems. This paper introduces a novel implicit "impulsive receptance method" (IRM) for the time domain analysis of such structures. The IRM's computational efficiency is largely immune to the number of modes used and dependent only on the number of nonlinear elements. This means that, apart from retaining numerical accuracy, a much more physically accurate solution is achievable within a short timeframe. Simulation tests on a realistically sized representative twin-spool aero-engine showed that the new method was around 40 times faster than a conventional implicit integration scheme. Preliminary results for a given rotor unbalance distribution revealed the varying degree of journal lift, orbit size and shape at the example engine's squeeze-film damper bearings, and the effect of end-sealing at these bearings.

A two steps solution approach to solving large nonlinear models: application to a problem of conjunctive use.

PubMed

Vieira, J; Cunha, M C

2011-01-01

This article describes a solution method of solving large nonlinear problems in two steps. The two steps solution approach takes advantage of handling smaller and simpler models and having better starting points to improve solution efficiency. The set of nonlinear constraints (named as complicating constraints) which makes the solution of the model rather complex and time consuming is eliminated from step one. The complicating constraints are added only in the second step so that a solution of the complete model is then found. The solution method is applied to a large-scale problem of conjunctive use of surface water and groundwater resources. The results obtained are compared with solutions determined with the direct solve of the complete model in one single step. In all examples the two steps solution approach allowed a significant reduction of the computation time. This potential gain of efficiency of the two steps solution approach can be extremely important for work in progress and it can be particularly useful for cases where the computation time would be a critical factor for having an optimized solution in due time.

Finite element modelling of non-linear magnetic circuits using Cosmic NASTRAN

NASA Technical Reports Server (NTRS)

Sheerer, T. J.

1986-01-01

The general purpose Finite Element Program COSMIC NASTRAN currently has the ability to model magnetic circuits with constant permeablilities. An approach was developed which, through small modifications to the program, allows modelling of non-linear magnetic devices including soft magnetic materials, permanent magnets and coils. Use of the NASTRAN code resulted in output which can be used for subsequent mechanical analysis using a variation of the same computer model. Test problems were found to produce theoretically verifiable results.

Magnetic Skyrmion as a Nonlinear Resistive Element: A Potential Building Block for Reservoir Computing

NASA Astrophysics Data System (ADS)

Prychynenko, Diana; Sitte, Matthias; Litzius, Kai; Krüger, Benjamin; Bourianoff, George; Kläui, Mathias; Sinova, Jairo; Everschor-Sitte, Karin

2018-01-01

Inspired by the human brain, there is a strong effort to find alternative models of information processing capable of imitating the high energy efficiency of neuromorphic information processing. One possible realization of cognitive computing involves reservoir computing networks. These networks are built out of nonlinear resistive elements which are recursively connected. We propose that a Skyrmion network embedded in magnetic films may provide a suitable physical implementation for reservoir computing applications. The significant key ingredient of such a network is a two-terminal device with nonlinear voltage characteristics originating from magnetoresistive effects, such as the anisotropic magnetoresistance or the recently discovered noncollinear magnetoresistance. The most basic element for a reservoir computing network built from "Skyrmion fabrics" is a single Skyrmion embedded in a ferromagnetic ribbon. In order to pave the way towards reservoir computing systems based on Skyrmion fabrics, we simulate and analyze (i) the current flow through a single magnetic Skyrmion due to the anisotropic magnetoresistive effect and (ii) the combined physics of local pinning and the anisotropic magnetoresistive effect.

Improvements to a method for the geometrically nonlinear analysis of compressively loaded stiffened composite panels

NASA Technical Reports Server (NTRS)

Stoll, Frederick

1993-01-01

The NLPAN computer code uses a finite-strip approach to the analysis of thin-walled prismatic composite structures such as stiffened panels. The code can model in-plane axial loading, transverse pressure loading, and constant through-the-thickness thermal loading, and can account for shape imperfections. The NLPAN code represents an attempt to extend the buckling analysis of the VIPASA computer code into the geometrically nonlinear regime. Buckling mode shapes generated using VIPASA are used in NLPAN as global functions for representing displacements in the nonlinear regime. While the NLPAN analysis is approximate in nature, it is computationally economical in comparison with finite-element analysis, and is thus suitable for use in preliminary design and design optimization. A comprehensive description of the theoretical approach of NLPAN is provided. A discussion of some operational considerations for the NLPAN code is included. NLPAN is applied to several test problems in order to demonstrate new program capabilities, and to assess the accuracy of the code in modeling various types of loading and response. User instructions for the NLPAN computer program are provided, including a detailed description of the input requirements and example input files for two stiffened-panel configurations.

Fast and Accurate Poisson Denoising With Trainable Nonlinear Diffusion.

PubMed

Feng, Wensen; Qiao, Peng; Chen, Yunjin; Wensen Feng; Peng Qiao; Yunjin Chen; Feng, Wensen; Chen, Yunjin; Qiao, Peng

2018-06-01

The degradation of the acquired signal by Poisson noise is a common problem for various imaging applications, such as medical imaging, night vision, and microscopy. Up to now, many state-of-the-art Poisson denoising techniques mainly concentrate on achieving utmost performance, with little consideration for the computation efficiency. Therefore, in this paper we aim to propose an efficient Poisson denoising model with both high computational efficiency and recovery quality. To this end, we exploit the newly developed trainable nonlinear reaction diffusion (TNRD) model which has proven an extremely fast image restoration approach with performance surpassing recent state-of-the-arts. However, the straightforward direct gradient descent employed in the original TNRD-based denoising task is not applicable in this paper. To solve this problem, we resort to the proximal gradient descent method. We retrain the model parameters, including the linear filters and influence functions by taking into account the Poisson noise statistics, and end up with a well-trained nonlinear diffusion model specialized for Poisson denoising. The trained model provides strongly competitive results against state-of-the-art approaches, meanwhile bearing the properties of simple structure and high efficiency. Furthermore, our proposed model comes along with an additional advantage, that the diffusion process is well-suited for parallel computation on graphics processing units (GPUs). For images of size , our GPU implementation takes less than 0.1 s to produce state-of-the-art Poisson denoising performance.

Theoretical and software considerations for nonlinear dynamic analysis

NASA Technical Reports Server (NTRS)

Schmidt, R. J.; Dodds, R. H., Jr.

1983-01-01

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.

Computer modeling of batteries from nonlinear circuit elements

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

Waaben, S.; Dyer, C.K.; Federico, J.

1985-06-01

Circuit analogs for a single battery cell have previously been composed of resistors, capacitors, and inductors. This work introduces a nonlinear circuit model for cell behavior. The circuit is configured around the PIN junction diode, whose charge-storage behavior has features similar to those of electrochemical cells. A user-friendly integrated circuit simulation computer program has reproduced a variety of complex cell responses including electrica isolation effects causing capacity loss, as well as potentiodynamic peaks and discharge phenomena hitherto thought to be thermodynamic in origin. However, in this work, they are shown to be simply due to spatial distribution of stored chargemore » within a practical electrode.« less

On a generalized laminate theory with application to bending, vibration, and delamination buckling in composite laminates

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

Barbero, E.J.

1989-01-01

In this study, a computational model for accurate analysis of composite laminates and laminates with including delaminated interfaces is developed. An accurate prediction of stress distributions, including interlaminar stresses, is obtained by using the Generalized Laminate Plate Theory of Reddy in which layer-wise linear approximation of the displacements through the thickness is used. Analytical as well as finite-element solutions of the theory are developed for bending and vibrations of laminated composite plates for the linear theory. Geometrical nonlinearity, including buckling and postbuckling are included and used to perform stress analysis of laminated plates. A general two dimensional theory of laminatedmore » cylindrical shells is also developed in this study. Geometrical nonlinearity and transverse compressibility are included. Delaminations between layers of composite plates are modelled by jump discontinuity conditions at the interfaces. The theory includes multiple delaminations through the thickness. Geometric nonlinearity is included to capture layer buckling. The strain energy release rate distribution along the boundary of delaminations is computed by a novel algorithm. The computational models presented herein are accurate for global behavior and particularly appropriate for the study of local effects.« less

Computer program for investigating effects of nonlinear suspension-system elastic properties on parachute inflation loads and motions

NASA Technical Reports Server (NTRS)

Poole, L. R.

1972-01-01

A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.

A hybrid linear/nonlinear training algorithm for feedforward neural networks.

PubMed

McLoone, S; Brown, M D; Irwin, G; Lightbody, A

1998-01-01

This paper presents a new hybrid optimization strategy for training feedforward neural networks. The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine. It is described for the multilayer perceptron (MLP) and radial basis function (RBF) networks and then extended to the local model network (LMN), a new feedforward structure in which a global nonlinear model is constructed from a set of locally valid submodels. Simulation results are presented demonstrating the superiority of the new hybrid training scheme compared to second-order gradient methods. It is particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

Yee, H. C.

2005-01-01

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations.

A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators

NASA Technical Reports Server (NTRS)

Smith, Ralph C.

1998-01-01

This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.

PubMed

Goto, Hayato

2016-02-22

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

NASA Astrophysics Data System (ADS)

Goto, Hayato

2016-02-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

An object-oriented computational model to study cardiopulmonary hemodynamic interactions in humans.

PubMed

Ngo, Chuong; Dahlmanns, Stephan; Vollmer, Thomas; Misgeld, Berno; Leonhardt, Steffen

2018-06-01

This work introduces an object-oriented computational model to study cardiopulmonary interactions in humans. Modeling was performed in object-oriented programing language Matlab Simscape, where model components are connected with each other through physical connections. Constitutive and phenomenological equations of model elements are implemented based on their non-linear pressure-volume or pressure-flow relationship. The model includes more than 30 physiological compartments, which belong either to the cardiovascular or respiratory system. The model considers non-linear behaviors of veins, pulmonary capillaries, collapsible airways, alveoli, and the chest wall. Model parameters were derisved based on literature values. Model validation was performed by comparing simulation results with clinical and animal data reported in literature. The model is able to provide quantitative values of alveolar, pleural, interstitial, aortic and ventricular pressures, as well as heart and lung volumes during spontaneous breathing and mechanical ventilation. Results of baseline simulation demonstrate the consistency of the assigned parameters. Simulation results during mechanical ventilation with PEEP trials can be directly compared with animal and clinical data given in literature. Object-oriented programming languages can be used to model interconnected systems including model non-linearities. The model provides a useful tool to investigate cardiopulmonary activity during spontaneous breathing and mechanical ventilation. Copyright © 2018 Elsevier B.V. All rights reserved.

Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

Symbolic computation of equivalence transformations and parameter reduction for nonlinear physical models

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.

2017-11-01

An efficient systematic procedure is provided for symbolic computation of Lie groups of equivalence transformations and generalized equivalence transformations of systems of differential equations that contain arbitrary elements (arbitrary functions and/or arbitrary constant parameters), using the software package GeM for Maple. Application of equivalence transformations to the reduction of the number of arbitrary elements in a given system of equations is discussed, and several examples are considered. The first computational example of generalized equivalence transformations where the transformation of the dependent variable involves an arbitrary constitutive function is presented. As a detailed physical example, a three-parameter family of nonlinear wave equations describing finite anti-plane shear displacements of an incompressible hyperelastic fiber-reinforced medium is considered. Equivalence transformations are computed and employed to radically simplify the model for an arbitrary fiber direction, invertibly reducing the model to a simple form that corresponds to a special fiber direction, and involves no arbitrary elements. The presented computation algorithm is applicable to wide classes of systems of differential equations containing arbitrary elements.

The development of global GRAPES 4DVAR

NASA Astrophysics Data System (ADS)

Liu, Yongzhu

2017-04-01

Four-dimensional variation data assimilation (4DVAR) has given a great contribution to the improvement of NWP system over the past twenty years. Therefore, our strategy is to develop an operational global 4D-Var system from the outset. The aim at the paper is to introduce the development of the global GRAPES four-dimensional variation data assimilation (4DVAR) using incremental analysis schemes and to presents results of a comparison between 4DVAR using 6-hour assimilation window and simplified physics during the minimization with three-dimensional variation data assimilation (3DVAR). The dynamical cores of the tangent-linear and adjoint models are developed directly based on the non-hydrostatic forecast model. In addition, the standard correctness checks have been performed. As well as the development adjoint codes, most of our work is focused on improving the computational efficiency since the bulk of the computational cost of 4D-Var is in the integration of the tangent-linear and adjoint models. In terms of tangent-linear model, the wall-clock time is reduced to about 1.2 times as much as one of nonlinear model through the optimizing of the software framework. The significant computational cost savings on adjoint model result from the removing the redundant recompilations of model trajectories. It is encouraging that the wall-clock time of adjoint model is less than 1.5 times as much as one of nonlinear model. The current difficulty is that the numerical scheme used within the linear model is based on strategically on the numeric of the corresponding nonlinear model. Further computational acceleration should be expected from the improvement on nonlinear numerical algorithm. A series of linearized physical parameterization schemes has been developed to improve the representation of perturbed fields in the linear model. It consists of horizontal and vertical diffusion, sub-grid scale orographic gravity wave drag, large-scale condensation and cumulus convection schemes. We also found the straightforward linearization based on the nonlinear physical scheme might lead to significant growing of spurious unstable perturbations. It is essential to simplify the linear physics with respect to the non-linear schemes. The improvement on the perturbed fields in the tangent-linear model is visible with the linear physics included, especially at the low level. GRAPES variation data assimilation system adopts the incremental approach. The work is ongoing to develop a pre-operational 4DVAR suite with 0.25° outer loop resolution and multiple outer-loops configurations. One 4DVAR analysis using 6-hour assimilation windows can be finished within 40-minutes when using the available conventional and satellite data. In summary, it was found that the analysis over the northern, southern hemispheres, tropical region and East Asian area of GRAPES 4DVAR performed better than GRAPES 3DVAR for one month experiments. Moreover, the forecast results show that northern and southern extra-tropical scores for GRAPES 4DVAR are already better than GRAPES 3DVAR, but the tropical performance needs further investigations. Therefore, the subsequent main improvements will aim to enhance its computational efficiency and accuracy in 2017. The global GRAPES 4DVAR is planned for operation in 2018.

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

Quon, Eliot; Platt, Andrew; Yu, Yi-Hsiang

Extreme loads are often a key cost driver for wave energy converters (WECs). As an alternative to exhaustive Monte Carlo or long-term simulations, the most likely extreme response (MLER) method allows mid- and high-fidelity simulations to be used more efficiently in evaluating WEC response to events at the edges of the design envelope, and is therefore applicable to system design analysis. The study discussed in this paper applies the MLER method to investigate the maximum heave, pitch, and surge force of a point absorber WEC. Most likely extreme waves were obtained from a set of wave statistics data based onmore » spectral analysis and the response amplitude operators (RAOs) of the floating body; the RAOs were computed from a simple radiation-and-diffraction-theory-based numerical model. A weakly nonlinear numerical method and a computational fluid dynamics (CFD) method were then applied to compute the short-term response to the MLER wave. Effects of nonlinear wave and floating body interaction on the WEC under the anticipated 100-year waves were examined by comparing the results from the linearly superimposed RAOs, the weakly nonlinear model, and CFD simulations. Overall, the MLER method was successfully applied. In particular, when coupled to a high-fidelity CFD analysis, the nonlinear fluid dynamics can be readily captured.« less

Fully Implicit, Nonlinear 3D Extended Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Chacon, Luis; Knoll, Dana

2003-10-01

Extended magnetohydrodynamics (XMHD) includes nonideal effects such as nonlinear, anisotropic transport and two-fluid (Hall) effects. XMHD supports multiple, separate time scales that make explicit time differencing approaches extremely inefficient. While a fully implicit implementation promises efficiency without sacrificing numerical accuracy,(D. A. Knoll et al., phJ. Comput. Phys.) 185 (2), 583-611 (2003) the nonlinear nature of the XMHD system and the numerical stiffness associated with the fast waves make this endeavor difficult. Newton-Krylov methods are, however, ideally suited for such a task. These synergistically combine Newton's method for nonlinear convergence, and Krylov techniques to solve the associated Jacobian (linear) systems. Krylov methods can be implemented Jacobian-free and can be preconditioned for efficiency. Successful preconditioning strategies have been developed for 2D incompressible resistive(L. Chacón et al., phJ. Comput. Phys). 178 (1), 15- 36 (2002) and Hall(L. Chacón and D. A. Knoll, phJ. Comput. Phys.), 188 (2), 573-592 (2003) MHD models. These are based on ``physics-based'' ideas, in which knowledge of the physics is exploited to derive well-conditioned (diagonally-dominant) approximations to the original system that are amenable to optimal solver technologies (multigrid). In this work, we will describe the status of the extension of the 2D preconditioning ideas for a 3D compressible, single-fluid XMHD model.

User document for computer programs for ring-stiffened shells of revolution

NASA Technical Reports Server (NTRS)

Cohen, G. A.

1973-01-01

A user manual and related program documentation is presented for six compatible computer programs for structural analysis of axisymmetric shell structures. The programs apply to a common structural model but analyze different modes of structural response. In particular, they are: (1) Linear static response under asymmetric loads; (2) Buckling of linear states under asymmetric loads; (3) Nonlinear static response under axisymmetric loads; (4) Buckling nonlinear states under axisymmetric (5) Imperfection sensitivity of buckling modes under axisymmetric loads; and (6) Vibrations about nonlinear states under axisymmetric loads. These programs treat branched shells of revolution with an arbitrary arrangement of a large number of open branches but with at most one closed branch.

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.

Computational Modeling of Ultrafast Pulse Propagation in Nonlinear Optical Materials

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Agrawal, Govind P.; Kwak, Dochan (Technical Monitor)

1996-01-01

There is an emerging technology of photonic (or optoelectronic) integrated circuits (PICs or OEICs). In PICs, optical and electronic components are grown together on the same chip. rib build such devices and subsystems, one needs to model the entire chip. Accurate computer modeling of electromagnetic wave propagation in semiconductors is necessary for the successful development of PICs. More specifically, these computer codes would enable the modeling of such devices, including their subsystems, such as semiconductor lasers and semiconductor amplifiers in which there is femtosecond pulse propagation. Here, the computer simulations are made by solving the full vector, nonlinear, Maxwell's equations, coupled with the semiconductor Bloch equations, without any approximations. The carrier is retained in the description of the optical pulse, (i.e. the envelope approximation is not made in the Maxwell's equations), and the rotating wave approximation is not made in the Bloch equations. These coupled equations are solved to simulate the propagation of femtosecond optical pulses in semiconductor materials. The simulations describe the dynamics of the optical pulses, as well as the interband and intraband.

Poster — Thur Eve — 44: Linearization of Compartmental Models for More Robust Estimates of Regional Hemodynamic, Metabolic and Functional Parameters using DCE-CT/PET Imaging

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

Blais, AR; Dekaban, M; Lee, T-Y

2014-08-15

Quantitative analysis of dynamic positron emission tomography (PET) data usually involves minimizing a cost function with nonlinear regression, wherein the choice of starting parameter values and the presence of local minima affect the bias and variability of the estimated kinetic parameters. These nonlinear methods can also require lengthy computation time, making them unsuitable for use in clinical settings. Kinetic modeling of PET aims to estimate the rate parameter k{sub 3}, which is the binding affinity of the tracer to a biological process of interest and is highly susceptible to noise inherent in PET image acquisition. We have developed linearized kineticmore » models for kinetic analysis of dynamic contrast enhanced computed tomography (DCE-CT)/PET imaging, including a 2-compartment model for DCE-CT and a 3-compartment model for PET. Use of kinetic parameters estimated from DCE-CT can stabilize the kinetic analysis of dynamic PET data, allowing for more robust estimation of k{sub 3}. Furthermore, these linearized models are solved with a non-negative least squares algorithm and together they provide other advantages including: 1) only one possible solution and they do not require a choice of starting parameter values, 2) parameter estimates are comparable in accuracy to those from nonlinear models, 3) significantly reduced computational time. Our simulated data show that when blood volume and permeability are estimated with DCE-CT, the bias of k{sub 3} estimation with our linearized model is 1.97 ± 38.5% for 1,000 runs with a signal-to-noise ratio of 10. In summary, we have developed a computationally efficient technique for accurate estimation of k{sub 3} from noisy dynamic PET data.« less

Decision Support Tool for Deep Energy Efficiency Retrofits in DoD Installations

DTIC Science & Technology

2014-01-01

representations (HDMR). Chemical Engineering Science, 57, 4445–4460. 2. Sobol ’, I., 2001. Global sensitivity indices for nonlinear mathematical...models and their Monte Carlo estimates. Mathematics and computers in simulation, 55, 271–280. 3. Sobol , I. and Kucherenko, S., 2009. Derivative based...representations (HDMR). Chemical Engineering Science, 57, 4445–4460. 16. Sobol ’, I., 2001. Global sensitivity indices for nonlinear mathematical models and

Operations research investigations of satellite power stations

NASA Technical Reports Server (NTRS)

Cole, J. W.; Ballard, J. L.

1976-01-01

A systems model reflecting the design concepts of Satellite Power Stations (SPS) was developed. The model is of sufficient scope to include the interrelationships of the following major design parameters: the transportation to and between orbits; assembly of the SPS; and maintenance of the SPS. The systems model is composed of a set of equations that are nonlinear with respect to the system parameters and decision variables. The model determines a figure of merit from which alternative concepts concerning transportation, assembly, and maintenance of satellite power stations are studied. A hybrid optimization model was developed to optimize the system's decision variables. The optimization model consists of a random search procedure and the optimal-steepest descent method. A FORTRAN computer program was developed to enable the user to optimize nonlinear functions using the model. Specifically, the computer program was used to optimize Satellite Power Station system components.

Estimating phase synchronization in dynamical systems using cellular nonlinear networks

NASA Astrophysics Data System (ADS)

Sowa, Robert; Chernihovskyi, Anton; Mormann, Florian; Lehnertz, Klaus

2005-06-01

We propose a method for estimating phase synchronization between time series using the parallel computing architecture of cellular nonlinear networks (CNN’s). Applying this method to time series of coupled nonlinear model systems and to electroencephalographic time series from epilepsy patients, we show that an accurate approximation of the mean phase coherence R —a bivariate measure for phase synchronization—can be achieved with CNN’s using polynomial-type templates.

Identification of cascade water tanks using a PWARX model

NASA Astrophysics Data System (ADS)

Mattsson, Per; Zachariah, Dave; Stoica, Petre

2018-06-01

In this paper we consider the identification of a discrete-time nonlinear dynamical model for a cascade water tank process. The proposed method starts with a nominal linear dynamical model of the system, and proceeds to model its prediction errors using a model that is piecewise affine in the data. As data is observed, the nominal model is refined into a piecewise ARX model which can capture a wide range of nonlinearities, such as the saturation in the cascade tanks. The proposed method uses a likelihood-based methodology which adaptively penalizes model complexity and directly leads to a computationally efficient implementation.

solveME: fast and reliable solution of nonlinear ME models.

PubMed

Yang, Laurence; Ma, Ding; Ebrahim, Ali; Lloyd, Colton J; Saunders, Michael A; Palsson, Bernhard O

2016-09-22

Genome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints. Here, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models using a quad-precision NLP solver (Quad MINOS). Our method was up to 45 % faster than binary search for six significant digits in growth rate. We also develop a fast, quad-precision flux variability analysis that is accelerated (up to 60× speedup) via solver warm-starts. Finally, we employ the tools developed to investigate growth-coupled succinate overproduction, accounting for proteome constraints. Just as genome-scale metabolic reconstructions have become an invaluable tool for computational and systems biologists, we anticipate that these fast and numerically reliable ME solution methods will accelerate the wide-spread adoption of ME models for researchers in these fields.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Identification of Linear and Nonlinear Aerodynamic Impulse Responses Using Digital Filter Techniques

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1997-01-01

This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.

Investigation on imperfection sensitivity of composite cylindrical shells using the nonlinearity reduction technique and the polynomial chaos method

NASA Astrophysics Data System (ADS)

Liang, Ke; Sun, Qin; Liu, Xiaoran

2018-05-01

The theoretical buckling load of a perfect cylinder must be reduced by a knock-down factor to account for structural imperfections. The EU project DESICOS proposed a new robust design for imperfection-sensitive composite cylindrical shells using the combination of deterministic and stochastic simulations, however the high computational complexity seriously affects its wider application in aerospace structures design. In this paper, the nonlinearity reduction technique and the polynomial chaos method are implemented into the robust design process, to significantly lower computational costs. The modified Newton-type Koiter-Newton approach which largely reduces the number of degrees of freedom in the nonlinear finite element model, serves as the nonlinear buckling solver to trace the equilibrium paths of geometrically nonlinear structures efficiently. The non-intrusive polynomial chaos method provides the buckling load with an approximate chaos response surface with respect to imperfections and uses buckling solver codes as black boxes. A fast large-sample study can be applied using the approximate chaos response surface to achieve probability characteristics of buckling loads. The performance of the method in terms of reliability, accuracy and computational effort is demonstrated with an unstiffened CFRP cylinder.

Web Platform for Sharing Modeling Software in the Field of Nonlinear Optics

NASA Astrophysics Data System (ADS)

Dubenskaya, Julia; Kryukov, Alexander; Demichev, Andrey

2018-02-01

We describe the prototype of a Web platform intended for sharing software programs for computer modeling in the rapidly developing field of the nonlinear optics phenomena. The suggested platform is built on the top of the HUBZero open-source middleware. In addition to the basic HUBZero installation we added to our platform the capability to run Docker containers via an external application server and to send calculation programs to those containers for execution. The presented web platform provides a wide range of features and might be of benefit to nonlinear optics researchers.

A Time Integration Algorithm Based on the State Transition Matrix for Structures with Time Varying and Nonlinear Properties

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2003-01-01

A variable order method of integrating the structural dynamics equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. When the time variation of the system can be modeled exactly by a polynomial it produces nearly exact solutions for a wide range of time step sizes. Solutions of a model nonlinear dynamic response exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with solutions obtained by established methods.

Study of improved modeling and solution procedures for nonlinear analysis. [aircraft-like structures

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1979-01-01

An evaluation of the ACTION computer code on an aircraft like structure is presented. This computer program proved adequate in predicting gross response parameters in structures which undergo severe localized cross sectional deformations.

EnviroLand: A Simple Computer Program for Quantitative Stream Assessment.

ERIC Educational Resources Information Center

Dunnivant, Frank; Danowski, Dan; Timmens-Haroldson, Alice; Newman, Meredith

2002-01-01

Introduces the Enviroland computer program which features lab simulations of theoretical calculations for quantitative analysis and environmental chemistry, and fate and transport models. Uses the program to demonstrate the nature of linear and nonlinear equations. (Author/YDS)

Computing eigenfunctions and eigenvalues of boundary-value problems with the orthogonal spectral renormalization method

NASA Astrophysics Data System (ADS)

Cartarius, Holger; Musslimani, Ziad H.; Schwarz, Lukas; Wunner, Günter

2018-03-01

The spectral renormalization method was introduced in 2005 as an effective way to compute ground states of nonlinear Schrödinger and Gross-Pitaevskii type equations. In this paper, we introduce an orthogonal spectral renormalization (OSR) method to compute ground and excited states (and their respective eigenvalues) of linear and nonlinear eigenvalue problems. The implementation of the algorithm follows four simple steps: (i) reformulate the underlying eigenvalue problem as a fixed-point equation, (ii) introduce a renormalization factor that controls the convergence properties of the iteration, (iii) perform a Gram-Schmidt orthogonalization process in order to prevent the iteration from converging to an unwanted mode, and (iv) compute the solution sought using a fixed-point iteration. The advantages of the OSR scheme over other known methods (such as Newton's and self-consistency) are (i) it allows the flexibility to choose large varieties of initial guesses without diverging, (ii) it is easy to implement especially at higher dimensions, and (iii) it can easily handle problems with complex and random potentials. The OSR method is implemented on benchmark Hermitian linear and nonlinear eigenvalue problems as well as linear and nonlinear non-Hermitian PT -symmetric models.

Computer simulation of the linear and nonlinear optical susceptibilities of p-nitroaniline in cyclohexane, 1,4-dioxane, and tetrahydrofuran in quadrupolar approximation. II. Local field effects and optical susceptibilitities.

PubMed

Reis, H; Papadopoulos, M G; Grzybowski, A

2006-09-21

This is the second part of a study to elucidate the local field effects on the nonlinear optical properties of p-nitroaniline (pNA) in three solvents of different multipolar character, that is, cyclohexane (CH), 1,4-dioxane (DI), and tetrahydrofuran (THF), employing a discrete description of the solutions. By the use of liquid structure information from molecular dynamics simulations and molecular properties computed by high-level ab initio methods, the local field and local field gradients on p-nitroaniline and the solvent molecules are computed in quadrupolar approximation. To validate the simulations and the induction model, static and dynamic (non)linear properties of the pure solvents are also computed. With the exception of the static dielectric constant of pure THF, a good agreement between computed and experimental refractive indices, dielectric constants, and third harmonic generation signals is obtained for the solvents. For the solutions, it is found that multipole moments up to two orders higher than quadrupole have a negligible influence on the local fields on pNA, if a simple distribution model is employed for the electric properties of pNA. Quadrupole effects are found to be nonnegligible in all three solvents but are especially pronounced in the 1,4-dioxane solvent, in which the local fields are similar to those in THF, although the dielectric constant of DI is 2.2 and that of the simulated THF is 5.4. The electric-field-induced second harmonic generation (EFISH) signal and the hyper-Rayleigh scattering signal of pNA in the solutions computed with the local field are in good to fair agreement with available experimental results. This confirms the effect of the "dioxane anomaly" also on nonlinear optical properties. Predictions based on an ellipsoidal Onsager model as applied by experimentalists are in very good agreement with the discrete model predictions. This is in contrast to a recent discrete reaction field calculation of pNA in 1,4-dioxane, which found that the predicted first hyperpolarizability of pNA deviated strongly from the predictions obtained using Onsager-Lorentz local field factors.

Fermi-Pasta-Ulam, solitons and the fabric of nonlinear and computational science: History, synergetics, and visiometricsa)

NASA Astrophysics Data System (ADS)

Zabusky, Norman J.

2005-03-01

This paper is mostly a history of the early years of nonlinear and computational physics and mathematics. I trace how the counterintuitive result of near-recurrence to an initial condition in the first scientific digital computer simulation led to the discovery of the soliton in a later computer simulation. The 1955 report by Fermi, Pasta, and Ulam (FPU) described their simulation of a one-dimensional nonlinear lattice which did not show energy equipartition. The 1965 paper by Zabusky and Kruskalshowed that the Korteweg-de Vries (KdV) nonlinear partial differential equation, a long wavelength model of the α-lattice (or cubic nonlinearity), derived by Kruskal, gave quantitatively the same results obtained by FPU. In 1967, Zabusky and Deem showed that a localized short wavelength initial excitation (then called an "optical" and now a "zone-boundary mode" excitation ) of the α-lattice revealed "n-curve" coherent states. If the initial amplitude was sufficiently large energy equipartition followed in a short time. The work of Kruskal and Miura (KM), Gardner and Greene (GG), and myself led to the appreciation of the infinity of denumerable invariants (conservation laws) for Hamiltonian systems and to a procedure by GGKM in 1967 for solving KdV exactly. The nonlinear science field exponentiated in diversity of linkages (as described in Appendix A). Included were pure and applied mathematics and all branches of basic and applied physics, including the first nonhydrodynamic application to optical solitons, as described in a brief essay (Appendix B) by Hasegawa. The growth was also manifest in the number of meetings held and institutes founded, as described briefly in Appendix D. Physicists and mathematicians in Japan, USA, and USSR (in the latter two, people associated with plasma physics) contributed to the diversification of the nonlinear paradigm which continues worldwide to the present. The last part of the paper (and Appendix C) discuss visiometrics: the visualization and quantification of simulation data, e.g., projection to lower dimensions, to facilitate understanding of nonlinear phenomena for modeling and prediction (or design). Finally, I present some recent developments that are linked to my early work by: Dritschel (vortex dynamics via contour dynamics/surgery in two and three dimensions); Friedland (pattern formation by synchronization in Hamiltonian nonlinear wave, vortex, plasma, systems, etc.); and the author ("n-curve" states and energy equipartition in a FPU lattice).

Fermi-Pasta-Ulam, solitons and the fabric of nonlinear and computational science: history, synergetics, and visiometrics.

