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At least 217 records · Page 12

Stability analysis of nonlinear systems by multiple time scaling

The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.

Morino, L.↗

Component-wise reduced order model lattice-type structure design

Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution of a mathematical model feasible. In this paper, we propose a topology optimization (TO) formulation that approximates the governing physics using component-wise reduced order modeling as introduced in Huynh et al. (2013); Eftang and Patera (2013), which can reduce solution time by multiple orders of magnitude over a full-order finite element model while providing a relative error in the solution of 1%. In addition, the offline training data set from such component-wise models is reusable, allowing its application to many design problems for only the cost of a single offline training phase, and the component-wise method is nearly embarrassingly parallel. We also show how the parameterization chosen in our optimization allows a simplification of the component-wise reduced order model (CWROM) not noted in previous literature, for further speedup of the optimization process. Furthermore, the sensitivity of the compliance with respect to the particular parameterization is derived solely at the component level. In numerical examples, we demonstrate a 1000x speedup over a full-order FEM model with relative error of 1% and show minimum compliance designs for two different cantilever beam examples, one smaller and one larger. Finally, error bounds for the displacement field, compliance, and compliance sensitivity of the CWROM are derived.

97 MATHEMATICS AND COMPUTING↗

Field Validation of a Grid-Interactive Efficient Building Software Solution

The U.S. General Services Administration's (GSA's) Green Proving Ground (GPG) program, in partnership with the National Laboratory of the Rockies (NLR), completed a field study of a Grid-Interactive Efficient Buildings (GEB) software solution. The study focused on a single testbed facility to test the GEB functionality of the software solution, along with other features. The testbed facility - a courthouse - is a common building type in GSA's vast building portfolio, offering potentially impactful findings on a scalable level. The study evaluated Prescriptive Data's technology, Nantum OS, a connected building operating system ("GEB Solution") which aggregates multiple sources of previously siloed building data and combines that data with external sources, such as weather information or utility signals, into a single integrated platform. A GEB Solution is a type of Energy Management Information System (EMIS). EMIS is defined as a system of devices, data services, and software applications that communicates with any building system or third-party data source to aggregate and transform data into new capabilities to aid in the optimization of energy use at the building, campus, or agency level. This specific GEB Solution is an EMIS with ASO, automated system optimization, offering supervisory control of certain aspects of the Building Automation System (BAS). Multiple features were evaluated including, but not limited to, Continuous Demand Management to avoid setting new monthly kilowatt (kW) peaks, energy efficiency for reduction of kilowatt hours (kWh) and natural gas consumption, and automated demand response (ADR) for purposes of lowering demand during a utility called Demand Response (DR) event. The testbed facility was the Foley Federal Building and US Courthouse ("Foley Federal Building") located in Las Vegas, NV. This is a 209,496 sq. ft. building constructed in the 1960s with major renovations in 2004. The facility was a good candidate due to the large prevalence of office and courthouse spaces in the GSA portfolio of buildings. It also has many features which allow integration into and control of the building and a strong facilities team to assist with the study. Quantitative and qualitative performance objectives were developed using GSA's GPG GEB project template along with input from the vendor and building facility staff; these are outlined in Table 1. The quantitative performance objectives focused on continuous demand management, energy efficiency, and automated demand response. The qualitative performance objectives focused on the ease of installation and commissioning as well as the operability of the GEB solution. Other performance metrics that are reported on include carbon reduction, cost effectiveness, and occupant acceptance.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Structure of the magnetopause inferred from one-dimensional hybrid simulations

The structure of the magnetopause is investigated by studying the interaction between two plasmas with solar wind and magnetospheric properties. Both Hall-MHD and hybrid (particle ions and fluid electrons) simulations are performed to compare and contrast the nature of the solutions in the fluid and the kinetic limits. It is shown that, in accordance with previous studies, the fluid solutions consist of multiple discontinuities and waves such as slow shocks and waves, as well as contact and rotational discontinuities. In contrast, the kinetic solutions consist of fewer discontinuities and include non-MHD boundaries. The difference between the two types of solutions are attributed to the absence of contact surfaces in collisionless plasmas and the possible Landau damping of slow waves. The kinetic solutions are found to be in a much better agreement with magnetopause observations, which have shown little evidence for the presence of slow shocks or contact discontinuities. The results of kinetic calculations suggest that the presence of a small but finite normal component of the magnetic field allows for the mixing of magnetosheath and magnetospheric plasmas and may, in part, be responsible for the formation of the boundary layer even during the periods of northward interplanetary magnetic field. These results also show that the necessary changes in the fields and the plasma parameters across the magnetopause do not occur simultaneously (i.e., in the same spatial location). As such, the magnetopause cannot be viewed as a single boundary but instead is a region which includes both abrupt and gradual changes in the fields and plasma parameters.

