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At least 703 records · Page 39

On the steady-state solutions of a nonlinear photonic lattice model

In this paper, we consider the steady-state solutions of the following equation related with nonlinear photonic lattice model Δu=(Pu)/(1+|u|{sup 2}+|v|{sup 2}) +λu, Δv=(Qv)/(1+|u|{sup 2}+|v|{sup 2}) +λv, where u, v are real-value function defined on R/(τ{sub 1}Z) × R/(τ{sub 2}Z). The existence and non-existence of non-constant semi-trivial (with only one component zero) solutions are considered.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect

Here, we consider gapped fractional quantum Hall states on the lowest Landau level when the Coulomb energy is much smaller than the cyclotron energy. We introduce two spectral densities, ρ T (ω) and $\bar{p}$ T (ω), which are proportional to the probabilities of absorption of circularly polarized gravitons by the quantum Hall system. We prove three sum rules relating these spectral densities with the shift S, the q 4 coefficient of the static structure factor S 4 , and the high-frequency shear modulus of the ground state μ ∞ , which is precisely defined. We confirm an inequality, first suggested by Haldane, that S 4 is bounded from below by |S–1|/8. The Laughlin wavefunction saturates this bound, which we argue to imply that systems with ground state wavefunctions close to Laughlin’s absorb gravitons of predominantly one circular polarization. We consider a nonlinear model where the sum rules are saturated by a single magneto-roton mode. In this model, the magneto-roton arises from the mixing between oscillations of an internal metric and the hydrodynamic motion. Implications for experiments are briefly discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

High precision control and deep learning-based corn stand counting algorithms for agricultural robot

This paper presents high precision control and deep learning-based corn stand counting algorithms for a low-cost, ultra-compact 3D printed and autonomous field robot for agricultural operations. Currently, plant traits, such as emergence rate, biomass, vigor, and stand counting, are measured manually. This is highly labor-intensive and prone to errors. The robot, termed TerraSentia, is designed to automate the measurement of plant traits for efficient phenotyping as an alternative to manual measurements. In this paper, we formulate a Nonlinear Moving Horizon Estimator that identifies key terrain parameters using onboard robot sensors and a learning-based Nonlinear Model Predictive Control that ensures high precision path tracking in the presence of unknown wheel-terrain interaction. Moreover, we develop a machine vision algorithm designed to enable an ultra-compact ground robot to count corn stands by driving through the fields autonomously. The algorithm leverages a deep network to detect corn plants in images, and a visual tracking model to re-identify detected objects at different time steps. We collected data from 53 corn plots in various fields for corn plants around 14 days after emergence (stage V3 - V4). The robot predictions have agreed well with the ground truth with C robot =1.02×C human -0.86 and a correlation coefficient R=0.96. The mean relative error given by the algorithm is -3.78%, and the standard deviation is 6.76%. These results indicate a first and significant step towards autonomous robot-based real-time phenotyping using low-cost, ultra-compact ground robots for corn and potentially other crops.

97 MATHEMATICS AND COMPUTING↗

Convolutions on the sphere: commutation with differential operators

We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the convolution. These properties make the new filtering operation particularly useful to analyzing and modeling nonlinear dynamics in spherical systems, such as in geophysics, astrophysics, and in inertial confinement fusion applications. An essential tool we use is the theory of scalar, vector, and tensor spherical harmonics. We then show that our generalized filtering operation is equivalent to the (traditional) convolution of scalar fields of the Helmholtz decomposition of vectors and tensors.

42 ENGINEERING↗

Lectures on renormalization and asymptotic safety

A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross–Neveu model, the nonlinear σ model, the sine–Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

PetIGA: A framework for high-performance isogeometric analysis

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equations, which simplifies the development of large-scale scientific codes, provides a rich environment for prototyping, and separates parallelism from algorithm choice. We describe the implementation of PetIGA, and exemplify its use by solving a model nonlinear problem. To illustrate the robustness and flexibility of PetIGA, we solve some challenging nonlinear partial differential equations that include problems in both solid and fluid mechanics. Lastly, we show strong scaling results on up to 4096 cores, which confirm the suitability of PetIGA for large scale simulations.

97 MATHEMATICS AND COMPUTING↗

Automated identification of dominant physical processes

The identification of processes that locally and approximately dominate dynamical system behavior has enabled significant advances in understanding and modeling nonlinear differential dynamical systems. Conventional methods of dominant process identification involve piecemeal and ad hoc (non-rigorous, informal) scaling analyses to identify dominant balances of governing equation terms and to delineate the spatiotemporal boundaries (boundaries in space and/or time) of each dominant balance. For the first time, we present an objective global measure of the fit of dominant balances to observations, which is desirable for automation, and was previously undefined. Furthermore, we propose a formal definition of the dominant balance identification problem in the form of an optimization problem. Here, we show that the optimization can be performed by various machine learning algorithms, enabling the automatic identification of dominant balances. Our method is algorithm agnostic and it eliminates reliance upon expert knowledge to identify dominant balances which are not known beforehand.

