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Aerodynamic mathematical modeling - basic concepts

This lecture is a review of the basic concepts involved In the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers. The review leads from Bryan's original formulation through the concepts of linear aerodynamic indicial functions and superposition to the extension of these concepts 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 torn, accommodating the discontinuous and double-valued behavior characteristic of hysteresis in the steady-state aerodynamic response

Murray Tobak↗

The Biological Effectiveness of Different Radiation Qualities for the Induction of Chromosome Damage in Human Lymphocytes

Chromosome aberrations were measured in human peripheral blood lymphocytes after in vitro exposure to 28Si- ions with energies ranging from 90 to 600 MeV/u, or to 56Fe-ions with energies ranging from 200 to 5,000 MeV/u. The LET of the various Fe beams in this study ranged from 145 to 440 keV/micron and the LET of the Si ions ranged from 48 to 158 keV/ m. Doses delivered were in the 10- to 200-cGy range. Dose-response curves for chromosome exchanges in cells at first division after exposure, measured using fluorescence in situ hybridization (FISH) with whole-chromosome probes, were fitted with linear or linear-quadratic functions. The relative biological effectiveness (RBE) was estimated from the initial slope of the dose-response curve for chromosome damage with respect to -rays. The estimates of RBE(sub max) values for total chromosome exchanges ranged from 4.4+/-0.4 to 31.5+/-2.6 for Fe ions, and 11.8+/-1.0 to 42.2+/-3.3 for Si ions. The highest RBE(sub max) value for Fe ions was obtained with the 600-Mev/u beam, and the highest RBE(sub max) value for Si ions was obtained with the 170 MeV/u beam. For both ions the RBEmax values increased with LET, reaching a maximum at about 180 keV/micron for Fe and about 100 keV/ m for Si, and decreasing with further increase in LET. Additional studies for low doses 28Si-ions down to 0.02 Gy will be discussed.

Hada, M.↗

The Biological Effectiveness of Different Radiation Qualities for the Induction of Chromosome Damage in Human Lymphocytes

Chromosome aberrations were measured in human peripheral blood lymphocytes after in vitro exposure to Si-28-ions with energies ranging from 90 to 600 MeV/u, Ti-48-ions with energies ranging from 240 to 1000 MeV/u, or to Fe-56-ions with energies ranging from 200 to 5,000 MeV/u. The LET of the various Si beams in this study ranged from 48 to 158 keV/ m, the LET of the Ti ions ranged from 107 to 240 keV/micron, and the LET of the Fe-ions ranged from 145 to 440 keV/ m. Doses delivered were in the 10- to 200-cGy range. Dose-response curves for chromosome exchanges in cells at first division after exposure, measured using fluorescence in situ hybridization (FISH) with whole-chromosome probes, were fitted with linear or linear-quadratic functions. The relative biological effectiveness (RBE) was estimated from the initial slope of the dose-response curve for chromosome damage with respect to gamma-rays. The estimates of RBEmax values for total chromosome exchanges ranged from 4.4+/-0.4 to 31.5+/-2.6 for Fe ions, 21.4+/-1.7 to 28.3+/-2.4 for Ti ions, and 11.8+/-1.0 to 42.2+/-3.3 for Si ions. The highest RBEmax value for Fe ions was obtained with the 600 MeV/u beam, the highest RBEmax value for Ti ions was obtained 1000 MeV/u beam, and the highest RBEmax value for Si ions was obtained with the 170 MeV/u beam. For Si and Fe ions the RBEmax values increased with LET, reaching a maximum at about 180 keV/micron for Fe and about 100 keV/micron for Si, and decreasing with further increase in LET. Additional studies for low doses Si-28-ions down to 0.02 Gy will be discussed.

Hada, M.↗

Control of the NASA Langley 16-Foot Transonic Tunnel with the Self-Organizing Map

A predictive, multiple model control strategy is developed based on an ensemble of local linear models of the nonlinear system dynamics for a transonic wind tunnel. The local linear models are estimated directly from the weights of a self-organizing map (SOM). Multiple self-organizing maps collectively model the global response of the wind tunnel to a finite set of representative prototype controls. These prototype controls partition the control space and incorporate experiential knowledge gained from decades of operation. Each SOM models the combination of the tunnel with one of the representative controls, over the entire range of operation. The SOM based linear models are used to predict the tunnel response to a larger family of control sequences which are clustered on the representative prototypes. The control sequence which corresponds to the prediction that best satisfies the requirements on the system output is applied as the external driving signal.