Omidi, N.↗

Potential of water quality wetlands to mitigate habitat losses from agricultural drainage modernization

Given widespread biodiversity declines, a growing global human population, and demands to improve water quality, there is an immediate need to explore land management solutions that support multiple ecosystem services. Agricultural water quality wetlands designed to provide both water quality benefits and wetland and grassland habitat are an emerging restoration solution that may reverse habitat declines in intensive agricultural areas. Installation of water quality wetlands in the Upper Midwest, USA, when considered alongside the repair and modification of aging agricultural tile drainage infrastructure, is a likely scenario that may mitigate nutrient pollution exported from agricultural systems and improve crop yields. The capacity of water quality wetlands to provide habitat within the wetland pool and the surrounding grassland is not well-studied, particularly with respect to potential habitat changes resulting from drainage infrastructure upgrades. For the current study, we produced spatially explicit models of 37 catchments distributed throughout an important region for agriculture and biodiversity, the Des Moines Lobe of Iowa. Four scenarios were considered - with and without improved drainage and with and without water quality wetlands - to estimate the net potential habitat implications of these scenarios for amphibians, grassland birds, and wild bees. Model results indicate that drainage modification alone will likely result in moderate direct losses of suitable amphibian habitat and large declines in overall habitat quality. However, inclusion of water quality wetlands at the catchment scale may mitigate these amphibian habitat losses while also increasing grassland bird and pollinator habitat. In conclusion, the impacts of water quality wetlands and drainage modernization on waterfowl in the region require additional study.

54 ENVIRONMENTAL SCIENCES↗

Field testing and validation of a low-cost MPC for demand flexibility for grid-interactive K-12 schools

K-12 school buildings account for the highest energy consumption within the public sector. Implementing advanced HVAC controls in grid-interactive K-12 schools could bring substantial economic advantages and grid flexibility. Our previous study demonstrated that a low-cost model predictive control (MPC) solution, which coordinates multiple packaged units, can enable demand flexibility without major hardware upgrades. However, a significant gap remains between academic pilots and market-ready scalable solutions. This paper extends the previous single-site pilot to a multi-site demonstration involving three school campuses (95 total units) through a commercial technology transfer process. Addressing the challenge of verifying performance with sparse field data, we present a new statistical approach using Bayesian methods to estimate the MPC’s effect on peak demand. Unlike traditional methods, this approach robustly quantifies uncertainty in non-normal, limited datasets. The results confirm the solution’s replicability, achieving a 21.6–38.9% reduction in HVAC peak demand (10.8–22.1% at the site-level) with > 98% probability across diverse locations. Finally, we document critical barriers to scaling software-as-a-service (SaaS) solutions–such as API instability and diverse legacy systems–and offer practical strategies to accelerate the commercial adoption of grid-interactive efficient buildings.

Ham, Sang Woo↗

Sub-pixel Spatial Resolution Micro-roughness Measurements with Interlaced Stitching

In this paper we describe a method to increase the spatial resolution of surface micro-roughness measurements. As the surface specifications for precision optics become more demanding, the metrology instruments must cover a broad spatial frequency range. Generally, multiple instruments are used to cover the full range of the specifications. For example, a Fizeau interferometer would be used to test low spatial frequency surface errors, a white light interferometer would be used for mid spatial frequency errors, and an AFM would be used for high spatial frequency errors. For some precision optics, three instruments would be necessary. However, in many applications, an increase in the spatial resolution of a metrology instrument could negate the need for multiple instruments. A solution to increase the spatial resolution of micro-roughness measurements obtained using white light interferometry with "interlaced stitching" will be presented. In "interlaced stitching", multiple interferometric measurements are made as the optic under test (or the CCD array) is laterally shifted at sub-pixel increments. The measurements are then combined to construct a measurement with higher spatial resolution. Initial results obtained while implementing a similar process used to increase the spatial resolution of measurements made with a commercially available Fizeau interferometer will be presented.

