Forcing Function Research Articles

Parametrization to Improve the Solution Accuracy of Problems Involving the Bi-Dimensional Dirac Delta in the Forcing Function

The representation of the Dirac delta, obtained by differentiating the parametric equation of the unit step with a riser, is used to solve two examples referring to problems of a different physical nature, each with the product of two deltas as a forcing function. Each problem was solved by an entirely different procedure. In comparison with non-parametric solutions, the present solutions are both more accurate and truer representations of the physics involved.

Stable components in extended-range forecasting during the continuous high temperature event in August 2013 over the mid-eastern China

Based on the continuous high temperature process over the mid-eastern China in August 2013, using the NCEP/NCAR (United States National Centers for Environmental Prediction/National Center for Atmospheric Research) daily average of 500 hPa height field, the wind field reanalysis data, and the NOAA (National Oceanic and Atmospheric Administration) reconstruction sea surface temperature (SST) data, through the selection method similar to the early adoption of SST forcing, band-pass filtering and empirical orthogonal function decomposition method to extract the 10-30 days of stable components, and through a stable component of diagnostic analysis, we investigate the mechanisms for sustaining and reducing high temperature process. Results show that by selecting and using the case that is the most similar to a pre-SST forcing 30-year climatology instead of the normal 30-year climatology (1981-2010), the steady-state component extracted climate proportion is reduced, and the proportion of anomalously stable components is significantly enhanced and the described influence strength and stability are improved significantly, which can more clearly show the extended maintenance mechanism of weather processes. It suggests that early consideration SST forcing in the extraction component is very necessary. Meanwhile, the analysis of extension of stable components shows that the process of maintaining and reducing high temperature is mainly caused by the combined effect of the Arctic Oscillation, continental high latitudes zonal circulation situation in Asia and the western Pacific subtropical high intensity and location.

Efficiently Generating the Ballistic Phase of Human-Like Aimed Movement

Human-like movement can be efficiently generated by driving a damped inertial plant toward a fixed target with position-based control, then switching to conventional feedback control as the desired endpoint is approached. Key characteristics of human motion, not easily replicated with traditional control architectures, result from tracking a position-based actuation template derived from human trials. Computation of the applied forcing function requires only linear scaling of this template, or displacement-normalized actuation program (DNAP). Simulated ballistic movements generated with the proposed method are shown to be consistent with human subject kinematic trajectories.

Transient response analysis of randomly parametrized finite element systems based on approximate balanced reduction

A model order reduction scheme of the transient response of large-scale randomly parametrized linear finite element system in state space form has been proposed. The reduced order model realization is aimed at preserving the invariant properties of the dynamic system model based on the dominant coupling characteristics of the specified system inputs and outputs. An a-priori model reduction strategy based on the balanced truncation method has been proposed in conjunction with the stochastic spectral Galerkin finite element method. Approximation of the dominant modes of the controllability Gramian has been performed with iterative Arnoldi scheme applied to Lyapunov equations. The reduced order representation of the randomly parametrized dynamical system has been obtained with Arnoldi–Lyapunov vector basis using an implicit time stepping algorithm. The performance and the computational efficacy of the proposed scheme has been illustrated with examples of randomly parametrized advection–diffusion–reaction problem under the action of transient external forcing functions. The convergence of the proposed reduced order scheme has been shown with a-posteriori error estimates.

Minimizing the acoustic power radiated by a fluid-loaded curved panel excited by turbulent boundary layer flow.

In order to address noise control problems in the design stage, structural-acoustic optimization procedures can be used to find the optimal design for reduced noise or vibration. However, most structural-acoustic optimization procedures are not general enough to include both heavy fluid loading and complex forcing functions. Additionally, it can be difficult to determine and assess trade-offs between weight and sound radiation. A structural-acoustic optimization approach is presented for minimizing the radiated power of structures with heavy fluid loading excited by complex forcing functions. The procedure is demonstrated on a curved underwater panel excited by a point drive and by turbulent boundary layer flow. To facilitate more efficient analysis, an uncorrelated pressure assumption is made for the turbulent boundary layer forcing function. The thicknesses of groups of elements were used as the design variables with an adaptive covariance matrix evolutionary strategy as the search algorithm. The objective function was a weighted sum of total sound power and panel mass and the Pareto front was computed to show the optimum trade-off between the two objectives. The optimal designs are presented which illustrate the best methods for reducing radiated sound and mass simultaneously.