Mark A. Motter↗

Occupational Experience Effects on Physiological and Perceptual Responses of Common Soldiering Tasks

Abstract Cohen BS, Redmond JE, Haven CC, Foulis SA, Canino MC, Frykman PN, Sharp MA. Occupational Experience Effects on Physiological and Perceptual Responses of Common Soldiering Tasks. J Strength Cond Res 37(4): 894–901, 2023—This study measured the impact of occupational experience (i.e., time spent deployed, in military service, and in job and task performance frequency in training, deployment, and study practice) on the physiological (heart rate [HR] and oxygen consumption [VO 2 ]) and perceptual (rate of perceived exertion [RPE]) responses to performance of critical physically demanding tasks (CPDTs). Five CPDTs (road march, build a fighting position, move under fire, evacuate a casualty, and drag a casualty to safety), common to all soldiers, were performed by 237 active duty soldiers. Linear regression models examined the association between measures of experience and physiological and perceptual performance responses to task demands. The level of significance was adjusted for multiple comparisons and set at ρ ≤ 0.0125 for this study. Significant and notable effect sizes included the impact of time spent deployed on the physiological measures of the road march (PostHR F = 24.84, p < 0.0001, β=-9.65), sandbag fill (PostHR F = 8.26, p = 0.005, β = −2.83), and sandbag carry (MeanHR F = 7.51, p = 0.007, β = −1.12; PostHR F = 7.35, p = 0.007, β = −0.87). For the road march task, there was a nearly 10 bpm decrease in postperformance HR for every year spent deployed. Road march, sandbag fill, and sandbag carry tasks PostHRs were also notably negatively associated with the experience measures of time in their MOS (job and time in military service but not for other physiological and perceptual responses, including VO 2 and RPE. Frequency of task performance in training, deployment, and study practice was not meaningfully associated with experience. The results suggest that increasing task familiarization through on-the-job occupational operational experience may result in greater proficiency and reduced physiological effort.

Sport Sciences↗

Time-domain technique for optimal design of digital-filter equalizers.

A technique is presented for the design of frequency-sampling and transversal digital filters from specified unit-impulse responses. The multiplier coefficients for the digital filter are specified by the use of a linear-programming algorithm. Examples include the design of digital filters to generate intersymbol-free pulses for data transmission over ideal bandlimited channels and to equalize data transmission channels that have known unit-impulse responses.

Burlage, D. W.↗

Electromechanical simulation and testing of actively controlled rotordynamic systems with piezoelectric actuators

A method is presented for simulating the coupled 'electromechanical' system to predict rotordynamic stability and unbalance response along with control system stability. The piezoelectric actuators and their amplifiers are represented as equivalent linear electrical circuits. The electromechanical system modeling approach is utilized to correlate test results from a double overhung rotor rig. The test results also show the effectiveness of the control system for suppressing the unbalance response of two modes using active stiffness and active damping.

Lin, Reng Rong↗

Nonlinear Analysis of Airfoil High-Intensity Gust Response Using a High-Order Prefactored Compact Code

The nonlinear response of symmetric and loaded airfoils to an impinging vortical gust is investigated in the parametric space of gust dimension, intensity, and frequency. The study, which was designed to investigate the validity limits for a linear analysis, is implemented by applying a nonlinear high-order prefactored compact code and comparing results with linear solutions from the GUST3D frequency-domain solver. Both the unsteady aerodynamic and acoustic gust responses are examined.

Crivellini, A.↗

Generation of linear dynamic models from a digital nonlinear simulation

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.