PubMed

Zabusky, Norman J

2005-03-01

This paper is mostly a history of the early years of nonlinear and computational physics and mathematics. I trace how the counterintuitive result of near-recurrence to an initial condition in the first scientific digital computer simulation led to the discovery of the soliton in a later computer simulation. The 1955 report by Fermi, Pasta, and Ulam (FPU) described their simulation of a one-dimensional nonlinear lattice which did not show energy equipartition. The 1965 paper by Zabusky and Kruskalshowed that the Korteweg-de Vries (KdV) nonlinear partial differential equation, a long wavelength model of the alpha-lattice (or cubic nonlinearity), derived by Kruskal, gave quantitatively the same results obtained by FPU. In 1967, Zabusky and Deem showed that a localized short wavelength initial excitation (then called an "optical" and now a "zone-boundary mode" excitation ) of the alpha-lattice revealed "n-curve" coherent states. If the initial amplitude was sufficiently large energy equipartition followed in a short time. The work of Kruskal and Miura (KM), Gardner and Greene (GG), and myself led to the appreciation of the infinity of denumerable invariants (conservation laws) for Hamiltonian systems and to a procedure by GGKM in 1967 for solving KdV exactly. The nonlinear science field exponentiated in diversity of linkages (as described in Appendix A). Included were pure and applied mathematics and all branches of basic and applied physics, including the first nonhydrodynamic application to optical solitons, as described in a brief essay (Appendix B) by Hasegawa. The growth was also manifest in the number of meetings held and institutes founded, as described briefly in Appendix D. Physicists and mathematicians in Japan, USA, and USSR (in the latter two, people associated with plasma physics) contributed to the diversification of the nonlinear paradigm which continues worldwide to the present. The last part of the paper (and Appendix C) discuss visiometrics: the visualization and quantification of simulation data, e.g., projection to lower dimensions, to facilitate understanding of nonlinear phenomena for modeling and prediction (or design). Finally, I present some recent developments that are linked to my early work by: Dritschel (vortex dynamics via contour dynamics/surgery in two and three dimensions); Friedland (pattern formation by synchronization in Hamiltonian nonlinear wave, vortex, plasma, systems, etc.); and the author ("n-curve" states and energy equipartition in a FPU lattice).

Differential morphology and image processing.

PubMed

Maragos, P

1996-01-01

Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision.

A kinematically driven anisotropic viscoelastic constitutive model applied to tires

NASA Technical Reports Server (NTRS)

Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.

1995-01-01

Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.

A kinematically driven anisotropic viscoelastic constitutive model applied to tires

NASA Astrophysics Data System (ADS)

Johnson, Arthur R.; Tanner, John A.; Mason, Angela J.

1995-08-01

Aircraft tires are composite structures manufactured with viscoelastic materials such as carbon black filled rubber and nylon cords. When loaded they experience large deflections and moderately large strains. Detailed structural models of tires require the use of either nonlinear shell or nonlinear three dimensional solid finite elements. Computational predictions of the dynamic response of tires must consider the composite viscoelastic material behavior in a realistic fashion. We describe a modification to a nonlinear anisotropic shell finite element so it can be used to model viscoelastic stresses during general deformations. The model is developed by introducing internal variables of the type used to model elastic strain energy. The internal variables are strains, curvatures, and transverse shear angles which are in a one-to-one correspondence with the generalized coordinates used to model the elastic strain energy for nonlinear response. A difference-relaxation equation is used to relate changes in the observable strain field to changes in the internal strain field. The internal stress state is introduced into the equilibrium equations by converting it to nodal loads associated with the element's displacement degrees of freedom. In this form the tangent matrix in the Newton-Raphson solution algorithm is not modified from its form for the nonlinear statics problem. Only the gradient vector is modified and the modification is not computationally costly. The existing finite element model for the Space Shuttle nose gear tire is used to provide examples of the algorithm. In the first example, the tire's rim is displaced at a constant rate up to a fixed value. In the second example, the tire's rim is enforced to follow a saw tooth load and unload curve to generate hysteresis loops.

Nonlinearity in Social Service Evaluation: A Primer on Agent-Based Modeling

ERIC Educational Resources Information Center

Israel, Nathaniel; Wolf-Branigin, Michael

2011-01-01

Measurement of nonlinearity in social service research and evaluation relies primarily on spatial analysis and, to a lesser extent, social network analysis. Recent advances in geographic methods and computing power, however, allow for the greater use of simulation methods. These advances now enable evaluators and researchers to simulate complex…

Probabilistic design of fibre concrete structures

NASA Astrophysics Data System (ADS)

Pukl, R.; Novák, D.; Sajdlová, T.; Lehký, D.; Červenka, J.; Červenka, V.

2017-09-01

Advanced computer simulation is recently well-established methodology for evaluation of resistance of concrete engineering structures. The nonlinear finite element analysis enables to realistically predict structural damage, peak load, failure, post-peak response, development of cracks in concrete, yielding of reinforcement, concrete crushing or shear failure. The nonlinear material models can cover various types of concrete and reinforced concrete: ordinary concrete, plain or reinforced, without or with prestressing, fibre concrete, (ultra) high performance concrete, lightweight concrete, etc. Advanced material models taking into account fibre concrete properties such as shape of tensile softening branch, high toughness and ductility are described in the paper. Since the variability of the fibre concrete material properties is rather high, the probabilistic analysis seems to be the most appropriate format for structural design and evaluation of structural performance, reliability and safety. The presented combination of the nonlinear analysis with advanced probabilistic methods allows evaluation of structural safety characterized by failure probability or by reliability index respectively. Authors offer a methodology and computer tools for realistic safety assessment of concrete structures; the utilized approach is based on randomization of the nonlinear finite element analysis of the structural model. Uncertainty of the material properties or their randomness obtained from material tests are accounted in the random distribution. Furthermore, degradation of the reinforced concrete materials such as carbonation of concrete, corrosion of reinforcement, etc. can be accounted in order to analyze life-cycle structural performance and to enable prediction of the structural reliability and safety in time development. The results can serve as a rational basis for design of fibre concrete engineering structures based on advanced nonlinear computer analysis. The presented methodology is illustrated on results from two probabilistic studies with different types of concrete structures related to practical applications and made from various materials (with the parameters obtained from real material tests).

Modeling transonic aerodynamic response using nonlinear systems theory for use with modern control theory

NASA Technical Reports Server (NTRS)

Silva, Walter A.

1993-01-01

The presentation begins with a brief description of the motivation and approach that has been taken for this research. This will be followed by a description of the Volterra Theory of Nonlinear Systems and the CAP-TSD code which is an aeroelastic, transonic CFD (Computational Fluid Dynamics) code. The application of the Volterra theory to a CFD model and, more specifically, to a CAP-TSD model of a rectangular wing with a NACA 0012 airfoil section will be presented.

Eddy current modeling in linear and nonlinear multifilamentary composite materials

NASA Astrophysics Data System (ADS)

Menana, Hocine; Farhat, Mohamad; Hinaje, Melika; Berger, Kevin; Douine, Bruno; Lévêque, Jean

2018-04-01

In this work, a numerical model is developed for a rapid computation of eddy currents in composite materials, adaptable for both carbon fiber reinforced polymers (CFRPs) for NDT applications and multifilamentary high temperature superconductive (HTS) tapes for AC loss evaluation. The proposed model is based on an integro-differential formulation in terms of the electric vector potential in the frequency domain. The high anisotropy and the nonlinearity of the considered materials are easily handled in the frequency domain.

An iterative hyperelastic parameters reconstruction for breast cancer assessment

NASA Astrophysics Data System (ADS)

Mehrabian, Hatef; Samani, Abbas

2008-03-01

In breast elastography, breast tissues usually undergo large compressions resulting in significant geometric and structural changes, and consequently nonlinear mechanical behavior. In this study, an elastography technique is presented where parameters characterizing tissue nonlinear behavior is reconstructed. Such parameters can be used for tumor tissue classification. To model the nonlinear behavior, tissues are treated as hyperelastic materials. The proposed technique uses a constrained iterative inversion method to reconstruct the tissue hyperelastic parameters. The reconstruction technique uses a nonlinear finite element (FE) model for solving the forward problem. In this research, we applied Yeoh and Polynomial models to model the tissue hyperelasticity. To mimic the breast geometry, we used a computational phantom, which comprises of a hemisphere connected to a cylinder. This phantom consists of two types of soft tissue to mimic adipose and fibroglandular tissues and a tumor. Simulation results show the feasibility of the proposed method in reconstructing the hyperelastic parameters of the tumor tissue.

Computational aspects in high intensity ultrasonic surgery planning.

PubMed

Pulkkinen, A; Hynynen, K

2010-01-01

Therapeutic ultrasound treatment planning is discussed and computational aspects regarding it are reviewed. Nonlinear ultrasound simulations were solved with a combined frequency domain Rayleigh and KZK model. Ultrasonic simulations were combined with thermal simulations and were used to compute heating of muscle tissue in vivo for four different focused ultrasound transducers. The simulations were compared with measurements and good agreement was found for large F-number transducers. However, at F# 1.9 the simulated rate of temperature rise was approximately a factor of 2 higher than the measured ones. The power levels used with the F# 1 transducer were too low to show any nonlinearity. The simulations were used to investigate the importance of nonlinarities generated in the coupling water, and also the importance of including skin in the simulations. Ignoring either of these in the model would lead to larger errors. Most notably, the nonlinearities generated in the water can enhance the focal temperature by more than 100%. The simulations also demonstrated that pulsed high power sonications may provide an opportunity to significantly (up to a factor of 3) reduce the treatment time. In conclusion, nonlinear propagation can play an important role in shaping the energy distribution during a focused ultrasound treatment and it should not be ignored in planning. However, the current simulation methods are accurate only with relatively large F-numbers and better models need to be developed for sharply focused transducers. Copyright 2009 Elsevier Ltd. All rights reserved.

Linear and nonlinear 2D finite element analysis of sloshing modes and pressures in rectangular tanks subject to horizontal harmonic motions

NASA Astrophysics Data System (ADS)

Virella, Juan C.; Prato, Carlos A.; Godoy, Luis A.

2008-05-01

The influence of nonlinear wave theory on the sloshing natural periods and their modal pressure distributions are investigated for rectangular tanks under the assumption of two-dimensional behavior. Natural periods and mode shapes are computed and compared for both linear wave theory (LWT) and nonlinear wave theory (NLWT) models, using the finite element package ABAQUS. Linear wave theory is implemented in an acoustic model, whereas a plane strain problem with large displacements is used in NLWT. Pressure distributions acting on the tank walls are obtained for the first three sloshing modes using both linear and nonlinear wave theory. It is found that the nonlinearity does not have significant effects on the natural sloshing periods. For the sloshing pressures on the tank walls, different distributions were found using linear and nonlinear wave theory models. However, in all cases studied, the linear wave theory conservatively estimated the magnitude of the pressure distribution, whereas larger pressures resultant heights were obtained when using the nonlinear theory. It is concluded that the nonlinearity of the surface wave does not have major effects in the pressure distribution on the walls for rectangular tanks.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

PubMed Central

Goto, Hayato

2016-01-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997

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.

Non-Darcy flow of water-based carbon nanotubes with nonlinear radiation and heat generation/absorption

NASA Astrophysics Data System (ADS)

Hayat, T.; Ullah, Siraj; Khan, M. Ijaz; Alsaedi, A.; Zaigham Zia, Q. M.

2018-03-01

Here modeling and computations are presented to introduce the novel concept of Darcy-Forchheimer three-dimensional flow of water-based carbon nanotubes with nonlinear thermal radiation and heat generation/absorption. Bidirectional stretching surface induces the flow. Darcy's law is commonly replace by Forchheimer relation. Xue model is implemented for nonliquid transport mechanism. Nonlinear formulation based upon conservation laws of mass, momentum and energy is first modeled and then solved by optimal homotopy analysis technique. Optimal estimations of auxiliary variables are obtained. Importance of influential variables on the velocity and thermal fields is interpreted graphically. Moreover velocity and temperature gradients are discussed and analyzed. Physical interpretation of influential variables is examined.

A comparison of washout filters using a human dynamic orientation model. M.S. Thesis

NASA Technical Reports Server (NTRS)

Riedel, S. A.

1977-01-01

The Ormsby model of human dynamic orientation, a discrete time computer program, was used to provide a vestibular explanation for observed differences between two washout schemes. These washout schemes, a linear washout and a nonlinear washout, were subjectively evaluated. It was found that the linear washout presented false rate cues, causing pilots to rate the simulation fidelity of the linear scheme much lower than the nonlinear scheme. By inputting these motion histories into the Ormsby model, it was shown that the linear filter causes discontinuities in the pilot's perceived angular velocity, resulting in the sensation of an anomalous rate cue. This phenomenon does not occur with the use of the nonlinear filter.

Joint nonlinearity effects in the design of a flexible truss structure control system

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1986-01-01

Nonlinear effects are introduced in the dynamics of large space truss structures by the connecting joints which are designed with rather important tolerances to facilitate the assembly of the structures in space. The purpose was to develop means to investigate the nonlinear dynamics of the structures, particularly the limit cycles that might occur when active control is applied to the structures. An analytical method was sought and derived to predict the occurrence of limit cycles and to determine their stability. This method is mainly based on the quasi-linearization of every joint using describing functions. This approach was proven successful when simple dynamical systems were tested. Its applicability to larger systems depends on the amount of computations it requires, and estimates of the computational task tend to indicate that the number of individual sources of nonlinearity should be limited. Alternate analytical approaches, which do not account for every single nonlinearity, or the simulation of a simplified model of the dynamical system should, therefore, be investigated to determine a more effective way to predict limit cycles in large dynamical systems with an important number of distributed nonlinearities.

Parameter estimation of a nonlinear Burger's model using nanoindentation and finite element-based inverse analysis

NASA Astrophysics Data System (ADS)

Hamim, Salah Uddin Ahmed

Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain behavior. Thus, theoretically it is possible to extract mechanical properties of a material through nanoindentation. However, due to various nonlinearities associated with nanoindentation the process of interpreting load-displacement data into material properties is difficult. Although, simple elastic behavior can be characterized easily, a method to characterize complicated material behavior such as nonlinear viscoelasticity is still lacking. In this study, a nanoindentation-based material characterization technique is developed to characterize soft materials exhibiting nonlinear viscoelasticity. Nanoindentation experiment was modeled in finite element analysis software (ABAQUS), where a nonlinear viscoelastic behavior was incorporated using user-defined subroutine (UMAT). The model parameters were calibrated using a process called inverse analysis. In this study, a surrogate model-based approach was used for the inverse analysis. The different factors affecting the surrogate model performance are analyzed in order to optimize the performance with respect to the computational cost.

Current structure of strongly nonlinear interfacial solitary waves

NASA Astrophysics Data System (ADS)

Semin, Sergey; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim; Churaev, Egor

2015-04-01

The characteristics of highly nonlinear solitary internal waves (solitons) in two-layer flow are computed within the fully nonlinear Navier-Stokes equations with use of numerical model of the Massachusetts Institute of Technology (MITgcm). The verification and adaptation of the model is based on the data from laboratory experiments [Carr & Davies, 2006]. The present paper also compares the results of our calculations with the computations performed in the framework of the fully nonlinear Bergen Ocean Model [Thiem et al, 2011]. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the interface and near the bottom are computed. The results demonstrated completely different trajectories at different depths of the model area. Thus, in the surface layer is observed the largest displacement of Lagrangian particles, which can be more than two and a half times larger than the characteristic width of the soliton. Located at the initial moment along the middle pycnocline fluid particles move along the elongated vertical loop at a distance of not more than one third of the width of the solitary wave. In the bottom layer of the fluid moves in the opposite direction of propagation of the internal wave, but under the influence of the reverse flow, when the bulk of the velocity field of the soliton ceases to influence the trajectory, it moves in the opposite direction. The magnitude of displacement of fluid particles in the bottom layer is not more than the half-width of the solitary wave. 1. Carr, M., and Davies, P.A. The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Phys. Fluids, 2006, vol. 18, No. 1, 1 - 10. 2. Thiem, O., Carr, M., Berntsen, J., and Davies, P.A. Numerical simulation of internal solitary wave-induced reverse flow and associated vortices in a shallow, two-layer fluid benthic boundary layer. Ocean Dynamics, 2011, vol. 61, No. 6, 857 - 872.

Gain optimization with non-linear controls

NASA Technical Reports Server (NTRS)

Slater, G. L.; Kandadai, R. D.

1984-01-01

An algorithm has been developed for the analysis and design of controls for non-linear systems. The technical approach is to use statistical linearization to model the non-linear dynamics of a system by a quasi-Gaussian model. A covariance analysis is performed to determine the behavior of the dynamical system and a quadratic cost function. Expressions for the cost function and its derivatives are determined so that numerical optimization techniques can be applied to determine optimal feedback laws. The primary application for this paper is centered about the design of controls for nominally linear systems but where the controls are saturated or limited by fixed constraints. The analysis is general, however, and numerical computation requires only that the specific non-linearity be considered in the analysis.

Finite element analysis of hysteresis effects in piezoelectric transducers

NASA Astrophysics Data System (ADS)

Simkovics, Reinhard; Landes, Hermann; Kaltenbacher, Manfred; Hoffelner, Johann; Lerch, Reinhard

2000-06-01

The design of ultrasonic transducers for high power applications, e.g. in medical therapy or production engineering, asks for effective computer aided design tools to analyze the occurring nonlinear effects. In this paper the finite-element-boundary-element package CAPA is presented that allows to model different types of electromechanical sensors and actuators. These transducers are based on various physical coupling effects, such as piezoelectricity or magneto- mechanical interactions. Their computer modeling requires the numerical solution of a multifield problem, such as coupled electric-mechanical fields or magnetic-mechanical fields as well as coupled mechanical-acoustic fields. With the reported software environment we are able to compute the dynamic behavior of electromechanical sensors and actuators by taking into account geometric nonlinearities, nonlinear wave propagation and ferroelectric as well as magnetic material nonlinearities. After a short introduction to the basic theory of the numerical calculation schemes, two practical examples will demonstrate the applicability of the numerical simulation tool. As a first example an ultrasonic thickness mode transducer consisting of a piezoceramic material used for high power ultrasound production is examined. Due to ferroelectric hysteresis, higher order harmonics can be detected in the actuators input current. Also in case of electrical and mechanical prestressing a resonance frequency shift occurs, caused by ferroelectric hysteresis and nonlinear dependencies of the material coefficients on electric field and mechanical stresses. As a second example, a power ultrasound transducer used in HIFU-therapy (high intensity focused ultrasound) is presented. Due to the compressibility and losses in the propagating fluid a nonlinear shock wave generation can be observed. For both examples a good agreement between numerical simulation and experimental data has been achieved.

Math modeling and computer mechanization for real time simulation of rotary-wing aircraft

NASA Technical Reports Server (NTRS)

Howe, R. M.

1979-01-01

Mathematical modeling and computer mechanization for real time simulation of rotary wing aircraft is discussed. Error analysis in the digital simulation of dynamic systems, such as rotary wing aircraft is described. The method for digital simulation of nonlinearities with discontinuities, such as exist in typical flight control systems and rotor blade hinges, is discussed.

Reduced-Order Modeling: New Approaches for Computational Physics

NASA Technical Reports Server (NTRS)

Beran, Philip S.; Silva, Walter A.

2001-01-01

In this paper, we review the development of new reduced-order modeling techniques and discuss their applicability to various problems in computational physics. Emphasis is given to methods ba'sed on Volterra series representations and the proper orthogonal decomposition. Results are reported for different nonlinear systems to provide clear examples of the construction and use of reduced-order models, particularly in the multi-disciplinary field of computational aeroelasticity. Unsteady aerodynamic and aeroelastic behaviors of two- dimensional and three-dimensional geometries are described. Large increases in computational efficiency are obtained through the use of reduced-order models, thereby justifying the initial computational expense of constructing these models and inotivatim,- their use for multi-disciplinary design analysis.

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.

Weighted Optimization-Based Distributed Kalman Filter for Nonlinear Target Tracking in Collaborative Sensor Networks.

PubMed

Chen, Jie; Li, Jiahong; Yang, Shuanghua; Deng, Fang

2017-11-01

The identification of the nonlinearity and coupling is crucial in nonlinear target tracking problem in collaborative sensor networks. According to the adaptive Kalman filtering (KF) method, the nonlinearity and coupling can be regarded as the model noise covariance, and estimated by minimizing the innovation or residual errors of the states. However, the method requires large time window of data to achieve reliable covariance measurement, making it impractical for nonlinear systems which are rapidly changing. To deal with the problem, a weighted optimization-based distributed KF algorithm (WODKF) is proposed in this paper. The algorithm enlarges the data size of each sensor by the received measurements and state estimates from its connected sensors instead of the time window. A new cost function is set as the weighted sum of the bias and oscillation of the state to estimate the "best" estimate of the model noise covariance. The bias and oscillation of the state of each sensor are estimated by polynomial fitting a time window of state estimates and measurements of the sensor and its neighbors weighted by the measurement noise covariance. The best estimate of the model noise covariance is computed by minimizing the weighted cost function using the exhaustive method. The sensor selection method is in addition to the algorithm to decrease the computation load of the filter and increase the scalability of the sensor network. The existence, suboptimality and stability analysis of the algorithm are given. The local probability data association method is used in the proposed algorithm for the multitarget tracking case. The algorithm is demonstrated in simulations on tracking examples for a random signal, one nonlinear target, and four nonlinear targets. Results show the feasibility and superiority of WODKF against other filtering algorithms for a large class of systems.

A method for the geometrically nonlinear analysis of compressively loaded prismatic composite structures

NASA Technical Reports Server (NTRS)

Stoll, Frederick; Gurdal, Zafer; Starnes, James H., Jr.

1991-01-01

A method was developed for the geometrically nonlinear analysis of the static response of thin-walled stiffened composite structures loaded in uniaxial or biaxial compression. The method is applicable to arbitrary prismatic configurations composed of linked plate strips, such as stiffened panels and thin-walled columns. The longitudinal ends of the structure are assumed to be simply supported, and geometric shape imperfections can be modeled. The method can predict the nonlinear phenomena of postbuckling strength and imperfection sensitivity which are exhibited by some buckling-dominated structures. The method is computer-based and is semi-analytic in nature, making it computationally economical in comparison to finite element methods. The method uses a perturbation approach based on the use of a series of buckling mode shapes to represent displacement contributions associated with nonlinear response. Displacement contributions which are of second order in the model amplitudes are incorported in addition to the buckling mode shapes. The principle of virtual work is applied using a finite basis of buckling modes, and terms through the third order in the model amplitudes are retained. A set of cubic nonlinear algebraic equations are obtained, from which approximate equilibrium solutions are determined. Buckling mode shapes for the general class of structure are obtained using the VIPASA analysis code within the PASCO stiffened-panel design code. Thus, subject to some additional restrictions in loading and plate anisotropy, structures which can be modeled with respect to buckling behavior by VIPASA can be analyzed with respect to nonlinear response using the new method. Results obtained using the method are compared with both experimental and analytical results in the literature. The configurations investigated include several different unstiffened and blade-stiffening panel configurations, featuring both homogeneous, isotropic materials, and laminated composite material.

NASA LeRC/Akron University Graduate Cooperative Fellowship Program and Graduate Student Researchers Program

NASA Technical Reports Server (NTRS)

Fertis, D. G.; Simon, A. L.

1981-01-01

The requisite methodology to solve linear and nonlinear problems associated with the static and dynamic analysis of rotating machinery, their static and dynamic behavior, and the interaction between the rotating and nonrotating parts of an engine is developed. Linear and nonlinear structural engine problems are investigated by developing solution strategies and interactive computational methods whereby the man and computer can communicate directly in making analysis decisions. Representative examples include modifying structural models, changing material, parameters, selecting analysis options and coupling with interactive graphical display for pre- and postprocessing capability.

High-resolution mapping of bifurcations in nonlinear biochemical circuits

NASA Astrophysics Data System (ADS)

Genot, A. J.; Baccouche, A.; Sieskind, R.; Aubert-Kato, N.; Bredeche, N.; Bartolo, J. F.; Taly, V.; Fujii, T.; Rondelez, Y.

2016-08-01

Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.

A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes

NASA Astrophysics Data System (ADS)

Ferhatoglu, Erhan; Cigeroglu, Ender; Özgüven, H. Nevzat

2018-07-01

In this paper, a new modal superposition method based on a hybrid mode shape concept is developed for the determination of steady state vibration response of nonlinear structures. The method is developed specifically for systems having nonlinearities where the stiffness of the system may take different limiting values. Stiffness variation of these nonlinear systems enables one to define different linear systems corresponding to each value of the limiting equivalent stiffness. Moreover, the response of the nonlinear system is bounded by the confinement of these linear systems. In this study, a modal superposition method utilizing novel hybrid mode shapes which are defined as linear combinations of the modal vectors of the limiting linear systems is proposed to determine periodic response of nonlinear systems. In this method the response of the nonlinear system is written in terms of hybrid modes instead of the modes of the underlying linear system. This provides decrease of the number of modes that should be retained for an accurate solution, which in turn reduces the number of nonlinear equations to be solved. In this way, computational time for response calculation is directly curtailed. In the solution, the equations of motion are converted to a set of nonlinear algebraic equations by using describing function approach, and the numerical solution is obtained by using Newton's method with arc-length continuation. The method developed is applied on two different systems: a lumped parameter model and a finite element model. Several case studies are performed and the accuracy and computational efficiency of the proposed modal superposition method with hybrid mode shapes are compared with those of the classical modal superposition method which utilizes the mode shapes of the underlying linear system.

Mixed convection flow of viscoelastic fluid by a stretching cylinder with heat transfer.

PubMed

Hayat, Tasawar; Anwar, Muhammad Shoaib; Farooq, Muhammad; Alsaedi, Ahmad

2015-01-01

Flow of viscoelastic fluid due to an impermeable stretching cylinder is discussed. Effects of mixed convection and variable thermal conductivity are present. Thermal conductivity is taken temperature dependent. Nonlinear partial differential system is reduced into the nonlinear ordinary differential system. Resulting nonlinear system is computed for the convergent series solutions. Numerical values of skin friction coefficient and Nusselt number are computed and discussed. The results obtained with the current method are in agreement with previous studies using other methods as well as theoretical ideas. Physical interpretation reflecting the contribution of influential parameters in the present flow is presented. It is hoped that present study serves as a stimulus for modeling further stretching flows especially in polymeric and paper production processes.

Mixed Convection Flow of Viscoelastic Fluid by a Stretching Cylinder with Heat Transfer

PubMed Central

Hayat, Tasawar; Anwar, Muhammad Shoaib; Farooq, Muhammad; Alsaedi, Ahmad

2015-01-01

Flow of viscoelastic fluid due to an impermeable stretching cylinder is discussed. Effects of mixed convection and variable thermal conductivity are present. Thermal conductivity is taken temperature dependent. Nonlinear partial differential system is reduced into the nonlinear ordinary differential system. Resulting nonlinear system is computed for the convergent series solutions. Numerical values of skin friction coefficient and Nusselt number are computed and discussed. The results obtained with the current method are in agreement with previous studies using other methods as well as theoretical ideas. Physical interpretation reflecting the contribution of influential parameters in the present flow is presented. It is hoped that present study serves as a stimulus for modeling further stretching flows especially in polymeric and paper production processes. PMID:25775032

Earthquake models using rate and state friction and fast multipoles

NASA Astrophysics Data System (ADS)

Tullis, T.

2003-04-01

The most realistic current earthquake models employ laboratory-derived non-linear constitutive laws. These are the rate and state friction laws having both a non-linear viscous or direct effect and an evolution effect in which frictional resistance depends on time of stationary contact and has a memory of past slip velocity that fades with slip. The frictional resistance depends on the log of the slip velocity as well as the log of stationary hold time, and the fading memory involves an approximately exponential decay with slip. Due to the nonlinearly of these laws, analytical earthquake models are not attainable and numerical models are needed. The situation is even more difficult if true dynamic models are sought that deal with inertial forces and slip velocities on the order of 1 m/s as are observed during dynamic earthquake slip. Additional difficulties that exist if the dynamic slip phase of earthquakes is modeled arise from two sources. First, many physical processes might operate during dynamic slip, but they are only poorly understood, the relative importance of the processes is unknown, and the processes are even more nonlinear than those described by the current rate and state laws. Constitutive laws describing such behaviors are still being developed. Second, treatment of inertial forces and the influence that dynamic stresses from elastic waves may have on slip on the fault requires keeping track of the history of slip on remote parts of the fault as far into the past as it takes waves to travel from there. This places even more stringent requirements on computer time. Challenges for numerical modeling of complete earthquake cycles are that both time steps and mesh sizes must be small. Time steps must be milliseconds during dynamic slip, and yet models must represent earthquake cycles 100 years or more in length; methods using adaptive step sizes are essential. Element dimensions need to be on the order of meters, both to approximate continuum behavior adequately and to model microseismicity as well as large earthquakes. In order to model significant sized earthquakes this requires millions of elements. Modeling methods like the boundary element method that involve Green's functions normally require computation times that increase with the number N of elements squared, so using large N becomes impossible. We have adapted the Fast Multipole method to this problem in which the influence of sufficiently remote elements are grouped together and the elements are indexed such that the computations more efficient when run on parallel computers. Compute time varies with N log N rather than N squared. Computer programs are available that use this approach (http://www.servogrid.org/slide/GEM/PARK). Whether the multipole approach can be adapted to dynamic modeling is unclear.

Manual of phosphoric acid fuel cell power plant optimization model and computer program

NASA Technical Reports Server (NTRS)

Lu, C. Y.; Alkasab, K. A.

1984-01-01

An optimized cost and performance model for a phosphoric acid fuel cell power plant system was derived and developed into a modular FORTRAN computer code. Cost, energy, mass, and electrochemical analyses were combined to develop a mathematical model for optimizing the steam to methane ratio in the reformer, hydrogen utilization in the PAFC plates per stack. The nonlinear programming code, COMPUTE, was used to solve this model, in which the method of mixed penalty function combined with Hooke and Jeeves pattern search was chosen to evaluate this specific optimization problem.

Nonlinear Structured Growth Mixture Models in Mplus and OpenMx

PubMed Central

Grimm, Kevin J.; Ram, Nilam; Estabrook, Ryne

2014-01-01

Growth mixture models (GMMs; Muthén & Muthén, 2000; Muthén & Shedden, 1999) are a combination of latent curve models (LCMs) and finite mixture models to examine the existence of latent classes that follow distinct developmental patterns. GMMs are often fit with linear, latent basis, multiphase, or polynomial change models because of their common use, flexibility in modeling many types of change patterns, the availability of statistical programs to fit such models, and the ease of programming. In this paper, we present additional ways of modeling nonlinear change patterns with GMMs. Specifically, we show how LCMs that follow specific nonlinear functions can be extended to examine the presence of multiple latent classes using the Mplus and OpenMx computer programs. These models are fit to longitudinal reading data from the Early Childhood Longitudinal Study-Kindergarten Cohort to illustrate their use. PMID:25419006

Computational dynamics of soft machines

NASA Astrophysics Data System (ADS)

Hu, Haiyan; Tian, Qiang; Liu, Cheng

2017-06-01

Soft machine refers to a kind of mechanical system made of soft materials to complete sophisticated missions, such as handling a fragile object and crawling along a narrow tunnel corner, under low cost control and actuation. Hence, soft machines have raised great challenges to computational dynamics. In this review article, recent studies of the authors on the dynamic modeling, numerical simulation, and experimental validation of soft machines are summarized in the framework of multibody system dynamics. The dynamic modeling approaches are presented first for the geometric nonlinearities of coupled overall motions and large deformations of a soft component, the physical nonlinearities of a soft component made of hyperelastic or elastoplastic materials, and the frictional contacts/impacts of soft components, respectively. Then the computation approach is outlined for the dynamic simulation of soft machines governed by a set of differential-algebraic equations of very high dimensions, with an emphasis on the efficient computations of the nonlinear elastic force vector of finite elements. The validations of the proposed approaches are given via three case studies, including the locomotion of a soft quadrupedal robot, the spinning deployment of a solar sail of a spacecraft, and the deployment of a mesh reflector of a satellite antenna, as well as the corresponding experimental studies. Finally, some remarks are made for future studies.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

NASA Astrophysics Data System (ADS)

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris; Khalil, Mohammad; Sarkar, Abhijit

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid-structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic system leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib-Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.

Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations

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

Sandhu, Rimple; Poirel, Dominique; Pettit, Chris

2016-07-01

A Bayesian model selection and parameter estimation algorithm is applied to investigate the influence of nonlinear and unsteady aerodynamic loads on the limit cycle oscillation (LCO) of a pitching airfoil in the transitional Reynolds number regime. At small angles of attack, laminar boundary layer trailing edge separation causes negative aerodynamic damping leading to the LCO. The fluid–structure interaction of the rigid, but elastically mounted, airfoil and nonlinear unsteady aerodynamics is represented by two coupled nonlinear stochastic ordinary differential equations containing uncertain parameters and model approximation errors. Several plausible aerodynamic models with increasing complexity are proposed to describe the aeroelastic systemmore » leading to LCO. The likelihood in the posterior parameter probability density function (pdf) is available semi-analytically using the extended Kalman filter for the state estimation of the coupled nonlinear structural and unsteady aerodynamic model. The posterior parameter pdf is sampled using a parallel and adaptive Markov Chain Monte Carlo (MCMC) algorithm. The posterior probability of each model is estimated using the Chib–Jeliazkov method that directly uses the posterior MCMC samples for evidence (marginal likelihood) computation. The Bayesian algorithm is validated through a numerical study and then applied to model the nonlinear unsteady aerodynamic loads using wind-tunnel test data at various Reynolds numbers.« less

Low-Dimensional Models for Physiological Systems: Nonlinear Coupling of Gas and Liquid Flows

NASA Astrophysics Data System (ADS)

Staples, A. E.; Oran, E. S.; Boris, J. P.; Kailasanath, K.