A heterogeneous stochastic FEM framework for elliptic PDEs

We introduce a new concept of sparsity for the stochastic elliptic operator −div(a(x,ω)∇(⋅)), which reflects the compactness of its inverse operator in the stochastic direction and allows for spatially heterogeneous stochastic structure. This new concept of sparsity motivates a heterogeneous stochastic finite element method (HSFEM) framework for linear elliptic equations, which discretizes the equations using the heterogeneous coupling of spatial basis with local stochastic basis to exploit the local stochastic structure of the solution space. We also provide a sampling method to construct the local stochastic basis for this framework using the randomized range finding techniques. The resulting HSFEM involves two stages and suits the multi-query setting: in the offline stage, the local stochastic structure of the solution space is identified; in the online stage, the equation can be efficiently solved for multiple forcing functions. An online error estimation and correction procedure through Monte Carlo sampling is given. Numerical results for several problems with high dimensional stochastic input are presented to demonstrate the efficiency of the HSFEM in the online stage.

A distributed parameter electromechanical and statistical model for energy harvesting from turbulence-induced vibration

Extensive research has been done on the topics of both turbulence-induced vibration and vibration based energy harvesting; however, little effort has been put into bringing these two topics together. Preliminary experimental studies have shown that piezoelectric structures excited by turbulent flow can produce significant amounts of useful power. This research could serve to benefit applications such as powering remote, self-sustained sensors in small rivers or air ventilation systems where turbulent fluid flow is a primary source of ambient energy. A novel solution for harvesting energy in these unpredictable fluid flow environments was explored by the authors in previous work, and a harvester prototype was developed. This prototype, called piezoelectric grass, has been the focus of many experimental studies. In this paper the authors present a theoretical analysis of the piezoelectric grass harvester modeled as a single unimorph cantilever beam exposed to turbulent cross-flow. This distributed parameter model was developed using a combination of both analytical and statistical techniques. The analytical portion uses a Rayleigh–Ritz approximation method to describe the beam dynamics, and utilizes piezoelectric constitutive relationships to define the electromechanical coupling effects. The statistical portion of the model defines the turbulence-induced forcing function distributed across the beam surface. The model presented in this paper was validated using results from several experimental case studies. Preliminary results show that the model agrees quite well with experimental data. A parameter optimization study was performed with the proposed model. This study demonstrated how a new harvester could be designed to achieve maximum power output in a given turbulent fluid flow environment.

A neuron model of stochastic resonance using rectangular pulse trains.

Stochastic resonance (SR) is the enhanced representation of a weak input signal by the addition of an optimal level of broadband noise to a nonlinear (threshold) system. Since its discovery in the 1980s the domain of input signals shown to be applicable to SR has greatly expanded, from strictly periodic inputs to now nearly any aperiodic forcing function. The perturbations (noise) used to generate SR have also expanded, from white noise to now colored noise or vibrational forcing. This study demonstrates that a new class of perturbations can achieve SR, namely, series of stochastically generated biphasic pulse trains. Using these pulse trains as 'noise' we show that a Hodgkin Huxley model neuron exhibits SR behavior when detecting weak input signals. This result is of particular interest to neuroscience because nearly all artificial neural stimulation is implemented with square current or voltage pulses rather than broadband noise, and this new method may facilitate the translation of the performance gains achievable through SR to neural prosthetics.