Daniele, C. J.↗

Gradient-Based Optimization of the Common Research Model Wing Subject to CFD-Based Gust and Flutter Constraints

The linearized frequency-domain method was recently implemented in the stabilized finite element solver in NASA’s FUN3D code. Previous work by the authors used this method for enforcing flutter constraints during gradient-based optimizations. More recently, the solver was expanded to account for continuous (also known as stochastic) gust responses. This paper expands on recent Common Research Model wing optimization work, which demonstrated gradient-based optimization with flutter and stochastic gust constraints, among others. While that work utilized FUN3D for static aeroelastic solutions but relied on doublet lattice aerodynamics for gust and flutter responses, the present work replaces these unsteady aerodynamic analyses with those of FUN3D’s linearized frequency-domain solver. With analytic derivatives available, gradient-based optimization is performed through the use of the OpenMDAO/MPhys libraries with over 700 shape, structural, and aerodynamic design variables and over 10 nonlinear constraints. Comparisons of analysis results and optimized designs are made between doublet lattice and linearized frequency-domain solutions.

aeroelasticity↗

Broadband Photoconductive Sampling in Gallium Phosphide

Abstract Direct measurements of the electric field of light enable new observations of light–matter interactions. In the near‐infrared and visible spectral ranges, this typically relies on techniques that exploit nonlinearities in gases or solids, which limits their sensitivity. Here, a method for the detection of broadband near‐infrared fields spanning more than one octave from 110 to 220 THz based on linear absorption in a semiconductor is demonstrated. This technique, which avoids complex vacuum setups and works under ambient conditions, employs linear photoconductive sampling (LPS) in gallium phosphide. Simulations reveal that the response function of LPS is concerned with the intensity envelope of the gate field, in contrast to electro‐optic sampling, relaxing the stringent temporal requirements on the gate pulse.

36 MATERIALS SCIENCE↗

FLASH Dose Rate Helium Ion Beams: First In Vitro Investigations

To establish and investigate the effects of dose, linear energy transfer (LET), and O{sub 2} concentration on biologic response to ultrahigh dose rate (uHDR; FLASH) helium ion beams compared with standard dose rate (SDR) irradiation.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

On the Breakdown of ENSO's Relationship With Thermocline Depth in the Central-Equatorial Pacific

Recent classification of El Nino-Southern Oscillation (ENSO) into two types, Eastern (EP) and Central (CP) events, has highlighted the importance of the central Pacific. We show here that the local correlation between ENSO subsurface temperatures (T sub ) in the upper 100-m and thermocline depth anomalies breaks down in the central equatorial Pacific, whereas T sub remains well correlated with sea surface height anomalies. This observed difference in the central equatorial Pacific is simulated by almost all climate models. It arises from a vertically slanted Tsub anomaly structure that is unique to the central equatorial Pacific. We show that this feature is an adiabatic response to wind-driving that is even present in a linear dynamic model, as long as the model has enough baroclinic modes to adequately represent the observed vertical complexity. Our findings have implications for better understanding the different importance of thermocline feedback in CP and EP events.

58 GEOSCIENCES↗

Customizable wave tailoring nonlinear materials enabled by bilevel inverse design

Abstract Passive wave transformation via nonlinearity is ubiquitous in settings from acoustics to optics and electromagnetics. It is well known that different nonlinearities yield different effects on propagating signals, which raises the question of “what precise nonlinearity is the best for a given wave tailoring application?” In this work, considering a one-dimensional spring-mass chain connected by polynomial springs (a variant of the Fermi-Pasta-Ulam-Tsingou system), we introduce a bilevel inverse design method which couples the shape optimization of structures for tailored constitutive responses with reduced-order nonlinear dynamical inverse design. We apply it to two qualitatively distinct problems—minimization of peak transmitted kinetic energy from impact, and pulse shape transformation—demonstrating our method’s breadth of applicability. For the impact problem, we obtain two fundamental insights. First, small differences in nonlinearity can drastically change the dynamic response of the system, from severely under- to outperforming a comparative linear system. Second, the oft-used strategy of impact mitigation via “energy locking” bistability can be significantly outperformed by our optimal nonlinearity. We validate this case with impact experiments and find excellent agreement. This study establishes a framework for broader passive nonlinear mechanical wave tailoring material design, with applications to computing, signal processing, shock mitigation, and autonomous materials.

Science & Technology - Other Topics↗

Quantum interferometry and pathway selectivity in the nonlinear response of photosynthetic excitons

We propose a time–frequency resolved spectroscopic technique which employs nonlinear interferometers to study exciton–exciton scattering in molecular aggregates. A higher degree of control over the contributing Liouville pathways is obtained as compared to classical light. We show how the nonlinear response can be isolated from the orders-of-magnitude stronger linear background by either phase matching or polarization filtering. Both arise due to averaging the signal over a large number of noninteracting, randomly oriented molecules. We apply our technique to the Frenkel exciton model which excludes charge separation for the photosystem II reaction center. We show how the sum of the entangled photon frequencies can be used to select two-exciton resonances, while their delay times reveal the single-exciton levels involved in the optical process.

