Sinusoidal Perturbation Research Articles

Mathematical modeling of Stokes flow in petal shaped pipes

A theoretical model is developed to characterize fully developed laminar flow (Stokes flow) in idealized petal shaped pipes by regarding the pipe wall as a circular boundary having sinusoidal perturbation (or, equivalently, surface roughness). Built upon the method of perturbation, the model quantifies the effects of the relative roughness and wave number of the pipe boundary on the Stokes flow. Approximate solutions of the velocity field, pressure gradient, and static flow resistivity are obtained. The same approach together with the method of Fourier transform is used to deal with low Reynolds flow in pipes having other cross-sectional morphologies such as triangle and square. Results obtained from computational fluid dynamics simulations are used to validate the theoretical model predictions, with good agreement achieved. The presence of surface roughness causes periodic fluctuation and global offset of velocity distribution and enlarges both the pressure gradient and static flow resistivity in petal shaped pipes.

On instabilities of growing bi-material interfaces

This study concerns with the evolution of morphological patterns that often arise on the interface of bi-material, so called metal-precipitate phase, due to the instability of the interfaces. The instability leads to growth or retraction of small perturbation, which may determine the formation of a variety of morphological patterns initially arising on surfaces of growing precipitates at small length scales. To better understand the cause of different patterns on the bi-material interfaces, an analytical study of the stability of the precipitate-matrix interface is performed. First, a wavy interface perturbation is used to examine the spontaneous variations that occur at the precipitate-matrix interface. Then, the analysis utilises Cerruti?s solution to compute the perturbed stress field surrounding the interface. It is shown that a virtually flat interface subjected to tension is in general unstable. The amplitude of sinusoidal perturbations decays for short wave lengths and grow for longer wave lengths. Both a critical wave length for which the perturbation amplitude is unaffected and a specific ditto which obtain maximum perturbation growth rate are derived

A Novel Inertia Identification Method and Its Application in PI Controllers of PMSM Drives

A novel method for inertia determination of a permanent magnet synchronous machine (PMSM) drive is proposed and analyzed, which employs a sinusoidal perturbation torque with a dc offset to drive the PMSM, and the amplitudes of reference sinusoidal torque and sinusoidal speed response are used to compute the system inertia. Compared with other methods, it is robust and fast to obtain the accurate quantity of the inertia. First, the inverter measures the resistances and inductances of a PMSM through a static voltage vector and stand-still frequency response experiments. The parameters are adopted to design the current proportion and integral controller and make both dq-axes currents to perform the first-order response. Second, the results of constant torque experiment employing the current controller are applied to get the friction coefficient and no-load torque. Third, a sinusoidal torque with a dc offset is applied and the response performs a sinusoidal speed with a constant offset. All the above experimental results and other preinstalled parameters are employed to get the system inertia, and the accuracy is verified by another experiment. As compensation for a position signal from a hall sensor, a corresponding method is also proposed to compute the sinusoidal speed response amplitude, which is the key in the procedure.

Study on the perturbation effect of the different vibration frequency and amplitude to the fusion pebble bed

The solid blanket is the main choice of the fusion reactor using the structure of pebble beds with beryllium as neutron multiplier and lithium silicate or lithium titanate as tritium breeder. The packing factor of the pebble bed is essential to the TBR(tritium breeder ratio), so it is important to study the mechanical behavior of particle system under the different kinds of the perturbations. In this paper, based on the mechanical behavior of solid pebble bed, the dynamic behavior of single particle system and mixed particle system under the different perturbation are simulated and analyzed by the EDEM software. The results show that, the perturbation can cause the packing factor of the particle system to increase continuously. In order to study the different way of the perturbation, three different typical models have been constructed. For the sinusoidal perturbation under the same strain, the stress of particle system decreases gradually, but the stress variation in the contraction and expansion process are different. The relationship between stress and vibration frequency roughly obeys the exponential decay law, and the stress drops faster with more violent disturbance. Then we use the mathematical model for fitting the relevant formula, which is valuable reference for engineering design in the future.

