Forcing Function Research Articles

Impact of Three Bleaching Events on the Reef Resiliency of Kāne‘ohe Bay, Hawai‘i

Coral bleaching events have been increasing in frequency and severity worldwide. The most prolonged global bleaching event began in 2014 and continued into 2017 impacting more reefs than any previous occurrence. Here we present the results of coral bleaching and mortality surveys conducted in Kāneʻohe Bay Oʻahu, Hawaiʻi and compare them to the only other widespread bleaching events to impact the main Hawaiian Islands in 1996 and 2014. Results from these surveys along with associated environmental factors were used to compare these events to gain a baseline understanding of the physical processes that influence localized bleaching dynamics under these extreme environmental conditions. Survey results show extensive variation in bleaching (1996- 62%, 2014- 45%, 2015- 30%) and cumulative mortality (1996- <1%, 2014- 13%, 2015- 22%) between years. Bleaching prevalence was observed to decrease in certain reef areas across events, suggesting some acclimation and/or resilience, but possible increase susceptibility to mortality. Long-term monitoring sites show a similar temporal pattern of coral mortality and decline in coral cover, but revealed some reefs remained relatively un-impacted by consecutive high temperature events. Across the three bleaching events, we found that although circulation patterns can facilitate heating, the duration and magnitude of the high temperature event were found to be the primary forcing functions for coral bleaching and mortality. Other localized primary drivers influencing water temperature such as irradiance, turbidity, and precipitation contributed to spatial variations. Recovery and resilience of this coral reef ecosystem is dependent on many factors including duration and magnitude of heating, resulting mortality levels, localized environmental factors in the bay, and coral species affected and their bleaching tolerances.

Probabilistic modelling of forces of hail

Numerical modelling techniques enable forcing function at the point of contact in a hail impact to be predicted, but many models available in commercial software have not been verified by experiments. A recently developed deterministic model is only able to simulate the impact action of an idealised spherical hailstone. Results recorded from the impact testing of non-spherical simulated hail ice specimens show wide scatters and are different to spherical specimens. A stochastic model has been developed in this study to incorporate the variability of the modelling parameters representing the behaviour of non-spherical ice specimens and to generate time histories of contact force for given impact scenarios. A probabilistic model which was developed previously to provide predictions of the distribution of the size of hailstones in a severe category hailstorm has also been further developed to provide predictions of the maximum contact force values in probabilistic terms. For any given pre-defined forcing function denting into the surface of a steel plate can be estimated by finite element analysis or experimentally on a test machine. The new knowledge base introduced in this paper can be used by manufacturers and designers to re-assess existing products and in making improvements to future installations taking into account cost–benefit considerations.

Comparison of forcing functions in magnetohydrodynamics

Results are presented of direct numerical simulations of incompressible, homogeneous magnetohydrodynamic turbulence without a mean magnetic field, subject to different mechanical forcing functions commonly used in the literature. Specifically, the forces are negative damping (which uses the large-scale velocity field as a forcing function), a nonhelical random force, and a nonhelical static sinusoidal force (analogous to helical ABC forcing). The time evolution of the three ideal invariants (energy, magnetic helicity and cross helicity), the time-averaged energy spectra, the energy ratios and the dissipation ratios are examined. All three forcing functions produce qualitatively similar steady states with regards to the time evolution of the energy and magnetic helicity. However, differences in the cross helicity evolution are observed, particularly in the case of the static sinusoidal method of energy injection. Indeed, an ensemble of sinusoidally-forced simulations with identical parameters shows significant variations in the cross helicity over long time periods, casting some doubt on the validity of the principle of ergodicity in systems in which the injection of helicity cannot be controlled. Cross helicity can unexpectedly enter the system through the forcing function and must be carefully monitored.

Modeling of Long-Term Evolution of Hydrophysical Fields of the Black Sea

The long-term evolution of the Black Sea dynamics (1980–2020) is reconstructed by numerical simulation. The model of the Black Sea circulation has 4.8 km horizontal spatial resolution and 40 levels in z-coordinates. The mixing processes in the upper layer are parameterized by Mellor-Yamada turbulent model. For the sea surface boundary conditions, atmospheric forcing functions were used, provided for the Black Sea region by the Euro mediterranean Center on Climate Change (CMCC) from the COSMO-CLM regional climate model. These data have a spatial resolution of 14 km and a daily temporal resolution. To evaluate the quality of the hydrodynamic fields derived from the simulation, they were compared with in-situ hydrological measurements and similar results from physical reanalysis of the Black Sea.