A Fast Immersed Boundary Fourier Pseudo-spectral Method for Simulation of the Incompressible Flows

Abstract The present paper is devoted to implementation of the immersed boundary technique into the Fourier pseudo-spectral solution of the vorticity-velocity formulation of the two-dimensional incompressible Navier-Stokes equations. The immersed boundary conditions are implemented via direct modification of the convection and diffusion terms, and therefore, in contrast to some other similar methods, there is not an explicit external forcing function in the present formulation. At the beginning of each time step, the solenoidal velocities (also satisfying the desired immersed boundary conditions), are obtained and fed into a conventional pseudo-spectral solver, together with a modified vorticity. The classical explicit fourth-order Runge-Kutta method is used in time integration, and the boundary conditions are set at the beginning of each sub-step, in order to increase the time accuracy. The method is employed in simulation of some different test cases, including the flow behind impulsively started circular cylinder, oscillating circular cylinder in fluid at rest and insect-like flapping wing motion. The results show accuracy and efficiency of the method.

Rotary and radial forcing effects on center-of-mass locomotion dynamics

Rotary and radial forcing are two common actuation methods for legged robots. However, these two orthogonal methods of center-of-mass (CoM) forcing have not been compared as potentially alternative strategies of actuation. In this paper, we compare the CoM stability and energetics of running with rotary and radial actuation through the simulation of two models: the rotary-forced spring-loaded inverted pendulum (rotary-forced-SLIP), and the radially-forced-SLIP. We model both radial and rotary actuation in the simplest way, applying them as a constant force during the stance portion of the gait. A simple application of constant rotary forcing throughout stance is capable of producing fully-asymptotically stable motion; however, a similarly constant application of radial forcing throughout the stance is not capable of producing stable solutions. We then allow both the applied rotary and radial forcing functions to turn on or off based on the occurrence of the mid-stance event, which breaks the symmetry of actuation during stance towards a net forward propulsion. We find that both a rotary force applied in the first half of stance and a radial force applied in the second half of stance, are capable of stabilizing running. Interestingly, these two forcing methods improve the motion stability in different ways. Rotary forcing first reduces then greatly increases the size of the stable parameter region when gradually increased. Radial forcing expands the stable parameter region, but only in a moderate way. Also, it is found that parameter region stabilized by rotary and radial forcing are largely complementary. Overall, rotary forcing can better stabilize running for both constant and event-based forcing functions that were attempted. This indicates that rotary forcing has an inherent capability of stabilizing running, even when minimal time-or-event-or-state feedback is present. Radial forcing, however, tends to be more energy efficient when compared to rotary forcing. In addition, a balanced stability and energy efficiency can be achieved by combining both forcing methods. These results may be applied in the future study of how legged animals move.

An Adaptive ANOVA-Based Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficient

AbstractIn this paper, we present an adaptive, analysis of variance (ANOVA)-based data-driven stochastic method (ANOVA-DSM) to study the stochastic partial differential equations (SPDEs) in the multi-query setting. Our new method integrates the advantages of both the adaptive ANOVA decomposition technique and the data-driven stochastic method. To handle high-dimensional stochastic problems, we investigate the use of adaptive ANOVA decomposition in the stochastic space as an effective dimension-reduction technique. To improve the slow convergence of the generalized polynomial chaos (gPC) method or stochastic collocation (SC) method, we adopt the data-driven stochastic method (DSM) for speed up. An essential ingredient of the DSM is to construct a set of stochastic basis under which the stochastic solutions enjoy a compact representation for a broad range of forcing functions and/or boundary conditions.Our ANOVA-DSM consists of offline and online stages. In the offline stage, the original high-dimensional stochastic problem is decomposed into a series of low-dimensional stochastic subproblems, according to the ANOVA decomposition technique. Then, for each subproblem, a data-driven stochastic basis is computed using the Karhunen-Loève expansion (KLE) and a two-level preconditioning optimization approach. Multiple trial functions are used to enrich the stochastic basis and improve the accuracy. In the online stage, we solve each stochastic subproblem for any given forcing function by projecting the stochastic solution into the data-driven stochastic basis constructed offline. In our ANOVA-DSM framework, solving the original highdimensional stochastic problem is reduced to solving a series of ANOVA-decomposed stochastic subproblems using the DSM. An adaptive ANOVA strategy is also provided to further reduce the number of the stochastic subproblems and speed up our method. To demonstrate the accuracy and efficiency of our method, numerical examples are presented for one- and two-dimensional elliptic PDEs with random coefficients.