2006-11-01

Current computational models of biological organisms focus on the details of a specific component of the organism. For example, very detailed models of the human heart, an aorta, a vein, or part of the respiratory or digestive system, are considered either independently from the rest of the body, or as interacting simply with other systems and components in the body. In actual biological organisms, these components and systems are strongly coupled and interact in complex, nonlinear ways leading to complicated global behavior. Here we describe a low-order computational model of two physiological systems, based loosely on a circulatory and respiratory system. Each system is represented as a one-dimensional fluid system with an interconnected series of mass sources, pumps, valves, and other network components, as appropriate, representing different physical organs and system components. Preliminary results from a first version of this model system are presented.

Improving the Efficiency of Abdominal Aortic Aneurysm Wall Stress Computations

PubMed Central

Zelaya, Jaime E.; Goenezen, Sevan; Dargon, Phong T.; Azarbal, Amir-Farzin; Rugonyi, Sandra

2014-01-01

An abdominal aortic aneurysm is a pathological dilation of the abdominal aorta, which carries a high mortality rate if ruptured. The most commonly used surrogate marker of rupture risk is the maximal transverse diameter of the aneurysm. More recent studies suggest that wall stress from models of patient-specific aneurysm geometries extracted, for instance, from computed tomography images may be a more accurate predictor of rupture risk and an important factor in AAA size progression. However, quantification of wall stress is typically computationally intensive and time-consuming, mainly due to the nonlinear mechanical behavior of the abdominal aortic aneurysm walls. These difficulties have limited the potential of computational models in clinical practice. To facilitate computation of wall stresses, we propose to use a linear approach that ensures equilibrium of wall stresses in the aneurysms. This proposed linear model approach is easy to implement and eliminates the burden of nonlinear computations. To assess the accuracy of our proposed approach to compute wall stresses, results from idealized and patient-specific model simulations were compared to those obtained using conventional approaches and to those of a hypothetical, reference abdominal aortic aneurysm model. For the reference model, wall mechanical properties and the initial unloaded and unstressed configuration were assumed to be known, and the resulting wall stresses were used as reference for comparison. Our proposed linear approach accurately approximates wall stresses for varying model geometries and wall material properties. Our findings suggest that the proposed linear approach could be used as an effective, efficient, easy-to-use clinical tool to estimate patient-specific wall stresses. PMID:25007052

Nonlinear digital signal processing in mental health: characterization of major depression using instantaneous entropy measures of heartbeat dynamics.

PubMed

Valenza, Gaetano; Garcia, Ronald G; Citi, Luca; Scilingo, Enzo P; Tomaz, Carlos A; Barbieri, Riccardo

2015-01-01

Nonlinear digital signal processing methods that address system complexity have provided useful computational tools for helping in the diagnosis and treatment of a wide range of pathologies. More specifically, nonlinear measures have been successful in characterizing patients with mental disorders such as Major Depression (MD). In this study, we propose the use of instantaneous measures of entropy, namely the inhomogeneous point-process approximate entropy (ipApEn) and the inhomogeneous point-process sample entropy (ipSampEn), to describe a novel characterization of MD patients undergoing affective elicitation. Because these measures are built within a nonlinear point-process model, they allow for the assessment of complexity in cardiovascular dynamics at each moment in time. Heartbeat dynamics were characterized from 48 healthy controls and 48 patients with MD while emotionally elicited through either neutral or arousing audiovisual stimuli. Experimental results coming from the arousing tasks show that ipApEn measures are able to instantaneously track heartbeat complexity as well as discern between healthy subjects and MD patients. Conversely, standard heart rate variability (HRV) analysis performed in both time and frequency domains did not show any statistical significance. We conclude that measures of entropy based on nonlinear point-process models might contribute to devising useful computational tools for care in mental health.

Research and development program for the development of advanced time-temperature dependent constitutive relationships. Volume 2: Programming manual

NASA Technical Reports Server (NTRS)

Cassenti, B. N.

1983-01-01

The results of a 10-month research and development program for nonlinear structural modeling with advanced time-temperature constitutive relationships are presented. The implementation of the theory in the MARC nonlinear finite element code is discussed, and instructions for the computational application of the theory are provided.

Getting off the Straight and Narrow: Exploiting Non-Linear, Interactive Narrative Structures in Digital Stories for Language Teaching

ERIC Educational Resources Information Center

Prosser, Andrew

2014-01-01

Digital storytelling is already used extensively in language education. Web documentaries, particularly in terms of design and narrative structure, provide an extension of the digital storytelling concept, specifically in terms of increased interactivity. Using a model of interactive, non-linear storytelling, originally derived from computer game…

Multi-linear model set design based on the nonlinearity measure and H-gap metric.

PubMed

Shaghaghi, Davood; Fatehi, Alireza; Khaki-Sedigh, Ali

2017-05-01

This paper proposes a model bank selection method for a large class of nonlinear systems with wide operating ranges. In particular, nonlinearity measure and H-gap metric are used to provide an effective algorithm to design a model bank for the system. Then, the proposed model bank is accompanied with model predictive controllers to design a high performance advanced process controller. The advantage of this method is the reduction of excessive switch between models and also decrement of the computational complexity in the controller bank that can lead to performance improvement of the control system. The effectiveness of the method is verified by simulations as well as experimental studies on a pH neutralization laboratory apparatus which confirms the efficiency of the proposed algorithm. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

NASA Astrophysics Data System (ADS)

Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

2018-01-01

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

An evolutionary firefly algorithm for the estimation of nonlinear biological model parameters.

PubMed

Abdullah, Afnizanfaizal; Deris, Safaai; Anwar, Sohail; Arjunan, Satya N V

2013-01-01

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test.

An Evolutionary Firefly Algorithm for the Estimation of Nonlinear Biological Model Parameters

PubMed Central

Abdullah, Afnizanfaizal; Deris, Safaai; Anwar, Sohail; Arjunan, Satya N. V.

2013-01-01

The development of accurate computational models of biological processes is fundamental to computational systems biology. These models are usually represented by mathematical expressions that rely heavily on the system parameters. The measurement of these parameters is often difficult. Therefore, they are commonly estimated by fitting the predicted model to the experimental data using optimization methods. The complexity and nonlinearity of the biological processes pose a significant challenge, however, to the development of accurate and fast optimization methods. We introduce a new hybrid optimization method incorporating the Firefly Algorithm and the evolutionary operation of the Differential Evolution method. The proposed method improves solutions by neighbourhood search using evolutionary procedures. Testing our method on models for the arginine catabolism and the negative feedback loop of the p53 signalling pathway, we found that it estimated the parameters with high accuracy and within a reasonable computation time compared to well-known approaches, including Particle Swarm Optimization, Nelder-Mead, and Firefly Algorithm. We have also verified the reliability of the parameters estimated by the method using an a posteriori practical identifiability test. PMID:23469172

An Asynchronous Recurrent Network of Cellular Automaton-Based Neurons and Its Reproduction of Spiking Neural Network Activities.

PubMed

Matsubara, Takashi; Torikai, Hiroyuki

2016-04-01

Modeling and implementation approaches for the reproduction of input-output relationships in biological nervous tissues contribute to the development of engineering and clinical applications. However, because of high nonlinearity, the traditional modeling and implementation approaches encounter difficulties in terms of generalization ability (i.e., performance when reproducing an unknown data set) and computational resources (i.e., computation time and circuit elements). To overcome these difficulties, asynchronous cellular automaton-based neuron (ACAN) models, which are described as special kinds of cellular automata that can be implemented as small asynchronous sequential logic circuits have been proposed. This paper presents a novel type of such ACAN and a theoretical analysis of its excitability. This paper also presents a novel network of such neurons, which can mimic input-output relationships of biological and nonlinear ordinary differential equation model neural networks. Numerical analyses confirm that the presented network has a higher generalization ability than other major modeling and implementation approaches. In addition, Field-Programmable Gate Array-implementations confirm that the presented network requires lower computational resources.

Improving Computational Efficiency of Prediction in Model-Based Prognostics Using the Unscented Transform

NASA Technical Reports Server (NTRS)

Daigle, Matthew John; Goebel, Kai Frank

2010-01-01

Model-based prognostics captures system knowledge in the form of physics-based models of components, and how they fail, in order to obtain accurate predictions of end of life (EOL). EOL is predicted based on the estimated current state distribution of a component and expected profiles of future usage. In general, this requires simulations of the component using the underlying models. In this paper, we develop a simulation-based prediction methodology that achieves computational efficiency by performing only the minimal number of simulations needed in order to accurately approximate the mean and variance of the complete EOL distribution. This is performed through the use of the unscented transform, which predicts the means and covariances of a distribution passed through a nonlinear transformation. In this case, the EOL simulation acts as that nonlinear transformation. In this paper, we review the unscented transform, and describe how this concept is applied to efficient EOL prediction. As a case study, we develop a physics-based model of a solenoid valve, and perform simulation experiments to demonstrate improved computational efficiency without sacrificing prediction accuracy.

A phenomenological approach to modeling chemical dynamics in nonlinear and two-dimensional spectroscopy.

PubMed

Ramasesha, Krupa; De Marco, Luigi; Horning, Andrew D; Mandal, Aritra; Tokmakoff, Andrei

2012-04-07

We present an approach for calculating nonlinear spectroscopic observables, which overcomes the approximations inherent to current phenomenological models without requiring the computational cost of performing molecular dynamics simulations. The trajectory mapping method uses the semi-classical approximation to linear and nonlinear response functions, and calculates spectra from trajectories of the system's transition frequencies and transition dipole moments. It rests on identifying dynamical variables important to the problem, treating the dynamics of these variables stochastically, and then generating correlated trajectories of spectroscopic quantities by mapping from the dynamical variables. This approach allows one to describe non-Gaussian dynamics, correlated dynamics between variables of the system, and nonlinear relationships between spectroscopic variables of the system and the bath such as non-Condon effects. We illustrate the approach by applying it to three examples that are often not adequately treated by existing analytical models--the non-Condon effect in the nonlinear infrared spectra of water, non-Gaussian dynamics inherent to strongly hydrogen bonded systems, and chemical exchange processes in barrier crossing reactions. The methods described are generally applicable to nonlinear spectroscopy throughout the optical, infrared and terahertz regions.

Development of a rotorcraft. Propulsion dynamics interface analysis, volume 2

NASA Technical Reports Server (NTRS)

Hull, R.

1982-01-01

A study was conducted to establish a coupled rotor/propulsion analysis that would be applicable to a wide range of rotorcraft systems. The effort included the following tasks: (1) development of a model structure suitable for simulating a wide range of rotorcraft configurations; (2) defined a methodology for parameterizing the model structure to represent a particular rotorcraft; (3) constructing a nonlinear coupled rotor/propulsion model as a test case to use in analyzing coupled system dynamics; and (4) an attempt to develop a mostly linear coupled model derived from the complete nonlinear simulations. Documentation of the computer models developed is presented.

Higher-order ice-sheet modelling accelerated by multigrid on graphics cards

NASA Astrophysics Data System (ADS)

Brædstrup, Christian; Egholm, David

2013-04-01

Higher-order ice flow modelling is a very computer intensive process owing primarily to the nonlinear influence of the horizontal stress coupling. When applied for simulating long-term glacial landscape evolution, the ice-sheet models must consider very long time series, while both high temporal and spatial resolution is needed to resolve small effects. The use of higher-order and full stokes models have therefore seen very limited usage in this field. However, recent advances in graphics card (GPU) technology for high performance computing have proven extremely efficient in accelerating many large-scale scientific computations. The general purpose GPU (GPGPU) technology is cheap, has a low power consumption and fits into a normal desktop computer. It could therefore provide a powerful tool for many glaciologists working on ice flow models. Our current research focuses on utilising the GPU as a tool in ice-sheet and glacier modelling. To this extent we have implemented the Integrated Second-Order Shallow Ice Approximation (iSOSIA) equations on the device using the finite difference method. To accelerate the computations, the GPU solver uses a non-linear Red-Black Gauss-Seidel iterator coupled with a Full Approximation Scheme (FAS) multigrid setup to further aid convergence. The GPU finite difference implementation provides the inherent parallelization that scales from hundreds to several thousands of cores on newer cards. We demonstrate the efficiency of the GPU multigrid solver using benchmark experiments.

Nonlinear predictive control of a boiler-turbine unit: A state-space approach with successive on-line model linearisation and quadratic optimisation.

PubMed

Ławryńczuk, Maciej

2017-03-01

This paper details development of a Model Predictive Control (MPC) algorithm for a boiler-turbine unit, which is a nonlinear multiple-input multiple-output process. The control objective is to follow set-point changes imposed on two state (output) variables and to satisfy constraints imposed on three inputs and one output. In order to obtain a computationally efficient control scheme, the state-space model is successively linearised on-line for the current operating point and used for prediction. In consequence, the future control policy is easily calculated from a quadratic optimisation problem. For state estimation the extended Kalman filter is used. It is demonstrated that the MPC strategy based on constant linear models does not work satisfactorily for the boiler-turbine unit whereas the discussed algorithm with on-line successive model linearisation gives practically the same trajectories as the truly nonlinear MPC controller with nonlinear optimisation repeated at each sampling instant. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Linear and nonlinear ARMA model parameter estimation using an artificial neural network

NASA Technical Reports Server (NTRS)

Chon, K. H.; Cohen, R. J.

1997-01-01

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

The YAV-8B simulation and modeling. Volume 2: Program listing

NASA Technical Reports Server (NTRS)

1983-01-01

Detailed mathematical models of varying complexity representative of the YAV-8B aircraft are defined and documented. These models are used in parameter estimation and in linear analysis computer programs while investigating YAV-8B aircraft handling qualities. Both a six degree of freedom nonlinear model and a linearized three degree of freedom longitudinal and lateral directional model were developed. The nonlinear model is based on the mathematical model used on the MCAIR YAV-8B manned flight simulator. This simulator model has undergone periodic updating based on the results of approximately 360 YAV-8B flights and 8000 hours of wind tunnel testing. Qualified YAV-8B flight test pilots have commented that the handling qualities characteristics of the simulator are quite representative of the real aircraft. These comments are validated herein by comparing data from both static and dynamic flight test maneuvers to the same obtained using the nonlinear program.

Numerical solution of turbulent flow past a backward facing step using a nonlinear K-epsilon model

NASA Technical Reports Server (NTRS)

Speziale, C. G.; Ngo, Tuan

1987-01-01

The problem of turbulent flow past a backward facing step is important in many technological applications and has been used as a standard test case to evaluate the performance of turbulence models in the prediction of separated flows. It is well known that the commonly used kappa-epsilon (and K-l) models of turbulence yield inaccurate predictions for the reattachment points in this problem. By an analysis of the mean vorticity transport equation, it will be argued that the intrinsically inaccurate prediction of normal Reynolds stress differences by the Kappa-epsilon and K-l models is a major contributor to this problem. Computations using a new nonlinear kappa-epsilon model (which alleviates this deficiency) are made with the TEACH program. Comparisons are made between the improved results predicted by this nonlinear kappa-epsilon model and those obtained from the linear kappa-epsilon model as well as from second-order closure models.

Efficient self-organizing multilayer neural network for nonlinear system modeling.

PubMed

Han, Hong-Gui; Wang, Li-Dan; Qiao, Jun-Fei

2013-07-01

It has been shown extensively that the dynamic behaviors of a neural system are strongly influenced by the network architecture and learning process. To establish an artificial neural network (ANN) with self-organizing architecture and suitable learning algorithm for nonlinear system modeling, an automatic axon-neural network (AANN) is investigated in the following respects. First, the network architecture is constructed automatically to change both the number of hidden neurons and topologies of the neural network during the training process. The approach introduced in adaptive connecting-and-pruning algorithm (ACP) is a type of mixed mode operation, which is equivalent to pruning or adding the connecting of the neurons, as well as inserting some required neurons directly. Secondly, the weights are adjusted, using a feedforward computation (FC) to obtain the information for the gradient during learning computation. Unlike most of the previous studies, AANN is able to self-organize the architecture and weights, and to improve the network performances. Also, the proposed AANN has been tested on a number of benchmark problems, ranging from nonlinear function approximating to nonlinear systems modeling. The experimental results show that AANN can have better performances than that of some existing neural networks. Crown Copyright © 2013. Published by Elsevier Ltd. All rights reserved.

A conservative numerical scheme for modeling nonlinear acoustic propagation in thermoviscous homogeneous media

NASA Astrophysics Data System (ADS)

Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.

2018-06-01

A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.

Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics

NASA Astrophysics Data System (ADS)

Ahmad, Iftikhar; Ahmad, Sufyan; Awais, Muhammad; Ul Islam Ahmad, Siraj; Asif Zahoor Raja, Muhammad

2018-05-01

The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.

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.

Cubical Mass-Spring Model design based on a tensile deformation test and nonlinear material model.

PubMed

San-Vicente, Gaizka; Aguinaga, Iker; Tomás Celigüeta, Juan

2012-02-01

Mass-Spring Models (MSMs) are used to simulate the mechanical behavior of deformable bodies such as soft tissues in medical applications. Although they are fast to compute, they lack accuracy and their design remains still a great challenge. The major difficulties in building realistic MSMs lie on the spring stiffness estimation and the topology identification. In this work, the mechanical behavior of MSMs under tensile loads is analyzed before studying the spring stiffness estimation. In particular, the performed qualitative and quantitative analysis of the behavior of cubical MSMs shows that they have a nonlinear response similar to hyperelastic material models. According to this behavior, a new method for spring stiffness estimation valid for linear and nonlinear material models is proposed. This method adjusts the stress-strain and compressibility curves to a given reference behavior. The accuracy of the MSMs designed with this method is tested taking as reference some soft-tissue simulations based on nonlinear Finite Element Method (FEM). The obtained results show that MSMs can be designed to realistically model the behavior of hyperelastic materials such as soft tissues and can become an interesting alternative to other approaches such as nonlinear FEM.

Real time optimal guidance of low-thrust spacecraft: an application of nonlinear model predictive control.

PubMed

Arrieta-Camacho, Juan José; Biegler, Lorenz T

2005-12-01

Real time optimal guidance is considered for a class of low thrust spacecraft. In particular, nonlinear model predictive control (NMPC) is utilized for computing the optimal control actions required to transfer a spacecraft from a low Earth orbit to a mission orbit. The NMPC methodology presented is able to cope with unmodeled disturbances. The dynamics of the transfer are modeled using a set of modified equinoctial elements because they do not exhibit singularities for zero inclination and zero eccentricity. The idea behind NMPC is the repeated solution of optimal control problems; at each time step, a new control action is computed. The optimal control problem is solved using a direct method-fully discretizing the equations of motion. The large scale nonlinear program resulting from the discretization procedure is solved using IPOPT--a primal-dual interior point algorithm. Stability and robustness characteristics of the NMPC algorithm are reviewed. A numerical example is presented that encourages further development of the proposed methodology: the transfer from low-Earth orbit to a molniya orbit.

Real-Time Detector of Human Fatigue: Detecting Lapses in Alertness

DTIC Science & Technology

2008-02-15

These coefficients and their variances, covariances and standard errors were computed simultaneously using HLM 6 (Raudenbush, Bryk, Cheong, & Congdon ...CA: Sage. Raudenbush, S. W., Bryk, A. S., Cheong, Y. F., & Congdon , R. T. (2004). HLM6: Hierarchical Linear and Nonlinear Modeling [Computer software

An adaptive model order reduction by proper snapshot selection for nonlinear dynamical problems

NASA Astrophysics Data System (ADS)

Nigro, P. S. B.; Anndif, M.; Teixeira, Y.; Pimenta, P. M.; Wriggers, P.

2016-04-01

Model Order Reduction (MOR) methods are employed in many fields of Engineering in order to reduce the processing time of complex computational simulations. A usual approach to achieve this is the application of Galerkin projection to generate representative subspaces (reduced spaces). However, when strong nonlinearities in a dynamical system are present and this technique is employed several times along the simulation, it can be very inefficient. This work proposes a new adaptive strategy, which ensures low computational cost and small error to deal with this problem. This work also presents a new method to select snapshots named Proper Snapshot Selection (PSS). The objective of the PSS is to obtain a good balance between accuracy and computational cost by improving the adaptive strategy through a better snapshot selection in real time (online analysis). With this method, it is possible a substantial reduction of the subspace, keeping the quality of the model without the use of the Proper Orthogonal Decomposition (POD).

Exploiting symmetries in the modeling and analysis of tires

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Andersen, Carl M.; Tanner, John A.

1987-01-01

A simple and efficient computational strategy for reducing both the size of a tire model and the cost of the analysis of tires in the presence of symmetry-breaking conditions (unsymmetry in the tire material, geometry, or loading) is presented. The strategy is based on approximating the unsymmetric response of the tire with a linear combination of symmetric and antisymmetric global approximation vectors (or modes). Details are presented for the three main elements of the computational strategy, which include: use of special three-field mixed finite-element models, use of operator splitting, and substantial reduction in the number of degrees of freedom. The proposed computational stategy is applied to three quasi-symmetric problems of tires: linear analysis of anisotropic tires, through use of semianalytic finite elements, nonlinear analysis of anisotropic tires through use of two-dimensional shell finite elements, and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry (and their combinations) exhibited by the tire response are identified.

Modification of 2-D Time-Domain Shallow Water Wave Equation using Asymptotic Expansion Method

NASA Astrophysics Data System (ADS)

Khairuman, Teuku; Nasruddin, MN; Tulus; Ramli, Marwan

2018-01-01

Generally, research on the tsunami wave propagation model can be conducted by using a linear model of shallow water theory, where a non-linear side on high order is ignored. In line with research on the investigation of the tsunami waves, the Boussinesq equation model underwent a change aimed to obtain an improved quality of the dispersion relation and non-linearity by increasing the order to be higher. To solve non-linear sides at high order is used a asymptotic expansion method. This method can be used to solve non linear partial differential equations. In the present work, we found that this method needs much computational time and memory with the increase of the number of elements.

Systematic Computation of Nonlinear Cellular and Molecular Dynamics with Low-Power CytoMimetic Circuits: A Simulation Study

PubMed Central

Papadimitriou, Konstantinos I.; Stan, Guy-Bart V.; Drakakis, Emmanuel M.

2013-01-01

This paper presents a novel method for the systematic implementation of low-power microelectronic circuits aimed at computing nonlinear cellular and molecular dynamics. The method proposed is based on the Nonlinear Bernoulli Cell Formalism (NBCF), an advanced mathematical framework stemming from the Bernoulli Cell Formalism (BCF) originally exploited for the modular synthesis and analysis of linear, time-invariant, high dynamic range, logarithmic filters. Our approach identifies and exploits the striking similarities existing between the NBCF and coupled nonlinear ordinary differential equations (ODEs) typically appearing in models of naturally encountered biochemical systems. The resulting continuous-time, continuous-value, low-power CytoMimetic electronic circuits succeed in simulating fast and with good accuracy cellular and molecular dynamics. The application of the method is illustrated by synthesising for the first time microelectronic CytoMimetic topologies which simulate successfully: 1) a nonlinear intracellular calcium oscillations model for several Hill coefficient values and 2) a gene-protein regulatory system model. The dynamic behaviours generated by the proposed CytoMimetic circuits are compared and found to be in very good agreement with their biological counterparts. The circuits exploit the exponential law codifying the low-power subthreshold operation regime and have been simulated with realistic parameters from a commercially available CMOS process. They occupy an area of a fraction of a square-millimetre, while consuming between 1 and 12 microwatts of power. Simulations of fabrication-related variability results are also presented. PMID:23393550

F-15B QuietSpike(TradeMark) Aeroservoelastic Flight Test Data Analysis

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.

2007-01-01

System identification or mathematical modelling is utilised in the aerospace community for the development of simulation models for robust control law design. These models are often described as linear, time-invariant processes and assumed to be uniform throughout the flight envelope. Nevertheless, it is well known that the underlying process is inherently nonlinear. The reason for utilising a linear approach has been due to the lack of a proper set of tools for the identification of nonlinear systems. Over the past several decades the controls and biomedical communities have made great advances in developing tools for the identification of nonlinear systems. These approaches are robust and readily applicable to aerospace systems. In this paper, we show the application of one such nonlinear system identification technique, structure detection, for the analysis of F-15B QuietSpike(TradeMark) aeroservoelastic flight test data. Structure detection is concerned with the selection of a subset of candidate terms that best describe the observed output. This is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modelling may be of critical importance for the development of robust, parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion which may save significant development time and costs. The objectives of this study are to demonstrate via analysis of F-15B QuietSpike(TradeMark) aeroservoelastic flight test data for several flight conditions (Mach number) that (i) linear models are inefficient for modelling aeroservoelastic data, (ii) nonlinear identification provides a parsimonious model description whilst providing a high percent fit for cross-validated data and (iii) the model structure and parameters vary as the flight condition is altered.

NDRAM: nonlinear dynamic recurrent associative memory for learning bipolar and nonbipolar correlated patterns.

PubMed

Chartier, Sylvain; Proulx, Robert

2005-11-01

This paper presents a new unsupervised attractor neural network, which, contrary to optimal linear associative memory models, is able to develop nonbipolar attractors as well as bipolar attractors. Moreover, the model is able to develop less spurious attractors and has a better recall performance under random noise than any other Hopfield type neural network. Those performances are obtained by a simple Hebbian/anti-Hebbian online learning rule that directly incorporates feedback from a specific nonlinear transmission rule. Several computer simulations show the model's distinguishing properties.

An Optimization Code for Nonlinear Transient Problems of a Large Scale Multidisciplinary Mathematical Model

NASA Astrophysics Data System (ADS)

Takasaki, Koichi

This paper presents a program for the multidisciplinary optimization and identification problem of the nonlinear model of large aerospace vehicle structures. The program constructs the global matrix of the dynamic system in the time direction by the p-version finite element method (pFEM), and the basic matrix for each pFEM node in the time direction is described by a sparse matrix similarly to the static finite element problem. The algorithm used by the program does not require the Hessian matrix of the objective function and so has low memory requirements. It also has a relatively low computational cost, and is suited to parallel computation. The program was integrated as a solver module of the multidisciplinary analysis system CUMuLOUS (Computational Utility for Multidisciplinary Large scale Optimization of Undense System) which is under development by the Aerospace Research and Development Directorate (ARD) of the Japan Aerospace Exploration Agency (JAXA).

Simulation of Jet Noise with OVERFLOW CFD Code and Kirchhoff Surface Integral

NASA Technical Reports Server (NTRS)

Kandula, M.; Caimi, R.; Voska, N. (Technical Monitor)

2002-01-01

An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow field are modeled with the aid of Spalart-Allmaras one-equation turbulence model. Appropriate acoustic and outflow boundary conditions were implemented to compute time-dependent acoustic pressure in the nonlinear source-field. Based on the specification of acoustic pressure, its temporal and normal derivatives on the Kirchhoff surface, the near-field and the far-field sound pressure levels are computed via Kirchhoff surface integral, with the Kirchhoff surface chosen to enclose the nonlinear sound source region described by the CFD code. The methods are validated by a comparison of the predictions of sound pressure levels with the available data for an axisymmetric turbulent supersonic (Mach 2) perfectly expanded jet.

Simulation of Supersonic Jet Noise with the Adaptation of Overflow CFD Code and Kirchhoff Surface Integral

NASA Technical Reports Server (NTRS)

Kandula, Max; Caimi, Raoul; Steinrock, T. (Technical Monitor)

2001-01-01

An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow field are modeled with the aid of Spalart-Allmaras one-equation turbulence model. Appropriate acoustic and outflow boundary conditions were implemented to compute time-dependent acoustic pressure in the nonlinear source-field. Based on the specification of acoustic pressure, its temporal and normal derivatives on the Kirchhoff surface, the near-field and the far-field sound pressure levels are computed via Kirchhoff surface integral, with the Kirchhoff surface chosen to enclose the nonlinear sound source region described by the CFD code. The methods are validated by a comparison of the predictions of sound pressure levels with the available data for an axisymmetric turbulent supersonic (Mach 2) perfectly expanded jet.

Plasmonic modes in nanowire dimers: A study based on the hydrodynamic Drude model including nonlocal and nonlinear effects

NASA Astrophysics Data System (ADS)

Moeferdt, Matthias; Kiel, Thomas; Sproll, Tobias; Intravaia, Francesco; Busch, Kurt

2018-02-01

A combined analytical and numerical study of the modes in two distinct plasmonic nanowire systems is presented. The computations are based on a discontinuous Galerkin time-domain approach, and a fully nonlinear and nonlocal hydrodynamic Drude model for the metal is utilized. In the linear regime, these computations demonstrate the strong influence of nonlocality on the field distributions as well as on the scattering and absorption spectra. Based on these results, second-harmonic-generation efficiencies are computed over a frequency range that covers all relevant modes of the linear spectra. In order to interpret the physical mechanisms that lead to corresponding field distributions, the associated linear quasielectrostatic problem is solved analytically via conformal transformation techniques. This provides an intuitive classification of the linear excitations of the systems that is then applied to the full Maxwell case. Based on this classification, group theory facilitates the determination of the selection rules for the efficient excitation of modes in both the linear and nonlinear regimes. This leads to significantly enhanced second-harmonic generation via judiciously exploiting the system symmetries. These results regarding the mode structure and second-harmonic generation are of direct relevance to other nanoantenna systems.

Passive dendrites enable single neurons to compute linearly non-separable functions.

PubMed

Cazé, Romain Daniel; Humphries, Mark; Gutkin, Boris

2013-01-01

Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally, we show how linearly non-separable functions can be computed by a generic two-compartment biophysical model and a realistic neuron model of the cerebellar stellate cell interneuron. Taken together our results demonstrate that passive dendrites are sufficient to enable neurons to compute linearly non-separable functions.

Passive Dendrites Enable Single Neurons to Compute Linearly Non-separable Functions

PubMed Central

Cazé, Romain Daniel; Humphries, Mark; Gutkin, Boris

2013-01-01

Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally, we show how linearly non-separable functions can be computed by a generic two-compartment biophysical model and a realistic neuron model of the cerebellar stellate cell interneuron. Taken together our results demonstrate that passive dendrites are sufficient to enable neurons to compute linearly non-separable functions. PMID:23468600

Stabilization of business cycles of finance agents using nonlinear optimal control

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

2017-11-01

Stabilization of the business cycles of interconnected finance agents is performed with the use of a new nonlinear optimal control method. First, the dynamics of the interacting finance agents and of the associated business cycles is described by a modeled of coupled nonlinear oscillators. Next, this dynamic model undergoes approximate linearization round a temporary operating point which is defined by the present value of the system's state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure is based on Taylor series expansion of the dynamic model and on the computation of Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms in the Taylor series expansion is considered as a disturbance which is compensated by the robustness of the control loop. Next, for the linearized model of the interacting finance agents, an H-infinity feedback controller is designed. The computation of the feedback control gain requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control scheme satisfies an H-infinity tracking performance criterion, which signifies elevated robustness against modelling uncertainty and external perturbations. Moreover, under moderate conditions the global asymptotic stability features of the control loop are proven.

Damage Tolerance of Sandwich Plates With Debonded Face Sheets

NASA Technical Reports Server (NTRS)

Sankar, Bhavani V.

2001-01-01

A nonlinear finite element analysis was performed to simulate axial compression of sandwich beams with debonded face sheets. The load - end-shortening diagrams were generated for a variety of specimens used in a previous experimental study. The energy release rate at the crack tip was computed using the J-integral, and plotted as a function of the load. A detailed stress analysis was performed and the critical stresses in the face sheet and the core were computed. The core was also modeled as an isotropic elastic-perfectly plastic material and a nonlinear post buckling analysis was performed. A Graeco-Latin factorial plan was used to study the effects of debond length, face sheet and core thicknesses, and core density on the load carrying capacity of the sandwich composite. It has been found that a linear buckling analysis is inadequate in determining the maximum load a debonded sandwich beam can carry. A nonlinear post-buckling analysis combined with an elastoplastic model of the core is required to predict the compression behavior of debonded sandwich beams.

Comparison of three newton-like nonlinear least-squares methods for estimating parameters of ground-water flow models

USGS Publications Warehouse

Cooley, R.L.; Hill, M.C.

1992-01-01

Three methods of solving nonlinear least-squares problems were compared for robustness and efficiency using a series of hypothetical and field problems. A modified Gauss-Newton/full Newton hybrid method (MGN/FN) and an analogous method for which part of the Hessian matrix was replaced by a quasi-Newton approximation (MGN/QN) solved some of the problems with appreciably fewer iterations than required using only a modified Gauss-Newton (MGN) method. In these problems, model nonlinearity and a large variance for the observed data apparently caused MGN to converge more slowly than MGN/FN or MGN/QN after the sum of squared errors had almost stabilized. Other problems were solved as efficiently with MGN as with MGN/FN or MGN/QN. Because MGN/FN can require significantly more computer time per iteration and more computer storage for transient problems, it is less attractive for a general purpose algorithm than MGN/QN.

Infrasound propagation in tropospheric ducts and acoustic shadow zones.