Phosphorus Budget of the Sundarban Mangrove Ecosystem: Box Model Approach

Phosphorus (P) cycling in mangroves plays an important role in productivity but the magnitude of atmospheric input in the mangrove P budget is still uncertain. This study applied a box model approach to assess P budget in the Indian Sundarban, the world’s largest mangrove ecosystem for conceptual understanding of P cycling and for better representation of transport and transformation of P within the mangrove ecosystem. The P content in the sediment (0.19–0.67 μg g−1) was found much below its maximum retention capacity (322 μg g−1) and was lower than the mean marine sediment (669 μg g−1). The C:N and C:P ratios were correlated (r 2 = 0.66, P < 0.01) and the major fraction of available P was recycled within the organic structure of mangrove ecosystem, thus maintaining productivity through conservation strategies. Atmospheric input accounted for 56.7% of total P input (16.06 Gg year−1) and 50% of total P output (14.7 Gg year−1) was attributed to plant uptake. Budget closing or unaccounted P (1.36 Gg) was only 8.5% of the total input. Two feedback pathways, i.e., input of P from dust fallout and biochemical mineralization of organic matter, significantly affected P availability. The findings of the study suggest that atmospheric deposition is of major importance as a natural and/or anthropogenic forcing function in the Sundarban mangrove system.

Robust Fault-Tolerant Tracking Control for Spacecraft Proximity Operations Using Time-Varying Sliding Mode

The capture of a free-floating tumbling object using an autonomous vehicle is a key technology for many future orbital missions. Spacecraft proximity operations will play an important role in guaranteeing the success of such missions. In this paper, we technically propose a tracking control scheme for proximity operations between a target and a pursuer spacecraft that ensures accurate relative position tracking as well as attitude synchronization. Specifically, an integrated six degrees of freedom dynamics model is first established to describe the relative motion of the pursuer with respect to the target. Then, a robust fault-tolerant controller is derived by combining the sliding mode control and the adaptive technique. The designed controller is proved to be not only robust against unexpected disturbances and adaptive to unknown and uncertain mass/inertia properties of the pursuer, but also able to accommodate a large class of actuator faults. In particular, by incorporating a novel time-varying forcing function into the sliding dynamics, the proposed control algorithm is able to guarantee the finite-time convergence of the translational and rotational tracking errors, and the convergence time as an explicit parameter can be assigned a priori by the designers. Furthermore, a theoretical analysis is also presented to assess the fault tolerance ability of the designed controller. Finally, numerous examples are carried out to evaluate the effectiveness and demonstrate the benefits of the overall control approach.

Periodic and transient motions of large woodpeckers

Two types of periodic and transient motions of large woodpeckers are considered. A drumming woodpecker may be modeled as a harmonic oscillator with a periodic forcing function. The transient behavior that occurs after the forcing is turned off suggests that the double knocks of Campephilus woodpeckers may be modeled in terms of a harmonic oscillator with an impulsive forcing, and this hypothesis is consistent with audio and video recordings. Wingbeats are another type of periodic and transient motion of large woodpeckers. A model for the flap rate in cruising flight is applied to the Pileated Woodpecker (Dryocopus pileatus) and the Ivory-billed Woodpecker (Campephilus principalis). During a brief transient just after taking off, the wing motion and flap rate of a large woodpecker may not be the same as in cruising flight. These concepts are relevant to videos that contain evidence for the persistence of the Ivory-billed Woodpecker.

Closed-Form Exact Solutions for Viscously Damped Free and Forced Vibrations of Longitudinal and Torsional Bars

This paper studies the viscously damped free and forced vibrations of longitudinal and torsional bars. The method is exact and yields closed form solution for the vibration displacement in contrast with the well-known eigenfunction superposition (ES) method, which requires expression of the distributed forcing functions and displacement response functions as infinite series sums of free vibration eigenfunctions. The viscously damped natural frequency equation and the critical viscous damping equation are exactly derived for the bars. Then the viscously damped free vibration frequencies and corresponding damped mode shapes are calculated and plotted, aside from the undamped free vibration and corresponding mode shapes typically computed and used in vibration problems. The longitudinal or torsional amplitude versus forcing frequency curves showing the forced response to distributed loadings are plotted for various viscous damping parameters. It is found that the viscous damping affects the natural frequencies and the corresponding mode shapes of longitudinal and torsional bars, especially for the fundamental frequency.

