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MASTODON has the capability to model stochastic nonlinear soil-structure interaction (NLSSI) in a dynamic probabilistic risk assessment framework. The NLSSI simulations include structural dynamics, time integration, dynamic porous media flow, nonlinear hysteretic soil constitutive models, geometric nonlinearities (gapping, sliding, and uplift). MASTODON is also the MOOSE based master application for dynamic PRA of external hazards.
We study the non-perturbative renormalization group flow of the nonlinear O(N) sigma model in two and three spacetime dimensions using a scheme that combines an effective local Hybrid Monte Carlo update routine, blockspin transformations and a Monte Carlo demon method. In two dimensions our results verify perturbative renormalizability. In three dimensions, we determine the flow diagram of the theory for various N and different truncations and find a non-trivial fixed point, which indicates non-perturbative renormalizability. It is related to the well-studied phase transition of the O(N) universality class and characterizes the continuum physics of the model. We compare the obtained renormalization group flows with recent investigations by means of the Functional Renormalization Group. - Highlights: • We compute the global flow diagram from lattice simulations. • Truncation of the effective action may lead to artificial fixed points. • Our optimization scheme effectively reduces truncation errors. • The Wilson–Fisher fixed point is identified as a non-trivial UV fixed point. • Asymptotic safety is realized for the 3D nonlinear sigma model.
The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.
We study out-of-equilibrium transport in disordered superconductors close to the superconducting transition. We consider a thin film connected by resistive tunnel interfaces to thermal reservoirs having different chemical potentials and temperatures. The nonequilibrium longitudinal current–current correlation function is calculated within the nonlinear sigma model description and nonlinear dependence on temperatures and chemical potentials is obtained. Different contributions are calculated, originating from the fluctuation-induced suppression of the quasiparticle density of states, Maki–Thompson and Aslamazov–Larkin processes. As a special case of our results, close-to-equilibrium we obtain the longitudinal ac conductivity using the fluctuation–dissipation theorem. -- Highlights: •Contributions to the current noise induced by superconducting fluctuations are calculated. •Nonequilibrium physics is studied. •Nonlinear dependence of the noise on temperatures and chemical potentials of the reservoirs is found.
We report our implementation of the magneto-frictional method in the Message Passing Interface Adaptive Mesh Refinement Versatile Advection Code (MPI-AMRVAC). The method aims at applications where local adaptive mesh refinement (AMR) is essential to make follow-up dynamical modeling affordable. We quantify its performance in both domain-decomposed uniform grids and block-adaptive AMR computations, using all frequently employed force-free, divergence-free, and other vector comparison metrics. As test cases, we revisit the semi-analytic solution of Low and Lou in both Cartesian and spherical geometries, along with the topologically challenging Titov–Démoulin model. We compare different combinations of spatial and temporal discretizations, and find that the fourth-order central difference with a local Lax–Friedrichs dissipation term in a single-step marching scheme is an optimal combination. The initial condition is provided by the potential field, which is the potential field source surface model in spherical geometry. Various boundary conditions are adopted, ranging from fully prescribed cases where all boundaries are assigned with the semi-analytic models, to solar-like cases where only the magnetic field at the bottom is known. Our results demonstrate that all the metrics compare favorably to previous works in both Cartesian and spherical coordinates. Cases with several AMR levels perform in accordance with their effective resolutions. The magneto-frictional method in MPI-AMRVAC allows us to model a region of interest with high spatial resolution and large field of view simultaneously, as required by observation-constrained extrapolations using vector data provided with modern instruments. The applications of the magneto-frictional method to observations are shown in an accompanying paper.
Irradiation creep plays a major role in the structural integrity of the graphite components in high temperature gas cooled reactors. Finite element procedures combined with a suitable irradiation creep model can be used to simulate the time-integrated structural integrity of complex shapes, such as the reactor core graphite reflector and fuel bricks. In the present work a comparative study was undertaken to understand the effect of linear and nonlinear irradiation creep on results of finite element based stress analysis. Numerical results were generated through finite element simulations of a typical graphite reflector.