PubMed

de Groot-Hedlin, Catherine D

2017-10-01

Numerical computations of the Navier-Stokes equations governing acoustic propagation are performed to investigate infrasound propagation in the troposphere and into acoustic shadow zones. An existing nonlinear finite-difference, time-domain (FDTD) solver that constrains input sound speed models to be axisymmetric is expanded to allow for advection and rigid, stair-step topography. The FDTD solver permits realistic computations along a given azimuth. It is applied to several environmental models to examine the effects of nonlinearity, topography, advection, and two-dimensional (2D) variations in wind and sound speeds on the penetration of infrasound into shadow zones. Synthesized waveforms are compared to a recording of a rocket motor fuel elimination event at the Utah Test and Training Range. Results show good agreement in the amplitude, duration, and spectra of synthesized and recorded waveforms for propagation through 2D atmospheric models whether or not topography, advection, or nonlinearity is explicitly included. However, infrasound propagation through a one-dimensional, range-averaged, atmospheric model yields waveforms with lower amplitudes and frequencies, suggesting that small-scale atmospheric variability causes significant scatter within the troposphere, leading to enhanced infrasound penetration into shadow zones. Thus, unresolved fine-scale atmospheric dynamics are not required to explain infrasound propagation into shadow zones.

Validation of a RANS transition model using a high-order weighted compact nonlinear scheme

NASA Astrophysics Data System (ADS)

Tu, GuoHua; Deng, XiaoGang; Mao, MeiLiang

2013-04-01

A modified transition model is given based on the shear stress transport (SST) turbulence model and an intermittency transport equation. The energy gradient term in the original model is replaced by flow strain rate to saving computational costs. The model employs local variables only, and then it can be conveniently implemented in modern computational fluid dynamics codes. The fifth-order weighted compact nonlinear scheme and the fourth-order staggered scheme are applied to discrete the governing equations for the purpose of minimizing discretization errors, so as to mitigate the confusion between numerical errors and transition model errors. The high-order package is compared with a second-order TVD method on simulating the transitional flow of a flat plate. Numerical results indicate that the high-order package give better grid convergence property than that of the second-order method. Validation of the transition model is performed for transitional flows ranging from low speed to hypersonic speed.

A 2D nonlinear multiring model for blood flow in large elastic arteries

NASA Astrophysics Data System (ADS)

Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves

2017-12-01

In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.

Computational system identification of continuous-time nonlinear systems using approximate Bayesian computation

NASA Astrophysics Data System (ADS)

Krishnanathan, Kirubhakaran; Anderson, Sean R.; Billings, Stephen A.; Kadirkamanathan, Visakan

2016-11-01

In this paper, we derive a system identification framework for continuous-time nonlinear systems, for the first time using a simulation-focused computational Bayesian approach. Simulation approaches to nonlinear system identification have been shown to outperform regression methods under certain conditions, such as non-persistently exciting inputs and fast-sampling. We use the approximate Bayesian computation (ABC) algorithm to perform simulation-based inference of model parameters. The framework has the following main advantages: (1) parameter distributions are intrinsically generated, giving the user a clear description of uncertainty, (2) the simulation approach avoids the difficult problem of estimating signal derivatives as is common with other continuous-time methods, and (3) as noted above, the simulation approach improves identification under conditions of non-persistently exciting inputs and fast-sampling. Term selection is performed by judging parameter significance using parameter distributions that are intrinsically generated as part of the ABC procedure. The results from a numerical example demonstrate that the method performs well in noisy scenarios, especially in comparison to competing techniques that rely on signal derivative estimation.

Wavelets, non-linearity and turbulence in fusion plasmas

NASA Astrophysics Data System (ADS)

van Milligen, B. Ph.

Introduction Linear spectral analysis tools Wavelet analysis Wavelet spectra and coherence Joint wavelet phase-frequency spectra Non-linear spectral analysis tools Wavelet bispectra and bicoherence Interpretation of the bicoherence Analysis of computer-generated data Coupled van der Pol oscillators A large eddy simulation model for two-fluid plasma turbulence A long wavelength plasma drift wave model Analysis of plasma edge turbulence from Langmuir probe data Radial coherence observed on the TJ-IU torsatron Bicoherence profile at the L/H transition on CCT Conclusions

Computational Methods for Structural Mechanics and Dynamics, part 1

NASA Technical Reports Server (NTRS)

Stroud, W. Jefferson (Editor); Housner, Jerrold M. (Editor); Tanner, John A. (Editor); Hayduk, Robert J. (Editor)

1989-01-01

The structural analysis methods research has several goals. One goal is to develop analysis methods that are general. This goal of generality leads naturally to finite-element methods, but the research will also include other structural analysis methods. Another goal is that the methods be amenable to error analysis; that is, given a physical problem and a mathematical model of that problem, an analyst would like to know the probable error in predicting a given response quantity. The ultimate objective is to specify the error tolerances and to use automated logic to adjust the mathematical model or solution strategy to obtain that accuracy. A third goal is to develop structural analysis methods that can exploit parallel processing computers. The structural analysis methods research will focus initially on three types of problems: local/global nonlinear stress analysis, nonlinear transient dynamics, and tire modeling.

Energy transport in weakly nonlinear wave systems with narrow frequency band excitation.

PubMed

Kartashova, Elena

2012-10-01

A novel discrete model (D model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of energy transport between modes, namely, intermittency and energy cascade, and gives the conditions under which each regime will take place. Conditions for the formation of a cascade, cascade direction, conditions for cascade termination, etc., are given and depend strongly on the choice of excitation parameters. The energy spectra of a cascade may be computed, yielding discrete and continuous energy spectra. The model does not require statistical assumptions, as all effects are derived from the interaction of distinct modes. In the example given-surface water waves with dispersion function ω(2)=gk and small nonlinearity-the D model predicts asymmetrical growth of side-bands for Benjamin-Feir instability, while the transition from discrete to continuous energy spectrum, excitation parameters properly chosen, yields the saturated Phillips' power spectrum ~g(2)ω(-5). The D model can be applied to the experimental and theoretical study of numerous wave systems appearing in hydrodynamics, nonlinear optics, electrodynamics, plasma, convection theory, etc.

Robust Nonlinear Neural Codes

NASA Astrophysics Data System (ADS)

Yang, Qianli; Pitkow, Xaq

2015-03-01

Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.

A new linear least squares method for T1 estimation from SPGR signals with multiple TRs

NASA Astrophysics Data System (ADS)

Chang, Lin-Ching; Koay, Cheng Guan; Basser, Peter J.; Pierpaoli, Carlo

2009-02-01

The longitudinal relaxation time, T1, can be estimated from two or more spoiled gradient recalled echo x (SPGR) images with two or more flip angles and one or more repetition times (TRs). The function relating signal intensity and the parameters are nonlinear; T1 maps can be computed from SPGR signals using nonlinear least squares regression. A widely-used linear method transforms the nonlinear model by assuming a fixed TR in SPGR images. This constraint is not desirable since multiple TRs are a clinically practical way to reduce the total acquisition time, to satisfy the required resolution, and/or to combine SPGR data acquired at different times. A new linear least squares method is proposed using the first order Taylor expansion. Monte Carlo simulations of SPGR experiments are used to evaluate the accuracy and precision of the estimated T1 from the proposed linear and the nonlinear methods. We show that the new linear least squares method provides T1 estimates comparable in both precision and accuracy to those from the nonlinear method, allowing multiple TRs and reducing computation time significantly.

An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

NASA Technical Reports Server (NTRS)

Murphy, Patrick Charles

1985-01-01

An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.

Non-linear homogenized and heterogeneous FE models for FRCM reinforced masonry walls in diagonal compression

NASA Astrophysics Data System (ADS)

Bertolesi, Elisa; Milani, Gabriele; Poggi, Carlo

2016-12-01

Two FE modeling techniques are presented and critically discussed for the non-linear analysis of tuff masonry panels reinforced with FRCM and subjected to standard diagonal compression tests. The specimens, tested at the University of Naples (Italy), are unreinforced and FRCM retrofitted walls. The extensive characterization of the constituent materials allowed adopting here very sophisticated numerical modeling techniques. In particular, here the results obtained by means of a micro-modeling strategy and homogenization approach are compared. The first modeling technique is a tridimensional heterogeneous micro-modeling where constituent materials (bricks, joints, reinforcing mortar and reinforcing grid) are modeled separately. The second approach is based on a two-step homogenization procedure, previously developed by the authors, where the elementary cell is discretized by means of three-noded plane stress elements and non-linear interfaces. The non-linear structural analyses are performed replacing the homogenized orthotropic continuum with a rigid element and non-linear spring assemblage (RBSM). All the simulations here presented are performed using the commercial software Abaqus. Pros and cons of the two approaches are herein discussed with reference to their reliability in reproducing global force-displacement curves and crack patterns, as well as to the rather different computational effort required by the two strategies.

Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models.

PubMed

Daunizeau, J; Friston, K J; Kiebel, S J

2009-11-01

In this paper, we describe a general variational Bayesian approach for approximate inference on nonlinear stochastic dynamic models. This scheme extends established approximate inference on hidden-states to cover: (i) nonlinear evolution and observation functions, (ii) unknown parameters and (precision) hyperparameters and (iii) model comparison and prediction under uncertainty. Model identification or inversion entails the estimation of the marginal likelihood or evidence of a model. This difficult integration problem can be finessed by optimising a free-energy bound on the evidence using results from variational calculus. This yields a deterministic update scheme that optimises an approximation to the posterior density on the unknown model variables. We derive such a variational Bayesian scheme in the context of nonlinear stochastic dynamic hierarchical models, for both model identification and time-series prediction. The computational complexity of the scheme is comparable to that of an extended Kalman filter, which is critical when inverting high dimensional models or long time-series. Using Monte-Carlo simulations, we assess the estimation efficiency of this variational Bayesian approach using three stochastic variants of chaotic dynamic systems. We also demonstrate the model comparison capabilities of the method, its self-consistency and its predictive power.

Nonlinear dispersion effects in elastic plates: numerical modelling and validation

NASA Astrophysics Data System (ADS)

Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.

2017-04-01

Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.

Non-linear aeroelastic prediction for aircraft applications

NASA Astrophysics Data System (ADS)

de C. Henshaw, M. J.; Badcock, K. J.; Vio, G. A.; Allen, C. B.; Chamberlain, J.; Kaynes, I.; Dimitriadis, G.; Cooper, J. E.; Woodgate, M. A.; Rampurawala, A. M.; Jones, D.; Fenwick, C.; Gaitonde, A. L.; Taylor, N. V.; Amor, D. S.; Eccles, T. A.; Denley, C. J.

2007-05-01

Current industrial practice for the prediction and analysis of flutter relies heavily on linear methods and this has led to overly conservative design and envelope restrictions for aircraft. Although the methods have served the industry well, it is clear that for a number of reasons the inclusion of non-linearity in the mathematical and computational aeroelastic prediction tools is highly desirable. The increase in available and affordable computational resources, together with major advances in algorithms, mean that non-linear aeroelastic tools are now viable within the aircraft design and qualification environment. The Partnership for Unsteady Methods in Aerodynamics (PUMA) Defence and Aerospace Research Partnership (DARP) was sponsored in 2002 to conduct research into non-linear aeroelastic prediction methods and an academic, industry, and government consortium collaborated to address the following objectives: To develop useable methodologies to model and predict non-linear aeroelastic behaviour of complete aircraft. To evaluate the methodologies on real aircraft problems. To investigate the effect of non-linearities on aeroelastic behaviour and to determine which have the greatest effect on the flutter qualification process. These aims have been very effectively met during the course of the programme and the research outputs include: New methods available to industry for use in the flutter prediction process, together with the appropriate coaching of industry engineers. Interesting results in both linear and non-linear aeroelastics, with comprehensive comparison of methods and approaches for challenging problems. Additional embryonic techniques that, with further research, will further improve aeroelastics capability. This paper describes the methods that have been developed and how they are deployable within the industrial environment. We present a thorough review of the PUMA aeroelastics programme together with a comprehensive review of the relevant research in this domain. This is set within the context of a generic industrial process and the requirements of UK and US aeroelastic qualification. A range of test cases, from simple small DOF cases to full aircraft, have been used to evaluate and validate the non-linear methods developed and to make comparison with the linear methods in everyday use. These have focused mainly on aerodynamic non-linearity, although some results for structural non-linearity are also presented. The challenges associated with time domain (coupled computational fluid dynamics-computational structural model (CFD-CSM)) methods have been addressed through the development of grid movement, fluid-structure coupling, and control surface movement technologies. Conclusions regarding the accuracy and computational cost of these are presented. The computational cost of time-domain methods, despite substantial improvements in efficiency, remains high. However, significant advances have been made in reduced order methods, that allow non-linear behaviour to be modelled, but at a cost comparable with that of the regular linear methods. Of particular note is a method based on Hopf bifurcation that has reached an appropriate maturity for deployment on real aircraft configurations, though only limited results are presented herein. Results are also presented for dynamically linearised CFD approaches that hold out the possibility of non-linear results at a fraction of the cost of time coupled CFD-CSM methods. Local linearisation approaches (higher order harmonic balance and continuation method) are also presented; these have the advantage that no prior assumption of the nature of the aeroelastic instability is required, but currently these methods are limited to low DOF problems and it is thought that these will not reach a level of maturity appropriate to real aircraft problems for some years to come. Nevertheless, guidance on the most likely approaches has been derived and this forms the basis for ongoing research. It is important to recognise that the aeroelastic design and qualification requires a variety of methods applicable at different stages of the process. The methods reported herein are mapped to the process, so that their applicability and complementarity may be understood. Overall, the programme has provided a suite of methods that allow realistic consideration of non-linearity in the aeroelastic design and qualification of aircraft. Deployment of these methods is underway in the industrial environment, but full realisation of the benefit of these approaches will require appropriate engagement with the standards community so that safety standards may take proper account of the inclusion of non-linearity.

A new physical model with multilayer architecture for facial expression animation using dynamic adaptive mesh.

PubMed

Zhang, Yu; Prakash, Edmond C; Sung, Eric

2004-01-01

This paper presents a new physically-based 3D facial model based on anatomical knowledge which provides high fidelity for facial expression animation while optimizing the computation. Our facial model has a multilayer biomechanical structure, incorporating a physically-based approximation to facial skin tissue, a set of anatomically-motivated facial muscle actuators, and underlying skull structure. In contrast to existing mass-spring-damper (MSD) facial models, our dynamic skin model uses the nonlinear springs to directly simulate the nonlinear visco-elastic behavior of soft tissue and a new kind of edge repulsion spring is developed to prevent collapse of the skin model. Different types of muscle models have been developed to simulate distribution of the muscle force applied on the skin due to muscle contraction. The presence of the skull advantageously constrain the skin movements, resulting in more accurate facial deformation and also guides the interactive placement of facial muscles. The governing dynamics are computed using a local semi-implicit ODE solver. In the dynamic simulation, an adaptive refinement automatically adapts the local resolution at which potential inaccuracies are detected depending on local deformation. The method, in effect, ensures the required speedup by concentrating computational time only where needed while ensuring realistic behavior within a predefined error threshold. This mechanism allows more pleasing animation results to be produced at a reduced computational cost.

Intelligence and Accidents: A Multilevel Model

DTIC Science & Technology

2006-05-06

individuals with low scores. Analysis Procedures The HLM 6 computer program (Raudenbush, Bryk, Cheong, & Congdon , 2004) was employed to conduct the...Cheong, Y. F., & Congdon , R. (2004). HLM 6: Hierarchical linear and nonlinear modeling. Chicago: Scientific Software International. Reynolds, D. H

Potential implementation of reservoir computing models based on magnetic skyrmions

NASA Astrophysics Data System (ADS)

Bourianoff, George; Pinna, Daniele; Sitte, Matthias; Everschor-Sitte, Karin

2018-05-01

Reservoir Computing is a type of recursive neural network commonly used for recognizing and predicting spatio-temporal events relying on a complex hierarchy of nested feedback loops to generate a memory functionality. The Reservoir Computing paradigm does not require any knowledge of the reservoir topology or node weights for training purposes and can therefore utilize naturally existing networks formed by a wide variety of physical processes. Most efforts to implement reservoir computing prior to this have focused on utilizing memristor techniques to implement recursive neural networks. This paper examines the potential of magnetic skyrmion fabrics and the complex current patterns which form in them as an attractive physical instantiation for Reservoir Computing. We argue that their nonlinear dynamical interplay resulting from anisotropic magnetoresistance and spin-torque effects allows for an effective and energy efficient nonlinear processing of spatial temporal events with the aim of event recognition and prediction.

Computer aided design of monolithic microwave and millimeter wave integrated circuits and subsystems

NASA Astrophysics Data System (ADS)

Ku, Walter H.; Gang, Guan-Wan; He, J. Q.; Ichitsubo, I.

1988-05-01

This final technical report presents results on the computer aided design of monolithic microwave and millimeter wave integrated circuits and subsystems. New results include analytical and computer aided device models of GaAs MESFETs and HEMTs or MODFETs, new synthesis techniques for monolithic feedback and distributed amplifiers and a new nonlinear CAD program for MIMIC called CADNON. This program incorporates the new MESFET and HEMT model and has been successfully applied to the design of monolithic millimeter-wave mixers.

Cost Considerations in Nonlinear Finite-Element Computing

NASA Technical Reports Server (NTRS)

Utku, S.; Melosh, R. J.; Islam, M.; Salama, M.

1985-01-01

Conference paper discusses computational requirements for finiteelement analysis using quasi-linear approach to nonlinear problems. Paper evaluates computational efficiency of different computer architecturtural types in terms of relative cost and computing time.

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.

Nonlinear Analysis of Two-phase Circumferential Motion in the Ablation Circumstance

NASA Astrophysics Data System (ADS)

Xiao-liang, Xu; Hai-ming, Huang; Zi-mao, Zhang

2010-05-01

In aerospace craft reentry and solid rocket propellant nozzle, thermal chemistry ablation is a complex process coupling with convection, heat transfer, mass transfer and chemical reaction. Based on discrete vortex method (DVM), thermal chemical ablation model and particle kinetic model, a computational module dealing with the two-phase circumferential motion in ablation circumstance is designed, the ablation velocity and circumferential field can be thus calculated. The calculated nonlinear time series are analyzed in chaotic identification method: relative chaotic characters such as correlation dimension and the maximum Lyapunov exponent are calculated, fractal dimension of vortex bulbs and particles distributions are also obtained, thus the nonlinear ablation process can be judged as a spatiotemporal chaotic process.

Optimizing Requirements Decisions with KEYS

NASA Technical Reports Server (NTRS)

Jalali, Omid; Menzies, Tim; Feather, Martin

2008-01-01

Recent work with NASA's Jet Propulsion Laboratory has allowed for external access to five of JPL's real-world requirements models, anonymized to conceal proprietary information, but retaining their computational nature. Experimentation with these models, reported herein, demonstrates a dramatic speedup in the computations performed on them. These models have a well defined goal: select mitigations that retire risks which, in turn, increases the number of attainable requirements. Such a non-linear optimization is a well-studied problem. However identification of not only (a) the optimal solution(s) but also (b) the key factors leading to them is less well studied. Our technique, called KEYS, shows a rapid way of simultaneously identifying the solutions and their key factors. KEYS improves on prior work by several orders of magnitude. Prior experiments with simulated annealing or treatment learning took tens of minutes to hours to terminate. KEYS runs much faster than that; e.g for one model, KEYS ran 13,000 times faster than treatment learning (40 minutes versus 0.18 seconds). Processing these JPL models is a non-linear optimization problem: the fewest mitigations must be selected while achieving the most requirements. Non-linear optimization is a well studied problem. With this paper, we challenge other members of the PROMISE community to improve on our results with other techniques.

Quantization of the nonlinear sigma model revisited

NASA Astrophysics Data System (ADS)

Nguyen, Timothy

2016-08-01

We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The symmetries we consider are twofold: (i) diffeomorphism covariance for a general target manifold; (ii) a transitive group of isometries when the target manifold is a homogeneous space. We show that there are no anomalies in case (i) and that (ii) is also anomaly-free under additional assumptions on the target homogeneous space, in agreement with the work of Friedan. We carry out some explicit computations for the O(N)-model. Finally, we show how a suitable notion of the renormalization group establishes the Ricci flow as the one loop renormalization group flow of the nonlinear sigma model.

The quadriceps muscle of knee joint modelling Using Hybrid Particle Swarm Optimization-Neural Network (PSO-NN)

NASA Astrophysics Data System (ADS)

Kamaruddin, Saadi Bin Ahmad; Marponga Tolos, Siti; Hee, Pah Chin; Ghani, Nor Azura Md; Ramli, Norazan Mohamed; Nasir, Noorhamizah Binti Mohamed; Ksm Kader, Babul Salam Bin; Saiful Huq, Mohammad

2017-03-01

Neural framework has for quite a while been known for its ability to handle a complex nonlinear system without a logical model and can learn refined nonlinear associations gives. Theoretically, the most surely understood computation to set up the framework is the backpropagation (BP) count which relies on upon the minimization of the mean square error (MSE). However, this algorithm is not totally efficient in the presence of outliers which usually exist in dynamic data. This paper exhibits the modelling of quadriceps muscle model by utilizing counterfeit smart procedures named consolidated backpropagation neural network nonlinear autoregressive (BPNN-NAR) and backpropagation neural network nonlinear autoregressive moving average (BPNN-NARMA) models in view of utilitarian electrical incitement (FES). We adapted particle swarm optimization (PSO) approach to enhance the performance of backpropagation algorithm. In this research, a progression of tests utilizing FES was led. The information that is gotten is utilized to build up the quadriceps muscle model. 934 preparing information, 200 testing and 200 approval information set are utilized as a part of the improvement of muscle model. It was found that both BPNN-NAR and BPNN-NARMA performed well in modelling this type of data. As a conclusion, the neural network time series models performed reasonably efficient for non-linear modelling such as active properties of the quadriceps muscle with one input, namely output namely muscle force.

Optimal remediation of unconfined aquifers: Numerical applications and derivative calculations

NASA Astrophysics Data System (ADS)

Mansfield, Christopher M.; Shoemaker, Christine A.

1999-05-01

This paper extends earlier work on derivative-based optimization for cost-effective remediation to unconfined aquifers, which have more complex, nonlinear flow dynamics than confined aquifers. Most previous derivative-based optimization of contaminant removal has been limited to consideration of confined aquifers; however, contamination is more common in unconfined aquifers. Exact derivative equations are presented, and two computationally efficient approximations, the quasi-confined (QC) and head independent from previous (HIP) unconfined-aquifer finite element equation derivative approximations, are presented and demonstrated to be highly accurate. The derivative approximations can be used with any nonlinear optimization method requiring derivatives for computation of either time-invariant or time-varying pumping rates. The QC and HIP approximations are combined with the nonlinear optimal control algorithm SALQR into the unconfined-aquifer algorithm, which is shown to compute solutions for unconfined aquifers in CPU times that were not significantly longer than those required by the confined-aquifer optimization model. Two of the three example unconfined-aquifer cases considered obtained pumping policies with substantially lower objective function values with the unconfined model than were obtained with the confined-aquifer optimization, even though the mean differences in hydraulic heads predicted by the unconfined- and confined-aquifer models were small (less than 0.1%). We suggest a possible geophysical index based on differences in drawdown predictions between unconfined- and confined-aquifer models to estimate which aquifers require unconfined-aquifer optimization and which can be adequately approximated by the simpler confined-aquifer analysis.

A model of the temporal dynamics of multisensory enhancement

PubMed Central

Rowland, Benjamin A.; Stein, Barry E.

2014-01-01

The senses transduce different forms of environmental energy, and the brain synthesizes information across them to enhance responses to salient biological events. We hypothesize that the potency of multisensory integration is attributable to the convergence of independent and temporally aligned signals derived from cross-modal stimulus configurations onto multisensory neurons. The temporal profile of multisensory integration in neurons of the deep superior colliculus (SC) is consistent with this hypothesis. The responses of these neurons to visual, auditory, and combinations of visual–auditory stimuli reveal that multisensory integration takes place in real-time; that is, the input signals are integrated as soon as they arrive at the target neuron. Interactions between cross-modal signals may appear to reflect linear or nonlinear computations on a moment-by-moment basis, the aggregate of which determines the net product of multisensory integration. Modeling observations presented here suggest that the early nonlinear components of the temporal profile of multisensory integration can be explained with a simple spiking neuron model, and do not require more sophisticated assumptions about the underlying biology. A transition from nonlinear “super-additive” computation to linear, additive computation can be accomplished via scaled inhibition. The findings provide a set of design constraints for artificial implementations seeking to exploit the basic principles and potency of biological multisensory integration in contexts of sensory substitution or augmentation. PMID:24374382

Finite element modeling and analysis of tires

NASA Technical Reports Server (NTRS)

Noor, A. K.; Andersen, C. M.

1983-01-01

Predicting the response of tires under various loading conditions using finite element technology is addressed. Some of the recent advances in finite element technology which have high potential for application to tire modeling problems are reviewed. The analysis and modeling needs for tires are identified. Reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment of combined loads, displacement-dependent and nonconservative loadings; development of simple and efficient mixed finite element models for shell analysis, identification of equivalent mixed and purely displacement models, and determination of the advantages of using mixed models; and effective computational models for large-rotation nonlinear problems, based on a total Lagrangian description of the deformation are included.

Distributed source model for the full-wave electromagnetic simulation of nonlinear terahertz generation.

PubMed

Fumeaux, Christophe; Lin, Hungyen; Serita, Kazunori; Withayachumnankul, Withawat; Kaufmann, Thomas; Tonouchi, Masayoshi; Abbott, Derek

2012-07-30

The process of terahertz generation through optical rectification in a nonlinear crystal is modeled using discretized equivalent current sources. The equivalent terahertz sources are distributed in the active volume and computed based on a separately modeled near-infrared pump beam. This approach can be used to define an appropriate excitation for full-wave electromagnetic numerical simulations of the generated terahertz radiation. This enables predictive modeling of the near-field interactions of the terahertz beam with micro-structured samples, e.g. in a near-field time-resolved microscopy system. The distributed source model is described in detail, and an implementation in a particular full-wave simulation tool is presented. The numerical results are then validated through a series of measurements on square apertures. The general principle can be applied to other nonlinear processes with possible implementation in any full-wave numerical electromagnetic solver.

A shock absorber model for structure-borne noise analyses

NASA Astrophysics Data System (ADS)

Benaziz, Marouane; Nacivet, Samuel; Thouverez, Fabrice

2015-08-01

Shock absorbers are often responsible for undesirable structure-borne noise in cars. The early numerical prediction of this noise in the automobile development process can save time and money and yet remains a challenge for industry. In this paper, a new approach to predicting shock absorber structure-borne noise is proposed; it consists in modelling the shock absorber and including the main nonlinear phenomena responsible for discontinuities in the response. The model set forth herein features: compressible fluid behaviour, nonlinear flow rate-pressure relations, valve mechanical equations and rubber mounts. The piston, base valve and complete shock absorber model are compared with experimental results. Sensitivity of the shock absorber response is evaluated and the most important parameters are classified. The response envelope is also computed. This shock absorber model is able to accurately reproduce local nonlinear phenomena and improves our state of knowledge on potential noise sources within the shock absorber.

Numerical Modeling of Nonlinear Thermodynamics in SMA Wires

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

Reynolds, D R; Kloucek, P

We present a mathematical model describing the thermodynamic behavior of shape memory alloy wires, as well as a computational technique to solve the resulting system of partial differential equations. The model consists of conservation equations based on a new Helmholtz free energy potential. The computational technique introduces a viscosity-based continuation method, which allows the model to handle dynamic applications where the temporally local behavior of solutions is desired. Computational experiments document that this combination of modeling and solution techniques appropriately predicts the thermally- and stress-induced martensitic phase transitions, as well as the hysteretic behavior and production of latent heat associatedmore » with such materials.« less

Modeling of Nonlinear Beat Signals of TAE's

NASA Astrophysics Data System (ADS)

Zhang, Bo; Berk, Herbert; Breizman, Boris; Zheng, Linjin

2012-03-01

Experiments on Alcator C-Mod reveal Toroidal Alfven Eigenmodes (TAE) together with signals at various beat frequencies, including those at twice the mode frequency. The beat frequencies are sidebands driven by quadratic nonlinear terms in the MHD equations. These nonlinear sidebands have not yet been quantified by any existing codes. We extend the AEGIS code to capture nonlinear effects by treating the nonlinear terms as a driving source in the linear MHD solver. Our goal is to compute the spatial structure of the sidebands for realistic geometry and q-profile, which can be directly compared with experiment in order to interpret the phase contrast imaging diagnostic measurements and to enable the quantitative determination of the Alfven wave amplitude in the plasma core

An efficient variable projection formulation for separable nonlinear least squares problems.

PubMed

Gan, Min; Li, Han-Xiong

2014-05-01

We consider in this paper a class of nonlinear least squares problems in which the model can be represented as a linear combination of nonlinear functions. The variable projection algorithm projects the linear parameters out of the problem, leaving the nonlinear least squares problems involving only the nonlinear parameters. To implement the variable projection algorithm more efficiently, we propose a new variable projection functional based on matrix decomposition. The advantage of the proposed formulation is that the size of the decomposed matrix may be much smaller than those of previous ones. The Levenberg-Marquardt algorithm using finite difference method is then applied to minimize the new criterion. Numerical results show that the proposed approach achieves significant reduction in computing time.

Probabilistic model of nonlinear penalties due to collision-induced timing jitter for calculation of the bit error ratio in wavelength-division-multiplexed return-to-zero systems

NASA Astrophysics Data System (ADS)

Sinkin, Oleg V.; Grigoryan, Vladimir S.; Menyuk, Curtis R.

2006-12-01

We introduce a fully deterministic, computationally efficient method for characterizing the effect of nonlinearity in optical fiber transmission systems that utilize wavelength-division multiplexing and return-to-zero modulation. The method accurately accounts for bit-pattern-dependent nonlinear distortion due to collision-induced timing jitter and for amplifier noise. We apply this method to calculate the error probability as a function of channel spacing in a prototypical multichannel return-to-zero undersea system.

Compressive Spectral Method for the Simulation of the Nonlinear Gravity Waves

PubMed Central

Bayındır, Cihan

2016-01-01

In this paper an approach for decreasing the computational effort required for the spectral simulations of the fully nonlinear ocean waves is introduced. The proposed approach utilizes the compressive sampling algorithm and depends on the idea of using a smaller number of spectral components compared to the classical spectral method. After performing the time integration with a smaller number of spectral components and using the compressive sampling technique, it is shown that the ocean wave field can be reconstructed with a significantly better efficiency compared to the classical spectral method. For the sparse ocean wave model in the frequency domain the fully nonlinear ocean waves with Jonswap spectrum is considered. By implementation of a high-order spectral method it is shown that the proposed methodology can simulate the linear and the fully nonlinear ocean waves with negligible difference in the accuracy and with a great efficiency by reducing the computation time significantly especially for large time evolutions. PMID:26911357

Nonlinear refraction and reflection travel time tomography

USGS Publications Warehouse

Zhang, Jiahua; ten Brink, Uri S.; Toksoz, M.N.

1998-01-01

We develop a rapid nonlinear travel time tomography method that simultaneously inverts refraction and reflection travel times on a regular velocity grid. For travel time and ray path calculations, we apply a wave front method employing graph theory. The first-arrival refraction travel times are calculated on the basis of cell velocities, and the later refraction and reflection travel times are computed using both cell velocities and given interfaces. We solve a regularized nonlinear inverse problem. A Laplacian operator is applied to regularize the model parameters (cell slownesses and reflector geometry) so that the inverse problem is valid for a continuum. The travel times are also regularized such that we invert travel time curves rather than travel time points. A conjugate gradient method is applied to minimize the nonlinear objective function. After obtaining a solution, we perform nonlinear Monte Carlo inversions for uncertainty analysis and compute the posterior model covariance. In numerical experiments, we demonstrate that combining the first arrival refraction travel times with later reflection travel times can better reconstruct the velocity field as well as the reflector geometry. This combination is particularly important for modeling crustal structures where large velocity variations occur in the upper crust. We apply this approach to model the crustal structure of the California Borderland using ocean bottom seismometer and land data collected during the Los Angeles Region Seismic Experiment along two marine survey lines. Details of our image include a high-velocity zone under the Catalina Ridge, but a smooth gradient zone between. Catalina Ridge and San Clemente Ridge. The Moho depth is about 22 km with lateral variations. Copyright 1998 by the American Geophysical Union.

Efficient critical design load case identification for floating offshore wind turbines with a reduced nonlinear model

NASA Astrophysics Data System (ADS)

Matha, Denis; Sandner, Frank; Schlipf, David

2014-12-01

Design verification of wind turbines is performed by simulation of design load cases (DLC) defined in the IEC 61400-1 and -3 standards or equivalent guidelines. Due to the resulting large number of necessary load simulations, here a method is presented to reduce the computational effort for DLC simulations significantly by introducing a reduced nonlinear model and simplified hydro- and aerodynamics. The advantage of the formulation is that the nonlinear ODE system only contains basic mathematic operations and no iterations or internal loops which makes it very computationally efficient. Global turbine extreme and fatigue loads such as rotor thrust, tower base bending moment and mooring line tension, as well as platform motions are outputs of the model. They can be used to identify critical and less critical load situations to be then analysed with a higher fidelity tool and so speed up the design process. Results from these reduced model DLC simulations are presented and compared to higher fidelity models. Results in frequency and time domain as well as extreme and fatigue load predictions demonstrate that good agreement between the reduced and advanced model is achieved, allowing to efficiently exclude less critical DLC simulations, and to identify the most critical subset of cases for a given design. Additionally, the model is applicable for brute force optimization of floater control system parameters.