Stoked nondynamos: sustaining field in magnetically non-closed systems

Much effort has gone into identifying and classifying systems that might be capable of dynamo action, i.e. capable of generating and sustaining magnetic field indefinitely against dissipative effects in a conducting fluid. However, it is difficult, if not almost technically impossible, to derive a method of determining in both an absolutely conclusive and a pragmatic manner whether a system is a dynamo or not in the nonlinear regime. This problem has generally been examined only for closed systems, despite the fact that most realistic situations of interest are not strictly closed. Here we examine the even more complex problem of whether a known nondynamo closed system can be distinguished pragmatically from a true dynamo when a small input of magnetic field to the system is allowed. We call such systems ‘stoked nondynamos’ owing to the ‘stoking’ or augmentation of the magnetic field in the system. It may seem obvious that magnetic energy can be sustained in such systems since there is an external source, but crucial questions remain regarding what level is maintained and whether such nondynamo systems can be distinguished from a true dynamo. In this paper, we perform 3D nonlinear numerical simulations with time-dependent ABC forcing possessing known dynamo properties. We find that magnetic field can indeed be maintained at a significant stationary level when stoking a system that is a nondynamo when not stoked. The maintained state results generally from an eventual rough balance of the rates of input and decay of magnetic field. We find that the relevance of this state is dictated by a parameter κ representing the correlation of the resultant field with the stoking forcing function. The interesting regime is where κ is small but non-zero, as this represents a middle ground between a state where the stoking has no effect on the pre-existing nondynamo properties and a state where the effect of stoking is easily detectable. We find that in this regime, (a) the saturated state is somewhat unexpectedly enhanced by a bias resulting from the random fluctuating statistics of the decay process, and (b) the state is indistinguishable from a true dynamo except via κ itself. Such results make the pragmatic identification of dynamos in real situations even more difficult than had previously been thought.

The ocean's role in polar climate change: asymmetric Arctic and Antarctic responses to greenhouse gas and ozone forcing.

In recent decades, the Arctic has been warming and sea ice disappearing. By contrast, the Southern Ocean around Antarctica has been (mainly) cooling and sea-ice extent growing. We argue here that interhemispheric asymmetries in the mean ocean circulation, with sinking in the northern North Atlantic and upwelling around Antarctica, strongly influence the sea-surface temperature (SST) response to anthropogenic greenhouse gas (GHG) forcing, accelerating warming in the Arctic while delaying it in the Antarctic. Furthermore, while the amplitude of GHG forcing has been similar at the poles, significant ozone depletion only occurs over Antarctica. We suggest that the initial response of SST around Antarctica to ozone depletion is one of cooling and only later adds to the GHG-induced warming trend as upwelling of sub-surface warm water associated with stronger surface westerlies impacts surface properties. We organize our discussion around ‘climate response functions’ (CRFs), i.e. the response of the climate to ‘step’ changes in anthropogenic forcing in which GHG and/or ozone-hole forcing is abruptly turned on and the transient response of the climate revealed and studied. Convolutions of known or postulated GHG and ozone-hole forcing functions with their respective CRFs then yield the transient forced SST response (implied by linear response theory), providing a context for discussion of the differing warming/cooling trends in the Arctic and Antarctic. We speculate that the period through which we are now passing may be one in which the delayed warming of SST associated with GHG forcing around Antarctica is largely cancelled by the cooling effects associated with the ozone hole. By mid-century, however, ozone-hole effects may instead be adding to GHG warming around Antarctica but with diminished amplitude as the ozone hole heals. The Arctic, meanwhile, responding to GHG forcing but in a manner amplified by ocean heat transport, may continue to warm at an accelerating rate.