Time Domain Simulation of Geomagnetically Induced Current (GIC) Flowing in 500‐kV Power Grid in Japan Including a Three‐Dimensional Ground Inhomogeneity

AbstractWe performed 3‐D time domain simulation of geomagnetically induced currents (GICs) flowing in the Japanese 500‐kV power grid. The three‐dimensional distribution of the geomagnetically induced electric field (GIE) was calculated by using the finite difference time domain method with a three‐dimensional electrical conductivity model constructed from a global relief model and a global map of sediment thickness. First, we imposed a uniform sheet current at 100‐km altitude with a sinusoidal perturbation to illuminate the influence of the structured ground conductivity on GIE and GIC. The simulation result shows that GIE exhibits localized, uneven distribution that can be attributed to charge accumulation due to the inhomogeneous conductivity below the Earth's surface. The charge accumulation becomes large when the conductivity gradient vector is parallel or antiparallel to the incident electric field. For given GIE, we calculated the GICs flowing in a simplified 500‐kV power grid network in Japan. The influence of the inhomogeneous ground conductivity on GIC appears to depend on a combination of the location of substations and the direction of the source current. Uneven distribution of the power grid system gives rise to intensification of the GICs flowing in remote areas where substations/power plants are distributed sparsely. Second, we imposed the sheet current with its intensity inferred from the ground magnetic disturbance for the magnetic storm of 27 May 2017. We compared the calculated GICs with the observed ones at substations around Tokyo and found a certain agreement when the uneven distribution of GIE is incorporated with the simulation.

Numerical simulation of incompressible gusty flow past a circular cylinder

Flow around a circular cylinder under the influence of a one dimensional gust is investigated in the present paper. In the present study the gusty flow which impinges on the cylinder is produced by superimposing a single harmonic sinusoidal transverse perturbation velocity component on uniform flow. A gust source region is defined for creating the perturbation velocity. Streamlines, vorticity and iso-velocity contours are used to physically interpret the flow field features. Temporal variations of force coefficients and stagnation-separation points on the cylinder surface are studied. Frequency spectrum of force coefficients reveal interesting facts about the variation of energy content in the gust frequency peak in comparison with vortex shedding frequency peak as a function of Reynolds number (Re) and the angular frequency of the gust (ω). Wherever possible, an attempt has been made to compare the flow features between uniform and gusty flow conditions. The present numerical work has been performed using ‘CFRUNS’ – a numerical scheme developed by Harichandan and Roy (2010) for solving incompressible two-dimensional Navier-Stokes equations using unstructured grid.

Driven thermal waves and determination of the thermal conductivity in a magnetized plasma

Results are presented from a basic heat transport experiment using a magnetized electron temperature filament that behaves as a thermal resonator. A small, crystal cathode injects low-energy electrons along the magnetic field into the afterglow of a large preexisting plasma forming a hot electron filament embedded in a colder plasma. A series of low amplitude, sinusoidal perturbations are added to the cathode discharge bias that create an oscillating heat source capable of driving thermal waves. Langmuir probe measurements demonstrate driven thermal oscillations and allow for the determination of the amplitude and parallel phase velocity of the thermal waves over a range of driver frequencies. The results conclusively show the presence of a thermal resonance and are used to verify the parallel thermal wave dispersion relation based on classical transport theory. A nonlinear transport code is used to verify the analysis procedure. This technique provides an alternative measure of the density normalized thermal conductivity, independent of the electron temperature.