Compressed air energy storage is suitable for large-scale electrical energy storage, which is important for integrating renewable energy sources into electric power systems. A typical compressed air energy storage plant consists of compressors, expanders, caverns, and a motor/generator set. Current cavern models used for compressed air energy storage are either accurate but highly nonlinear or linear but inaccurate. The application of highly nonlinear cavern models in power system optimization problems renders them computationally challenging to solve. In this regard, an accurate bilinear cavern model for compressed air energy storage is proposed. The charging and discharging processes in a cavern are divided into several real/virtual states. The first law of thermodynamics and ideal gas law are then utilized to derive a cavern model, i.e., a model for the variation of temperature and pressure in these processes. Thereafter, the heat transfer between the air in the cavern and the cavern wall is considered and integrated into the cavern model. By subsequently eliminating several negligible terms, the cavern model reduces to a bilinear model. The accuracy of the bilinear cavern model is verified via comparison with both an accurate nonlinear model and two sets of field-measured data. The bilinear cavern model can be easily linearized and is then suitable for integration into optimization problems considering compressed air energy storage. This is verified via comparatively solving a self-scheduling problem of compressed air energy storage using different cavern models.
It is hard to identify nonlinear biological models strictly from data, with results that are often sensitive to experimental conditions. Automated experimental workflows and liquid handling enables unprecedented throughput, as well as the capacity to generate extremely large datasets. We seek to develop generalized identifiability conditions for informing the design of automated experiments to discover predictive nonlinear biological models. For linear systems, identifiability is characterized by persistence of excitation conditions. For nonlinear systems, no such persistence of excitation conditions exist. We use the input-Koopman operator method to model nonlinear systems and derive identifiability conditions for openloop systems initialized from a single initial condition. We show that nonlinear identifiability is intrinsically tied to the rank of a given dataset’s power spectral density, transformed through the lifted Koopman observable space. We illustrate these identifiability conditions with a simulated synthetic gene circuit model, the repressilator. We illustrate how rank degeneracy in datasets results in overfitted nonlinear models of the repressilator, resulting in poor predictive accuracy. Our findings provide novel experimental design criteria for discovery of globally predictive nonlinear models of biological phenomena.
Handbook on nonlinear mathematical models for electronic components
We study lattice SU(2) Yang-Mills theory with dimension d{>=}4. The model can be expressed as a (d-1)-dimensional O(4) nonlinear {sigma} model in a d-dimensional heat bath. As is well known, the nonlinear {sigma} model alone shows a phase transition. If the quark confinement is a consequence of the absence of a phase transition for the Yang-Mills theory, then the fluctuations of the heat bath must destroy the long-range order of the nonlinear {sigma} model. In order to clarify whether this is true, we replace the fluctuations of the heat bath with Gaussian random variables, and obtain a Langevin equation which yields the effective action of the nonlinear {sigma} model by analyzing the Fokker-Planck equation. It turns out that the fluctuations indeed destroy the long-range order of the nonlinear {sigma} model within a mean-field approximation estimating a critical point, whereas for the corresponding U(1) gauge theory, the phase transition to the massless phase remains against the fluctuations.
In the performance period of this work under a DOE contract, the co-PIs, Philip Gill and Henry Abarbanel, developed new methods for statistical data assimilation for problems of DOE interest, including geophysical and biological problems. This included numerical optimization algorithms for variational principles, new parallel processing Monte Carlo routines for performing the path integrals of statistical data assimilation. These results have been summarized in the monograph: “Predicting the Future: Completing Models of Observed Complex Systems” by Henry Abarbanel, published by Spring-Verlag in June 2013. Additional results and details have appeared in the peer reviewed literature.
The plasma physical analog model (an extension of the damped, harmonic-oscillator dripping faucet model) is employed to consider explicitly the effect of time-varying the inputs. This work is equivalent to considering the effects of northward and southward turnings of the interplanetary magnetic field for various periods of time. It is found that relatively extended episodes (not less than 2 hours) of turned-on input with shorter (about 1 hour) periods of turned-off input lead to model behavior much like the continuously driven case. Going to short input intervals with longer periods of zero input leads to highly irregular and dramatically fluctuating episodes of magnetotail unloading. These results give an insight into the diversity of apparent magnetospheric responses during relatively isolated substorm conditions. This work shows the absolutely critical interdependence (in a nonlinear dynamical system) of input phasing and internal magnetospheric response cycles.