Modelling the effects of climate change on a Caribbean coral reef food web

Global climate change and local anthropogenic pressures are among the primary factors leading to the decline of functional biodiversity and critical habitats in coral reefs. Coral bleaching, the potential decreases in dissolved oxygen concentration (deoxygenation) and pH (acidification) in the oceans can induce severe changes in coral reef ecosystem biodiversity and functionality. The main objective of this study was to apply four Ecopath with Ecosim models of a Caribbean coral reef system to individually and collectively model the effects of coral bleaching on the trophic web, deoxygenation on fish, and acidification on calcifying organisms. These three sources of stress were used as forcing functions on several trophic groups depending on the model. The forcing functions were scaled according to the species’ responses achieved in previously tested climate change marine models. For the bleaching model, a mediation function was also considered that represents the degree of coral reef protection on small and intermediate fish groups. The dynamic models were constructed from an extensive database of 171 reef fish species (abundance and biomass) and benthic communities from 13 coral reefs that were evenly distributed parallel to approximately 400km of the Mexican Caribbean coast as well as fishery landings in this area. Simulations driven with these different forcing and mediation functions predicted different changes in the biomasses of fish and non-fish functional groups as well as the biomass of the functional groups of fished species. Coral bleaching and pH reduction caused a phase shift to a decrease in coral biomass and an increase in primary producer biomass. This shift produced a cascading decrease in the biomass of small and intermediate fish groups. Additionally, the fished functional group biomass increased with coral bleaching but decreased with the effects of decreased oxygen on fish and pH on calcifying organisms. The biomasses of certain macroinvertebrate functional groups were predicted to respond favourably to the combined effect of the sources of stress. However, when all the sources of stress were combined, we found a general decrease of biomass in fish, non-fish, and some commercially valuable fish and macroinvertebrate functional groups, suggesting that the combined effects of stress induced synergistic effects as a result of global climate change and overfishing, which can result in a potential loss of biodiversity and ecosystem services in coral reefs.

Paperless reporting and electronically verifying clinical investigations.

The purpose of this paper is to outline considerations and steps taken to introduce electronic reporting and verification from systems design and multidisciplinary collaborations to gap analysis and devising solutions. It also evaluates carefully placed forcing functions' impact on verification rates. A multidisciplinary workgroup was formed to stop print and establish electronic reporting. The electronic verification's success was assessed by weekly activity analysis. Introducing a verification forcing function markedly improved verification activity. Thereafter, non-verified results stabilized at 7 percent up to 75 weeks post-implementation. This paper illustrates how results reporting and verification could be implemented in a tertiary hospital using a mixed electronic and paper record. Factors that were critical to success include stakeholder engagement and applying systems design that focussed on patient safety as a key priority. The electronic reporting system was augmented by strategically inserted forcing functions, clear clinical-responsibility lines and ancillary alert systems. The systems design method's value in managing non-critical but abnormal results appears to have been under-appreciated. This paper describes how systems design could be used to improve health information delivery and management.

SU‐E‐T‐248: Near Real‐Time Analysis of Radiation Delivery and Imaging, Accuracy to Ensure Patient Safety

Purpose:To develop and optimize an effective software method for comparing planned to delivered control point machine parameters for all VARIAN TrueBeam treatments so as to permit (1) assessment of a large patient pool throughout their treatment course to quantify treatment technique specific systematic and random uncertainty of observables, (2) quantify the site specific daily imaging shifts required for target alignment, and (3) define tolerance levels for mechanical parameters and imaging parameters based on statistical analysis data gathered, and the dosimetric impact of variations.Methods:Treatment and imaging log files were directly compared to plan parameters for Eclipse and Pinnacle planned treatments via 3D, IMRT, control point, RapidArc, and electrons. Each control point from all beams/arcs (7984) for all fractions (1940) of all patients treated over six months were analyzed. At each control point gantry angle, collimator angle, couch angle, jaw positions, MLC positions, MU were compared. Additionally per‐treatment isocenter shifts were calculated.Results were analyzed as a whole in treatment type subsets:IMRT, 3D, RapidArc; and in treatment site subsets: brain, chest/mediastinum, esophagus, H&N, lung, pelvis, prostate. Results: Daily imaging isocenter shifts from initial external tattoo alignment were dependent on the treatment site with < 0.5 cm translational shifts for H&N, Brain, and lung SBRT, while pelvis, esophagus shifts were ∼1 cm. Mechanical delivery parameters were within tolerance levels for all sub‐beams. The largest variations were for RapidArc plans: gantry angle 0.11±0.12,collimator angle 0.00±0.00, jaw positions 0.48±0.26, MLC leaf positions 0.66±0.08, MU 0.14±0.34.Conclusion:Per‐control point validation reveals deviations between planned and delivered parameters. If used in a near real‐time error checking system, patient safety can be improved by equipping the treatment delivery system with additional forcing functions which by‐pass human error avenues.