Vortex-Induced Vibration Optimization of a Wide Streamline Box Girder by Wind Tunnel Test

Although the streamline box girder exhibits an excellent aerodynamic performance, they are often suffer severe Vortex-Induced Vibrations (VIVs) due to complicated separation and reattachment of air flows. It is necessary to apply control measures on the streamline box girder to suppress VIV. In this study, the VIV optimizations of a super wide streamline box girder were conducted via a series of section model wind tunnel tests. The effects of wind fairings, inspection vehicle rails, guide vanes, traffic barriers and handrails on the heaving VIV performance of the wide streamline box girder were analyzed. The test results show that the inspection vehicle rail and handrail are the main members to induce the heaving VIV of the box girder. A sharper wind fairing without changing the distance of railings is favorable to the heaving VIV performance. However, the countermeasures of changing the position of inspection vehicle rail and installing guide vanes under the girder have slight influences on reducing heaving VIV responses. Inspired by the spanwise sinusoidal perturbation method, the traffic barriers sealed with plates by regular intervals along the bridge deck can suppress the heaving VIV of the box girder successfully. The porosity of handrails has a significant effect on the heaving VIV. By using a sharp wind fairing and circular simplified handrails, the VIV performance of the wide streamline box girder was greatly improved. Their mitigation abilities were verified by a large-scale section model wind tunnel test.

The influence of layer-interface geometry on single-layer folding

Abstract Geometrical heterogeneities along layer interfaces play a key role in determining the geometries of folds developed during shortening of competent layers. We present a series of numerical simulations to investigate the influence of initial sinusoidal perturbations on the folding of single layers. Models consist of a competent viscous single layer embedded in a softer matrix, with the layer orientated parallel to the shortening direction. We first generalize the wide spectrum of sinusoidal perturbations accounting for asymmetries along and across a competent single layer, using two parameters: transversal asymmetry ( A ′) and longitudinal asymmetry ( φ ). These two parameters allow the transition between classical fold shapes and pinch and swell geometries to be studied. The parameter A ′ describes the development of fold hinges with different geometries between the upper and lower layer interfaces, and abnormal curvatures between the outer and inner arcs of fold hinges. The parameter φ induces a strong polarity on the folds, with a systematic preferred orientation of the pinch and swell regions of the layer, even if there is no shear component parallel to the layer. Our results demonstrate the importance of structural inheritance on the resulting fold geometries, and suggest that caution must be taken when using certain types of asymmetrical folds as strain markers and kinematic indicators.

Mitochondrial chaotic dynamics: Redox-energetic behavior at the edge of stability

Mitochondria serve multiple key cellular functions, including energy generation, redox balance, and regulation of apoptotic cell death, thus making a major impact on healthy and diseased states. Increasingly recognized is that biological network stability/instability can play critical roles in determining health and disease. We report for the first-time mitochondrial chaotic dynamics, characterizing the conditions leading from stability to chaos in this organelle. Using an experimentally validated computational model of mitochondrial function, we show that complex oscillatory dynamics in key metabolic variables, arising at the “edge” between fully functional and pathological behavior, sets the stage for chaos. Under these conditions, a mild, regular sinusoidal redox forcing perturbation triggers chaotic dynamics with main signature traits such as sensitivity to initial conditions, positive Lyapunov exponents, and strange attractors. At the “edge” mitochondrial chaos is exquisitely sensitive to the antioxidant capacity of matrix Mn superoxide dismutase as well as to the amplitude and frequency of the redox perturbation. These results have potential implications both for mitochondrial signaling determining health maintenance, and pathological transformation, including abnormal cardiac rhythms.

Cellular Automata Modeling of Ostwald Ripening and Rayleigh Instability.

A cellular automata (CA) approach to modeling both Ostwald ripening and Rayleigh instability was developed. Curvature-driven phase interface migration was implemented to CA model, and novel CA rules were introduced to ensure the conservation of phase volume fraction of nearly equilibrium two-phase system. For transient Ostwald ripening, it is shown that the temporal growth exponent m is evolving with time and non-integer temporal exponents between 2 and 3 are predicted. The varying temporal growth exponent m is related to the particle size distributions (PSDs) evolution. With an initial wide PSD, it becomes narrowed toward steady state. With an initial narrow PSD, it becomes widened at first and then narrowed toward steady state. For Rayleigh instability, two cases (one with sinusoidal perturbation on the surface of the long cylinder, and the other with grain boundaries in the interior of the long cylinder) were simulated, and the breakup of the long cylinder was shown for both cases. In the end, a system containing long cylinders with interior grain boundaries was simulated, which demonstrated the integration of Rayleigh instability and Ostwald ripening relating to the spheroidization of the lamellar structure.