Mooney, James T.↗

Provably conservative approximations to complex reliability models

Complex models can be the bases for derivation of provably conservative and optimistic reliability models that incorporate a reduced state space and fewer transitions; they accordingly possess solutions that are more cost-effective than those of the original complex models. Design space can thereby be extensively explored without incurring the expense of multiple complex model solutions. A conservative-optimistic pair of derived models produces a band that includes the solution to the complex model. Sensitivity analysis can be performed on this pair of models to determine those parameters of the original model that are most sensitive to change and therefore require further expense in obtaining tighter specifications.

Smotherman, M.↗

Improving Navigation Analysis with OD-D: The Visually Interactive Orbit Determination Dashboard

Orbit determination requires iterative analysis with the goal of converging on as accurate of a solution as possible, a process that can be time and labor intensive. To increase the efficiency of this analysis, we provide a diagnostic tool capable of comprehensively displaying multiple orbit determination solutions by leveraging data visualization techniques. This work details the design and visualization decisions made in the creation of the Orbit Determination Dashboard, a tool aimed at giving users an interactive workspace for understanding how changes to input parameters of orbit determination models affect their solutions.

Jah, Moriba↗

An Analytic Benchmark for Neutron Boltzmann Transport with Downscattering—Part I: Flux and Eigenvalue Solutions

Computing in the energy dimension is one of the greatest challenges confronting present-day deterministic neutron transport solvers. Accurately resolving the neutron flux as neutrons downscatter across resonances in the nuclear cross sections currently requires considerable computing power and suffers from approximation errors. Flux uncertainty resulting from the uncertainty of the resonance structure is the single-largest cause of reactivity uncertainty. Any additional reference solution for the critical neutron downscattering problem with resonance phenomena would be a boon to verification and validation of neutronics codes. This paper establishes a benchmark to verify the accuracy of neutron transport criticality solvers along the energy dimension. For the first time, the analytic solution of the flux amplitude is derived in the particular case of an infinite homogeneous medium with isotropic scattering in the center of mass and an arbitrary number of no-threshold, neutral particle reaction resonances (e.g., radiative capture, fission, and resonance scattering). Furthermore, original analytic expressions are established to quantify the discrepancy between the ψ k (E) and ψ α (E) flux amplitudes, respective solutions of the multiplication factor k, or the exponential time-evolution frequency α eigenproblems. The physical study of these relations led to analysis of their first-order relative difference near the criticality condition α=0. Finally, numerical solutions are provided to a benchmark problem constituted of the first resonance of 239 Pu, the 6.67-eV resonance of 238 U, and a scattering isotope with a flat cross section, allowing for the computational verification of the energy resolution of current neutron transport criticality codes. Through these novel results, this analytic benchmark can serve as a reference to verify the energy resolution and sensitivity analysis of neutron transport criticality calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Non-linear analysis of vibrations of irregular plates

A numerical perturbation method is used to investigate the forced vibrations of irregular plates. Nonlinear terms associated with the midplane stretching are retained in the analysis. The numerical part of the method involves the use of linear, finite element techniques to determine the free oscillation mode shapes and frequencies and to obtain the linear midplane stress resultants caused by the midplane stretching. Representing the solution as an expansion in terms of these linear mode shapes, these modes and the resultants are used to determine the equations governing the time-dependent coefficients of this expansion. These equations are solved by using the method of multiple scales. Specific solutions are given for the main-resonant vibrations of an elliptical plate in the presence of internal resonances. The results indicate that modes other than the driven mode can be drawn into the steady state response. Though the excitation is composed of a single harmonic, the response may not be periodic. Moreover, the particular types of responses that can occur are highly dependent on the mode being excited and are sensitive to small geometrical changes.

Lobitz, D. W.↗

Similarity solutions of jet flows using a multiple-scale turbulence model

An accurate finite difference scheme is used to study the performance of a newly developed multiple-scale turbulence model in the similarity region of plane/radial/round jet flows. Under the assumption that molecular viscosity can be neglected, the governing equations contain a hidden eigenvalue which corresponds to the sharp boundary of the flowfield. It is found that this eigenvalue is the locus of the free boundary separating the turbulent shear flow and the irrotational ambient fluid.