42 ENGINEERING↗

Ambient temperature and added heat wave effects on hospitalizations in California from 1999 to 2009

Highlights: • We examined temperature and heat wave links to hospitalizations in California. • Heat waves set as minimum 2 days above climate zone- and month-specific threshold. • Temperature linked with many hospital visit types (e.g. diabetes, ischemic stroke). • Added heat wave associations observed (e.g. acute renal failure), but less often. • Associations sometimes differed by demographic and region. Investigators have examined how heat waves or incremental changes in temperature affect health outcomes, but few have examined both simultaneously. We utilized distributed lag nonlinear models (DLNM) to explore temperature associations and evaluate possible added heat wave effects on hospitalizations in 16 climate zones throughout California from May through October 1999–2009. We define heat waves as a period when daily mean temperatures were above the zone- and month-specific 95th percentile for at least two consecutive days. DLNMs were used to estimate climate zone-specific non-linear temperature and heat wave effects, which were then combined using random effects meta-analysis to produce an overall estimate for each. With higher temperatures, admissions for acute renal failure, appendicitis, dehydration, ischemic stroke, mental health, non-infectious enteritis, and primary diabetes were significantly increased, with added effects from heat waves observed for acute renal failure and dehydration. Higher temperatures also predicted statistically significant decreases in hypertension admissions, respiratory admissions, and respiratory diseases with secondary diagnoses of diabetes, though heat waves independently predicted an added increase in risk for both respiratory types. Our findings provide evidence that both heat wave and temperature exposures can exert effects independently.

54 ENVIRONMENTAL SCIENCES↗

Hippocampal Dosimetry Predicts Neurocognitive Function Impairment After Fractionated Stereotactic Radiotherapy for Benign or Low-Grade Adult Brain Tumors

Purpose: To prospectively evaluate the association between hippocampal dose and long-term neurocognitive function (NCF) impairment for benign or low-grade adult brain tumors treated with fractionated stereotactic radiotherapy (FSRT). Methods and Materials: Adult patients with benign or low-grade adult brain tumors were treated with FSRT per institutional practice. No attempt was made to spare the hippocampus. NCF testing was conducted at baseline and 18 months follow-up, on a prospective clinical trial. Regression-based standardized z scores were calculated by using similar healthy control individuals evaluated at the same test-retest interval. NCF impairment was defined as a z score {<=}-1.5. After delineation of the bilateral hippocampi according to the Radiation Therapy Oncology Group contouring atlas, dose-volume histograms were generated for the left and right hippocampi and for the composite pair. Biologically equivalent doses in 2-Gy fractions (EQD{sub 2}) assuming an {alpha}/{beta} ratio of 2 Gy were computed. Fisher's exact test and binary logistic regression were used for univariate and multivariate analyses, respectively. Dose-response data were fit to a nonlinear model. Results: Of 29 patients enrolled in this trial, 18 completed both baseline and 18-month NCF testing. An EQD{sub 2} to 40% of the bilateral hippocampi >7.3 Gy was associated with impairment in Wechsler Memory Scale-III Word List (WMS-WL) delayed recall (odds ratio [OR] 19.3; p = 0.043). The association between WMS-WL delayed recall and EQD{sub 2} to 100% of the bilateral hippocampi >0.0 Gy trended to significance (OR 14.8; p = 0.068). Conclusion: EQD{sub 2} to 40% of the bilateral hippocampi greater than 7.3 Gy is associated with long-term impairment in list-learning delayed recall after FSRT for benign or low-grade adult brain tumors. Given that modern intensity-modulated radiotherapy techniques can reduce the dose to the bilateral hippocampi below this dosimetric threshold, patients should be enrolled in ongoing prospective trials of hippocampal sparing during cranial irradiation to confirm these preliminary results.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Development of a nearshore oscillating surge wave energy converter with variable geometry

This paper presents an analysis of a novel wave energy converter concept that combines an oscillating surge wave energy converter (OSWEC) with control surfaces. The control surfaces allow for a variable device geometry that enables the hydrodynamic properties to be adapted with respect to structural loading, absorption range and power-take-off capability. The device geometry is adjusted on a sea state-to-sea state time scale and combined with wave-to-wave manipulation of the power take-off (PTO) to provide greater control over the capture efficiency, capacity factor, and design loads. This work begins with a sensitivity study of the hydrodynamic coefficients with respect to device width, support structure thickness, and geometry. A linear frequency domain analysis is used to evaluate device performance in terms of absorbed power, foundation loads, and PTO torque. Previous OSWEC studies included nonlinear hydrodynamics, in response a nonlinear model that includes a quadratic viscous damping torque that was linearized via the Lorentz linearization. Inclusion of the quadratic viscous torque led to construction of an optimization problem that incorporated motion and PTO constraints. Results from this study found that, when transitioning from moderate-to-large sea states the novel OSWEC was capable of reducing structural loads while providing a near constant power output.