The paper studies with finite difference nonlinear circulation models the uncertainties in interesting flow properties, such as western boundary current transport, potential and kinetic energy, owing to the uncertainty in the driving surface boundary condition. The procedure is based upon nonlinear optimization methods. The same calculations permit quantitative study of the importance of new information as a function of type, region of measurement and accuracy, providing a method to study various observing strategies. Uncertainty in a model parameter, the bottom friction coefficient, is studied in conjunction with uncertain measurements. The model is free to adjust the bottom friction coefficient such that an objective function is minimized while fitting a set of data to within prescribed bounds. The relative importance of the accuracy of the knowledge about the friction coefficient with respect to various kinds of observations is then quantified, and the possible range of the friction coefficients is calculated.
We develop the halo model of large-scale structure as an accurate tool for probing primordial non-Gaussianity. In this study we focus on understanding the matter clustering at several redshifts in the context of primordial non-Gaussianity that is a quadratic correction to the local Gaussian potential, characterized by the parameter f{sub NL}. In our formulation of the halo model we pay special attention to the effect of halo exclusion and show that this can potentially solve the long-standing problem of excess power on large scales in this model. The halo model depends on the mass function, clustering of halo centers, and the density profiles. We test these ingredients using a large ensemble of high-resolution Gaussian and non-Gaussian numerical simulations, covering f{sub NL}={l_brace}0,+100,-100{r_brace}. In particular, we provide a first exploration of how halo density profiles change in the presence of primordial non-Gaussianity. We find that for f{sub NL} positive (negative) high-mass haloes have an increased (decreased) core density, so being more (less) concentrated than in the Gaussian case. We also examine the halo bias and show that, if the halo model is correct, then there is a small asymmetry in the scale dependence of the bias on very large scales, which arises because the Gaussian bias must be renormalized. We show that the matter power spectrum is modified by {approx}2.5% and {approx}3.5% on scales k{approx}1.0 h Mpc{sup -1} at z=0 and z=1, respectively. Our halo model calculation reproduces the absolute amplitude to within < or approx. 10% and the ratio of non-Gaussian to Gaussian spectra to within < or approx. 1%. We also measure the matter correlation function and find similarly good levels of agreement between the halo model and the data. We anticipate that this modeling will be useful for constraining f{sub NL} from measurements of the shear correlation function in future weak lensing surveys such as Euclid.
The managers in Federal agencies are challenged to control the extensive activities in government and still provide high-quality products and services to the American taxpayers. Considering today's complex social and economic environment and the $3.8 billion daily cost of operating the Federal Government, it is evident that there is a need to develop decision-making tools for accurate resource allocation and total quality management. The goal of this thesis is to provide a methodical process that will aid managers in Federal Government to make budgetary decisions based on the cost of services, the agency's objectives, and the customers' perception of the agency's product. A general resource allocation procedure was developed in this study that can be applied to any government organization. A government organization, hereafter the 'organization,' is assumed to be a multidivision enterprise. This procedure was applied to a small organization for the proof of the concept. This organization is the Technical Services Directorate (TSD) at the NASA Lewis Research Center in Cleveland, Ohio. As part of the procedure, a nonlinear programming model was developed to account for the resources of the organization, the outputs produced by the organization, the decision-maker's views, and the customers' satisfaction with the organization. The information on the resources of the organization was acquired from current budget levels of the organization and the human resources assigned to the divisions. The outputs of the organization were defined and measured by identifying metrics that assess the outputs, the most challenging task in this study. The decision-maker's views are represented in the model as weights assigned to the various outputs and were quantified by using the analytic hierarchy process. The customer's opinions regarding the outputs of the organization were collected through questionnaires that were designed for each division individually. Following the philosophy of total quality management, information on customers' satisfaction is presented in the model as the quality of output. The model is a nonlinear one whose objective is to maximize customers' satisfaction such that the total cost of operation does not exceed the organization's budget. This model represents a structured approach or policy mechanism, at the agency level, to make capital investment decisions based on the priorities of the agency and the quality of outputs. This procedure applied to TSD resulted in a resources allocation scheme that was reasonable and acceptable to the decision-makers and, as expected, dependent on the assumptions and accuracy of the data used in the model.