Maximizing Map Sensitivity and Higher Derivatives Via Extremum Seeking

We present a generalization to the scalar Newton-based extremum seeking algorithm which, through perturbation-induced measurements of an unknown steady-state input-to-output map, maximizes the map's higher derivatives. As with other extremum seeking (ES) problems, the scheme relies on derivative estimators and learning dynamics operating in different time scales. We provide analysis for the typical deterministic (sinusoidal) perturbation of the optimal parameter estimate. Also, we alternatively include a stochastic method where the map is perturbed via the sinusoid of Brownian motion about the boundary of a circle. By properly demodulating the map output corresponding to the manner in which it is perturbed, the ES algorithm maximizes the $n{\rm th}$ derivative only through measurements of the map. The Newton-based ES approach removes the dependence of the convergence rate on the unknown Hessian of the higher derivative, an effort to improve performance over standard gradient-based ES. Our design stems from the existing multivariable Newton-based ES algorithm where a differential Riccati equation estimates the inverse Hessian of the function to be maximized. Algebraically computing a direct estimate of the inverse Hessian is susceptible to singularity, whereas employing the Riccati filter removes that potential. We prove local stability of the algorithm for general nonlinear equilibrium profiles of dynamic maps and compare the Newton-based method against the gradient-based method. We also extend this abstraction to multiplayer noncooperative games but limit our attention to a two-player game for notational simplicity and length considerations.

The Stability Analysis of a Multi-Port Single-Phase Solid-State Transformer in the Electromagnetic Timescale

This paper proposes an overall practical stability assessment for a multi-port single-phase solid-state transformer (MS3T) in the electromagnetic timescale. When multiple stable subsystems are combined into one MS3T, the newly formed MS3T has a certain possibility to be unstable. Thus, this paper discusses the stability assessment of the MS3T in detail. First and foremost, the structure of the MS3T and its three stage control strategies are proposed. Furthermore, the stability analysis of each of the MS3T’s subsystems is achieved through the closed loop transfer function of each subsystem, respectively, including an AC-DC front-end side converter, dual active bridge (DAB) with a high-frequency (HF) or medium-frequency (MF) transformer, and back-end side incorporating DC-AC and dc-dc converters. Furthermore, the practical impedance stability criterion in the electromagnetic timescale, which only requires two current sensors and one external high-bandwidth small-signal sinusoidal perturbation current source, is proposed by the Gershgorin theorem and Kirchhoff laws. Finally, the overall stability assessment, based on a modified impedance criterion for the MS3T is investigated. The overall practical stability assessment of the MS3T can be validated through extensive simulation and hardware results.

Analytical and numerical study of normal shock response in a uniform duct

The response of an inviscid shock to external pressure perturbations in a constant area duct is analyzed in terms of fundamental processes like perturbation propagation and its interaction with shock. The results of these elementary processes are formulated analytically and with a Riemann wave tracking method to enable the prediction of shock movement for both upstream and downstream perturbations. The predictions thus obtained are compared with the finite-volume based numerical simulations of the Euler equations. This study shows that the shock responds nonlinearly to perturbations and the nonlinearity has a cumulative effect. Contact surfaces generated during the interaction of normal shock with perturbations, which was ignored in previous investigations, are shown to be important in order to capture this cumulative nonlinearity. The nonlinearity alters the positive and negative duty cycles, which results in a net displacement of shock after responding to one full cycle of sinusoidal perturbation. This drift in shock location is pronounced at low supersonic Mach numbers (1.2–3) but is also present at higher Mach numbers. Furthermore, it is demonstrated that the duty cycle variations are higher for perturbations originating downstream of shock than those originating upstream. The variations in frequency and amplitude are found to merely scale the response and do not introduce any new physics.