16 TIDAL AND WAVE POWER↗

On the late-time growth of the two-dimensional Richtmyer–Meshkov instability in shock tube experiments [On the late-time growth of the 2D Richtmyer–Meshkov instability in shock tube experiments]

In the present study, shock tube experiments are used to study the very late-time development of the Richtmyer–Meshkov instability from a diffuse, nearly sinusoidal, initial perturbation into a fully turbulent flow. The interface is generated by two opposing gas flows and a perturbation is formed on the interface by transversely oscillating the shock tube to create a standing wave. The puncturing of a diaphragm generates a Mach $1. 2$ shock wave that then impacts a density gradient composed of air and SF 6 , causing the Richtmyer–Meshkov instability to develop in the 2.0 m long test section. The instability is visualized with planar Mie scattering in which smoke particles in the air are illuminated by a Nd:YLF laser sheet, and images are recorded using four high-speed video cameras operating at 6 kHz that allow the recording of the time history of the instability. In addition, particle image velocimetry (PIV) is implemented using a double-pulsed Nd:YAG laser with images recorded using a single CCD camera. Initial modal content, amplitude, and growth rates are reported from the Mie scattering experiments while vorticity and circulation measurements are made using PIV. Amplitude measurements show good early-time agreement but relatively poor late-time agreement with existing nonlinear models. The model of Goncharov agrees with growth rate measurements at intermediate times but fails at late experimental times. Measured background acceleration present in the experiment suggests that the late-time growth rate may be influenced by Rayleigh–Taylor instability induced by the interfacial acceleration. Numerical simulations conducted using the LLNL codes Ares and Miranda show that this acceleration may be caused by the growth of boundary layers, and must be accounted for to produce good agreement with models and simulations. Adding acceleration to the Richtmyer–Meshkov buoyancy–drag model produces improved agreement. It is found that the growth rate and amplitude trends are also modelled well by the Likhachev–Jacobs vortex model. Here, circulation measurements also show good agreement with the circulation value extracted by fitting the vortex model to the experimental data.

42 ENGINEERING↗

The effect of initial conditions on mixing transition of the Richtmyer–Meshkov instability

We investigate the late-time Richtmyer–Meshkov instability (RMI) growth of sinuous perturbations on an air/sulphur hexafluoride interface (Atwood number, A ~ 0.67 ) subjected to a Mach 1.2 planar shock wave at Los Alamos National Laboratory's vertical shock tube facility. Interface perturbations are established using a novel membraneless technique where cross-flowing air and SF 6 separated by an oscillating splitter plate create a perturbed density interface. The interface formed has multi-modal features and residual small perturbations, however, a dominant mode is still noticeable. The late-time perturbation growths scale with $ka_0$ initial conditions (where $k$ is the wavenumber and $a_0$ is the initial amplitude of the dominant mode) as measured at the pre-shock interface. Past nonlinear models based on potential-flow theory, heuristic/interpolation approaches, Padé approximants and numerical simulations are evaluated against present experimental results. Accounting for an explicit $ka_0$ dependence in Sadot et al.'s model, we propose an empirical rational function that captures the asymptotic behaviour of perturbation growth for a broad range of initial conditions ( 0.30 $≤ ka_0 ≤$ 0.86 ). The onset of mixing transition and its initial condition dependence are investigated with respect to the minimum state criterion ($Re =$ 1.6 $\times$ 10 5 ) for unsteady flows by Zhou. Earlier mixing transitions for higher ka0 initial conditions are noted from local and global Reynolds number estimates which are corroborated by the existence of an inertial sub-range and formation of mixing regions indicating the physical significance of the minimum state criterion in RMI flows. The transition is accompanied by the increasing teapot-like appearance of joint probability density functions of $p–q$ (invariants of the reduced velocity gradient tensor), establishing the technique as a useful tool for turbulence detection in two-dimensional diagnostics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Economic NMPC for a Reversible Solid Oxide Cell