Fluid dynamics approach to free reed physics

The periodic vibration of a free reed subject to a steady pressure gradient (bellows pressure) is examined from a fluid dynamics approach. In this analytic study, the self-excited forcing function is modeled from the static and dynamic pressures acting on the vibrating tongue surface. A first formulation includes standard mounting of the reed over a cavity, with a hole that accommodates a mean air flow to the outside. A second formulation includes in addition a resonant air geometry that could include non-standard operation, such as pitch bending.

Ecosystem approach to fisheries: Exploring environmental and trophic effects on Maximum Sustainable Yield (MSY) reference point estimates.

We present a comprehensive analysis of estimation of fisheries Maximum Sustainable Yield (MSY) reference points using an ecosystem model built for Mille Lacs Lake, the second largest lake within Minnesota, USA. Data from single-species modelling output, extensive annual sampling for species abundances, annual catch-survey, stomach-content analysis for predatory-prey interactions, and expert opinions were brought together within the framework of an Ecopath with Ecosim (EwE) ecosystem model. An increase in the lake water temperature was observed in the last few decades; therefore, we also incorporated a temperature forcing function in the EwE model to capture the influences of changing temperature on the species composition and food web. The EwE model was fitted to abundance and catch time-series for the period 1985 to 2006. Using the ecosystem model, we estimated reference points for most of the fished species in the lake at single-species as well as ecosystem levels with and without considering the influence of temperature change; therefore, our analysis investigated the trophic and temperature effects on the reference points. The paper concludes that reference points such as MSY are not stationary, but change when (1) environmental conditions alter species productivity and (2) fishing on predators alters the compensatory response of their prey. Thus, it is necessary for the management to re-estimate or re-evaluate the reference points when changes in environmental conditions and/or major shifts in species abundance or community structure are observed.

Fully discrete second-order backward difference method for Kelvin-Voigt fluid flow model

In this article, based on a second-order backward difference method, a completely discrete scheme is discussed for a Kelvin-Voigt viscoelastic fluid flow model with nonzero forcing function, which is either independent of time or in L ∞ (L 2). After deriving some a priori bounds for the solution of a semidiscrete Galerkin finite element scheme, a second-order backward difference method is applied for temporal discretization. Then, a priori estimates in Dirichlet norm are derived, which are valid uniformly in time using a combination of discrete Gronwall’s lemma and Stolz-Cesaro’s classical result on sequences. Moreover, an existence of a discrete global attractor for the discrete problem is established. Further, optimal a priori error estimates are obtained, whose bounds may depend exponentially in time. Under uniqueness condition, these estimates are shown to be uniform in time. Finally, several numerical experiments are conducted to confirm our theoretical findings.

Evaluating the Global Internal Wave Model IDEMIX Using Finestructure Methods

AbstractSmall-scale turbulent mixing affects large-scale ocean processes such as the global overturning circulation but remains unresolved in ocean models. Since the breaking of internal gravity waves is a major source of this mixing, consistent parameterizations take internal wave energetics into account. The model Internal Wave Dissipation, Energy and Mixing (IDEMIX) predicts the internal wave energy, dissipation rates, and diapycnal diffusivities based on a simplification of the spectral radiation balance of the wave field and can be used as a mixing module in global numerical simulations. In this study, it is evaluated against finestructure estimates of turbulent dissipation rates derived from Argo float observations. In addition, a novel method to compute internal gravity wave energy from finescale strain information alone is presented and applied. IDEMIX well reproduces the magnitude and the large-scale variations of the Argo-derived dissipation rate and energy level estimates. Deficiencies arise with respect to the detailed vertical structure or the spatial extent of mixing hot spots. This points toward the need to improve the forcing functions in IDEMIX, both by implementing additional physical detail and by better constraining the processes already included in the model. A prominent example is the energy transfer from the mesoscale eddies to the internal gravity waves, which is identified as an essential contributor to turbulent mixing in idealized simulations but needs to be better understood through the help of numerical, analytical, and observational studies in order to be represented realistically in ocean models.