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.

Experimental Control of Thermocapillary Convection in a Liquid Bridge

NASA Technical Reports Server (NTRS)

Petrov, Valery; Schatz, Michael F.; Muehlner, Kurt A.; VanHook, Stephen J.; McCormick, W. D.; Swift, Jack B.; Swinney, Harry L.

1996-01-01

We demonstrate the stabilization of an isolated unstable periodic orbit in a liquid bridge convection experiment. A model independent, nonlinear control algorithm uses temperature measurements near the liquid interface to compute control perturbations which are applied by a thermoelectric element. The algorithm employs a time series reconstruction of a nonlinear control surface in a high dimensional phase space to alter the system dynamics.

Wing Leading Edge RCC Rapid Response Damage Prediction Tool (IMPACT2)

NASA Technical Reports Server (NTRS)

Clark, Robert; Cottter, Paul; Michalopoulos, Constantine

2013-01-01

This rapid response computer program predicts Orbiter Wing Leading Edge (WLE) damage caused by ice or foam impact during a Space Shuttle launch (Program "IMPACT2"). The program was developed after the Columbia accident in order to assess quickly WLE damage due to ice, foam, or metal impact (if any) during a Shuttle launch. IMPACT2 simulates an impact event in a few minutes for foam impactors, and in seconds for ice and metal impactors. The damage criterion is derived from results obtained from one sophisticated commercial program, which requires hours to carry out simulations of the same impact events. The program was designed to run much faster than the commercial program with prediction of projectile threshold velocities within 10 to 15% of commercial-program values. The mathematical model involves coupling of Orbiter wing normal modes of vibration to nonlinear or linear springmass models. IMPACT2 solves nonlinear or linear impact problems using classical normal modes of vibration of a target, and nonlinear/ linear time-domain equations for the projectile. Impact loads and stresses developed in the target are computed as functions of time. This model is novel because of its speed of execution. A typical model of foam, or other projectile characterized by material nonlinearities, impacting an RCC panel is executed in minutes instead of hours needed by the commercial programs. Target damage due to impact can be assessed quickly, provided that target vibration modes and allowable stress are known.

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.

Membrane hydrophone phase characteristics through nonlinear acoustics measurements.

PubMed

Bloomfield, Philip E; Gandhi, Gaurav; Lewin, Peter A

2011-11-01

This work considers the need for both the amplitude and phase to fully characterize polyvinylidene fluoride (PVDF) membrane hydrophones and presents a comprehensive discussion of the nonlinear acoustic measurements utilized to extract the phase information and the experimental results taken with two widely used PVDF membrane hydrophones up to 100 MHz. A semi-empirical computer model utilized the hyperbolic propagation operator to predict the nonlinear pressure field and provide the complex frequency response of the corresponding source transducer. The PVDF hydrophone phase characteristics, which were obtained directly from the difference between the computer-modeled nonlinear field simulation and the corresponding measured harmonic frequency phase values, agree to within 10% with the phase predictions obtained from receive-transfer-function simulations based on software modeling of the membrane's physical properties. Cable loading effects and membrane hydrophone resonances were distinguished and identified through a series of impedance measurements and receive transfer function simulations on the hydrophones including their hard-wired coaxial cables. The results obtained indicate that the PVDF membrane hydrophone's phase versus frequency plot exhibits oscillations about a monotonically decreasing line. The maxima and minima inflection point slopes occur at the membrane thickness resonances and antiresonances, respectively. A cable resonance was seen at 100 MHz for the hydrophone with a 1-m cable attached, but not seen for the hydrophone with a shorter 0.65-m cable.

Sparsity enabled cluster reduced-order models for control

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L.

2018-01-01

Characterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible.

Data Assimilation on a Quantum Annealing Computer: Feasibility and Scalability

NASA Astrophysics Data System (ADS)

Nearing, G. S.; Halem, M.; Chapman, D. R.; Pelissier, C. S.

2014-12-01

Data assimilation is one of the ubiquitous and computationally hard problems in the Earth Sciences. In particular, ensemble-based methods require a large number of model evaluations to estimate the prior probability density over system states, and variational methods require adjoint calculations and iteration to locate the maximum a posteriori solution in the presence of nonlinear models and observation operators. Quantum annealing computers (QAC) like the new D-Wave housed at the NASA Ames Research Center can be used for optimization and sampling, and therefore offers a new possibility for efficiently solving hard data assimilation problems. Coding on the QAC is not straightforward: a problem must be posed as a Quadratic Unconstrained Binary Optimization (QUBO) and mapped to a spherical Chimera graph. We have developed a method for compiling nonlinear 4D-Var problems on the D-Wave that consists of five steps: Emulating the nonlinear model and/or observation function using radial basis functions (RBF) or Chebyshev polynomials. Truncating a Taylor series around each RBF kernel. Reducing the Taylor polynomial to a quadratic using ancilla gadgets. Mapping the real-valued quadratic to a fixed-precision binary quadratic. Mapping the fully coupled binary quadratic to a partially coupled spherical Chimera graph using ancilla gadgets. At present the D-Wave contains 512 qbits (with 1024 and 2048 qbit machines due in the next two years); this machine size allows us to estimate only 3 state variables at each satellite overpass. However, QAC's solve optimization problems using a physical (quantum) system, and therefore do not require iterations or calculation of model adjoints. This has the potential to revolutionize our ability to efficiently perform variational data assimilation, as the size of these computers grows in the coming years.

Transient responses of phosphoric acid fuel cell power plant system. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Lu, Cheng-Yi

1983-01-01

An analytical and computerized study of the steady state and transient response of a phosphoric acid fuel cell (PAFC) system was completed. Parametric studies and sensitivity analyses of the PAFC system's operation were accomplished. Four non-linear dynamic models of the fuel cell stack, reformer, shift converters, and heat exchangers were developed based on nonhomogeneous non-linear partial differential equations, which include the material, component, energy balance, and electrochemical kinetic features. Due to a lack of experimental data for the dynamic response of the components only the steady state results were compared with data from other sources, indicating reasonably good agreement. A steady state simulation of the entire system was developed using, nonlinear ordinary differential equations. The finite difference method and trial-and-error procedures were used to obtain a solution. Using the model, a PAFC system, that was developed under NASA Grant, NCC3-17, was improved through the optimization of the heat exchanger network. Three types of cooling configurations for cell plates were evaluated to obtain the best current density and temperature distributions. The steady state solutions were used as the initial conditions in the dynamic model. The transient response of a simplified PAFC system, which included all of the major components, subjected to a load change was obtained. Due to the length of the computation time for the transient response calculations, analysis on a real-time computer was not possible. A simulation of the real-time calculations was developed on a batch type computer. The transient response characteristics are needed for the optimization of the design and control of the whole PAFC system. All of the models, procedures and simulations were programmed in Fortran and run on IBM 370 computers at Cleveland State University and the NASA Lewis Research Center.

The influence of surface roughness on the contact stiffness and the contact filter effect in nonlinear wheel-track interaction

NASA Astrophysics Data System (ADS)

Lundberg, Oskar E.; Nordborg, Anders; Lopez Arteaga, Ines

2016-03-01

A state-dependent contact model including nonlinear contact stiffness and nonlinear contact filtering is used to calculate contact forces and rail vibrations with a time-domain wheel-track interaction model. In the proposed method, the full three-dimensional contact geometry is reduced to a point contact in order to lower the computational cost and to reduce the amount of required input roughness-data. Green's functions including the linear dynamics of the wheel and the track are coupled with a point contact model, leading to a numerically efficient model for the wheel-track interaction. Nonlinear effects due to the shape and roughness of the wheel and the rail surfaces are included in the point contact model by pre-calculation of functions for the contact stiffness and contact filters. Numerical results are compared to field measurements of rail vibrations for passenger trains running at 200 kph on a ballast track. Moreover, the influence of vehicle pre-load and different degrees of roughness excitation on the resulting wheel-track interaction is studied by means of numerical predictions.

Variational methods in supersymmetric lattice field theory: The vacuum sector

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

Duncan, A.; Meyer-Ortmanns, H.; Roskies, R.

1987-12-15

The application of variational methods to the computation of the spectrum in supersymmetric lattice theories is considered, with special attention to O(N) supersymmetric sigma models. Substantial cancellations are found between bosonic and fermionic contributions even in approximate Ansa$uml: tze for the vacuum wave function. The nonlinear limit of the linear sigma model is studied in detail, and it is shown how to construct an appropriate non-Gaussian vacuum wave function for the nonlinear model. The vacuum energy is shown to be of order unity in lattice units in the latter case, after infinite cancellations.

Finite Dimensional Approximations for Continuum Multiscale Problems

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

Berlyand, Leonid

2017-01-24

The completed research project concerns the development of novel computational techniques for modeling nonlinear multiscale physical and biological phenomena. Specifically, it addresses the theoretical development and applications of the homogenization theory (coarse graining) approach to calculation of the effective properties of highly heterogenous biological and bio-inspired materials with many spatial scales and nonlinear behavior. This theory studies properties of strongly heterogeneous media in problems arising in materials science, geoscience, biology, etc. Modeling of such media raises fundamental mathematical questions, primarily in partial differential equations (PDEs) and calculus of variations, the subject of the PI’s research. The focus of completed researchmore » was on mathematical models of biological and bio-inspired materials with the common theme of multiscale analysis and coarse grain computational techniques. Biological and bio-inspired materials offer the unique ability to create environmentally clean functional materials used for energy conversion and storage. These materials are intrinsically complex, with hierarchical organization occurring on many nested length and time scales. The potential to rationally design and tailor the properties of these materials for broad energy applications has been hampered by the lack of computational techniques, which are able to bridge from the molecular to the macroscopic scale. The project addressed the challenge of computational treatments of such complex materials by the development of a synergistic approach that combines innovative multiscale modeling/analysis techniques with high performance computing.« less

CALCULATION OF NONLINEAR CONFIDENCE AND PREDICTION INTERVALS FOR GROUND-WATER FLOW MODELS.

USGS Publications Warehouse

Cooley, Richard L.; Vecchia, Aldo V.

1987-01-01

A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually-calibrated ground-water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that inclusion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.

Nonlinear computations shaping temporal processing of precortical vision.

PubMed

Butts, Daniel A; Cui, Yuwei; Casti, Alexander R R

2016-09-01

Computations performed by the visual pathway are constructed by neural circuits distributed over multiple stages of processing, and thus it is challenging to determine how different stages contribute on the basis of recordings from single areas. In the current article, we address this problem in the lateral geniculate nucleus (LGN), using experiments combined with nonlinear modeling capable of isolating various circuit contributions. We recorded cat LGN neurons presented with temporally modulated spots of various sizes, which drove temporally precise LGN responses. We utilized simultaneously recorded S-potentials, corresponding to the primary retinal ganglion cell (RGC) input to each LGN cell, to distinguish the computations underlying temporal precision in the retina from those in the LGN. Nonlinear models with excitatory and delayed suppressive terms were sufficient to explain temporal precision in the LGN, and we found that models of the S-potentials were nearly identical, although with a lower threshold. To determine whether additional influences shaped the response at the level of the LGN, we extended this model to use the S-potential input in combination with stimulus-driven terms to predict the LGN response. We found that the S-potential input "explained away" the major excitatory and delayed suppressive terms responsible for temporal patterning of LGN spike trains but revealed additional contributions, largely PULL suppression, to the LGN response. Using this novel combination of recordings and modeling, we were thus able to dissect multiple circuit contributions to LGN temporal responses across retina and LGN, and set the foundation for targeted study of each stage. Copyright © 2016 the American Physiological Society.

Center for Parallel Optimization.

DTIC Science & Technology

1996-03-19

A NEW OPTIMIZATION BASED APPROACH TO IMPROVING GENERALIZATION IN MACHINE LEARNING HAS BEEN PROPOSED AND COMPUTATIONALLY VALIDATED ON SIMPLE LINEAR MODELS AS WELL AS ON HIGHLY NONLINEAR SYSTEMS SUCH AS NEURAL NETWORKS.

Investigation of non-uniform airflow signal oscillation during high frequency chest compression

PubMed Central

Sohn, Kiwon; Warwick, Warren J; Lee, Yong W; Lee, Jongwon; Holte, James E

2005-01-01

Background High frequency chest compression (HFCC) is a useful and popular therapy for clearing bronchial airways of excessive or thicker mucus. Our observation of respiratory airflow of a subject during use of HFCC showed the airflow oscillation by HFCC was strongly influenced by the nonlinearity of the respiratory system. We used a computational model-based approach to analyse the respiratory airflow during use of HFCC. Methods The computational model, which is based on previous physiological studies and represented by an electrical circuit analogue, was used for simulation of in vivo protocol that shows the nonlinearity of the respiratory system. Besides, airflow was measured during use of HFCC. We compared the simulation results to either the measured data or the previous research, to understand and explain the observations. Results and discussion We could observe two important phenomena during respiration pertaining to the airflow signal oscillation generated by HFCC. The amplitudes of HFCC airflow signals varied depending on spontaneous airflow signals. We used the simulation results to investigate how the nonlinearity of airway resistance, lung capacitance, and inertance of air characterized the respiratory airflow. The simulation results indicated that lung capacitance or the inertance of air is also not a factor in the non-uniformity of HFCC airflow signals. Although not perfect, our circuit analogue model allows us to effectively simulate the nonlinear characteristics of the respiratory system. Conclusion We found that the amplitudes of HFCC airflow signals behave as a function of spontaneous airflow signals. This is due to the nonlinearity of the respiratory system, particularly variations in airway resistance. PMID:15904523

Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code

NASA Astrophysics Data System (ADS)

Buyadzhi, V. V.; Glushkov, A. V.; Khetselius, O. Yu; Kuznetsova, A. A.; Buyadzhi, A. A.; Prepelitsa, G. P.; Ternovsky, V. B.

2017-10-01

A general, uniform chaos-geometric computational approach to analysis, modelling and prediction of the non-linear dynamics of quantum and laser systems (laser and quantum generators system etc) with elements of the deterministic chaos is briefly presented. The approach is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov’s exponents analysis, and surrogate data method, prediction models etc There are firstly presented the numerical data on the topological and dynamical invariants (in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunov’s exponents, Kolmogorov’s entropy and other parameters) for laser system (the semiconductor GaAs/GaAlAs laser with a retarded feedback) dynamics in a chaotic and hyperchaotic regimes.

A computational model of the human hand 93-ERI-053

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

Hollerbach, K.; Axelrod, T.

1996-03-01

The objectives of the Computational Hand Modeling project were to prove the feasibility of the Laboratory`s NIKE3D finite element code to orthopaedic problems. Because of the great complexity of anatomical structures and the nonlinearity of their behavior, we have focused on a subset of joints of the hand and lower extremity and have developed algorithms to model their behavior. The algorithms developed here solve fundamental problems in computational biomechanics and can be expanded to describe any other joints of the human body. This kind of computational modeling has never successfully been attempted before, due in part to a lack ofmore » biomaterials data and a lack of computational resources. With the computational resources available at the National Laboratories and the collaborative relationships we have established with experimental and other modeling laboratories, we have been in a position to pursue our innovative approach to biomechanical and orthopedic modeling.« less

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.

Multi-disease analysis of maternal antibody decay using non-linear mixed models accounting for censoring.

PubMed

Goeyvaerts, Nele; Leuridan, Elke; Faes, Christel; Van Damme, Pierre; Hens, Niel

2015-09-10

Biomedical studies often generate repeated measures of multiple outcomes on a set of subjects. It may be of interest to develop a biologically intuitive model for the joint evolution of these outcomes while assessing inter-subject heterogeneity. Even though it is common for biological processes to entail non-linear relationships, examples of multivariate non-linear mixed models (MNMMs) are still fairly rare. We contribute to this area by jointly analyzing the maternal antibody decay for measles, mumps, rubella, and varicella, allowing for a different non-linear decay model for each infectious disease. We present a general modeling framework to analyze multivariate non-linear longitudinal profiles subject to censoring, by combining multivariate random effects, non-linear growth and Tobit regression. We explore the hypothesis of a common infant-specific mechanism underlying maternal immunity using a pairwise correlated random-effects approach and evaluating different correlation matrix structures. The implied marginal correlation between maternal antibody levels is estimated using simulations. The mean duration of passive immunity was less than 4 months for all diseases with substantial heterogeneity between infants. The maternal antibody levels against rubella and varicella were found to be positively correlated, while little to no correlation could be inferred for the other disease pairs. For some pairs, computational issues occurred with increasing correlation matrix complexity, which underlines the importance of further developing estimation methods for MNMMs. Copyright © 2015 John Wiley & Sons, Ltd.

Control of nonlinear flexible space structures

NASA Astrophysics Data System (ADS)

Shi, Jianjun

With the advances made in computer technology and efficiency of numerical algorithms over last decade, the MPC strategies have become quite popular among control community. However, application of MPC or GPC to flexible space structure control has not been explored adequately in the literature. The work presented in this thesis primarily focuses on application of GPC to control of nonlinear flexible space structures. This thesis is particularly devoted to the development of various approximate dynamic models, design and assessment of candidate controllers, and extensive numerical simulations for a realistic multibody flexible spacecraft, namely, Jupiter Icy Moons Orbiter (JIMO)---a Prometheus class of spacecraft proposed by NASA for deep space exploratory missions. A stable GPC algorithm is developed for Multi-Input-Multi-Output (MIMO) systems. An end-point weighting (penalty) is used in the GPC cost function to guarantee the nominal stability of the closed-loop system. A method is given to compute the desired end-point state from the desired output trajectory. The methodologies based on Fake Algebraic Riccati Equation (FARE) and constrained nonlinear optimization, are developed for synthesis of state weighting matrix. This makes this formulation more practical. A stable reconfigurable GPC architecture is presented and its effectiveness is demonstrated on both aircraft as well as spacecraft model. A representative in-orbit maneuver is used for assessing the performance of various control strategies using various design models. Different approximate dynamic models used for analysis include linear single body flexible structure, nonlinear single body flexible structure, and nonlinear multibody flexible structure. The control laws evaluated include traditional GPC, feedback linearization-based GPC (FLGPC), reconfigurable GPC, and nonlinear dissipative control. These various control schemes are evaluated for robust stability and robust performance in the presence of parametric uncertainties and input disturbances. Finally, the conclusions are made with regard to the efficacy of these controllers and potential directions for future research.

An efficient model for coupling structural vibrations with acoustic radiation

NASA Technical Reports Server (NTRS)

Frendi, Abdelkader; Maestrello, Lucio; Ting, LU

1993-01-01

The scattering of an incident wave by a flexible panel is studied. The panel vibration is governed by the nonlinear plate equations while the loading on the panel, which is the pressure difference across the panel, depends on the reflected and transmitted waves. Two models are used to calculate this structural-acoustic interaction problem. One solves the three dimensional nonlinear Euler equations for the flow-field coupled with the plate equations (the fully coupled model). The second uses the linear wave equation for the acoustic field and expresses the load as a double integral involving the panel oscillation (the decoupled model). The panel oscillation governed by a system of integro-differential equations is solved numerically and the acoustic field is then defined by an explicit formula. Numerical results are obtained using the two models for linear and nonlinear panel vibrations. The predictions given by these two models are in good agreement but the computational time needed for the 'fully coupled model' is 60 times longer than that for 'the decoupled model'.

Computational Medicine: Translating Models to Clinical Care

PubMed Central

Winslow, Raimond L.; Trayanova, Natalia; Geman, Donald; Miller, Michael I.

2013-01-01

Because of the inherent complexity of coupled nonlinear biological systems, the development of computational models is necessary for achieving a quantitative understanding of their structure and function in health and disease. Statistical learning is applied to high-dimensional biomolecular data to create models that describe relationships between molecules and networks. Multiscale modeling links networks to cells, organs, and organ systems. Computational approaches are used to characterize anatomic shape and its variations in health and disease. In each case, the purposes of modeling are to capture all that we know about disease and to develop improved therapies tailored to the needs of individuals. We discuss advances in computational medicine, with specific examples in the fields of cancer, diabetes, cardiology, and neurology. Advances in translating these computational methods to the clinic are described, as well as challenges in applying models for improving patient health. PMID:23115356

An Investigation of High-Order Shock-Capturing Methods for Computational Aeroacoustics

NASA Technical Reports Server (NTRS)

Casper, Jay; Baysal, Oktay

1997-01-01

Topics covered include: Low-dispersion scheme for nonlinear acoustic waves in nonuniform flow; Computation of acoustic scattering by a low-dispersion scheme; Algorithmic extension of low-dispersion scheme and modeling effects for acoustic wave simulation; The accuracy of shock capturing in two spatial dimensions; Using high-order methods on lower-order geometries; and Computational considerations for the simulation of discontinuous flows.

A Novel Shape Parameterization Approach

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

1999-01-01

This paper presents a novel parameterization approach for complex shapes suitable for a multidisciplinary design optimization application. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft objects animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in a similar manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity analysis tools (e.g., nonlinear computational fluid dynamics and detailed finite element modeling). This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, and camber. The results are presented for a multidisciplinary design optimization application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, performance, and a simple propulsion module.

Atomic switch networks-nanoarchitectonic design of a complex system for natural computing.

PubMed

Demis, E C; Aguilera, R; Sillin, H O; Scharnhorst, K; Sandouk, E J; Aono, M; Stieg, A Z; Gimzewski, J K

2015-05-22

Self-organized complex systems are ubiquitous in nature, and the structural complexity of these natural systems can be used as a model to design new classes of functional nanotechnology based on highly interconnected networks of interacting units. Conventional fabrication methods for electronic computing devices are subject to known scaling limits, confining the diversity of possible architectures. This work explores methods of fabricating a self-organized complex device known as an atomic switch network and discusses its potential utility in computing. Through a merger of top-down and bottom-up techniques guided by mathematical and nanoarchitectonic design principles, we have produced functional devices comprising nanoscale elements whose intrinsic nonlinear dynamics and memorization capabilities produce robust patterns of distributed activity and a capacity for nonlinear transformation of input signals when configured in the appropriate network architecture. Their operational characteristics represent a unique potential for hardware implementation of natural computation, specifically in the area of reservoir computing-a burgeoning field that investigates the computational aptitude of complex biologically inspired systems.

Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

2000-01-01

This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in the same manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminate plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling) analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.

Multidisciplinary Aerodynamic-Structural Shape Optimization Using Deformation (MASSOUD)

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

2000-01-01

This paper presents a multidisciplinary shape parameterization approach. The approach consists of two basic concepts: (1) parameterizing the shape perturbations rather than the geometry itself and (2) performing the shape deformation by means of the soft object animation algorithms used in computer graphics. Because the formulation presented in this paper is independent of grid topology, we can treat computational fluid dynamics and finite element grids in a similar manner. The proposed approach is simple, compact, and efficient. Also, the analytical sensitivity derivatives are easily computed for use in a gradient-based optimization. This algorithm is suitable for low-fidelity (e.g., linear aerodynamics and equivalent laminated plate structures) and high-fidelity (e.g., nonlinear computational fluid dynamics and detailed finite element modeling analysis tools. This paper contains the implementation details of parameterizing for planform, twist, dihedral, thickness, camber, and free-form surface. Results are presented for a multidisciplinary design optimization application consisting of nonlinear computational fluid dynamics, detailed computational structural mechanics, and a simple performance module.

Ventilatory Patterning in a Mouse Model of Stroke

PubMed Central

Koo, Brian B; Strohl, Kingman P; Gillombardo, Carl B; Jacono, Frank J

2010-01-01

Cheyne-Stokes respiration (CSR) is a breathing pattern characterized by waxing and waning of breath volume and frequency, and is often recognized following stroke, when causal pathways are often obscure. We used an animal model to address the hypothesis that cerebral infarction is a mechanism for producing breathing instability. Fourteen male A/J mice underwent either stroke (n=7) or sham (n=7) procedure. Ventilation was measured using whole body plethysmography. Respiratory rate (RR), tidal volume (VT) and minute ventilation (Ve) mean values and coefficient of variation were computed for ventilation and oscillatory behavior. In addition, the ventilatory data were computationally fit to models to quantify autocorrelation, mutual information, sample entropy and a nonlinear complexity index. At the same time post procedure, stroke when compared to sham animal breathing consisted of a lower RR and autocorrelation, higher coefficient of variation for VT and higher coefficient of variation for Ve. Mutual information and the nonlinear complexity index were higher in breathing following stroke which also demonstrated a waxing/waning pattern. The absence of stroke in the sham animals was verified anatomically. We conclude that ventilatory pattern following cerebral infarction demonstrated increased variability with increased nonlinear patterning and a waxing/waning pattern, consistent with CSR. PMID:20472101

Deformed Palmprint Matching Based on Stable Regions.

PubMed

Wu, Xiangqian; Zhao, Qiushi

2015-12-01

Palmprint recognition (PR) is an effective technology for personal recognition. A main problem, which deteriorates the performance of PR, is the deformations of palmprint images. This problem becomes more severe on contactless occasions, in which images are acquired without any guiding mechanisms, and hence critically limits the applications of PR. To solve the deformation problems, in this paper, a model for non-linearly deformed palmprint matching is derived by approximating non-linear deformed palmprint images with piecewise-linear deformed stable regions. Based on this model, a novel approach for deformed palmprint matching, named key point-based block growing (KPBG), is proposed. In KPBG, an iterative M-estimator sample consensus algorithm based on scale invariant feature transform features is devised to compute piecewise-linear transformations to approximate the non-linear deformations of palmprints, and then, the stable regions complying with the linear transformations are decided using a block growing algorithm. Palmprint feature extraction and matching are performed over these stable regions to compute matching scores for decision. Experiments on several public palmprint databases show that the proposed models and the KPBG approach can effectively solve the deformation problem in palmprint verification and outperform the state-of-the-art methods.

A Computer Model of the Cardiovascular System for Effective Learning.

ERIC Educational Resources Information Center

Rothe, Carl F.

1980-01-01

Presents a model of the cardiovascular system which solves a set of interacting, possibly nonlinear, differential equations. Figures present a schematic diagram of the model and printouts that simulate normal conditions, exercise, hemorrhage, reduced contractility. The nine interacting equations used to describe the system are described in the…

The viscoelastic standard nonlinear solid model: predicting the response of the lumbar intervertebral disk to low-frequency vibrations.

PubMed

Groth, Kevin M; Granata, Kevin P

2008-06-01

Due to the mathematical complexity of current musculoskeletal spine models, there is a need for computationally efficient models of the intervertebral disk (IVD). The aim of this study is to develop a mathematical model that will adequately describe the motion of the IVD under axial cyclic loading as well as maintain computational efficiency for use in future musculoskeletal spine models. Several studies have successfully modeled the creep characteristics of the IVD using the three-parameter viscoelastic standard linear solid (SLS) model. However, when the SLS model is subjected to cyclic loading, it underestimates the load relaxation, the cyclic modulus, and the hysteresis of the human lumbar IVD. A viscoelastic standard nonlinear solid (SNS) model was used to predict the response of the human lumbar IVD subjected to low-frequency vibration. Nonlinear behavior of the SNS model was simulated by a strain-dependent elastic modulus on the SLS model. Parameters of the SNS model were estimated from experimental load deformation and stress-relaxation curves obtained from the literature. The SNS model was able to predict the cyclic modulus of the IVD at frequencies of 0.01 Hz, 0.1 Hz, and 1 Hz. Furthermore, the SNS model was able to quantitatively predict the load relaxation at a frequency of 0.01 Hz. However, model performance was unsatisfactory when predicting load relaxation and hysteresis at higher frequencies (0.1 Hz and 1 Hz). The SLS model of the lumbar IVD may require strain-dependent elastic and viscous behavior to represent the dynamic response to compressive strain.

An Efficient Numerical Approach for Nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin; Vedula, Prakash

2009-03-01

Fokker-Planck equations which are nonlinear with respect to their probability densities that occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, classical fermions and bosons can be challenging to solve numerically. To address some underlying challenges in obtaining numerical solutions, we propose a quadrature based moment method for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations. In this approach the distribution function is represented as a collection of Dirac delta functions with corresponding quadrature weights and locations, that are in turn determined from constraints based on evolution of generalized moments. Properties of the distribution function can be obtained by solution of transport equations for quadrature weights and locations. We will apply this computational approach to study a wide range of problems, including the Desai-Zwanzig Model (for nonlinear muscular contraction) and multivariate nonlinear Fokker-Planck equations describing classical fermions and bosons, and will also demonstrate good agreement with results obtained from Monte Carlo and other standard numerical methods.

Computational Nonlinear Morphology with Emphasis on Semitic Languages. Studies in Natural Language Processing.

ERIC Educational Resources Information Center

Kiraz, George Anton

This book presents a tractable computational model that can cope with complex morphological operations, especially in Semitic languages, and less complex morphological systems present in Western languages. It outlines a new generalized regular rewrite rule system that uses multiple finite-state automata to cater to root-and-pattern morphology,…

Difference-Equation/Flow-Graph Circuit Analysis

NASA Technical Reports Server (NTRS)

Mcvey, I. M.

1988-01-01

Numerical technique enables rapid, approximate analyses of electronic circuits containing linear and nonlinear elements. Practiced in variety of computer languages on large and small computers; for circuits simple enough, programmable hand calculators used. Although some combinations of circuit elements make numerical solutions diverge, enables quick identification of divergence and correction of circuit models to make solutions converge.

Analytic and computational modelling of super-radiant pulse compression in plasma and comparisons with experiment

NASA Astrophysics Data System (ADS)

Shvets, Gennady; Kalmykov, Serguei; Dreher, Matthias; Meyer-Ter-Vehn, Juergen

2003-10-01

The strongly non-linear regime of Raman backscattering [1,2] holds the promise of compressing long low-intensity laser beams into ultra-short high intensity pulses. As the short pulse is amplified by the long counter-propagating pump via backscattering the pump off the nonlinear plasma wave, its duration shrinks and intensity grows. The increase of the bandwidth of the amplified pulse only occurs in the nonlinear amplification regime, and is its most telling signature. Recent experiments at MPQ carried out in the strongly nonlinear regime reveal two previously unobserved features: (i) bandwidth expansion, and (ii) breakdown of the initially smooth amplified pulse into several spikes. Using semi-analytic model and particle-in-cell simulations, we explain the multiple pulse formation by the synchrotron motion of plasma electrons in the ponderomotive potential. Self-similar solutions consisting of multiple spikes are derived, and their nonlinear frequency shifts evaluated. The nonlinear focusing of the pulse by the pump is predicted and compared with experimental observations. [1] G. Shvets et. al., Phys. Rev. Lett. 81, 4879 (1998). [2] A. Pukhov, Rep. Progr. Phys. 66, 47 (1998).

Multivariate moment closure techniques for stochastic kinetic models

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

Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.

2015-09-07

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporallymore » evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.« less

A precise integration method for solving coupled vehicle-track dynamics with nonlinear wheel-rail contact

NASA Astrophysics Data System (ADS)

Zhang, J.; Gao, Q.; Tan, S. J.; Zhong, W. X.

2012-10-01

A new method is proposed as a solution for the large-scale coupled vehicle-track dynamic model with nonlinear wheel-rail contact. The vehicle is simplified as a multi-rigid-body model, and the track is treated as a three-layer beam model. In the track model, the rail is assumed to be an Euler-Bernoulli beam supported by discrete sleepers. The vehicle model and the track model are coupled using Hertzian nonlinear contact theory, and the contact forces of the vehicle subsystem and the track subsystem are approximated by the Lagrange interpolation polynomial. The response of the large-scale coupled vehicle-track model is calculated using the precise integration method. A more efficient algorithm based on the periodic property of the track is applied to calculate the exponential matrix and certain matrices related to the solution of the track subsystem. Numerical examples demonstrate the computational accuracy and efficiency of the proposed method.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee

2015-08-01

This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.

Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach

PubMed Central

Duarte, Belmiro P. M.; Wong, Weng Kee

2014-01-01

Summary This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted. PMID:26512159

Aerodynamic mathematical modeling - basic concepts

NASA Technical Reports Server (NTRS)

Tobak, M.; Schiff, L. B.

1981-01-01

The mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers is reviewed. Bryan's original formulation, linear aerodynamic indicial functions, and superposition are considered. These concepts are extended into the nonlinear regime. The nonlinear generalization yields a form for the aerodynamic response that can be built up from the responses to a limited number of well defined characteristic motions, reproducible in principle either in wind tunnel experiments or flow field computations. A further generalization leads to a form accommodating the discontinuous and double valued behavior characteristics of hysteresis in the steady state aerodynamic response.

Fluid moments of the nonlinear Landau collision operator

DOE PAGES

Hirvijoki, E.; Lingam, M.; Pfefferle, D.; ...

2016-08-09

An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. In conclusion, the proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to arbitrary collisionality and flow.

CAD of control systems: Application of nonlinear programming to a linear quadratic formulation

NASA Technical Reports Server (NTRS)

Fleming, P.

1983-01-01

The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.

Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations

NASA Astrophysics Data System (ADS)

Szalai, Robert; Ehrhardt, David; Haller, George

2017-06-01

In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here, a methodology to compute analytically both the shape of SSMs and their corresponding backbone curves from a data-assimilating model fitted to experimental vibration signals. This model identification utilizes Taken's delay-embedding theorem, as well as a least square fit to the Taylor expansion of the sampling map associated with that embedding. The SSMs are then constructed for the sampling map using the parametrization method for invariant manifolds, which assumes that the manifold is an embedding of, rather than a graph over, a spectral subspace. Using examples of both synthetic and real experimental data, we demonstrate that this approach reproduces backbone curves with high accuracy.

An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control.

PubMed

Neilson, Peter D; Neilson, Megan D

2005-09-01

Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.

A Computing Method for Sound Propagation Through a Nonuniform Jet Stream

NASA Technical Reports Server (NTRS)

Padula, S. L.; Liu, C. H.

1974-01-01

Understanding the principles of jet noise propagation is an essential ingredient of systematic noise reduction research. High speed computer methods offer a unique potential for dealing with complex real life physical systems whereas analytical solutions are restricted to sophisticated idealized models. The classical formulation of sound propagation through a jet flow was found to be inadequate for computer solutions and a more suitable approach was needed. Previous investigations selected the phase and amplitude of the acoustic pressure as dependent variables requiring the solution of a system of nonlinear algebraic equations. The nonlinearities complicated both the analysis and the computation. A reformulation of the convective wave equation in terms of a new set of dependent variables is developed with a special emphasis on its suitability for numerical solutions on fast computers. The technique is very attractive because the resulting equations are linear in nonwaving variables. The computer solution to such a linear system of algebraic equations may be obtained by well-defined and direct means which are conservative of computer time and storage space. Typical examples are illustrated and computational results are compared with available numerical and experimental data.

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

A Computational/Experimental Study of Two Optimized Supersonic Transport Designs and the Reference H Baseline

NASA Technical Reports Server (NTRS)

Cliff, Susan E.; Baker, Timothy J.; Hicks, Raymond M.; Reuther, James J.

1999-01-01

Two supersonic transport configurations designed by use of non-linear aerodynamic optimization methods are compared with a linearly designed baseline configuration. One optimized configuration, designated Ames 7-04, was designed at NASA Ames Research Center using an Euler flow solver, and the other, designated Boeing W27, was designed at Boeing using a full-potential method. The two optimized configurations and the baseline were tested in the NASA Langley Unitary Plan Supersonic Wind Tunnel to evaluate the non-linear design optimization methodologies. In addition, the experimental results are compared with computational predictions for each of the three configurations from the Enter flow solver, AIRPLANE. The computational and experimental results both indicate moderate to substantial performance gains for the optimized configurations over the baseline configuration. The computed performance changes with and without diverters and nacelles were in excellent agreement with experiment for all three models. Comparisons of the computational and experimental cruise drag increments for the optimized configurations relative to the baseline show excellent agreement for the model designed by the Euler method, but poorer comparisons were found for the configuration designed by the full-potential code.

Initial Computations of Vertical Displacement Events with NIMROD

NASA Astrophysics Data System (ADS)

Bunkers, Kyle; Sovinec, C. R.

2014-10-01

Disruptions associated with vertical displacement events (VDEs) have potential for causing considerable physical damage to ITER and other tokamak experiments. We report on initial computations of generic axisymmetric VDEs using the NIMROD code [Sovinec et al., JCP 195, 355 (2004)]. An implicit thin-wall computation has been implemented to couple separate internal and external regions without numerical stability limitations. A simple rectangular cross-section domain generated with the NIMEQ code [Howell and Sovinec, CPC (2014)] modified to use a symmetry condition at the midplane is used to test linear and nonlinear axisymmetric VDE computation. As current in simulated external coils for large- R / a cases is varied, there is a clear n = 0 stability threshold which lies below the decay-index criterion for the current-loop model of a tokamak to model VDEs [Mukhovatov and Shafranov, Nucl. Fusion 11, 605 (1971)]; a scan of wall distance indicates the offset is due to the influence of the conducting wall. Results with a vacuum region surrounding a resistive wall will also be presented. Initial nonlinear computations show large vertical displacement of an intact simulated tokamak. This effort is supported by U.S. Department of Energy Grant DE-FG02-06ER54850.

Time-optimal aircraft pursuit-evasion with a weapon envelope constraint

NASA Technical Reports Server (NTRS)

Menon, P. K. A.; Duke, E. L.

1990-01-01

The optimal pursuit-evasion problem between two aircraft, including nonlinear point-mass vehicle models and a realistic weapon envelope, is analyzed. Using a linear combination of flight time and the square of the vehicle acceleration as the performance index, a closed-form solution is obtained in nonlinear feedback form. Due to its modest computational requirements, this guidance law can be used for onboard real-time implementation.

Model of the non-linear stress-strain behavior of a 2D-SiC/SiC ceramic matrix composite (CMC)

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

Guillaumat, L; Lamon, J.

The non-linear stress-strain behaviour of a 2D-SiC/SiC composite reinforced with fabrics of fiber bundles was predicted from properties of major constituents. A finite element analysis was employed for stress computation. The different steps of matrix damage identified experimentally were duplicated in the mesh. Predictions compared satisfactorily with experimental data.

Nonlinear analysis of pupillary dynamics.

PubMed

Onorati, Francesco; Mainardi, Luca Tommaso; Sirca, Fabiola; Russo, Vincenzo; Barbieri, Riccardo

2016-02-01

Pupil size reflects autonomic response to different environmental and behavioral stimuli, and its dynamics have been linked to other autonomic correlates such as cardiac and respiratory rhythms. The aim of this study is to assess the nonlinear characteristics of pupil size of 25 normal subjects who participated in a psychophysiological experimental protocol with four experimental conditions, namely “baseline”, “anger”, “joy”, and “sadness”. Nonlinear measures, such as sample entropy, correlation dimension, and largest Lyapunov exponent, were computed on reconstructed signals of spontaneous fluctuations of pupil dilation. Nonparametric statistical tests were performed on surrogate data to verify that the nonlinear measures are an intrinsic characteristic of the signals. We then developed and applied a piecewise linear regression model to detrended fluctuation analysis (DFA). Two joinpoints and three scaling intervals were identified: slope α0, at slow time scales, represents a persistent nonstationary long-range correlation, whereas α1 and α2, at middle and fast time scales, respectively, represent long-range power-law correlations, similarly to DFA applied to heart rate variability signals. Of the computed complexity measures, α0 showed statistically significant differences among experimental conditions (p<0.001). Our results suggest that (a) pupil size at constant light condition is characterized by nonlinear dynamics, (b) three well-defined and distinct long-memory processes exist at different time scales, and (c) autonomic stimulation is partially reflected in nonlinear dynamics. (c) autonomic stimulation is partially reflected in nonlinear dynamics.

Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids

NASA Astrophysics Data System (ADS)

Aureli, M.; Basaran, M. E.; Porfiri, M.

2012-03-01

In this paper, we study flexural vibrations of a cantilever beam with thin rectangular cross section submerged in a quiescent viscous fluid and undergoing oscillations whose amplitude is comparable with its width. The structure is modeled using Euler-Bernoulli beam theory and the distributed hydrodynamic loading is described by a single complex-valued hydrodynamic function which accounts for added mass and fluid damping experienced by the structure. We perform a parametric 2D computational fluid dynamics analysis of an oscillating rigid lamina, representative of a generic beam cross section, to understand the dependence of the hydrodynamic function on the governing flow parameters. We find that increasing the frequency and amplitude of the vibration elicits vortex shedding and convection phenomena which are, in turn, responsible for nonlinear hydrodynamic damping. We establish a manageable nonlinear correction to the classical hydrodynamic function developed for small amplitude vibration and we derive a computationally efficient reduced order modal model for the beam nonlinear oscillations. Numerical and theoretical results are validated by comparison with ad hoc designed experiments on tapered beams and multimodal vibrations and with data available in the literature. Findings from this work are expected to find applications in the design of slender structures of interest in marine applications, such as biomimetic propulsion systems and energy harvesting devices.

Data-Driven Nonlinear Subspace Modeling for Prediction and Control of Molten Iron Quality Indices in Blast Furnace Ironmaking

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

Zhou, Ping; Song, Heda; Wang, Hong

Blast furnace (BF) in ironmaking is a nonlinear dynamic process with complicated physical-chemical reactions, where multi-phase and multi-field coupling and large time delay occur during its operation. In BF operation, the molten iron temperature (MIT) as well as Si, P and S contents of molten iron are the most essential molten iron quality (MIQ) indices, whose measurement, modeling and control have always been important issues in metallurgic engineering and automation field. This paper develops a novel data-driven nonlinear state space modeling for the prediction and control of multivariate MIQ indices by integrating hybrid modeling and control techniques. First, to improvemore » modeling efficiency, a data-driven hybrid method combining canonical correlation analysis and correlation analysis is proposed to identify the most influential controllable variables as the modeling inputs from multitudinous factors would affect the MIQ indices. Then, a Hammerstein model for the prediction of MIQ indices is established using the LS-SVM based nonlinear subspace identification method. Such a model is further simplified by using piecewise cubic Hermite interpolating polynomial method to fit the complex nonlinear kernel function. Compared to the original Hammerstein model, this simplified model can not only significantly reduce the computational complexity, but also has almost the same reliability and accuracy for a stable prediction of MIQ indices. Last, in order to verify the practicability of the developed model, it is applied in designing a genetic algorithm based nonlinear predictive controller for multivariate MIQ indices by directly taking the established model as a predictor. Industrial experiments show the advantages and effectiveness of the proposed approach.« less

Predicted Risk of Radiation-Induced Cancers After Involved Field and Involved Node Radiotherapy With or Without Intensity Modulation for Early-Stage Hodgkin Lymphoma in Female Patients

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

Weber, Damien C., E-mail: damien.weber@unige.ch; Johanson, Safora; Peguret, Nicolas

2011-10-01

Purpose: To assess the excess relative risk (ERR) of radiation-induced cancers (RIC) in female patients with Hodgkin lymphoma (HL) female patients treated with conformal (3DCRT), intensity modulated (IMRT), or volumetric modulated arc (RA) radiation therapy. Methods and Materials: Plans for 10 early-stage HL female patients were computed for 3DCRT, IMRT, and RA with involved field RT (IFRT) and involvednode RT (INRT) radiation fields. Organs at risk dose--volume histograms were computed and inter-compared for IFRT vs. INRT and 3DCRT vs. IMRT/RA, respectively. The ERR for cancer induction in breasts, lungs, and thyroid was estimated using both linear and nonlinear models. Results:more » The mean estimated ERR for breast, lung, and thyroid were significantly lower (p < 0.01) with INRT than with IFRT planning, regardless of the radiation delivery technique used, assuming a linear dose-risk relationship. We found that using the nonlinear model, the mean ERR values were significantly (p < 0.01) increased with IMRT or RA compared to those with 3DCRT planning for the breast, lung, and thyroid, using an IFRT paradigm. After INRT planning, IMRT or RA increased the risk of RIC for lung and thyroid only. Conclusions: In this comparative planning study, using a nonlinear dose--risk model, IMRT or RA increased the estimated risk of RIC for breast, lung, and thyroid for HL female patients. This study also suggests that INRT planning, compared to IFRT planning, may reduce the ERR of RIC when risk is predicted using a linear model. Observing the opposite effect, with a nonlinear model, however, questions the validity of these biologically parameterized models.« less

Nonlinear simulations with and computational issues for NIMROD

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

Sovinec, C R

The NIMROD (Non-Ideal Magnetohydrodynamics with Rotation, Open Discussion) code development project was commissioned by the US Department of Energy in February, 1996 to provide the fusion research community with a computational tool for studying low-frequency behavior in experiments. Specific problems of interest include the neoclassical evolution of magnetic islands and the nonlinear behavior of tearing modes in the presence of rotation and nonideal walls in tokamaks; they also include topics relevant to innovative confinement concepts such as magnetic turbulence. Besides having physics models appropriate for these phenomena, an additional requirement is the ability to perform the computations in realistic geometries.more » The NIMROD Team is using contemporary management and computational methods to develop a computational tool for investigating low-frequency behavior in plasma fusion experiments. The authors intend to make the code freely available, and are taking steps to make it as easy to learn and use as possible. An example application for NIMROD is the nonlinear toroidal RFP simulation--the first in a series to investigate how toroidal geometry affects MHD activity in RFPs. Finally, the most important issue facing the project is execution time, and they are exploring better matrix solvers and a better parallel decomposition to address this.« less

Modeling and comparative study of linear and nonlinear controllers for rotary inverted pendulum

NASA Astrophysics Data System (ADS)

Lima, Byron; Cajo, Ricardo; Huilcapi, Víctor; Agila, Wilton

2017-01-01

The rotary inverted pendulum (RIP) is a problem difficult to control, several studies have been conducted where different control techniques have been applied. Literature reports that, although problem is nonlinear, classical PID controllers presents appropriate performances when applied to the system. In this paper, a comparative study of the performances of linear and nonlinear PID structures is carried out. The control algorithms are evaluated in the RIP system, using indices of performance and power consumption, which allow the categorization of control strategies according to their performance. This article also presents the modeling system, which has been estimated some of the parameters involved in the RIP system, using computer-aided design tools (CAD) and experimental methods or techniques proposed by several authors attended. The results indicate a better performance of the nonlinear controller with an increase in the robustness and faster response than the linear controller.

A study of the parallel algorithm for large-scale DC simulation of nonlinear systems

NASA Astrophysics Data System (ADS)

Cortés Udave, Diego Ernesto; Ogrodzki, Jan; Gutiérrez de Anda, Miguel Angel

Newton-Raphson DC analysis of large-scale nonlinear circuits may be an extremely time consuming process even if sparse matrix techniques and bypassing of nonlinear models calculation are used. A slight decrease in the time required for this task may be enabled on multi-core, multithread computers if the calculation of the mathematical models for the nonlinear elements as well as the stamp management of the sparse matrix entries are managed through concurrent processes. This numerical complexity can be further reduced via the circuit decomposition and parallel solution of blocks taking as a departure point the BBD matrix structure. This block-parallel approach may give a considerable profit though it is strongly dependent on the system topology and, of course, on the processor type. This contribution presents the easy-parallelizable decomposition-based algorithm for DC simulation and provides a detailed study of its effectiveness.

Nonlinear finite amplitude torsional vibrations of cantilevers in viscous fluids

NASA Astrophysics Data System (ADS)

Aureli, Matteo; Pagano, Christopher; Porfiri, Maurizio

2012-06-01

In this paper, we study torsional vibrations of cantilever beams undergoing moderately large oscillations within a quiescent viscous fluid. The structure is modeled as an Euler-Bernoulli beam, with thin rectangular cross section, under base excitation. The distributed hydrodynamic loading experienced by the vibrating structure is described through a complex-valued hydrodynamic function which incorporates added mass and fluid damping elicited by moderately large rotations. We conduct a parametric study on the two dimensional computational fluid dynamics of a pitching rigid lamina, representative of a generic beam cross section, to investigate the dependence of the hydrodynamic function on the governing flow parameters. As the frequency and amplitude of the oscillation increase, vortex shedding and convection phenomena increase, thus resulting into nonlinear hydrodynamic damping. We derive a handleable nonlinear correction to the classical hydrodynamic function developed for small amplitude torsional vibrations for use in a reduced order nonlinear modal model and we validate theoretical results against experimental findings.

Nonlinear Analysis and Modeling of Tires

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.

1996-01-01

The objective of the study was to develop efficient modeling techniques and computational strategies for: (1) predicting the nonlinear response of tires subjected to inflation pressure, mechanical and thermal loads; (2) determining the footprint region, and analyzing the tire pavement contact problem, including the effect of friction; and (3) determining the sensitivity of the tire response (displacements, stresses, strain energy, contact pressures and contact area) to variations in the different material and geometric parameters. Two computational strategies were developed. In the first strategy the tire was modeled by using either a two-dimensional shear flexible mixed shell finite elements or a quasi-three-dimensional solid model. The contact conditions were incorporated into the formulation by using a perturbed Lagrangian approach. A number of model reduction techniques were applied to substantially reduce the number of degrees of freedom used in describing the response outside the contact region. The second strategy exploited the axial symmetry of the undeformed tire, and uses cylindrical coordinates in the development of three-dimensional elements for modeling each of the different parts of the tire cross section. Model reduction techniques are also used with this strategy.

Testing alternative ground water models using cross-validation and other methods

USGS Publications Warehouse

Foglia, L.; Mehl, S.W.; Hill, M.C.; Perona, P.; Burlando, P.

2007-01-01

Many methods can be used to test alternative ground water models. Of concern in this work are methods able to (1) rank alternative models (also called model discrimination) and (2) identify observations important to parameter estimates and predictions (equivalent to the purpose served by some types of sensitivity analysis). Some of the measures investigated are computationally efficient; others are computationally demanding. The latter are generally needed to account for model nonlinearity. The efficient model discrimination methods investigated include the information criteria: the corrected Akaike information criterion, Bayesian information criterion, and generalized cross-validation. The efficient sensitivity analysis measures used are dimensionless scaled sensitivity (DSS), composite scaled sensitivity, and parameter correlation coefficient (PCC); the other statistics are DFBETAS, Cook's D, and observation-prediction statistic. Acronyms are explained in the introduction. Cross-validation (CV) is a computationally intensive nonlinear method that is used for both model discrimination and sensitivity analysis. The methods are tested using up to five alternative parsimoniously constructed models of the ground water system of the Maggia Valley in southern Switzerland. The alternative models differ in their representation of hydraulic conductivity. A new method for graphically representing CV and sensitivity analysis results for complex models is presented and used to evaluate the utility of the efficient statistics. The results indicate that for model selection, the information criteria produce similar results at much smaller computational cost than CV. For identifying important observations, the only obviously inferior linear measure is DSS; the poor performance was expected because DSS does not include the effects of parameter correlation and PCC reveals large parameter correlations. ?? 2007 National Ground Water Association.

Computational aspects of the nonlinear normal mode initialization of the GLAS 4th order GCM

NASA Technical Reports Server (NTRS)

Navon, I. M.; Bloom, S. C.; Takacs, L.

1984-01-01

Using the normal modes of the GLAS 4th Order Model, a Machenhauer nonlinear normal mode initialization (NLNMI) was carried out for the external vertical mode using the GLAS 4th Order shallow water equations model for an equivalent depth corresponding to that associated with the external vertical mode. A simple procedure was devised which was directed at identifying computational modes by following the rate of increase of BAL sub M, the partial (with respect to the zonal wavenumber m) sum of squares of the time change of the normal mode coefficients (for fixed vertical mode index) varying over the latitude index L of symmetric or antisymmetric gravity waves. A working algorithm is presented which speeds up the convergence of the iterative Machenhauer NLNMI. A 24 h integration using the NLNMI state was carried out using both Matsuno and leap-frog time-integration schemes; these runs were then compared to a 24 h integration starting from a non-initialized state. The maximal impact of the nonlinear normal mode initialization was found to occur 6-10 hours after the initial time.

Nonlinear Modeling of Forced Magnetic Reconnection with Transient Perturbations

NASA Astrophysics Data System (ADS)

Beidler, Matthew T.; Callen, James D.; Hegna, Chris C.; Sovinec, Carl R.

2017-10-01

Externally applied 3D magnetic fields in tokamaks can penetrate into the plasma and lead to forced magnetic reconnection, and hence magnetic islands, on resonant surfaces. Analytic theory has been reasonably successful in describing many aspects of this paradigm with regard to describing the time asymptotic-steady state. However, understanding the nonlinear evolution into a low-slip, field-penetrated state, especially how MHD events such as sawteeth and ELMs precipitate this transition, is in its early development. We present nonlinear computations employing the extended-MHD code NIMROD, building on previous work by incorporating a temporally varying external perturbation as a simple model for an MHD event that produces resonant magnetic signals. A parametric series of proof-of-principle computations and accompanying analytical theory characterize the transition into a mode-locked state with an emphasis on detailing the temporal evolution properties. Supported by DOE OFES Grants DE-FG02-92ER54139, DE-FG02-86ER53218, and the U.S. DOE FES Postdoctoral Research program administered by ORISE and managed by ORAU under DOE contract DE-SC0014664.

Advances and trends in structures and dynamics; Proceedings of the Symposium, Washington, DC, October 22-25, 1984

NASA Technical Reports Server (NTRS)

Noor, A. K. (Editor); Hayduk, R. J. (Editor)

1985-01-01

Among the topics discussed are developments in structural engineering hardware and software, computation for fracture mechanics, trends in numerical analysis and parallel algorithms, mechanics of materials, advances in finite element methods, composite materials and structures, determinations of random motion and dynamic response, optimization theory, automotive tire modeling methods and contact problems, the damping and control of aircraft structures, and advanced structural applications. Specific topics covered include structural design expert systems, the evaluation of finite element system architectures, systolic arrays for finite element analyses, nonlinear finite element computations, hierarchical boundary elements, adaptive substructuring techniques in elastoplastic finite element analyses, automatic tracking of crack propagation, a theory of rate-dependent plasticity, the torsional stability of nonlinear eccentric structures, a computation method for fluid-structure interaction, the seismic analysis of three-dimensional soil-structure interaction, a stress analysis for a composite sandwich panel, toughness criterion identification for unidirectional composite laminates, the modeling of submerged cable dynamics, and damping synthesis for flexible spacecraft structures.

Nonlinear optics quantum computing with circuit QED.

PubMed

Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M

2013-02-08

One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.

DYGABCD: A program for calculating linear A, B, C, and D matrices from a nonlinear dynamic engine simulation

NASA Technical Reports Server (NTRS)

Geyser, L. C.

1978-01-01

A digital computer program, DYGABCD, was developed that generates linearized, dynamic models of simulated turbofan and turbojet engines. DYGABCD is based on an earlier computer program, DYNGEN, that is capable of calculating simulated nonlinear steady-state and transient performance of one- and two-spool turbojet engines or two- and three-spool turbofan engines. Most control design techniques require linear system descriptions. For multiple-input/multiple-output systems such as turbine engines, state space matrix descriptions of the system are often desirable. DYGABCD computes the state space matrices commonly referred to as the A, B, C, and D matrices required for a linear system description. The report discusses the analytical approach and provides a users manual, FORTRAN listings, and a sample case.

Nonlinear effective theory of dark energy

NASA Astrophysics Data System (ADS)

Cusin, Giulia; Lewandowski, Matthew; Vernizzi, Filippo

2018-04-01

We develop an approach to parametrize cosmological perturbations beyond linear order for general dark energy and modified gravity models characterized by a single scalar degree of freedom. We derive the full nonlinear action, focusing on Horndeski theories. In the quasi-static, non-relativistic limit, there are a total of six independent relevant operators, three of which start at nonlinear order. The new nonlinear couplings modify, beyond linear order, the generalized Poisson equation relating the Newtonian potential to the matter density contrast. We derive this equation up to cubic order in perturbations and, in a companion article [1], we apply it to compute the one-loop matter power spectrum. Within this approach, we also discuss the Vainshtein regime around spherical sources and the relation between the Vainshtein scale and the nonlinear scale for structure formation.

Comparison of linear and nonlinear implementation of the compartmental tissue uptake model for dynamic contrast-enhanced MRI.

PubMed

Kallehauge, Jesper F; Sourbron, Steven; Irving, Benjamin; Tanderup, Kari; Schnabel, Julia A; Chappell, Michael A

2017-06-01

Fitting tracer kinetic models using linear methods is much faster than using their nonlinear counterparts, although this comes often at the expense of reduced accuracy and precision. The aim of this study was to derive and compare the performance of the linear compartmental tissue uptake (CTU) model with its nonlinear version with respect to their percentage error and precision. The linear and nonlinear CTU models were initially compared using simulations with varying noise and temporal sampling. Subsequently, the clinical applicability of the linear model was demonstrated on 14 patients with locally advanced cervical cancer examined with dynamic contrast-enhanced magnetic resonance imaging. Simulations revealed equal percentage error and precision when noise was within clinical achievable ranges (contrast-to-noise ratio >10). The linear method was significantly faster than the nonlinear method, with a minimum speedup of around 230 across all tested sampling rates. Clinical analysis revealed that parameters estimated using the linear and nonlinear CTU model were highly correlated (ρ ≥ 0.95). The linear CTU model is computationally more efficient and more stable against temporal downsampling, whereas the nonlinear method is more robust to variations in noise. The two methods may be used interchangeably within clinical achievable ranges of temporal sampling and noise. Magn Reson Med 77:2414-2423, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.

Improving accuracy of electrochemical capacitance and solvation energetics in first-principles calculations

NASA Astrophysics Data System (ADS)

Sundararaman, Ravishankar; Letchworth-Weaver, Kendra; Schwarz, Kathleen A.

2018-04-01

Reliable first-principles calculations of electrochemical processes require accurate prediction of the interfacial capacitance, a challenge for current computationally efficient continuum solvation methodologies. We develop a model for the double layer of a metallic electrode that reproduces the features of the experimental capacitance of Ag(100) in a non-adsorbing, aqueous electrolyte, including a broad hump in the capacitance near the potential of zero charge and a dip in the capacitance under conditions of low ionic strength. Using this model, we identify the necessary characteristics of a solvation model suitable for first-principles electrochemistry of metal surfaces in non-adsorbing, aqueous electrolytes: dielectric and ionic nonlinearity, and a dielectric-only region at the interface. The dielectric nonlinearity, caused by the saturation of dipole rotational response in water, creates the capacitance hump, while ionic nonlinearity, caused by the compactness of the diffuse layer, generates the capacitance dip seen at low ionic strength. We show that none of the previously developed solvation models simultaneously meet all these criteria. We design the nonlinear electrochemical soft-sphere solvation model which both captures the capacitance features observed experimentally and serves as a general-purpose continuum solvation model.

Mapping nonlinear shallow-water tides: a look at the past and future

NASA Astrophysics Data System (ADS)

Andersen, Ole B.; Egbert, Gary D.; Erofeeva, Svetlana Y.; Ray, Richard D.

2006-12-01

Overtides and compound tides are generated by nonlinear mechanisms operative primarily in shallow waters. Their presence complicates tidal analysis owing to the multitude of new constituents and their possible frequency overlap with astronomical tides. The science of nonlinear tides was greatly advanced by the pioneering researches of Christian Le Provost who employed analytical theory, physical modeling, and numerical modeling in many extensive studies, especially of the tides of the English Channel. Le Provost’s complementary work with satellite altimetry motivates our attempts to merge these two interests. After a brief review, we describe initial steps toward the assimilation of altimetry into models of nonlinear tides via generalized inverse methods. A series of barotropic inverse solutions is computed for the M_4 tide over the northwest European Shelf. Future applications of altimetry to regions with fewer in situ measurements will require improved understanding of error covariance models because these control the tradeoffs between fitting hydrodynamics and data, a delicate issue in coastal regions. While M_4 can now be robustly determined along the Topex/Poseidon satellite ground tracks, many other compound tides face serious aliasing problems.

Modeling the Nonlinear, Strain Rate Dependent Deformation of Woven Ceramic Matrix Composites With Hydrostatic Stress Effects Included

NASA Technical Reports Server (NTRS)

Goldberg, Robert K.; Carney, Kelly S.

2004-01-01

An analysis method based on a deformation (as opposed to damage) approach has been developed to model the strain rate dependent, nonlinear deformation of woven ceramic matrix composites with a plain weave fiber architecture. In the developed model, the differences in the tension and compression response have also been considered. State variable based viscoplastic equations originally developed for metals have been modified to analyze the ceramic matrix composites. To account for the tension/compression asymmetry in the material, the effective stress and effective inelastic strain definitions have been modified. The equations have also been modified to account for the fact that in an orthotropic composite the in-plane shear stiffness is independent of the stiffness in the normal directions. The developed equations have been implemented into a commercially available transient dynamic finite element code, LS-DYNA, through the use of user defined subroutines (UMATs). The tensile, compressive, and shear deformation of a representative plain weave woven ceramic matrix composite are computed and compared to experimental results. The computed values correlate well to the experimental data, demonstrating the ability of the model to accurately compute the deformation response of woven ceramic matrix composites.

Circuit transients due to negative bias arcs-II. [on solar cell power systems in low earth orbit

NASA Technical Reports Server (NTRS)

Metz, R. N.

1986-01-01

Two new models of negative-bias arcing on a solar cell power system in Low Earth Orbit are presented. One is an extended, analytical model and the other is a non-linear, numerical model. The models are based on an earlier analytical model in which the interactions between solar cell interconnects and the space plasma as well as the parameters of the power circuit are approximated linearly. Transient voltages due to arcs struck at the negative thermal of the solar panel are calculated in the time domain. The new models treat, respectively, further linear effects within the solar panel load circuit and non-linear effects associated with the plasma interactions. Results of computer calculations with the models show common-mode voltage transients of the electrically floating solar panel struck by an arc comparable to the early model but load transients that differ substantially from the early model. In particular, load transients of the non-linear model can be more than twice as great as those of the early model and more than twenty times as great as the extended, linear model.

DYCAST: A finite element program for the crash analysis of structures

NASA Technical Reports Server (NTRS)

Pifko, A. B.; Winter, R.; Ogilvie, P.

1987-01-01

DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors.

Nonlinear 3D MHD verification study: SpeCyl and PIXIE3D codes for RFP and Tokamak plasmas

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Cappello, S.; Chacon, L.

2010-11-01

A strong emphasis is presently placed in the fusion community on reaching predictive capability of computational models. An essential requirement of such endeavor is the process of assessing the mathematical correctness of computational tools, termed verification [1]. We present here a successful nonlinear cross-benchmark verification study between the 3D nonlinear MHD codes SpeCyl [2] and PIXIE3D [3]. Excellent quantitative agreement is obtained in both 2D and 3D nonlinear visco-resistive dynamics for reversed-field pinch (RFP) and tokamak configurations [4]. RFP dynamics, in particular, lends itself as an ideal non trivial test-bed for 3D nonlinear verification. Perspectives for future application of the fully-implicit parallel code PIXIE3D to RFP physics, in particular to address open issues on RFP helical self-organization, will be provided. [4pt] [1] M. Greenwald, Phys. Plasmas 17, 058101 (2010) [0pt] [2] S. Cappello and D. Biskamp, Nucl. Fusion 36, 571 (1996) [0pt] [3] L. Chac'on, Phys. Plasmas 15, 056103 (2008) [0pt] [4] D. Bonfiglio, L. Chac'on and S. Cappello, Phys. Plasmas 17 (2010)

Are human spontaneous otoacoustic emissions generated by a chain of coupled nonlinear oscillators?

PubMed

Wit, Hero P; van Dijk, Pim

2012-08-01

Spontaneous otoacoustic emissions (SOAEs) are generated by self-sustained cochlear oscillators. Properties of a computational model for a linear array of active oscillators with nearest neighbor coupling are investigated. The model can produce many experimentally well-established properties of SOAEs.

All-optical reservoir computing.

PubMed

Duport, François; Schneider, Bendix; Smerieri, Anteo; Haelterman, Marc; Massar, Serge

2012-09-24

Reservoir Computing is a novel computing paradigm that uses a nonlinear recurrent dynamical system to carry out information processing. Recent electronic and optoelectronic Reservoir Computers based on an architecture with a single nonlinear node and a delay loop have shown performance on standardized tasks comparable to state-of-the-art digital implementations. Here we report an all-optical implementation of a Reservoir Computer, made of off-the-shelf components for optical telecommunications. It uses the saturation of a semiconductor optical amplifier as nonlinearity. The present work shows that, within the Reservoir Computing paradigm, all-optical computing with state-of-the-art performance is possible.

State-variable analysis of non-linear circuits with a desk computer

NASA Technical Reports Server (NTRS)

Cohen, E.

1981-01-01

State variable analysis was used to analyze the transient performance of non-linear circuits on a desk top computer. The non-linearities considered were not restricted to any circuit element. All that is required for analysis is the relationship defining each non-linearity be known in terms of points on a curve.

Dynamics of Numerics & Spurious Behaviors in CFD Computations. Revised

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Sweby, Peter K.

1997-01-01

The global nonlinear behavior of finite discretizations for constant time steps and fixed or adaptive grid spacings is studied using tools from dynamical systems theory. Detailed analysis of commonly used temporal and spatial discretizations for simple model problems is presented. The role of dynamics in the understanding of long time behavior of numerical integration and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in computational fluid dynamics (CFD) is explored. The study is complemented with examples of spurious behavior observed in steady and unsteady CFD computations. The CFD examples were chosen to illustrate non-apparent spurious behavior that was difficult to detect without extensive grid and temporal refinement studies and some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations where the physics of the problem under study is not well understood and numerical simulations are the only viable means of solution, extreme care must be taken in both computation and interpretation of the numerical data. The goal of this paper is to explore the important role that dynamical systems theory can play in the understanding of the global nonlinear behavior of numerical algorithms and to aid the identification of the sources of numerical uncertainties in CFD.

Identification of Linear and Nonlinear Sensory Processing Circuits from Spiking Neuron Data.

PubMed

Florescu, Dorian; Coca, Daniel

2018-03-01

Inferring mathematical models of sensory processing systems directly from input-output observations, while making the fewest assumptions about the model equations and the types of measurements available, is still a major issue in computational neuroscience. This letter introduces two new approaches for identifying sensory circuit models consisting of linear and nonlinear filters in series with spiking neuron models, based only on the sampled analog input to the filter and the recorded spike train output of the spiking neuron. For an ideal integrate-and-fire neuron model, the first algorithm can identify the spiking neuron parameters as well as the structure and parameters of an arbitrary nonlinear filter connected to it. The second algorithm can identify the parameters of the more general leaky integrate-and-fire spiking neuron model, as well as the parameters of an arbitrary linear filter connected to it. Numerical studies involving simulated and real experimental recordings are used to demonstrate the applicability and evaluate the performance of the proposed algorithms.