Reversible solid oxide fuel cells (rSOCs) offer the flexibility to operate in tandem with the electric grid by switching between fuel cell and electrolysis modes based on real-time electricity prices. However, their complex, tightly coupled dynamic behavior poses significant challenges in determining optimal operating strategies. In this work, we present an economic nonlinear model predictive control (E-NMPC) framework to optimize the operation of rSOCs. The proposed E-NMPC is applied to a detailed rSOC flowsheet model that includes a utility scale rSOC module as well as balance-of-plant equipment necessary for thermal management. Our results demonstrate that in fuel cell mode, the E-NMPC strategy reduces hydrogen consumption compared to conventional set-point tracking NMPC, while maintaining the same level of electricity output. Also, in electrolysis mode, the E-NMPC yields a marginal improvement in hydrogen production. In addition, we explore the integration of a battery with the rSOC system to enhance flexibility in meeting electricity production and consumption targets.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Optimal Design of Sustainable Ammonia-Based Food–Energy–Water Systems with Nitrogen Management

As the basis for virtually any form of nitrogen fertilizers, ammonia plays a vital role in agriculture; in addition, there has been an increased interest in its use as a carbon-free energy carrier. However, ammonia is also associated with two major environmental concerns: CO 2 emissions from the conventional production process and nitrogen pollution from the excessive use of ammonia-based fertilizers. To mitigate these environmental impacts, we develop an optimization framework for the design of a sustainable ammonia-based agricultural system that synergistically integrates the production of ammonia from renewable resources and effective measures for nitrogen management. The proposed model captures the effect of intermittency by incorporating both design and detailed operational decisions. Here, by applying a multiscale time representation that reduces the problem size and a tailored surrogate model that accurately approximates model nonlinearity, we are able to achieve optimal solutions within reasonable computation times. A computational case study is conducted using real-world data from a local farm in Morris, Minnesota, and the results indicate the trade-off between cost and nitrogen loss. Importantly, we show that practicing effective nitrogen management can significantly reduce the nitrogen loss with only a small increase in net present cost.

10 SYNTHETIC FUELS↗

Self-focusing of circularly polarized laser pulse propagating through a magnetized non-Maxwellian plasma

Self-focusing of an intense circularly polarized laser pulse propagating through a magnetized non-Maxwellian plasma is investigated. Based on a relativistic two-fluid model, nonlinear equation describing dynamics of the slowly varying amplitude is obtained. The evolution of laser spot size is studied and effect of non-Maxwellian distribution of charge density on the spot size is considered. It is shown that the existence of super-thermal particles leads to the enhancement of the self-focusing quality of plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Safety assessment of historical masonry churches based on pre-assigned kinematic limit analysis, FE limit and pushover analyses

This study presents some results of a comprehensive numerical analysis on three masonry churches damaged by the recent Emilia-Romagna (Italy) seismic events occurred in May 2012. The numerical study comprises: (a) pushover analyses conducted with a commercial code, standard nonlinear material models and two different horizontal load distributions; (b) FE kinematic limit analyses performed using a non-commercial software based on a preliminary homogenization of the masonry materials and a subsequent limit analysis with triangular elements and interfaces; (c) kinematic limit analyses conducted in agreement with the Italian code and based on the a-priori assumption of preassigned failure mechanisms, where the masonry material is considered unable to withstand tensile stresses. All models are capable of giving information on the active failure mechanism and the base shear at failure, which, if properly made non-dimensional with the weight of the structure, gives also an indication of the horizontal peak ground acceleration causing the collapse of the church. The results obtained from all three models indicate that the collapse is usually due to the activation of partial mechanisms (apse, façade, lateral walls, etc.). Moreover the horizontal peak ground acceleration associated to the collapse is largely lower than that required in that seismic zone by the Italian code for ordinary buildings. These outcomes highlight that structural upgrading interventions would be extremely beneficial for the considerable reduction of the seismic vulnerability of such kind of historical structures.

42 ENGINEERING↗

The benefits of CMB delensing

The effects of gravitational lensing of the cosmic microwave background (CMB) have been measured at high significance with existing data and will be measured even more precisely in future surveys. Reversing the effects of lensing on the observed CMB temperature and polarization maps provides a variety of benefits. Delensed CMB spectra have sharper acoustic peaks and more prominent damping tails, allowing for improved inferences of cosmological parameters that impact those features. Delensing reduces B-mode power, aiding the search for primordial gravitational waves and allowing for lower variance reconstruction of lensing and other sources of secondary CMB anisotropies. Lensing-induced power spectrum covariances are reduced by delensing, simplifying analyses and improving constraints on primordial non-Gaussianities. Biases that result from incorrectly modeling nonlinear and baryonic feedback effects on the lensing power spectrum are mitigated by delensing. All of these benefits are possible without any changes to experimental or survey design. Here, we develop a self-consistent, iterative, all-orders treatment of CMB delensing on the curved sky and demonstrate the impact that delensing will have with future surveys.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