Dynamic and tribological study of a planetary gearbox with local nonlinearities

A planetary gearbox model comprising five spur gears (sun, ring and three planets) and the carrier has been developed and analysed. The influence of gear teeth backlash and friction during mixed regime of lubrication has been taken into consideration. Greenwood and Tripp model is employed, while viscous friction is calculated analytically using the functions of Evans and Johnson. A combined tribodynamics modeling approach has been implemented and modal analysis is performed in order to predict the coupled mechanism of tribological and dynamic behavior, subjected to backlash and excited at the gear meshing frequency. The software used for the simulations is ADAMS MSc (Student Edition), where the model variables (concerning gear geometry and forcing functions) have been added in a parametric way. The results showed that small variations of the dynamic transmission error affect notably the viscous friction through changing the contact load between the engaged teeth pairs. Also, higher values of the Stribeck oil parameter due to higher film thickness or lower surface roughness in the mixed lubrication regime lead to reduction of the boundary friction, whereas a reduction of the total generated friction occurs when increasing the angular velocity of the input gear body (due to higher film thickness and smaller asperity interactions). The above lead to reduced power loss of the mechanism. Finally, a characterization of the system dynamics is presented using the calculated eigenvalues and eigenmodes of the corresponding linearized system. Potential interactions with the gear meshing frequency of the system are also examined.

Unsteady Non-Premixed Methane/Oxygen Flame Structures at Supercritical Pressures

ABSTRACTUnsteady non-premixed flame structures of methane/oxygen mixtures are investigated at supercritical pressures, representative of liquid rocket engines combustion chamber operating conditions. A general-fluid formulation of the flamelet equations is used and deviations from ideality of the thermodynamic properties are taken into account by means of a computationally efficient cubic equation of state written in a general three-parameter fashion. The effects of pressure and scalar dissipation rate are investigated in the context of prototypical unsteady laminar flame configurations, such as autoignition and re-ignition/quenching. In auto-igniting flamelets, real gas effects are observed to influence different flame regions depending on the thermodynamic pressure. Moreover, the mixture ensuing from methane oxidation is never observed to reach a saturated (two-phase) thermodynamic region. Re-ignition and quenching phenomena are analyzed using a time dependent forcing function for the scalar dissipation rate, in order to investigate the response of the real gas flame structures to typical turbulent perturbations. The role of pressure on the critical strain values that a real gas laminar flame can sustain without quenching is investigated and compared to its ideal gas counterpart.

Identification of non-linear parameter of a cantilever beam model with boundary condition non-linearity in the presence of noise: an NSI- and ANN-based approach

In this study the non-linear system identification (NSI) and parameter estimation of a model of a cantilever beam with non-linear stiffness attached to its free end are investigated. For this purpose, the impulse response of the beam model, in the presence of added measurement noise, is obtained by solving the weak form of the governing equation of motion via Rayleigh–Ritz method. The non-linear interaction model (NIM) including a set of intrinsic modal oscillators (IMOs) is constructed based on intrinsic mode functions (IMFs), which are derived by applying empirical mode decomposition (EMD) on the noise-contaminated response signals. For reducing the effect of noise and increasing the accuracy of extracted IMFs, the EMD-based noise reduction is employed, followed by the modification of the IMF amplitudes by introducing a “beta-factor” criterion. The changes in the amplitudes of the forcing functions associated with IMOs are used to extract features to estimate the non-linear parameter of the system. To this end, an artificial neural network has been trained to establish the non-linear relationship between the non-linearity of the system and the forcing functions of IMOs.

Large Eddy Simulation of Low Swirl Flames Under External Flow Excitations

Low swirl flame characteristics under external flow excitations are numerically investigated using large eddy simulations with a dynamically thickened flame combustion model. A finite volume scheme on a Cartesian grid with a dynamic one equation eddy viscosity subgrid scale model is used for large eddy simulations. The excitations are imposed on inlet velocity profiles by a sinusoidal forcing function over a wide range of amplitudes and frequencies. Present investigation shows that although, the swirling motion of the low swirl flame is not intense enough to induce a recirculation zone in ensemble averaged results, external flow excitations increase the local swirl number upstream of the flame front. Such increase in the local swirl number is at maximum value when the low swirl flame is excited at the dominant frequency of the flow field, which in turn induces a vortex breakdown and hence a central recirculation zone. The strength and size of the time averaged recirculation zone depend on both the amplitude and frequency of the excitations. Moreover, phase-locked results indicate that external flow excitations induce local swirl fluctuations ahead of the flame front which alter the strength of the recirculation zone at different phase angles of the excitations.