Statistical linearization for multi-input/multi-output nonlinearities

NASA Technical Reports Server (NTRS)

Lin, Ching-An; Cheng, Victor H. L.

1991-01-01

Formulas are derived for the computation of the random input-describing functions for MIMO nonlinearities; these straightforward and rigorous derivations are based on the optimal mean square linear approximation. The computations involve evaluations of multiple integrals. It is shown that, for certain classes of nonlinearities, multiple-integral evaluations are obviated and the computations are significantly simplified.

Analyzing the relationships between reflection source DPOAEs and SFOAEs using a computational model

NASA Astrophysics Data System (ADS)

Wen, Haiqi; Bowling, Thomas; Meaud, Julien

2018-05-01

Distortion product otoacoustic emissions (DPOAEs) are sounds generated by the cochlea in response to a stimulus that consists of two primary tones. DPOAEs consist of a mixture of emissions arising from two different mechanisms: nonlinear distortion and coherent reflection. Stimulus Frequency Otoacoustic Emissions (SFOAEs) are sounds generated by the cochlea in response to a pure tone; SFOAEs are commonly hypothesized to be generated due to coherent reflection. Nonlinearity of the outer hair cells (OHCs) provides nonlinear amplification to the traveling wave while reflections occur due to pre-existing micromechanical impedance perturbations. In this work, DPOAEs are obtained from a time domain computational model coupling a lumped parameter middle ear model with a multiphysics mechanical-electrical-acoustical model of cochlea. Cochlear roughness is intro-duced by perturbing the value of the OHC electromechanical coupling coefficient to account for the putative inhomogeneities inside the cochlea. The DPOAEs emitted in the ear canal are decomposed into distortion source and reflection source components. The reflection source component of DPOAEs is compared to SFOAEs obtained using a frequency-domain implementation of the model, to help us understand how distortion source and reflection source contributes to total DPOAEs. Moreover, the group delays of reflection sources OAEs are compared to group delays in the basilar membrane velocity to clarify the relationship between basilar membrane and OAE group delays.

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

NASA Technical Reports Server (NTRS)

Koppenhoefer, Kyle C.; Gullerud, Arne S.; Ruggieri, Claudio; Dodds, Robert H., Jr.; Healy, Brian E.

1998-01-01

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

Computer program for nonlinear static stress analysis of shuttle thermal protection system: User's manual

NASA Technical Reports Server (NTRS)

Giles, G. L.; Wallas, M.

1981-01-01

User documentation is presented for a computer program which considers the nonlinear properties of the strain isolator pad (SIP) in the static stress analysis of the shuttle thermal protection system. This program is generalized to handle an arbitrary SIP footprint including cutouts for instrumentation and filler bar. Multiple SIP surfaces are defined to model tiles in unique locations such as leading edges, intersections, and penetrations. The nonlinearity of the SIP is characterized by experimental stress displacement data for both normal and shear behavior. Stresses in the SIP are calculated using a Newton iteration procedure to determine the six rigid body displacements of the tile which develop reaction forces in the SIP to equilibrate the externally applied loads. This user documentation gives an overview of the analysis capabilities, a detailed description of required input data and an example to illustrate use of the program.

One-dimensional nonlinear theory for rectangular helix traveling-wave tube

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

Fu, Chengfang, E-mail: fchffchf@126.com; Zhao, Bo; Yang, Yudong

A 1-D nonlinear theory of a rectangular helix traveling-wave tube (TWT) interacting with a ribbon beam is presented in this paper. The RF field is modeled by a transmission line equivalent circuit, the ribbon beam is divided into a sequence of thin rectangular electron discs with the same cross section as the beam, and the charges are assumed to be uniformly distributed over these discs. Then a method of computing the space-charge field by solving Green's Function in the Cartesian Coordinate-system is fully described. Nonlinear partial differential equations for field amplitudes and Lorentz force equations for particles are solved numericallymore » using the fourth-order Runge-Kutta technique. The tube's gain, output power, and efficiency of the above TWT are computed. The results show that increasing the cross section of the ribbon beam will improve a rectangular helix TWT's efficiency and reduce the saturated length.« less

Stochastic Multiscale Analysis and Design of Engine Disks

DTIC Science & Technology

2010-07-28

shown recently to fail when used with data-driven non-linear stochastic input models (KPCA, IsoMap, etc.). Need for scalable exascale computing algorithms Materials Process Design and Control Laboratory Cornell University

Nonlinear vibration analysis of bladed disks with dry friction dampers

NASA Astrophysics Data System (ADS)

Ciğeroğlu, Ender; Özgüven, H. Nevzat

2006-08-01

In this work, a new model is proposed for the vibration analysis of turbine blades with dry friction dampers. The aim of the study is to develop a multiblade model that is accurate and yet easy to be analyzed so that it can be used efficiently in the design of friction dampers. The suggested nonlinear model for a bladed disk assembly includes all the blades with blade to blade and/or blade to cover plate dry friction dampers. An important feature of the model is that both macro-slip and micro-slip models are used in representing dry friction dampers. The model is simple to be analyzed as it is the case in macro-slip model, and yet it includes the features of more realistic micro-slip model. The nonlinear multidegree-of-freedom (mdof) model of bladed disk system is analyzed in frequency domain by applying a quasi-linearization technique, which transforms the nonlinear differential equations into a set of nonlinear algebraic equations. The solution method employed reduces the computational effort drastically compared to time solution methods for nonlinear systems, which makes it possible to obtain a more realistic model by the inclusion of all blades around the disk, disk itself and all friction dampers since in general system parameters are not identical throughout the geometry. The validation of the method is demonstrated by comparing the results obtained in this study with those given in literature and also with results obtained by time domain analysis. In the case studies presented the effect of friction damper parameters on vibration characteristics of tuned and mistuned bladed disk systems is studied by using a 20 blade system. It is shown that the method presented can be used to find the optimum friction damper values in a bladed disk assembly.

Electromechanical quantum simulators

NASA Astrophysics Data System (ADS)

Tacchino, F.; Chiesa, A.; LaHaye, M. D.; Carretta, S.; Gerace, D.

2018-06-01

Digital quantum simulators are among the most appealing applications of a quantum computer. Here we propose a universal, scalable, and integrated quantum computing platform based on tunable nonlinear electromechanical nano-oscillators. It is shown that very high operational fidelities for single- and two-qubits gates can be achieved in a minimal architecture, where qubits are encoded in the anharmonic vibrational modes of mechanical nanoresonators, whose effective coupling is mediated by virtual fluctuations of an intermediate superconducting artificial atom. An effective scheme to induce large single-phonon nonlinearities in nanoelectromechanical devices is explicitly discussed, thus opening the route to experimental investigation in this direction. Finally, we explicitly show the very high fidelities that can be reached for the digital quantum simulation of model Hamiltonians, by using realistic experimental parameters in state-of-the-art devices, and considering the transverse field Ising model as a paradigmatic example.

Monte Carlo Volcano Seismic Moment Tensors

NASA Astrophysics Data System (ADS)

Waite, G. P.; Brill, K. A.; Lanza, F.

2015-12-01

Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.

Models, Databases, and Simulation Tools Needed for the Realization of Integrated Computational Materials Engineering. Proceedings of the Symposium Held at Materials Science and Technology 2010

NASA Technical Reports Server (NTRS)

Arnold, Steven M. (Editor); Wong, Terry T. (Editor)

2011-01-01

Topics covered include: An Annotative Review of Multiscale Modeling and its Application to Scales Inherent in the Field of ICME; and A Multiscale, Nonlinear, Modeling Framework Enabling the Design and Analysis of Composite Materials and Structures.

VBA: A Probabilistic Treatment of Nonlinear Models for Neurobiological and Behavioural Data

PubMed Central

Daunizeau, Jean; Adam, Vincent; Rigoux, Lionel

2014-01-01

This work is in line with an on-going effort tending toward a computational (quantitative and refutable) understanding of human neuro-cognitive processes. Many sophisticated models for behavioural and neurobiological data have flourished during the past decade. Most of these models are partly unspecified (i.e. they have unknown parameters) and nonlinear. This makes them difficult to peer with a formal statistical data analysis framework. In turn, this compromises the reproducibility of model-based empirical studies. This work exposes a software toolbox that provides generic, efficient and robust probabilistic solutions to the three problems of model-based analysis of empirical data: (i) data simulation, (ii) parameter estimation/model selection, and (iii) experimental design optimization. PMID:24465198

LS-DYNA Implementation of Polymer Matrix Composite Model Under High Strain Rate Impact

NASA Technical Reports Server (NTRS)

Zheng, Xia-Hua; Goldberg, Robert K.; Binienda, Wieslaw K.; Roberts, Gary D.

2003-01-01

A recently developed constitutive model is implemented into LS-DYNA as a user defined material model (UMAT) to characterize the nonlinear strain rate dependent behavior of polymers. By utilizing this model within a micromechanics technique based on a laminate analogy, an algorithm to analyze the strain rate dependent, nonlinear deformation of a fiber reinforced polymer matrix composite is then developed as a UMAT to simulate the response of these composites under high strain rate impact. The models are designed for shell elements in order to ensure computational efficiency. Experimental and numerical stress-strain curves are compared for two representative polymers and a representative polymer matrix composite, with the analytical model predicting the experimental response reasonably well.

Nonlinear dynamic macromodeling techniques for audio systems

NASA Astrophysics Data System (ADS)

Ogrodzki, Jan; Bieńkowski, Piotr

2015-09-01

This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.

Multivariable control of the Space Shuttle Remote Manipulator System using linearization by state feedback. M.S. Thesis

NASA Technical Reports Server (NTRS)

Gettman, Chang-Ching LO

1993-01-01

This thesis develops and demonstrates an approach to nonlinear control system design using linearization by state feedback. The design provides improved transient response behavior allowing faster maneuvering of payloads by the SRMS. Modeling uncertainty is accounted for by using a second feedback loop designed around the feedback linearized dynamics. A classical feedback loop is developed to provide the easy implementation required for the relatively small on board computers. Feedback linearization also allows the use of higher bandwidth model based compensation in the outer loop, since it helps maintain stability in the presence of the nonlinearities typically neglected in model based designs.

Optimal fixed-finite-dimensional compensator for Burgers' equation with unbounded input/output operators

NASA Technical Reports Server (NTRS)

Burns, John A.; Marrekchi, Hamadi

1993-01-01

The problem of using reduced order dynamic compensators to control a class of nonlinear parabolic distributed parameter systems was considered. Concentration was on a system with unbounded input and output operators governed by Burgers' equation. A linearized model was used to compute low-order-finite-dimensional control laws by minimizing certain energy functionals. Then these laws were applied to the nonlinear model. Standard approaches to this problem employ model/controller reduction techniques in conjunction with linear quadratic Gaussian (LQG) theory. The approach used is based on the finite dimensional Bernstein/Hyland optimal projection theory which yields a fixed-finite-order controller.

Transit-time and age distributions for nonlinear time-dependent compartmental systems.

PubMed

Metzler, Holger; Müller, Markus; Sierra, Carlos A

2018-02-06

Many processes in nature are modeled using compartmental systems (reservoir/pool/box systems). Usually, they are expressed as a set of first-order differential equations describing the transfer of matter across a network of compartments. The concepts of age of matter in compartments and the time required for particles to transit the system are important diagnostics of these models with applications to a wide range of scientific questions. Until now, explicit formulas for transit-time and age distributions of nonlinear time-dependent compartmental systems were not available. We compute densities for these types of systems under the assumption of well-mixed compartments. Assuming that a solution of the nonlinear system is available at least numerically, we show how to construct a linear time-dependent system with the same solution trajectory. We demonstrate how to exploit this solution to compute transit-time and age distributions in dependence on given start values and initial age distributions. Furthermore, we derive equations for the time evolution of quantiles and moments of the age distributions. Our results generalize available density formulas for the linear time-independent case and mean-age formulas for the linear time-dependent case. As an example, we apply our formulas to a nonlinear and a linear version of a simple global carbon cycle model driven by a time-dependent input signal which represents fossil fuel additions. We derive time-dependent age distributions for all compartments and calculate the time it takes to remove fossil carbon in a business-as-usual scenario.

Atomic switch networks—nanoarchitectonic design of a complex system for natural computing

NASA Astrophysics Data System (ADS)

Demis, E. C.; Aguilera, R.; Sillin, H. O.; Scharnhorst, K.; Sandouk, E. J.; Aono, M.; Stieg, A. Z.; Gimzewski, J. K.

2015-05-01

Self-organized complex systems are ubiquitous in nature, and the structural complexity of these natural systems can be used as a model to design new classes of functional nanotechnology based on highly interconnected networks of interacting units. Conventional fabrication methods for electronic computing devices are subject to known scaling limits, confining the diversity of possible architectures. This work explores methods of fabricating a self-organized complex device known as an atomic switch network and discusses its potential utility in computing. Through a merger of top-down and bottom-up techniques guided by mathematical and nanoarchitectonic design principles, we have produced functional devices comprising nanoscale elements whose intrinsic nonlinear dynamics and memorization capabilities produce robust patterns of distributed activity and a capacity for nonlinear transformation of input signals when configured in the appropriate network architecture. Their operational characteristics represent a unique potential for hardware implementation of natural computation, specifically in the area of reservoir computing—a burgeoning field that investigates the computational aptitude of complex biologically inspired systems.

Modeling of stress/strain behavior of fiber-reinforced ceramic matrix composites including stress redistribution

NASA Technical Reports Server (NTRS)

Mital, Subodh K.; Murthy, Pappu L. N.; Chamis, Christos C.

1994-01-01

A computational simulation procedure is presented for nonlinear analyses which incorporates microstress redistribution due to progressive fracture in ceramic matrix composites. This procedure facilitates an accurate simulation of the stress-strain behavior of ceramic matrix composites up to failure. The nonlinearity in the material behavior is accounted for at the constituent (fiber/matrix/interphase) level. This computational procedure is a part of recent upgrades to CEMCAN (Ceramic Matrix Composite Analyzer) computer code. The fiber substructuring technique in CEMCAN is used to monitor the damage initiation and progression as the load increases. The room-temperature tensile stress-strain curves for SiC fiber reinforced reaction-bonded silicon nitride (RBSN) matrix unidirectional and angle-ply laminates are simulated and compared with experimentally observed stress-strain behavior. Comparison between the predicted stress/strain behavior and experimental stress/strain curves is good. Collectively the results demonstrate that CEMCAN computer code provides the user with an effective computational tool to simulate the behavior of ceramic matrix composites.

A flexible cure rate model for spatially correlated survival data based on generalized extreme value distribution and Gaussian process priors.

PubMed

Li, Dan; Wang, Xia; Dey, Dipak K

2016-09-01

Our present work proposes a new survival model in a Bayesian context to analyze right-censored survival data for populations with a surviving fraction, assuming that the log failure time follows a generalized extreme value distribution. Many applications require a more flexible modeling of covariate information than a simple linear or parametric form for all covariate effects. It is also necessary to include the spatial variation in the model, since it is sometimes unexplained by the covariates considered in the analysis. Therefore, the nonlinear covariate effects and the spatial effects are incorporated into the systematic component of our model. Gaussian processes (GPs) provide a natural framework for modeling potentially nonlinear relationship and have recently become extremely powerful in nonlinear regression. Our proposed model adopts a semiparametric Bayesian approach by imposing a GP prior on the nonlinear structure of continuous covariate. With the consideration of data availability and computational complexity, the conditionally autoregressive distribution is placed on the region-specific frailties to handle spatial correlation. The flexibility and gains of our proposed model are illustrated through analyses of simulated data examples as well as a dataset involving a colon cancer clinical trial from the state of Iowa. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Numerical aspects in modeling high Deborah number flow and elastic instability

NASA Astrophysics Data System (ADS)

Kwon, Youngdon

2014-05-01

Investigating highly nonlinear viscoelastic flow in 2D domain, we explore problem as well as property possibly inherent in the streamline upwinding technique (SUPG) and then present various results of elastic instability. The mathematically stable Leonov model written in tensor-logarithmic formulation is employed in the framework of finite element method for spatial discretization of several representative problem domains. For enhancement of computation speed, decoupled integration scheme is applied for shear thinning and Boger-type fluids. From the analysis of 4:1 contraction flow at low and moderate values of the Deborah number (De) the solution with SUPG method does not show noticeable difference from the one by the computation without upwinding. On the other hand, in the flow regime of high De, especially in the state of elastic instability the SUPG significantly distorts the flow field and the result differs considerably from the solution acquired straightforwardly. When the strength of elastic flow and thus the nonlinearity further increase, the computational scheme with upwinding fails to converge and evolutionary solution does not become available any more. All this result suggests that extreme care has to be taken on occasions where upwinding is applied, and one has to first of all prove validity of this algorithm in the case of high nonlinearity. On the contrary, the straightforward computation with no upwinding can efficiently model representative phenomena of elastic instability in such benchmark problems as 4:1 contraction flow, flow over a circular cylinder and flow over asymmetric array of cylinders. Asymmetry of the flow field occurring in the symmetric domain, enhanced spatial and temporal fluctuation of dynamic variables and flow effects caused by extension hardening are properly described in this study.

Hierarchy of simulation models for a turbofan gas engine

NASA Technical Reports Server (NTRS)

Longenbaker, W. E.; Leake, R. J.

1977-01-01

Steady-state and transient performance of an F-100-like turbofan gas engine are modeled by a computer program, DYNGEN, developed by NASA. The model employs block data maps and includes about 25 states. Low-order nonlinear analytical and linear techniques are described in terms of their application to the model. Experimental comparisons illustrating the accuracy of each model are presented.

Statistical Metamodeling and Sequential Design of Computer Experiments to Model Glyco-Altered Gating of Sodium Channels in Cardiac Myocytes.

PubMed

Du, Dongping; Yang, Hui; Ednie, Andrew R; Bennett, Eric S

2016-09-01

Glycan structures account for up to 35% of the mass of cardiac sodium ( Nav ) channels. To question whether and how reduced sialylation affects Nav activity and cardiac electrical signaling, we conducted a series of in vitro experiments on ventricular apex myocytes under two different glycosylation conditions, reduced protein sialylation (ST3Gal4(-/-)) and full glycosylation (control). Although aberrant electrical signaling is observed in reduced sialylation, realizing a better understanding of mechanistic details of pathological variations in INa and AP is difficult without performing in silico studies. However, computer model of Nav channels and cardiac myocytes involves greater levels of complexity, e.g., high-dimensional parameter space, nonlinear and nonconvex equations. Traditional linear and nonlinear optimization methods have encountered many difficulties for model calibration. This paper presents a new statistical metamodeling approach for efficient computer experiments and optimization of Nav models. First, we utilize a fractional factorial design to identify control variables from the large set of model parameters, thereby reducing the dimensionality of parametric space. Further, we develop the Gaussian process model as a surrogate of expensive and time-consuming computer models and then identify the next best design point that yields the maximal probability of improvement. This process iterates until convergence, and the performance is evaluated and validated with real-world experimental data. Experimental results show the proposed algorithm achieves superior performance in modeling the kinetics of Nav channels under a variety of glycosylation conditions. As a result, in silico models provide a better understanding of glyco-altered mechanistic details in state transitions and distributions of Nav channels. Notably, ST3Gal4(-/-) myocytes are shown to have higher probabilities accumulated in intermediate inactivation during the repolarization and yield a shorter refractory period than WTs. The proposed statistical design of computer experiments is generally extensible to many other disciplines that involve large-scale and computationally expensive models.

An efficient computational method for the approximate solution of nonlinear Lane-Emden type equations arising in astrophysics

NASA Astrophysics Data System (ADS)

Singh, Harendra

2018-04-01

The key purpose of this article is to introduce an efficient computational method for the approximate solution of the homogeneous as well as non-homogeneous nonlinear Lane-Emden type equations. Using proposed computational method given nonlinear equation is converted into a set of nonlinear algebraic equations whose solution gives the approximate solution to the Lane-Emden type equation. Various nonlinear cases of Lane-Emden type equations like standard Lane-Emden equation, the isothermal gas spheres equation and white-dwarf equation are discussed. Results are compared with some well-known numerical methods and it is observed that our results are more accurate.

A novel auto-tuning PID control mechanism for nonlinear systems.

PubMed

Cetin, Meric; Iplikci, Serdar

2015-09-01

In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Experimental Design for Stochastic Models of Nonlinear Signaling Pathways Using an Interval-Wise Linear Noise Approximation and State Estimation.

PubMed

Zimmer, Christoph

2016-01-01

Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models.

Reduced order surrogate modelling (ROSM) of high dimensional deterministic simulations

NASA Astrophysics Data System (ADS)

Mitry, Mina

Often, computationally expensive engineering simulations can prohibit the engineering design process. As a result, designers may turn to a less computationally demanding approximate, or surrogate, model to facilitate their design process. However, owing to the the curse of dimensionality, classical surrogate models become too computationally expensive for high dimensional data. To address this limitation of classical methods, we develop linear and non-linear Reduced Order Surrogate Modelling (ROSM) techniques. Two algorithms are presented, which are based on a combination of linear/kernel principal component analysis and radial basis functions. These algorithms are applied to subsonic and transonic aerodynamic data, as well as a model for a chemical spill in a channel. The results of this thesis show that ROSM can provide a significant computational benefit over classical surrogate modelling, sometimes at the expense of a minor loss in accuracy.

Effect of nonlinearity in hybrid kinetic Monte Carlo-continuum models.

PubMed

Balter, Ariel; Lin, Guang; Tartakovsky, Alexandre M

2012-01-01

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a kinetic Monte Carlo (KMC) model for a surface to a finite-difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition-dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition-dissolution model including competitive adsorption, which leads to a nonlinear rate, and show that in this case the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.

Effect of Nonlinearity in Hybrid Kinetic Monte Carlo-Continuum Models

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

Balter, Ariel I.; Lin, Guang; Tartakovsky, Alexandre M.

2012-04-23

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a KMC model for a surface to a finite difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and also show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition/dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition/dissolution model including competitive adsorption, which leadsmore » to a nonlinear rate, and show that, in this case, the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.« less

Reduced-Order Modeling for Flutter/LCO Using Recurrent Artificial Neural Network

NASA Technical Reports Server (NTRS)

Yao, Weigang; Liou, Meng-Sing

2012-01-01

The present study demonstrates the efficacy of a recurrent artificial neural network to provide a high fidelity time-dependent nonlinear reduced-order model (ROM) for flutter/limit-cycle oscillation (LCO) modeling. An artificial neural network is a relatively straightforward nonlinear method for modeling an input-output relationship from a set of known data, for which we use the radial basis function (RBF) with its parameters determined through a training process. The resulting RBF neural network, however, is only static and is not yet adequate for an application to problems of dynamic nature. The recurrent neural network method [1] is applied to construct a reduced order model resulting from a series of high-fidelity time-dependent data of aero-elastic simulations. Once the RBF neural network ROM is constructed properly, an accurate approximate solution can be obtained at a fraction of the cost of a full-order computation. The method derived during the study has been validated for predicting nonlinear aerodynamic forces in transonic flow and is capable of accurate flutter/LCO simulations. The obtained results indicate that the present recurrent RBF neural network is accurate and efficient for nonlinear aero-elastic system analysis

Nonlinear transient analysis by energy minimization: A theoretical basis for the ACTION computer code. [predicting the response of a lightweight aircraft during a crash

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1980-01-01

The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems.

Multi-scale Eulerian model within the new National Environmental Modeling System

NASA Astrophysics Data System (ADS)

Janjic, Zavisa; Janjic, Tijana; Vasic, Ratko

2010-05-01

The unified Non-hydrostatic Multi-scale Model on the Arakawa B grid (NMMB) is being developed at NCEP within the National Environmental Modeling System (NEMS). The finite-volume horizontal differencing employed in the model preserves important properties of differential operators and conserves a variety of basic and derived dynamical and quadratic quantities. Among these, conservation of energy and enstrophy improves the accuracy of nonlinear dynamics of the model. Within further model development, advection schemes of fourth order of formal accuracy have been developed. It is argued that higher order advection schemes should not be used in the thermodynamic equation in order to preserve consistency with the second order scheme used for computation of the pressure gradient force. Thus, the fourth order scheme is applied only to momentum advection. Three sophisticated second order schemes were considered for upgrade. Two of them, proposed in Janjic(1984), conserve energy and enstrophy, but with enstrophy calculated differently. One of them conserves enstrophy as computed by the most accurate second order Laplacian operating on stream function. The other scheme conserves enstrophy as computed from the B grid velocity. The third scheme (Arakawa 1972) is arithmetic mean of the former two. It does not conserve enstrophy strictly, but it conserves other quadratic quantities that control the nonlinear energy cascade. Linearization of all three schemes leads to the same second order linear advection scheme. The second order term of the truncation error of the linear advection scheme has a special form so that it can be eliminated by simply preconditioning the advected quantity. Tests with linear advection of a cone confirm the advantage of the fourth order scheme. However, if a localized, large amplitude and high wave-number pattern is present in initial conditions, the clear advantage of the fourth order scheme disappears. In real data runs, problems with noisy data may appear due to mountains. Thus, accuracy and formal accuracy may not be synonymous. The nonlinear fourth order schemes are quadratic conservative and reduce to the Arakawa Jacobian in case of non-divergent flow. In case of general flow the conservation properties of the new momentum advection schemes impose stricter constraint on the nonlinear cascade than the original second order schemes. However, for non-divergent flow, the conservation properties of the fourth order schemes cannot be proven in the same way as those of the original second order schemes. Therefore, nonlinear tests were carried out in order to check how well the fourth order schemes control the nonlinear energy cascade. In the tests nonlinear shallow water equations are solved in a rotating rectangular domain (Janjic, 1984). The domain is covered with only 17 x 17 grid points. A diagnostic quantity is used to monitor qualitative changes in the spectrum over 116 days of simulated time. All schemes maintained meaningful solutions throughout the test. Among the second order schemes, the best result was obtained with the scheme that conserved enstrophy as computed by the second order Laplacian of the stream function. It was closely followed by the Arakawa (1972) scheme, while the remaining scheme was distant third. The fourth order schemes ranked in the same order, and were competitive throughout the experiments with their second order counterparts in preventing accumulation of energy at small scales. Finally, the impact was examined of the fourth order momentum advection on global medium range forecasts. The 500 mb anomaly correlation coefficient is used as a measure of success of the forecasts. Arakawa, A., 1972: Design of the UCLA general circulation model. Tech. Report No. 7, Department of Meteorology, University of California, Los Angeles, 116 pp. Janjic, Z. I., 1984: Non-linear advection schemes and energy cascade on semi-staggered grids. Monthly Weather Review, 112, 1234-1245.

Breaking Computational Barriers: Real-time Analysis and Optimization with Large-scale Nonlinear Models via Model Reduction

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

Carlberg, Kevin Thomas; Drohmann, Martin; Tuminaro, Raymond S.

2014-10-01

Model reduction for dynamical systems is a promising approach for reducing the computational cost of large-scale physics-based simulations to enable high-fidelity models to be used in many- query (e.g., Bayesian inference) and near-real-time (e.g., fast-turnaround simulation) contexts. While model reduction works well for specialized problems such as linear time-invariant systems, it is much more difficult to obtain accurate, stable, and efficient reduced-order models (ROMs) for systems with general nonlinearities. This report describes several advances that enable nonlinear reduced-order models (ROMs) to be deployed in a variety of time-critical settings. First, we present an error bound for the Gauss-Newton with Approximatedmore » Tensors (GNAT) nonlinear model reduction technique. This bound allows the state-space error for the GNAT method to be quantified when applied with the backward Euler time-integration scheme. Second, we present a methodology for preserving classical Lagrangian structure in nonlinear model reduction. This technique guarantees that important properties--such as energy conservation and symplectic time-evolution maps--are preserved when performing model reduction for models described by a Lagrangian formalism (e.g., molecular dynamics, structural dynamics). Third, we present a novel technique for decreasing the temporal complexity --defined as the number of Newton-like iterations performed over the course of the simulation--by exploiting time-domain data. Fourth, we describe a novel method for refining projection-based reduced-order models a posteriori using a goal-oriented framework similar to mesh-adaptive h -refinement in finite elements. The technique allows the ROM to generate arbitrarily accurate solutions, thereby providing the ROM with a 'failsafe' mechanism in the event of insufficient training data. Finally, we present the reduced-order model error surrogate (ROMES) method for statistically quantifying reduced- order-model errors. This enables ROMs to be rigorously incorporated in uncertainty-quantification settings, as the error model can be treated as a source of epistemic uncertainty. This work was completed as part of a Truman Fellowship appointment. We note that much additional work was performed as part of the Fellowship. One salient project is the development of the Trilinos-based model-reduction software module Razor , which is currently bundled with the Albany PDE code and currently allows nonlinear reduced-order models to be constructed for any application supported in Albany. Other important projects include the following: 1. ROMES-equipped ROMs for Bayesian inference: K. Carlberg, M. Drohmann, F. Lu (Lawrence Berkeley National Laboratory), M. Morzfeld (Lawrence Berkeley National Laboratory). 2. ROM-enabled Krylov-subspace recycling: K. Carlberg, V. Forstall (University of Maryland), P. Tsuji, R. Tuminaro. 3. A pseudo balanced POD method using only dual snapshots: K. Carlberg, M. Sarovar. 4. An analysis of discrete v. continuous optimality in nonlinear model reduction: K. Carlberg, M. Barone, H. Antil (George Mason University). Journal articles for these projects are in progress at the time of this writing.« less

Low-complexity nonlinear adaptive filter based on a pipelined bilinear recurrent neural network.

PubMed

Zhao, Haiquan; Zeng, Xiangping; He, Zhengyou

2011-09-01

To reduce the computational complexity of the bilinear recurrent neural network (BLRNN), a novel low-complexity nonlinear adaptive filter with a pipelined bilinear recurrent neural network (PBLRNN) is presented in this paper. The PBLRNN, inheriting the modular architectures of the pipelined RNN proposed by Haykin and Li, comprises a number of BLRNN modules that are cascaded in a chained form. Each module is implemented by a small-scale BLRNN with internal dynamics. Since those modules of the PBLRNN can be performed simultaneously in a pipelined parallelism fashion, it would result in a significant improvement of computational efficiency. Moreover, due to nesting module, the performance of the PBLRNN can be further improved. To suit for the modular architectures, a modified adaptive amplitude real-time recurrent learning algorithm is derived on the gradient descent approach. Extensive simulations are carried out to evaluate the performance of the PBLRNN on nonlinear system identification, nonlinear channel equalization, and chaotic time series prediction. Experimental results show that the PBLRNN provides considerably better performance compared to the single BLRNN and RNN models.

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

PubMed

Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F

2018-02-13

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

Probabilistic risk assessment for CO2 storage in geological formations: robust design and support for decision making under uncertainty

NASA Astrophysics Data System (ADS)

Oladyshkin, Sergey; Class, Holger; Helmig, Rainer; Nowak, Wolfgang

2010-05-01

CO2 storage in geological formations is currently being discussed intensively as a technology for mitigating CO2 emissions. However, any large-scale application requires a thorough analysis of the potential risks. Current numerical simulation models are too expensive for probabilistic risk analysis and for stochastic approaches based on brute-force repeated simulation. Even single deterministic simulations may require parallel high-performance computing. The multiphase flow processes involved are too non-linear for quasi-linear error propagation and other simplified stochastic tools. As an alternative approach, we propose a massive stochastic model reduction based on the probabilistic collocation method. The model response is projected onto a orthogonal basis of higher-order polynomials to approximate dependence on uncertain parameters (porosity, permeability etc.) and design parameters (injection rate, depth etc.). This allows for a non-linear propagation of model uncertainty affecting the predicted risk, ensures fast computation and provides a powerful tool for combining design variables and uncertain variables into one approach based on an integrative response surface. Thus, the design task of finding optimal injection regimes explicitly includes uncertainty, which leads to robust designs of the non-linear system that minimize failure probability and provide valuable support for risk-informed management decisions. We validate our proposed stochastic approach by Monte Carlo simulation using a common 3D benchmark problem (Class et al. Computational Geosciences 13, 2009). A reasonable compromise between computational efforts and precision was reached already with second-order polynomials. In our case study, the proposed approach yields a significant computational speedup by a factor of 100 compared to Monte Carlo simulation. We demonstrate that, due to the non-linearity of the flow and transport processes during CO2 injection, including uncertainty in the analysis leads to a systematic and significant shift of predicted leakage rates towards higher values compared with deterministic simulations, affecting both risk estimates and the design of injection scenarios. This implies that, neglecting uncertainty can be a strong simplification for modeling CO2 injection, and the consequences can be stronger than when neglecting several physical phenomena (e.g. phase transition, convective mixing, capillary forces etc.). The authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart. Keywords: polynomial chaos; CO2 storage; multiphase flow; porous media; risk assessment; uncertainty; integrative response surfaces

A nonlinear bi-level programming approach for product portfolio management.

