Forcing Function Research Articles

Numerical study of seasonal circulation and variability over the inner shelf of the northern South China Sea

This study examines seasonal circulation, hydrography, and associated spatial variability over the inner shelf of the northern South China Sea (NSCS) using a nested-grid coastal ocean circulation model. The model external forcing consists of tides, atmospheric forcing, and open boundary conditions based on the global ocean circulation and hydrography reanalysis produced by the Hybrid Coordinate Ocean model. Five numerical experiments are conducted with different combinations of external forcing functions to examine main physical processes affecting the seasonal circulation in the study region. Model results demonstrate that the monthly mean circulation in the study region features the Guangdong Coastal Current (GCC) over coastal waters and the South China Sea Warm Current (SCSWC) in the offshore deep waters. The GCC produced by the model flows nearly southwestward in winter months and northwestward in summer months, which agrees with previous studies. The SCSWC flows roughly northeastward and is well defined in summer months. In winter months, by comparison, the SCSWC is superseded by the southwestward strong wind-driven currents. Analysis of model results in five different experiments demonstrates that the monthly mean circulation over coastal and inner shelf waters of the NSCS can be approximated by barotropic currents forced by the southwestward monsoon winds in winter months. In summer months, by comparison, the monthly mean circulation in the study region is affected significantly by baroclinic dynamics associated with freshwater runoff from the Pearl River and advection of warm and saline waters carried by the SCSWC over the NSCS.

Experimental Investigation of a Forced-Response Condition in a Multistage Compressor

It is nearly impossible to remove all resonant crossings from the operating range of a multistage compressor; thus, designers rely on models to predict the resonant response amplitude to determine if the crossing is acceptable. An accurate model can reduce unexpected forced-response problems encountered during engine testing. Although work has been done to improve such models, the confidence in these models comes from validation with quality test data including both the aerodynamic forcing function and the response of the blade row. Recent trends in turbomachinery, including higher blade loadings and use of integrally bladed rotors, lead to increased potential for forced-response issues. The Campbell diagram crossing for the excitation associated with the upstream and downstream vane rows on the embedded rotor first torsion vibratory mode is measured. The rotor response will be characterized with tip-timing measurements and the aerodynamic forcing functions measured. Unsteady casing pressures over the vibrating rotor are also acquired. This represents one of the few datasets detailing a forced-response condition in a multistage compressor, and the understanding gained from these experiments will be valuable in developing robust compressor designs.

Effect of switching uncertainty on a boost converter under a coloured noise influence

The noise processes associated with dynamical systems have limited bandwidth having finite, non-zero correlation time enabling us to model them as the Ornstein–Uhlenbeck process. The confluence of the deterministic system dynamics with these noisy forcing functions may trigger a series of unwarranted complex, peculiar phenomenon or stability issues in the system under different initial conditions and noise intensities. Thus, revisiting the system dynamics in the Ornstein–Uhlenbeck setting using the estimation and filtration algorithms seems an accurate and imperative choice. The Ito calculus, a very powerful classical tool, is used to evaluate the performance of stochastic differential equations. However, the Ito calculus cannot be directly applied to the systems under the influence of the Ornstein–Uhlenbeck process and we come across what is more fondly called as the curse of dimensionality, the augmented state vector approach. This paper develops a system theoretic-estimation algorithm for a switched-mode DC–DC power converter driven by the Ornstein–Uhlenbeck process. This is a novel attempt in this research direction. The algorithm is tested under a various data set and initial conditions to validate the findings.

Using Best Evidence to Reduce the Rate of Surgical Site Infection

Poster Presentation Objective To create a surgical site infection prevention bundle by examining population characteristics, context of care, and prioritization of evidence‐based interventions. Design Quality improvement plan‐do‐study‐act (PDSA) methodology with a small‐scale iterative approach to three cycles of improvement was used to create a surgical site infection (SSI) prevention bundle. Sample All women with cesarean births in scheduled day surgery operating suites and labor room operating suites at an academic medical center with 5500 births annually. Methods Care improvement process consisting of a common cause analysis of our readmission cases to determine the characteristics of our population. Next, we examined the literature on SSI prevention and treatment related to these characteristics. Three areas with significant variation from evidence‐based practice were identified: antibiotic prophylaxis, skin preparation, and education. Implementation Strategies To plan cycle one, we assessed antibiotic stewardship of participants. Overall 32% of participants and 31% of readmission participants did not adhere to guidelines To act, a forcing function in our order sets yielded a 100% compliance rate, and none of the participants in the test of change cycle ( N = 20) was readmitted. In the second cycle, we assessed skin preparation and found significant variation in processes. After education and implementation of new interventions, we found 100% compliance. The last cycle focused on patient education. To plan, we called 20 participants to assess their knowledge, what they were taught, and their current wound status. We found that we were teaching patients the signs and symptoms of infection but not prevention. Participants reported variation in care, limited education on wound care, and no education on hand hygiene; 20% reported wound deviation. Interventions applied included focused nursing education on wound care and hand hygiene when caring for infants, including a care package with materials to support the education at home. Reassessment revealed increased knowledge and wound care and no reports of wound deviations. Results SSI rates decreased during 10 months from 2.41% to 0.61% to zero. Days between SSI readmissions increased from 2 days to 68 days at present. Conclusion/Implications for Nursing Practice Developing a context and population focused evidence‐based prioritized care bundle can result in improved patient outcomes. Nursing interventions based on knowing the patient can yield sustainable results.