Developing and applying metamodels of high resolution process-based simulations for high throughput exposure assessment of organic chemicals in riverine ecosystems

As defined by Wikipedia (https://en.wikipedia.org/wiki/Metamodeling), “(a) metamodel or surrogate model is a model of a model, and metamodeling is the process of generating such metamodels.” The goals of metamodeling include, but are not limited to (1) developing functional or statistical relationships between a model's input and output variables for model analysis, interpretation, or information consumption by users' clients; (2) quantifying a model's sensitivity to alternative or uncertain forcing functions, initial conditions, or parameters; and (3) characterizing the model's response or state space. Using five models developed by the US Environmental Protection Agency, we generate a metamodeling database of the expected environmental and biological concentrations of 644 organic chemicals released into nine US rivers from wastewater treatment works (WTWs) assuming multiple loading rates and sizes of populations serviced. The chemicals of interest have log n-octanol/water partition coefficients (logKOW) ranging from 3 to 14, and the rivers of concern have mean annual discharges ranging from 1.09 to 3240m3/s. Log-linear regression models are derived to predict mean annual dissolved and total water concentrations and total sediment concentrations of chemicals of concern based on their logKOW, Henry's Law Constant, and WTW loading rate and on the mean annual discharges of the receiving rivers. Metamodels are also derived to predict mean annual chemical concentrations in fish, invertebrates, and periphyton. We corroborate a subset of these metamodels using field studies focused on brominated flame retardants and discuss their application for high throughput screening of exposures to human and ecological populations and for analysis and interpretation of field data.

Revisiting the inhomogeneously driven sine–Gordon equation

The sine–Gordonequation is a semilinear wave equation used to model many physical phenomenon like seismic events that includes earthquakes, slow slip and after-slip processes, dislocation in solids etc. Solution of homogeneous sine–Gordon equation exhibit soliton like structure that propagates without change in its shape and structure. The question whether solution of sine–Gordon equation still exhibit soliton like behavior under an external forcing has been challenging as it is extremely difficult to obtain an exact solution even under simple forcing like constant. In this study solution to an inhomogeneous sine–Gordon equation with Heaviside forcing function is analyzed. Various one-dimensional test cases like kink and breather with no flux and non-reflecting boundary conditions are studied.

Modeling compressible multiphase flows with dispersed particles in both dense and dilute regimes

Many important explosives and energetics applications involve multiphase formulations employing dispersed particles. While considerable progress has been made toward developing mathematical models and computational methodologies for these flows, significant challenges remain. In this work, we apply a mathematical model for compressible multiphase flows with dispersed particles to existing shock and explosive dispersal problems from the literature. The model is cast in an Eulerian framework, treats all phases as compressible, is hyperbolic, and satisfies the second law of thermodynamics. It directly applies the continuous-phase pressure gradient as a forcing function for particle acceleration and thereby retains relaxed characteristics for the dispersed particle phase that remove the constituent material sound velocity from the eigenvalues. This is consistent with the expected characteristics of dispersed particle phases and can significantly improve the stable time-step size for explicit methods. The model is applied to test cases involving the shock and explosive dispersal of solid particles and compared to data from the literature. Computed results compare well with experimental measurements, providing confidence in the model and computational methods applied.

An Enhanced Patient-Specific Computer Model Using an Iterative Multi-Staged Algorithm

Background: A previously introduced patient-specific computer model was applied to predict outcomes of the balloon occlusion test (BOT). The goal of this work was to propose an enhanced patient-specific computer model using a new iterative multi-staged algorithm. Method: This work presents an enhanced patient-specific computer model which converts several more terminals from generic, to patient-specific, resistances and also makes the aortic pressure and the stiffness coefficient patient-specific. A new iterative multi-staged algorithm is proposed to determine the terminal resistances, the aortic pressure, and the stiffness coefficient using vessel sizes and vessel flows measured by quantitative magnetic resonance angiography (qMRA) and cuff pressure. The predictions of the BOT were also evaluated for the validation of the proposed model. Results: The predictions from the proposed model were accurate in comparison with the clinical outcomes of the two BOTs. The computed stiffness coefficients were consistent with the ages of the two patients. The correlation coefficients between the flow measurements and the computed flows using the proposed computer model at baseline for the two patients were 0.9861 and 0.9995, respectively. The computed aortic pressures were also comparable in waveform shape with the actual aortic pressure measurements obtained during the BOT using a catheter-transducer. Conclusion: The present study makes the computer model more patient-specific with a new algorithm using non-invasive data from qMRA and cuff pressure. The six more sectors have made the terminal resistances more patient-specific. The patient-specific aortic pressure has made the forcing function patient-specific. And the stiffness coefficient has made the compliance patient-specific. J Neurol Res. 2017;7(3):25-38 doi: https://doi.org/10.14740/jnr435w