Chen, C. P.↗

Multimodal Bayesian registration of noisy functions using Hamiltonian Monte Carlo

Functional data registration is a necessary processing step for many applications. The observed data can be inherently noisy, often due to measurement error or natural process uncertainty; which most functional alignment methods cannot handle. A pair of functions can also have multiple optimal alignment solutions, which is not addressed in current literature. In this paper, a flexible Bayesian approach to functional alignment is presented, which appropriately accounts for noise in the data without any pre-smoothing required. Additionally, by running parallel MCMC chains, the method can account for multiple optimal alignments via the multi-modal posterior distribution of the warping functions. To most efficiently sample the warping functions, the approach relies on a modification of the standard Hamiltonian Monte Carlo to be well-defined on the infinite-dimensional Hilbert space. In this work, this flexible Bayesian alignment method is applied to both simulated data and real data sets to show its efficiency in handling noisy functions and successfully accounting for multiple optimal alignments in the posterior; characterizing the uncertainty surrounding the warping functions.

97 MATHEMATICS AND COMPUTING↗

Violation of the Vogt-Russell theorem for homogeneous nondegenerate stars

A systematic study is made of the number and types of solutions of the equilibrium equations of stellar structure, in the case of homogeneous stars of Population I over the mass range 2-1000 solar masses, with four different opacity representations. A variant of the usual fitting method permits the simultaneous investigation of convergence and tendency toward multiplicity of the solutions. Quadratic interpolation and extrapolation of Carson's new opacity tables produces a very large opacity at low temperatures that greatly affects the loose outer layers of massive stars, while leaving the cores practically unaffected. As a result, over a small mass range, well above 100 solar masses, triple solutions exist, always near an effective temperature of log Te = 4.73. A simple classification of the known exceptions to the Vogt-Russell theorem on the uniqueness of stellar structure is given.

Stothers, R.↗

General-Purpose Time-Accurate Adaptive-Grid Method

Adaptive-grid method provides for generation of time-accurate grids used to solve wide variety of problems numerically. Intended use in computation of compressible flows. Part of solution method including algebraic grid-movement scheme; algorithm solving, by use of explicit numerical-integration scheme, Euler equations of unsteady flow; and temporal coupling routine utilizing grid-prediction/correction method to link dynamic grid with Euler-equation-solving algorithm. Improves ability to adapt grid to multiple features of solution and involves use of coarse grid in prediction stage of temporal coupling reducing central-processing-unit cost of obtaining new grid.

Bockelie, Michael J.↗

Fully Nonlinear Modeling and Analysis of Precision Membranes

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

Pai, P. Frank↗

Cluster Variation Method Analysis of Correlations and Entropy in BCC Solid Solutions

Solid solutions occur when multiple chemical species share sites of a common crystal lattice. Although the single site occupation is random, chemical interaction preferences bias the occupation probabilities of neighboring sites, and this bias reduced the entropy of mixing below its ideal value. Sufficiently strong bias leads to symmetry-breaking phase transitions. Here, we apply the cluster variation method to explore solid solutions on body centered cubic lattices in the context of two specific compounds that exhibit opposite ordering trends. Employing density functional theory to model the energetics, we show that CuZn exhibits an order-disorder transition to the CsCl prototype structure, while AlLi instead takes the NaTl prototype structure, and we evaluate their temperature-dependent order parameters, correlations and entropies.

36 MATERIALS SCIENCE↗

Novel Electric Nucleation Technique for Growing Large Single Crystal in Space

We present, herein, an electrical model for growing crystals without a seed which might not be free of defects and thereby still hinder the growth of a perfect crystal in space. The system is designed to confine nucleation to a single site automatically in an under saturated solution to avoid multiple nucleation. The technique is based on the effect of electrostriction, which is the tendency of a material to become more compressed in the presence of an electric field. The system is designed to create an electrical potential well between two hyperboloid electrodes with applied voltage at low frequency. The induced potential well between the electrodes oscillates at low frequency and attracts the solute and condenses it into the region of maximum field intensity. The alternating voltage prevents molecules with intrinsic charge from being attracted to the electrodes. The continuous presence of the electric field during the duration of the experiment, provides a continuous migration of the molecules toward the trapping site. This will eliminate the creation of a depletion region around the nucleation center and will enhance the crystal growth rate. Aside from the above mentioned advantages, the system is compact, safe to operate, and inexpensive to build.

Abdeldayem, Hossin↗