Science & Technology - Other Topics↗

An energy-dependent electro-thermal response model of CUORE cryogenic calorimeter

The Cryogenic Underground Observatory for Rare Events (CUORE) is the most sensitive experiment searching for neutrinoless double-beta decay (0νββ) in 130 Te. CUORE uses a cryogenic array of 988 TeO 2 calorimeters operated at ~10 mK with a total mass of 741 kg. To further increase the sensitivity, the detector response must be well understood. Here, we present a non-linear thermal model for the CUORE experiment on a detector-by-detector basis. We have examined both equilibrium and dynamic electro-thermal models of detectors by numerically fitting non-linear differential equations to the detector data of a subset of CUORE channels which are well characterized and representative of all channels. Further, we demonstrate that the hot-electron effect and electric-field dependence of resistance in NTD-Ge thermistors alone are inadequate to describe our detectors' energy-dependent pulse shapes. We introduce an empirical second-order correction factor in the exponential temperature dependence of the thermistor, which produces excellent agreement with energy-dependent pulse shape data up to 6 MeV. We also present a noise analysis using the fitted thermal parameters and show that the intrinsic thermal noise is negligible compared to the observed noise for our detectors.

47 OTHER INSTRUMENTATION↗

Key environmental and production factors for understanding variation in switchgrass chemical attributes

Abstract Switchgrass ( Panicum virgatum L.) is a promising feedstock for bioenergy and bioproducts; however, its inherent variability in chemical attributes creates challenges for uniform conversion efficiencies and product quality. It is necessary to understand the range of variation and factors (i.e., field management, environmental) influencing chemical attributes for process improvement and risk assessment. The objectives of this study were to (1) examine the impact of nitrogen fertilizer application rate, year, and location on switchgrass chemical attributes, (2) examine the relationships among chemical attributes, weather and soil data, and (3) develop models to predict chemical attributes using environmental factors. Switchgrass samples from a field study spanning four locations including upland cultivars, one location including a lowland cultivar, and between three and six harvest years were assessed for glucan, xylan, lignin, volatiles, carbon, nitrogen, and ash concentrations. Using variance estimation, location/cultivar, nitrogen application rate, and year explained 65%–96% of the variation for switchgrass chemical attributes. Location/cultivar × year interaction was a significant factor for all chemical attributes indicating environmental‐based influences. Nitrogen rate was less influential. Production variables and environmental conditions occurring during the switchgrass field trials were used to successfully predict chemical attributes using linear regression models. Upland switchgrass results highlight the complexity in plant responses to growing conditions because all production and environmental variables had strong relationships with one or more chemical attributes. Lowland switchgrass was limited to observations of year‐to‐year environmental variability and nitrogen application rate. All explanatory variable categories were important for lowland switchgrass models but stand age and precipitation relationships were particularly strong. The relationships found in this study can be used to understand spatial and temporal variation in switchgrass chemical attributes. The ability to predict chemical attributes critical for conversion processes in a geospatial/temporal manner would provide state‐of‐the‐art knowledge for risk assessment in the bioenergy and bioproducts industry.

09 BIOMASS FUELS↗

On the bulk compaction of brittle granular materials, Part II: Representing interparticle comminution by K COMP

An applied and empirical compaction fracture resistance parameter, K COMP , was developed to represent the compression-induced interparticle-comminution response of granular brittle materials (e.g., ceramic or glass particles). The development of K COMP is an outcome from Part I of this three-paper series. The K COMP represents a continuum response of compaction fracture resistance and was adapted from established Griffith linear elastic fracture mechanics theory. From that, the K COMP relates macroscopically applied compressive stress to a corresponding inverse-square-root representative particle size, where the latter is estimated from an entire particle size distribution or specific surface area measurement. In conclusion, the K COMP value was not constant over a wide range of stresses for all examined brittle granular materials, and this is indicative of a change in the dominant mode of permanent deformation at higher compaction stresses.

brittle↗