Reaping the potentials of nonlinear energy harvesting with tunable damping and modulation of the forcing functions

The fundamental features of nonlinear dynamical systems are investigated in the context of vibration-based energy harvesting. A generalized, global, multi-frequency resonance condition is shown to exist in nonlinear systems where the energy harvesting efficiency has been maximized. Results show that damping and modulation of the excitation play critical roles in facilitating the frequency match required for resonance by tuning the frequencies of the system and modifying the frequency content of the excitation.

Physical forcing and physical/biochemical variability of the Mediterranean Sea: a review of unresolved issues and directions for future research

Abstract. This paper is the outcome of a workshop held in Rome in November 2011 on the occasion of the 25th anniversary of the POEM (Physical Oceanography of the Eastern Mediterranean) program. In the workshop discussions, a number of unresolved issues were identified for the physical and biogeochemical properties of the Mediterranean Sea as a whole, i.e., comprising the Western and Eastern sub-basins. Over the successive two years, the related ideas were discussed among the group of scientists who participated in the workshop and who have contributed to the writing of this paper. Three major topics were identified, each of them being the object of a section divided into a number of different sub-sections, each addressing a specific physical, chemical or biological issue: 1. Assessment of basin-wide physical/biochemical properties, of their variability and interactions. 2. Relative importance of external forcing functions (wind stress, heat/moisture fluxes, forcing through straits) vs. internal variability. 3. Shelf/deep sea interactions and exchanges of physical/biogeochemical properties and how they affect the sub-basin circulation and property distribution. Furthermore, a number of unresolved scientific/methodological issues were also identified and are reported in each sub-section after a short discussion of the present knowledge. They represent the collegial consensus of the scientists contributing to the paper. Naturally, the unresolved issues presented here constitute the choice of the authors and therefore they may not be exhaustive and/or complete. The overall goal is to stimulate a broader interdisciplinary discussion among the scientists of the Mediterranean oceanographic community, leading to enhanced collaborative efforts and exciting future discoveries.

Dynamic and Pushover Analysis of 8 Storey Building (G+8) Using ETAB Nonlinear

Nonlinear Dynamic analysis can be done by direct integration of the equations of motion by step by step procedures. Direct integration provides the most powerful and informative analysis for any given earthquake motion. A time dependent forcing function (earthquake accelerogram) is applied and the corresponding response-history of the structure during the earthquake is computed. That is, the moment and force diagrams at each of a series of prescribed intervals throughout the applied motion can be found. Computer programs have been written for both linear elastic and non-linear inelastic material behaviour using step-by-step integration procedures. One such program is ETAB in which three-dimensional non-linear analyses can be carried out taking as input the three orthogonal accelerogram components from a given earthquake, and applying them simultaneously to the structure.

Asymptotic stability and regularity of solutions for a magnetoelastic system in bounded domains

We prove the existence of strong time-periodic solutions and their asymptotic stability with the total energy of the perturbations decaying to zero at an exponential decay rate as t→∞ for a semilinear (nonlinearly coupled) magnetoelastic system in bounded, simply connected three-dimensional domain. The mathematical model includes a mechanical dissipation and a periodic forcing function of period T. In the second part of the paper, we consider a magnetoelastic system in the form of a semilinear initial-boundary-value problem in a bounded, simply connected two-dimensional domain. We use the LaSalle invariance principle to obtain results on the asymptotic behavior of solutions. This second result was obtained for the system under the action of only one dissipation (the natural dissipation of the system).