Existence of globally attracting fixed points of viscous Burgers equation with constant forcing. A computer assisted proof

We present a computer assisted method for proving the existence of globally attracting fixed points of dissipative PDEs. An application to the viscous Burgers equation with periodic boundary conditions and a forcing function constant in time is presented as a case study. We establish the existence of a locally attracting fixed point by using rigorous numerics techniques. To prove that the fixed point is, in fact, globally attracting we introduce a technique relying on a construction of an absorbing set, capturing any sufficiently regular initial condition after a finite time. Then the absorbing set is rigorously integrated forward in time to verify that any sufficiently regular initial condition is in the basin of attraction of the fixed point.

Application of an Adaptive Neuro Fuzzy Inference System for Low Speed Planetary Gearbox Vibration Control

The gear pair assembly remains one of the major vibration sources in power transmission systems of mechanical rotating machinery. The gear vibration signature is often dominated by several high-level tonal peaks that occur at the fundamental gear mesh and its harmonics. The primary forcing function is produced by the gear transmission error excitation resulting from tooth profile errors, misalignment and elastic deformation. The excessive dynamic response generated can frequently lead to structural fatigue failure. Therefore, it is highly desirable to control the low-speed planetary gearbox rotational vibration acceleration levels. To achieve this goal, the present study demonstrates a method by which these vibrations produced due to the primary forcing function originating from the mesh points can be controlled. Hence, to deal with both the meshing stiffness generation and vibration transmissibility processes more effectively, the control system must be applied close to the gear's connection. This close proximity will allow the application of a single controller. Selection of the proper rule base depending upon the situation can be achieved by the use of an adaptive neuro-fuzzy inference system (ANFIS) controller as an integrated approach for purposes of control to yield excellent results, and this is the highlight of this paper. The results presented in the paper show that the outputs take less time to stabilize. Moreover, due to incorporation of the ANFIS controller with the plant, it is observed that the gearbox reaches the desired vibration very quickly in relatively shorter time.

Improved mirror position estimation using resonant quantum smoothing

Quantum parameter estimation, the ability to precisely obtain a classical value in a quantum system, is very important to many key quantum technologies. Many of these technologies rely on an optical probe, either coherent or squeezed states to make a precise measurement of a parameter ultimately limited by quantum mechanics. We use this technique to theoretically model, simulate and validate by experiment the measurement and precise estimation of the position of a cavity mirror. In non-resonant systems, the achieved estimation enhancement from quantum smoothing over optimal filtering has not exceeded a factor two, even when squeezed state probes were used. Using a coherent state probe, we show that using quantum smoothing on a mechanically resonant structure driven by a resonant forcing function can result significantly greater improvement in parameter estimation than with non-resonant systems. In this work, we show that it is possible to achieve a smoothing improvement by a factor in excess of three times over optimal filtering. By using intra-cavity light as the probe we obtain finer precision than has been achieved with the equivalent quantum resources in free-space.

Solution method for a boundary value problem with fuzzy forcing function

In this paper, we present a new approach to a non-homogeneous fuzzy boundary value problem. We consider a linear differential equation with real coefficients but with a fuzzy forcing function and fuzzy boundary values. We assume that the forcing function is a triangular fuzzy function. Unlike previous studies, we look for a solution that is a fuzzy set of real functions (not a fuzzy-valued function). Each of these real functions satisfies the boundary value problem with some membership degree. We have developed a method that finds this solution, and demonstrated its effectiveness using a test example.To show that the approach can be extended to other types of fuzzy numbers, we extended it to the trapezoidal case. For a particular example, we used the product t-norm to demonstrate how a new solution type can be obtained.

The MJO skeleton model with observation‐based background state and forcing

The Madden–Julian Oscillation (MJO) skeleton model, a nonlinear oscillator model, has previously been shown to have solutions which exhibit several features in common with observed MJOs. In prior studies, model solutions have been found using mathematically simple (constant or sinusoidal) identical moistening and radiative forcing functions. Here we investigate whether this model can also produce realistic regional variability. To do this, observation‐based forcing functions are prescribed for latent heat flux and radiative cooling, and model solutions –both linear and nonlinear –are studied. In the stochastic nonlinear model, solutions reproduce the climatological mean convective activity well and the climatological variance reasonably well for such a simple model. In the linearized model, the solutions are found to contain additional structure including a realistic wave envelope of convective activity centred over the warm pool. These linear solutions are then used to identify and compare significant MJO activity in both reanalysis data and stochastic model solutions. Additional potential uses for these analytical and numerical solutions are discussed.