PubMed

Ma, Shuang

2016-01-01

Product portfolio management (PPM) is a critical decision-making for companies across various industries in today's competitive environment. Traditional studies on PPM problem have been motivated toward engineering feasibilities and marketing which relatively pay less attention to other competitors' actions and the competitive relations, especially in mathematical optimization domain. The key challenge lies in that how to construct a mathematical optimization model to describe this Stackelberg game-based leader-follower PPM problem and the competitive relations between them. The primary work of this paper is the representation of a decision framework and the optimization model to leverage the PPM problem of leader and follower. A nonlinear, integer bi-level programming model is developed based on the decision framework. Furthermore, a bi-level nested genetic algorithm is put forward to solve this nonlinear bi-level programming model for leader-follower PPM problem. A case study of notebook computer product portfolio optimization is reported. Results and analyses reveal that the leader-follower bi-level optimization model is robust and can empower product portfolio optimization.

Computer Language For Optimization Of Design

NASA Technical Reports Server (NTRS)

Scotti, Stephen J.; Lucas, Stephen H.

1991-01-01

SOL is computer language geared to solution of design problems. Includes mathematical modeling and logical capabilities of computer language like FORTRAN; also includes additional power of nonlinear mathematical programming methods at language level. SOL compiler takes SOL-language statements and generates equivalent FORTRAN code and system calls. Provides syntactic and semantic checking for recovery from errors and provides detailed reports containing cross-references to show where each variable used. Implemented on VAX/VMS computer systems. Requires VAX FORTRAN compiler to produce executable program.

Adaptation of a program for nonlinear finite element analysis to the CDC STAR 100 computer

NASA Technical Reports Server (NTRS)

Pifko, A. B.; Ogilvie, P. L.

1978-01-01

The conversion of a nonlinear finite element program to the CDC STAR 100 pipeline computer is discussed. The program called DYCAST was developed for the crash simulation of structures. Initial results with the STAR 100 computer indicated that significant gains in computation time are possible for operations on gloval arrays. However, for element level computations that do not lend themselves easily to long vector processing, the STAR 100 was slower than comparable scalar computers. On this basis it is concluded that in order for pipeline computers to impact the economic feasibility of large nonlinear analyses it is absolutely essential that algorithms be devised to improve the efficiency of element level computations.

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.

Experiences on p-Version Time-Discontinuous Galerkin's Method for Nonlinear Heat Transfer Analysis and Sensitivity Analysis

NASA Technical Reports Server (NTRS)

Hou, Gene

2004-01-01

The focus of this research is on the development of analysis and sensitivity analysis equations for nonlinear, transient heat transfer problems modeled by p-version, time discontinuous finite element approximation. The resulting matrix equation of the state equation is simply in the form ofA(x)x = c, representing a single step, time marching scheme. The Newton-Raphson's method is used to solve the nonlinear equation. Examples are first provided to demonstrate the accuracy characteristics of the resultant finite element approximation. A direct differentiation approach is then used to compute the thermal sensitivities of a nonlinear heat transfer problem. The report shows that only minimal coding effort is required to enhance the analysis code with the sensitivity analysis capability.

A computer program to obtain time-correlated gust loads for nonlinear aircraft using the matched-filter-based method

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Pototzky, Anthony S.; Perry, Boyd, III

1994-01-01

NASA Langley Research Center has, for several years, conducted research in the area of time-correlated gust loads for linear and nonlinear aircraft. The results of this work led NASA to recommend that the Matched-Filter-Based One-Dimensional Search Method be used for gust load analyses of nonlinear aircraft. This manual describes this method, describes a FORTRAN code which performs this method, and presents example calculations for a sample nonlinear aircraft model. The name of the code is MFD1DS (Matched-Filter-Based One-Dimensional Search). The program source code, the example aircraft equations of motion, a sample input file, and a sample program output are all listed in the appendices.

The pEst version 2.1 user's manual

NASA Technical Reports Server (NTRS)

Murray, James E.; Maine, Richard E.

1987-01-01

This report is a user's manual for version 2.1 of pEst, a FORTRAN 77 computer program for interactive parameter estimation in nonlinear dynamic systems. The pEst program allows the user complete generality in definig the nonlinear equations of motion used in the analysis. The equations of motion are specified by a set of FORTRAN subroutines; a set of routines for a general aircraft model is supplied with the program and is described in the report. The report also briefly discusses the scope of the parameter estimation problem the program addresses. The report gives detailed explanations of the purpose and usage of all available program commands and a description of the computational algorithms used in the program.

Nonlinear feedback guidance law for aero-assisted orbit transfer maneuvers

NASA Technical Reports Server (NTRS)

Menon, P. K. A.

1992-01-01

Aero-assisted orbit transfer vehicles have the potential for significantly reducing the fuel requirements in certain classes of orbit transfer operations. Development of a nonlinear feedback guidance law for performing aero-assisted maneuvers that accomplish simultaneous change of all the orbital elements with least vehicle acceleration magnitude is discussed. The analysis is based on a sixth order nonlinear point-mass vehicle model with lift, bank angle, thrust and drag modulation as the control variables. The guidance law uses detailed vehicle aerodynamic and the atmosphere models in the feedback loop. Higher-order gravitational harmonics, planetary atmosphere rotation and ambient winds are included in the formulation. Due to modest computational requirements, the guidance law is implementable on-board an orbit transfer vehicle. The guidance performance is illustrated for three sets of boundary conditions.

Kalman filter control of a model of spatiotemporal cortical dynamics

PubMed Central

Schiff, Steven J; Sauer, Tim

2007-01-01

Recent advances in Kalman filtering to estimate system state and parameters in nonlinear systems have offered the potential to apply such approaches to spatiotemporal nonlinear systems. We here adapt the nonlinear method of unscented Kalman filtering to observe the state and estimate parameters in a computational spatiotemporal excitable system that serves as a model for cerebral cortex. We demonstrate the ability to track spiral wave dynamics, and to use an observer system to calculate control signals delivered through applied electrical fields. We demonstrate how this strategy can control the frequency of such a system, or quench the wave patterns, while minimizing the energy required for such results. These findings are readily testable in experimental applications, and have the potential to be applied to the treatment of human disease. PMID:18310806

A unified perspective on robot control - The energy Lyapunov function approach

NASA Technical Reports Server (NTRS)

Wen, John T.

1990-01-01

A unified framework for the stability analysis of robot tracking control is presented. By using an energy-motivated Lyapunov function candidate, the closed-loop stability is shown for a large family of control laws sharing a common structure of proportional and derivative feedback and a model-based feedforward. The feedforward can be zero, partial or complete linearized dynamics, partial or complete nonlinear dynamics, or linearized or nonlinear dynamics with parameter adaptation. As result, the dichotomous approaches to the robot control problem based on the open-loop linearization and nonlinear Lyapunov analysis are both included in this treatment. Furthermore, quantitative estimates of the trade-offs between different schemes in terms of the tracking performance, steady state error, domain of convergence, realtime computation load and required a prior model information are derived.

A nonlinear macromodel of the bipolar integrated circuit operational amplifier for electromagnetic interference analysis

NASA Astrophysics Data System (ADS)

Chen, G. K. C.

1981-06-01

A nonlinear macromodel for the bipolar transistor integrated circuit operational amplifier is derived from the macromodel proposed by Boyle. The nonlinear macromodel contains only two nonlinear transistors in the input stage in a differential amplifier configuration. Parasitic capacitance effects are represented by capacitors placed at the collectors and emitters of the input transistors. The nonlinear macromodel is effective in predicting the second order intermodulation effect of operational amplifiers in a unity gain buffer amplifier configuration. The nonlinear analysis computer program NCAP is used for the analysis. Accurate prediction of demodulation of amplitude modulated RF signals with RF carrier frequencies in the 0.05 to 100 MHz range is achieved. The macromodel predicted results, presented in the form of second order nonlinear transfer function, come to within 6 dB of the full model predictions for the 741 type of operational amplifiers for values of the second order transfer function greater than -40 dB.

The Elementary Operations of Human Vision Are Not Reducible to Template-Matching

PubMed Central

Neri, Peter

2015-01-01

It is generally acknowledged that biological vision presents nonlinear characteristics, yet linear filtering accounts of visual processing are ubiquitous. The template-matching operation implemented by the linear-nonlinear cascade (linear filter followed by static nonlinearity) is the most widely adopted computational tool in systems neuroscience. This simple model achieves remarkable explanatory power while retaining analytical tractability, potentially extending its reach to a wide range of systems and levels in sensory processing. The extent of its applicability to human behaviour, however, remains unclear. Because sensory stimuli possess multiple attributes (e.g. position, orientation, size), the issue of applicability may be asked by considering each attribute one at a time in relation to a family of linear-nonlinear models, or by considering all attributes collectively in relation to a specified implementation of the linear-nonlinear cascade. We demonstrate that human visual processing can operate under conditions that are indistinguishable from linear-nonlinear transduction with respect to substantially different stimulus attributes of a uniquely specified target signal with associated behavioural task. However, no specific implementation of a linear-nonlinear cascade is able to account for the entire collection of results across attributes; a satisfactory account at this level requires the introduction of a small gain-control circuit, resulting in a model that no longer belongs to the linear-nonlinear family. Our results inform and constrain efforts at obtaining and interpreting comprehensive characterizations of the human sensory process by demonstrating its inescapably nonlinear nature, even under conditions that have been painstakingly fine-tuned to facilitate template-matching behaviour and to produce results that, at some level of inspection, do conform to linear filtering predictions. They also suggest that compliance with linear transduction may be the targeted outcome of carefully crafted nonlinear circuits, rather than default behaviour exhibited by basic components. PMID:26556758

Phase space analysis for anisotropic universe with nonlinear bulk viscosity

NASA Astrophysics Data System (ADS)

Sharif, M.; Mumtaz, Saadia

2018-06-01

In this paper, we discuss phase space analysis of locally rotationally symmetric Bianchi type I universe model by taking a noninteracting mixture of dust like and viscous radiation like fluid whose viscous pressure satisfies a nonlinear version of the Israel-Stewart transport equation. An autonomous system of equations is established by defining normalized dimensionless variables. In order to investigate stability of the system, we evaluate corresponding critical points for different values of the parameters. We also compute power-law scale factor whose behavior indicates different phases of the universe model. It is found that our analysis does not provide a complete immune from fine-tuning because the exponentially expanding solution occurs only for a particular range of parameters. We conclude that stable solutions exist in the presence of nonlinear model for bulk viscosity with different choices of the constant parameter m for anisotropic universe.

Nonlinear Dynamic Models in Advanced Life Support

NASA Technical Reports Server (NTRS)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Prosthetic avian vocal organ controlled by a freely behaving bird based on a low dimensional model of the biomechanical periphery.

PubMed

Arneodo, Ezequiel M; Perl, Yonatan Sanz; Goller, Franz; Mindlin, Gabriel B

2012-01-01

Because of the parallels found with human language production and acquisition, birdsong is an ideal animal model to study general mechanisms underlying complex, learned motor behavior. The rich and diverse vocalizations of songbirds emerge as a result of the interaction between a pattern generator in the brain and a highly nontrivial nonlinear periphery. Much of the complexity of this vocal behavior has been understood by studying the physics of the avian vocal organ, particularly the syrinx. A mathematical model describing the complex periphery as a nonlinear dynamical system leads to the conclusion that nontrivial behavior emerges even when the organ is commanded by simple motor instructions: smooth paths in a low dimensional parameter space. An analysis of the model provides insight into which parameters are responsible for generating a rich variety of diverse vocalizations, and what the physiological meaning of these parameters is. By recording the physiological motor instructions elicited by a spontaneously singing muted bird and computing the model on a Digital Signal Processor in real-time, we produce realistic synthetic vocalizations that replace the bird's own auditory feedback. In this way, we build a bio-prosthetic avian vocal organ driven by a freely behaving bird via its physiologically coded motor commands. Since it is based on a low-dimensional nonlinear mathematical model of the peripheral effector, the emulation of the motor behavior requires light computation, in such a way that our bio-prosthetic device can be implemented on a portable platform.

Alternatives for jet engine control

NASA Technical Reports Server (NTRS)

Sain, M. K.; Yurkovich, S.; Hill, J. P.; Kingler, T. A.

1983-01-01

The development of models of tensor type for a digital simulation of the quiet, clean safe engine (QCSE) gas turbine engine; the extension, to nonlinear multivariate control system design, of the concepts of total synthesis which trace their roots back to certain early investigations under this grant; the role of series descriptions as they relate to questions of scheduling in the control of gas turbine engines; the development of computer-aided design software for tensor modeling calculations; further enhancement of the softwares for linear total synthesis, mentioned above; and calculation of the first known examples using tensors for nonlinear feedback control are discussed.

Application of the thermorheologically complex nonlinear Adam-Gibbs model for the glass transition to molecular motion in hydrated proteins.

PubMed

Hodge, Ian M

2006-08-01

The nonlinear thermorheologically complex Adam Gibbs (extended "Scherer-Hodge") model for the glass transition is applied to enthalpy relaxation data reported by Sartor, Mayer, and Johari for hydrated methemoglobin. A sensible range in values for the average localized activation energy is obtained (100-200 kJ mol(-1)). The standard deviation in the inferred Gaussian distribution of activation energies, computed from the reported KWW beta-parameter, is approximately 30% of the average, consistent with the suggestion that some relaxation processes in hydrated proteins have exceptionally low activation energies.

A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

NASA Astrophysics Data System (ADS)

Matouš, Karel; Geers, Marc G. D.; Kouznetsova, Varvara G.; Gillman, Andrew

2017-02-01

Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

Intensity dependence of focused ultrasound lesion position

NASA Astrophysics Data System (ADS)

Meaney, Paul M.; Cahill, Mark D.; ter Haar, Gail R.

1998-04-01

Knowledge of the spatial distribution of intensity loss from an ultrasonic beam is critical to predicting lesion formation in focused ultrasound surgery. To date most models have used linear propagation models to predict the intensity profiles needed to compute the temporally varying temperature distributions. These can be used to compute thermal dose contours that can in turn be used to predict the extent of thermal damage. However, these simulations fail to adequately describe the abnormal lesion formation behavior observed for in vitro experiments in cases where the transducer drive levels are varied over a wide range. For these experiments, the extent of thermal damage has been observed to move significantly closer to the transducer with increasing transducer drive levels than would be predicted using linear propagation models. The simulations described herein, utilize the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear propagation model with the parabolic approximation for highly focused ultrasound waves, to demonstrate that the positions of the peak intensity and the lesion do indeed move closer to the transducer. This illustrates that for accurate modeling of heating during FUS, nonlinear effects must be considered.

A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

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

Matouš, Karel, E-mail: kmatous@nd.edu; Geers, Marc G.D.; Kouznetsova, Varvara G.

2017-02-01

Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platformmore » in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.« less

Two Studies of Complex Nonlinear Systems: Engineered Granular Crystals and Coarse-Graining Optimization Problems

NASA Astrophysics Data System (ADS)

Pozharskiy, Dmitry

In recent years a nonlinear, acoustic metamaterial, named granular crystals, has gained prominence due to its high accessibility, both experimentally and computationally. The observation of a wide range of dynamical phenomena in the system, due to its inherent nonlinearities, has suggested its importance in many engineering applications related to wave propagation. In the first part of this dissertation, we explore the nonlinear dynamics of damped-driven granular crystals. In one case, we consider a highly nonlinear setting, also known as a sonic vacuum, and derive a nonlinear analogue of a linear spectrum, corresponding to resonant periodic propagation and antiresonances. Experimental studies confirm the computational findings and the assimilation of experimental data into a numerical model is demonstrated. In the second case, global bifurcations in a precompressed granular crystal are examined, and their involvement in the appearance of chaotic dynamics is demonstrated. Both results highlight the importance of exploring the nonlinear dynamics, to gain insight into how a granular crystal responds to different external excitations. In the second part, we borrow established ideas from coarse-graining of dynamical systems, and extend them to optimization problems. We combine manifold learning algorithms, such as Diffusion Maps, with stochastic optimization methods, such as Simulated Annealing, and show that we can retrieve an ensemble, of few, important parameters that should be explored in detail. This framework can lead to acceleration of convergence when dealing with complex, high-dimensional optimization, and could potentially be applied to design engineered granular crystals.

Modeling and reduction with applications to semiconductor processing

NASA Astrophysics Data System (ADS)

Newman, Andrew Joseph

This thesis consists of several somewhat distinct but connected parts, with an underlying motivation in problems pertaining to control and optimization of semiconductor processing. The first part (Chapters 3 and 4) addresses problems in model reduction for nonlinear state-space control systems. In 1993, Scherpen generalized the balanced truncation method to the nonlinear setting. However, the Scherpen procedure is not easily computable and has not yet been applied in practice. We offer a method for computing a working approximation to the controllability energy function, one of the main objects involved in the method. Moreover, we show that for a class of second-order mechanical systems with dissipation, under certain conditions related to the dissipation, an exact formula for the controllability function can be derived. We then present an algorithm for a numerical implementation of the Morse-Palais lemma, which produces a local coordinate transformation under which a real-valued function with a non-degenerate critical point is quadratic on a neighborhood of the critical point. Application of the algorithm to the controllabilty function plays a key role in computing the balanced representation. We then apply our methods and algorithms to derive balanced realizations for nonlinear state-space models of two example mechanical systems: a simple pendulum and a double pendulum. The second part (Chapter 5) deals with modeling of rapid thermal chemical vapor deposition (RTCVD) for growth of silicon thin films, via first-principles and empirical analysis. We develop detailed process-equipment models and study the factors that influence deposition uniformity, such as temperature, pressure, and precursor gas flow rates, through analysis of experimental and simulation results. We demonstrate that temperature uniformity does not guarantee deposition thickness uniformity in a particular commercial RTCVD reactor of interest. In the third part (Chapter 6) we continue the modeling effort, specializing to a control system for RTCVD heat transfer. We then develop and apply ad-hoc versions of prominent model reduction approaches to derive reduced models and perform a comparative study.

An artificial nonlinear diffusivity method for supersonic reacting flows with shocks

NASA Astrophysics Data System (ADS)

Fiorina, B.; Lele, S. K.

2007-03-01

A computational approach for modeling interactions between shocks waves, contact discontinuities and reactions zones with a high-order compact scheme is investigated. To prevent the formation of spurious oscillations around shocks, artificial nonlinear viscosity [A.W. Cook, W.H. Cabot, A high-wavenumber viscosity for high resolution numerical method, J. Comput. Phys. 195 (2004) 594-601] based on high-order derivative of the strain rate tensor is used. To capture temperature and species discontinuities a nonlinear diffusivity based on the entropy gradient is added. It is shown that the damping of 'wiggles' is controlled by the model constants and is largely independent of the mesh size and the shock strength. The same holds for the numerical shock thickness and allows a determination of the L2 error. In the shock tube problem, with fluids of different initial entropy separated by the diaphragm, an artificial diffusivity is required to accurately capture the contact surface. Finally, the method is applied to a shock wave propagating into a medium with non-uniform density/entropy and to a CJ detonation wave. Multi-dimensional formulation of the model is presented and is illustrated by a 2D oblique wave reflection from an inviscid wall, by a 2D supersonic blunt body flow and by a Mach reflection problem.

The numerical dynamic for highly nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Lafon, A.; Yee, H. C.

1992-01-01

Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

Adaptive Crack Modeling with Interface Solid Elements for Plain and Fiber Reinforced Concrete Structures.

PubMed

Zhan, Yijian; Meschke, Günther

2017-07-08

The effective analysis of the nonlinear behavior of cement-based engineering structures not only demands physically-reliable models, but also computationally-efficient algorithms. Based on a continuum interface element formulation that is suitable to capture complex cracking phenomena in concrete materials and structures, an adaptive mesh processing technique is proposed for computational simulations of plain and fiber-reinforced concrete structures to progressively disintegrate the initial finite element mesh and to add degenerated solid elements into the interfacial gaps. In comparison with the implementation where the entire mesh is processed prior to the computation, the proposed adaptive cracking model allows simulating the failure behavior of plain and fiber-reinforced concrete structures with remarkably reduced computational expense.

Adaptive Crack Modeling with Interface Solid Elements for Plain and Fiber Reinforced Concrete Structures

PubMed Central

Zhan, Yijian

2017-01-01

The effective analysis of the nonlinear behavior of cement-based engineering structures not only demands physically-reliable models, but also computationally-efficient algorithms. Based on a continuum interface element formulation that is suitable to capture complex cracking phenomena in concrete materials and structures, an adaptive mesh processing technique is proposed for computational simulations of plain and fiber-reinforced concrete structures to progressively disintegrate the initial finite element mesh and to add degenerated solid elements into the interfacial gaps. In comparison with the implementation where the entire mesh is processed prior to the computation, the proposed adaptive cracking model allows simulating the failure behavior of plain and fiber-reinforced concrete structures with remarkably reduced computational expense. PMID:28773130

From Occasional Choices to Inevitable Musts: A Computational Model of Nicotine Addiction

PubMed Central

Metin, Selin; Sengor, N. Serap

2012-01-01

Although, there are considerable works on the neural mechanisms of reward-based learning and decision making, and most of them mention that addiction can be explained by malfunctioning in these cognitive processes, there are very few computational models. This paper focuses on nicotine addiction, and a computational model for nicotine addiction is proposed based on the neurophysiological basis of addiction. The model compromises different levels ranging from molecular basis to systems level, and it demonstrates three different possible behavioral patterns which are addict, nonaddict, and indecisive. The dynamical behavior of the proposed model is investigated with tools used in analyzing nonlinear dynamical systems, and the relation between the behavioral patterns and the dynamics of the system is discussed. PMID:23251144

Linear and Non-Linear Visual Feature Learning in Rat and Humans

PubMed Central

Bossens, Christophe; Op de Beeck, Hans P.

2016-01-01

The visual system processes visual input in a hierarchical manner in order to extract relevant features that can be used in tasks such as invariant object recognition. Although typically investigated in primates, recent work has shown that rats can be trained in a variety of visual object and shape recognition tasks. These studies did not pinpoint the complexity of the features used by these animals. Many tasks might be solved by using a combination of relatively simple features which tend to be correlated. Alternatively, rats might extract complex features or feature combinations which are nonlinear with respect to those simple features. In the present study, we address this question by starting from a small stimulus set for which one stimulus-response mapping involves a simple linear feature to solve the task while another mapping needs a well-defined nonlinear combination of simpler features related to shape symmetry. We verified computationally that the nonlinear task cannot be trivially solved by a simple V1-model. We show how rats are able to solve the linear feature task but are unable to acquire the nonlinear feature. In contrast, humans are able to use the nonlinear feature and are even faster in uncovering this solution as compared to the linear feature. The implications for the computational capabilities of the rat visual system are discussed. PMID:28066201

Development and application of unified algorithms for problems in computational science

NASA Technical Reports Server (NTRS)

Shankar, Vijaya; Chakravarthy, Sukumar

1987-01-01

A framework is presented for developing computationally unified numerical algorithms for solving nonlinear equations that arise in modeling various problems in mathematical physics. The concept of computational unification is an attempt to encompass efficient solution procedures for computing various nonlinear phenomena that may occur in a given problem. For example, in Computational Fluid Dynamics (CFD), a unified algorithm will be one that allows for solutions to subsonic (elliptic), transonic (mixed elliptic-hyperbolic), and supersonic (hyperbolic) flows for both steady and unsteady problems. The objectives are: development of superior unified algorithms emphasizing accuracy and efficiency aspects; development of codes based on selected algorithms leading to validation; application of mature codes to realistic problems; and extension/application of CFD-based algorithms to problems in other areas of mathematical physics. The ultimate objective is to achieve integration of multidisciplinary technologies to enhance synergism in the design process through computational simulation. Specific unified algorithms for a hierarchy of gas dynamics equations and their applications to two other areas: electromagnetic scattering, and laser-materials interaction accounting for melting.

Mathematical and computational modelling of skin biophysics: a review

PubMed Central

2017-01-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas. PMID:28804267

Mathematical and computational modelling of skin biophysics: a review

NASA Astrophysics Data System (ADS)

Limbert, Georges

2017-07-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas.

Prognostic characteristics of the lowest-mode internal waves in the Sea of Okhotsk

NASA Astrophysics Data System (ADS)

Kurkin, Andrey; Kurkina, Oxana; Zaytsev, Andrey; Rybin, Artem; Talipova, Tatiana

2017-04-01

The nonlinear dynamics of short-period internal waves on ocean shelves is well described by generalized nonlinear evolutionary models of Korteweg - de Vries type. Parameters of these models such as long wave propagation speed, nonlinear and dispersive coefficients can be calculated using hydrological data (sea water density stratification), and therefore have geographical and seasonal variations. The internal wave parameters for the basin of the Sea of Okhotsk are computed on a base of recent version of hydrological data source GDEM V3.0. Geographical and seasonal variability of internal wave characteristics is investigated. It is shown that annually or seasonally averaged data can be used for linear parameters. The nonlinear parameters are more sensitive to temporal averaging of hydrological data and detailed data are preferable to use. The zones for nonlinear parameters to change their signs (so-called "turning points") are selected. Possible internal waveforms appearing in the process of internal tide transformation including the solitary waves changing polarities are simulated for the hydrological conditions in the Sea of Okhotsk shelf to demonstrate different scenarios of internal wave adjustment, transformation, refraction and cylindrical divergence.

Nonlinear mechanics of non-rigid origami: an efficient computational approach

NASA Astrophysics Data System (ADS)

Liu, K.; Paulino, G. H.

2017-10-01

Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on `bar-and-hinge' models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.

Nonlinear mechanics of non-rigid origami: an efficient computational approach.

PubMed

Liu, K; Paulino, G H

2017-10-01

Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on 'bar-and-hinge' models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.

Nonlinear plasma wave models in 3D fluid simulations of laser-plasma interaction

NASA Astrophysics Data System (ADS)

Chapman, Thomas; Berger, Richard; Arrighi, Bill; Langer, Steve; Banks, Jeffrey; Brunner, Stephan

2017-10-01

Simulations of laser-plasma interaction (LPI) in inertial confinement fusion (ICF) conditions require multi-mm spatial scales due to the typical laser beam size and durations of order 100 ps in order for numerical laser reflectivities to converge. To be computationally achievable, these scales necessitate a fluid-like treatment of light and plasma waves with a spatial grid size on the order of the light wave length. Plasma waves experience many nonlinear phenomena not naturally described by a fluid treatment, such as frequency shifts induced by trapping, a nonlinear (typically suppressed) Landau damping, and mode couplings leading to instabilities that can cause the plasma wave to decay rapidly. These processes affect the onset and saturation of stimulated Raman and Brillouin scattering, and are of direct interest to the modeling and prediction of deleterious LPI in ICF. It is not currently computationally feasible to simulate these Debye length-scale phenomena in 3D across experimental scales. Analytically-derived and/or numerically benchmarked models of processes occurring at scales finer than the fluid simulation grid offer a path forward. We demonstrate the impact of a range of kinetic processes on plasma reflectivity via models included in the LPI simulation code pF3D. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

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.

A new adaptive multiple modelling approach for non-linear and non-stationary systems

NASA Astrophysics Data System (ADS)

Chen, Hao; Gong, Yu; Hong, Xia

2016-07-01

This paper proposes a novel adaptive multiple modelling algorithm for non-linear and non-stationary systems. This simple modelling paradigm comprises K candidate sub-models which are all linear. With data available in an online fashion, the performance of all candidate sub-models are monitored based on the most recent data window, and M best sub-models are selected from the K candidates. The weight coefficients of the selected sub-model are adapted via the recursive least square (RLS) algorithm, while the coefficients of the remaining sub-models are unchanged. These M model predictions are then optimally combined to produce the multi-model output. We propose to minimise the mean square error based on a recent data window, and apply the sum to one constraint to the combination parameters, leading to a closed-form solution, so that maximal computational efficiency can be achieved. In addition, at each time step, the model prediction is chosen from either the resultant multiple model or the best sub-model, whichever is the best. Simulation results are given in comparison with some typical alternatives, including the linear RLS algorithm and a number of online non-linear approaches, in terms of modelling performance and time consumption.

A nonlinear optimal control approach to stabilization of a macroeconomic development model

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

2017-11-01

A nonlinear optimal (H-infinity) control approach is proposed for the problem of stabilization of the dynamics of a macroeconomic development model that is known as the Grossman-Helpman model of endogenous product cycles. The dynamics of the macroeconomic development model is divided in two parts. The first one describes economic activities in a developed country and the second part describes variation of economic activities in a country under development which tries to modify its production so as to serve the needs of the developed country. The article shows that through control of the macroeconomic model of the developed country, one can finally control the dynamics of the economy in the country under development. The control method through which this is achieved is the nonlinear H-infinity control. The macroeconomic model for the country under development undergoes approximate linearization round a temporary operating point. This is defined at each time instant by the present value of the system's state vector and the last value of the control input vector that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. For the linearized model an H-infinity feedback controller is computed. The controller's gain is calculated by solving an algebraic Riccati equation at each iteration of the control method. The asymptotic stability of the control approach is proven through Lyapunov analysis. This assures that the state variables of the macroeconomic model of the country under development will finally converge to the designated reference values.

Nonlinear transport for a dilute gas in steady Couette flow

NASA Astrophysics Data System (ADS)

Garzó, V.; López de Haro, M.

1997-03-01

Transport properties of a dilute gas subjected to arbitrarily large velocity and temperature gradients (steady planar Couette flow) are determined. The results are obtained from the so-called ellipsoidal statistical (ES) kinetic model, which is an extension of the well-known BGK kinetic model to account for the correct Prandtl number. At a hydrodynamic level, the solution is characterized by constant pressure, and linear velocity and parabolic temperature profiles with respect to a scaled variable. The transport coefficients are explicitly evaluated as nonlinear functions of the shear rate. A comparison with previous results derived from a perturbative solution of the Boltzmann equation as well as from other kinetic models is carried out. Such a comparison shows that the ES predictions are in better agreement with the Boltzmann results than those of the other approximations. In addition, the velocity distribution function is also computed. Although the shear rates required for observing non-Newtonian effects are experimentally unrealizable, the conclusions obtained here may be relevant for analyzing computer results.

Modeling boundary-layer transition in direct and large-eddy simulations using parabolized stability equations

NASA Astrophysics Data System (ADS)

Lozano-Durán, A.; Hack, M. J. P.; Moin, P.

2018-02-01

We examine the potential of the nonlinear parabolized stability equations (PSE) to provide an accurate yet computationally efficient treatment of the growth of disturbances in H-type transition to turbulence. The PSE capture the nonlinear interactions that eventually induce breakdown to turbulence and can as such identify the onset of transition without relying on empirical correlations. Since the local PSE solution at the onset of transition is a close approximation of the Navier-Stokes equations, it provides a natural inflow condition for direct numerical simulations (DNS) and large-eddy simulations (LES) by avoiding nonphysical transients. We show that a combined PSE-DNS approach, where the pretransitional region is modeled by the PSE, can reproduce the skin-friction distribution and downstream turbulent statistics from a DNS of the full domain. When the PSE are used in conjunction with wall-resolved and wall-modeled LES, the computational cost in both the laminar and turbulent regions is reduced by several orders of magnitude compared to DNS.

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

NASA Astrophysics Data System (ADS)

Arendt, V.; Shalchi, A.

2018-06-01

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker-Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.

Nonlinear dynamics as an engine of computation.

PubMed

Kia, Behnam; Lindner, John F; Ditto, William L

2017-03-06

Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Nonlinear dynamics as an engine of computation

PubMed Central

Lindner, John F.; Ditto, William L.

2017-01-01

Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics—cybernetical physics—opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation. This article is part of the themed issue ‘Horizons of cybernetical physics’. PMID:28115619

Modeling of Biomaterials for Non-Linear Optical Applications.

DTIC Science & Technology

1995-01-01

Computational chemistry methods were used to explore the molecular conformations of a variety of optoelectronic biopolymers -spiropyran chromophore...investigated. These polypeptides are compositionally representative of the naturally occurring amino acid sequences in silk and wool, having respectively

Fuzzy logic based robotic controller

NASA Technical Reports Server (NTRS)

Attia, F.; Upadhyaya, M.

1994-01-01

Existing Proportional-Integral-Derivative (PID) robotic controllers rely on an inverse kinematic model to convert user-specified cartesian trajectory coordinates to joint variables. These joints experience friction, stiction, and gear backlash effects. Due to lack of proper linearization of these effects, modern control theory based on state space methods cannot provide adequate control for robotic systems. In the presence of loads, the dynamic behavior of robotic systems is complex and nonlinear, especially where mathematical modeling is evaluated for real-time operators. Fuzzy Logic Control is a fast emerging alternative to conventional control systems in situations where it may not be feasible to formulate an analytical model of the complex system. Fuzzy logic techniques track a user-defined trajectory without having the host computer to explicitly solve the nonlinear inverse kinematic equations. The goal is to provide a rule-based approach, which is closer to human reasoning. The approach used expresses end-point error, location of manipulator joints, and proximity to obstacles as fuzzy variables. The resulting decisions are based upon linguistic and non-numerical information. This paper presents a solution to the conventional robot controller which is independent of computationally intensive kinematic equations. Computer simulation results of this approach as obtained from software implementation are also discussed.

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