The (1 + 1)-dimensional nonlinear O(3) {sigma} model involving an explicitly broken symmetry is considered. Sphalerons are known to exist in this model. These sphalerons are of a topological origin and are embedded kinks of the sine-Gordon model. In the case of a compact spatial manifold S{sup 1}, sine-Gordon multikinks exist in the model. It is shown that the model admits a nonstatic generalization of the sine-Gordon kink/multikink, Q kink/multikink. Explicit expressions are obtained for the dependence of the Q kink energy and charge on the phase frequency of rotation. The Q kink is studied for stability, and expressions are obtained for the eigenfunctions and eigenfrequencies of the operator of quadratic fluctuations. It is shown that the Q kink is unstable over the entire admissible frequency range {omega} Element-Of [-1, 1]. The one-loop quantum correction to the static-kink mass is calculated, and the Q-kink zero mode is quantized. It is shown that, in a general static case, the field equations of the model are integrable in quadratures.
An improved description for nonlinear plasma wakefields with phase velocities near the speed of light is presented and compared against fully kinetic particle-in-cell simulations. These wakefields are excited by intense particle beams or lasers pushing plasma electrons radially outward, creating an ion bubble surrounded by a sheath of electrons characterized by the source term S≡−1enp(ρ−Jz/c), where ρ and Jz are the charge and axial current densities, respectively. Previously, the sheath source term was described phenomenologically with a positive-definite function, resulting in a positive definite wake potential. In reality, the wake potential is negative at the rear of the ion column which is important for self-injection and accurate beam loading models. To account for this, we introduce a multi-sheath model in which the source term, S, of the plasma wake can be negative in regions outside the ion bubble. Using this model, we obtain a new expression for the wake potential and a modified differential equation for the bubble radius. Numerical results obtained from these equations are validated against particle-in-cell simulations for unloaded and loaded wakes. The new model provides accurate predictions of the shape and duration of trailing bunch current profiles that flatten plasma wakefields. It is also used to design a trailing bunch for a desired longitudinally varying loaded wakefield. We present beam loading results for laser wakefields and discuss how the model can be improved for laser drivers in future work. Finally, we discuss differences between the predictions of the multi- and single-sheath models for beam loading.
Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of a set of partial differential equations (PDEs) using conventional techniques (e.g., finite element, finite volume, finite difference methods) where the discretization may contain a very large number of degrees of freedom. As a result of this more compact representation, the resulting projection-based reduced order models (ROMs) can achieve considerable computational speedups, which are especially useful in real-time or multi-query analyses. One known deficiency of projection-based ROMs is that they can suffer from a lack of robustness, stability and accuracy, especially in the predictive regime, which ultimately limits their useful application. Another research gap that has prevented the widespread adoption of ROMs within the modeling and simulation community is the lack of theoretical and algorithmic foundations necessary for the “plug-and-play” integration of these models into existing multi-scale and multi-physics frameworks. This paper describes a new methodology that has the potential to address both of the aforementioned deficiencies by coupling projection-based ROMs with each other as well as with conventional FOMs by means of the Schwarz alternating method [41]. Leveraging recent work that adapted the Schwarz alternating method to enable consistent and concurrent multiscale coupling of finite element FOMs in solid mechanics [35, 36], we present a new extension of the Schwarz framework that enables FOM-ROM and ROM-ROM coupling, following a domain decomposition of the physical geometry on which a PDE is posed. In order to maintain efficiency and achieve computation speed-ups, we employ hyper-reduction via the Energy-Conserving Sampling and Weighting (ECSW) approach [13]. We evaluate the proposed coupling approach in the reproductive as well as in the predictive regime on a canonical test case that involves the dynamic propagation of a traveling wave in a nonlinear hyper-elastic material.