Determination of forcing functions in the wave equation. Part I: the space-dependent case

We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the study has importance and significance to non-intrusive and non-destructive testing of materials. This inverse force problem is linear, the solution is unique, but the problem is still ill-posed since, in general, the solution does not exist and, even if it exists, it does not depend continuously upon the input data. Numerically, the finite difference method combined with the Tikhonov regularization are employed in order to obtain a stable solution. Several orders of regularization are investigated. The choice of the regularization parameter is based on the L-curve method. Numerical results show that the solution is accurate for exact data and stable for noisy data. An extension to the case of multiple additive forces is also addressed. In a companion paper, in Part II, the time-dependent force identification will be undertaken.

Determination of forcing functions in the wave equation. Part II: the time-dependent case

An unknown time-dependent force function in the wave equation is investigated in this study. This is a natural continuation of Part I [J Eng Math 2015, this volume], where the space-dependent force identification has been considered. Additional data are given by a space integral average measurement of the displacement. This linear inverse problem has a unique solution, but it is still ill-posed since small errors in the input data cause large errors in the output solution. Consequently, when the input data are contaminated with noise, we use the Tikhonov regularization method in order to obtain a stable solution. The choice of the regularization parameter is based on the L-curve method. Numerical results show that the solution is accurate for exact data and stable for noisy data.

Approximate Analytical Solution to Diurnal Atmospheric Boundary-Layer Growth Under Well-Watered Conditions

Simplified numerical models of the atmospheric boundary layer (ABL) are useful both for understanding the underlying dynamics and potentially providing parsimonious modelling approaches for inclusion in larger models. Herein the governing equations of a simplified slab model of the uniformly mixed, purely convective, diurnal ABL are shown to allow immediate solutions for the potential temperature and specific humidity as functions of the ABL height and net radiation when expressed in integral form. By employing a linearized saturation vapour relation, the height of the mixed layer is shown to obey a non-linear ordinary differential equation with quadratic dependence on ABL height. A perturbation solution provides general analytical approximations, of which the leading term is shown to represent the contribution under equilibrium evaporation. These solutions allow the diurnal evolution of the height, potential temperature, and specific humidity (i.e., also vapour pressure deficit) of the mixed layer to be expressed analytically for arbitrary radiative forcing functions.

Simulation of solid body motion in a Newtonian fluid using a vorticity-based pseudo-spectral immersed boundary method augmented by the radial basis functions

The moving boundary conditions are implemented into the Fourier pseudo-spectral solution of the two-dimensional incompressible Navier–Stokes equations (NSE) in the vorticity-velocity form, using the radial basis functions (RBF). Without explicit definition of an external forcing function, the desired immersed boundary conditions are imposed by direct modification of the convection and diffusion terms. At the beginning of each time-step the solenoidal velocities, satisfying the desired moving boundary conditions, along with a modified vorticity are obtained and used in modification of the convection and diffusion terms of the vorticity evolution equation. Time integration is performed by the explicit fourth-order Runge–Kutta method and the boundary conditions are set at the beginning of each sub-step. The method is applied to a couple of moving boundary problems and more than second-order of accuracy in space is demonstrated for the Reynolds numbers up to Re = 550. Moreover, performance of the method is shown in comparison with the classical Fourier pseudo-spectral method.

The initial value problem for interval-valued second-order differential equations under generalized H-differentiability

In this paper the interval-valued second-order differential equations under generalized Hukuhara differentiability (ISDEs) are introduced. Under suitable conditions we obtain the existence and uniqueness results of solutions to ISDEs. To prove this assertion we use idea of contraction principle and successive approximations. Furthermore, we use the method based on properties of linear transformations (LTM) to find the explicit solution of initial value problem for linear second-order differential equation with interval-valued forcing function and with interval initial values (IIVP). We apply the linear transformations method to two example problems including a vibrating mass and an electrical circuit. Finally, the method based on the analysis of a solution to real-valued second-order differential equation is investigated to solve interval-valued second-order differential equations with interval-valued coefficients, interval-valued forcing function and interval initial values. Some examples are presented to illustrate applicability of the proposed method.

A Multilevel Numerical Approach with Application in Time-Domain Electromagnetics

AbstractAn algebraic multilevel method is proposed for efficiently simulating linear wave propagation using higher-order numerical schemes. This method is used in conjunction with the Finite Volume Time Domain (FVTD) technique for the numerical solution of the time-domain Maxwell’s equations in electromagnetic scattering problems. In the multilevel method the solution is cycled through spatial operators of varying orders of accuracy, while maintaining highest-order accuracy at coarser approximation levels through the use of the relative truncation error as a forcing function. Higher-order spatial accuracy can be enforced using the multilevel method at a fraction of the computational cost incurred in a conventional higher-order implementation. The multilevel method is targeted towards electromagnetic scattering problems at large electrical sizes which usually require long simulation times due to the use of very fine meshes dictated by point-per-wavelength requirements to accurately model wave propagation over long distances.

Stability Analysis for the Deployment of Unmanned Surface Vehicles

Motion control schemes are generally classified into three categories (point stabilization, trajectory tracking, and path following). This paper deals with the problem which is associated with the initial deployment of a group of Unmanned Surface Vehicle (USVs) and corresponding point stabilization. To keep the formation of a group of USVs, it is necessary to set the relationship between each vehicle. A forcing functions such as potential fields are designed to keep the formation and a graph Laplacian is used to represent the connectivity between vehicle. In case of fixed topology of the graph representing the communication between the vehicles, the graph Laplacian is assumed constant. However the graph topologies are allowed to change as the vehicles move, and the system dynamics become discontinuous in nature because the graph Laplacian changes as time passes. To check the stability in the stage of deployment, the system is modeled with Kronecker algebra notation. Filippov’s calculus of differential equations with discontinuous right hand sides is then used to formally characterize the behavior of USVs. The stability of the system is analyzed with Lyapunov’s stability theory and LaSalle’s invariance principle, and the validity is shown by checking the variation of state norm.

Glacial cycles drive variations in the production of oceanic crust.

Glacial cycles redistribute water between oceans and continents, causing pressure changes in the upper mantle, with consequences for the melting of Earth's interior. Using Plio-Pleistocene sea-level variations as a forcing function, theoretical models of mid-ocean ridge dynamics that include melt transport predict temporal variations in crustal thickness of hundreds of meters. New bathymetry from the Australian-Antarctic ridge shows statistically significant spectral energy near the Milankovitch periods of 23, 41, and 100 thousand years, which is consistent with model predictions. These results suggest that abyssal hills, one of the most common bathymetric features on Earth, record the magmatic response to changes in sea level. The models and data support a link between glacial cycles at the surface and mantle melting at depth, recorded in the bathymetric fabric of the sea floor.

Fuzzy Euler differential equation

In this work, we state a Fuzzy Euler differential equation, Here we investigate problems with fuzzy coefficients, fuzzy initial values and fuzzy forcing functions. Our strategy is based by the change of variables and reduced Fuzzy Euler differential equation to fuzzy initial value problem for a second-order linear fuzzy differential equation. Finally we present an example by using our proposed strategy.

The American Counterculture of War: Supporting Foreign Insurgencies and the American Discourse of War

The U.S. Army Special Forces and the Central Intelligence Agency (CIA) trace their legacy back to the Office of Strategic Services (OSS). But the history and legacy of special operations, especially the use of unconventional warfare, goes back much further in American history. After closely examining the historical literature that discusses the American ways, cultures, and dominant traditions of war, this article asserts that unconventional warfare, the practice of supporting insurgencies, represents a counterculture of war that is rising and beginning to influence the discourse on strategy, war, and warfare in America. The article speculates that the rise of this counterculture could be a forcing function for better strategy and strategic thinking.

The Quasigeostrophic Omega Equation: Reappraisal, Refinements, and Relevance

Abstract A two-component study is undertaken of the classical quasigeostrophic (QG) omega equation. First, a reappraisal is undertaken of extant formulations of the equation’s so-called forcing function. It pinpoints shortcomings of various formulations and prompts consideration of alternative forms. Particular consideration is given to the contribution of flow deformation to the forcing function, and to the role of the advection of the geostrophic flow by the thermal wind (the R vector). The latter is closely related to the Q vector, the horizontal component of the ageostrophic vorticity, and the forcing function itself. The reexamination promotes further examination of the physical interpretation and diagnostic use of the omega equation particularly for assessing richly structured subsynoptic flow features. Second, consideration is given to the dynamics associated with the equation and its more general utility. It is shown that the R vector is intrinsic to a quasigeostrophic cascade to finer-scaled flow, and that a fundamental feature of the QG omega equation—the in-phase relationship between cloud-diabatic heating and the attendant vertical velocity—has important potential ramifications for the assimilation of data in numerical weather prediction (NWP) models. Finally, it is shown that, in the context of considering NWP model output, mild generalizations of the quasigeostrophic R vector retain interpretative value for flow settings beyond geostrophy and warrant consideration when addressing some contemporary NWP challenges.