Ureolytic Biofilm Formation from a Microbial Consortium on Graphite

Urea Hydrolysis by Biofilms composed of urease producing bacteria are of primordial interest in several fields 1. The ureolysis at circumneutral pH requires water and a proton producing two molecules of ammonium ions and one molecule of bicarbonate ion. The consumption of one proton increases the pH and carbonate mineral precipitation (biomineralization) may proceed when calcium or other divalent cations are present 1. This biochemical process can be useful for applications such as building materials, soil stabilization, and contaminant remediation; it is also of interest to industrial, agricultural and wastewater treatment 1. To increase the ureolysis rate new methods should be sought to maintain bacterial cells adhered to different solid surfaces However, biofilms are generally studied by imaging, rheological and physical techniques which are difficult to implement and do not represent an efficient form of “metabolic” evaluation, thus it is necessary to develop alternative techniques that allow the direct study of the biofilms properties. In light of this scenario, the present work proposes the selection of a microbial consortium from cow dung and the study of the formation and growth of an ureolytic biofilm on graphite surfaces by Electrochemical Impedance Spectroscopy (EIS) without noticeable modifications of the biofilm. EIS spectra were obtained at open circuit potential (OCP) (without additional electric perturbation apart from sinusoidal perturbation ±10 mV), during the time of immersion of graphite in the culture medium, in the absence (Control) and presence of bacteria (Biotic). The results (figure 1) indicate that the spectra of both control and biotic conditions exhibit just one time constant. Moreover, spectra adjustment to equivalent electric circuits indicates that the biofilm adhesion is directly related to the modification of the capacitance, while the generation of ammonium ions directly influences the decrease in electrical resistance of the culture medium. The biofilm maturation and its interaction with the graphite surface induces lower charge transfer resistance, which can be applied as a novel technology for the urea hydrolysis. SEM and CLSM images confirm the presence of ureolytic biofilm and confirm the interpretations obtained by EIS. Figure 1. Evolution of Bode plots obtained on a graphite surface (0.283 cm2) during the time of immersion. Solid symbols identify frequency where the impedance was obtained. The lines are simulated EIS diagrams constructed with the electric parameter values obtained from the best fit of EIS experimental spectra. The study systems: a) and c) Control (without bacteria), and b) and d) Biotic: with microbial consortium inoculum. Funding This research was supported by the National Council for Science and Technology (CONACyT) México and for the scholarship 328072. References J. M. Connolly, B. Jackson, A. P. Rothman, I. Klapper, and R. Gerlach, npj Biofilms Microbiomes, 1, 15014 (2015) http://www.nature.com/articles/npjbiofilms201514. Figure 1

Optimal control of single stage LiBr/water absorption chiller

Low-capacity refrigeration and space conditioning systems have increased significantly in the last years, increasing primary energy demand. For this reason, it is important to start implementing refrigeration and space conditioning system that can be driven by unconventional energy sources, such as a single stage lithium bromide absorption refrigeration chiller since it can be powered by a low grade heat source. Therefore, we establish an optimal control strategy to operate these systems. For the implementation of the optimum control a dynamic model to evaluate the system is developed and discretized and solved using the interior point optimization (IPOPT) solver. The cases studied where a step and a sinusoidal perturbation on the hot water inlet temperature. The results obtained are promising because, through the implementation of the optimal control strategy, the coefficient of performance (COP) of the refrigeration system was significantly improved, reducing operational cost and all this without affecting the cold water outlet temperature.

Wrinkles in soft dielectric plates

We show that a smooth giant voltage actuation of soft dielectric plates is not easily obtained in practice. In principle one can exploit, through pre-deformation, the snap-through behavior of their loading curve to deliver a large stretch prior to electric breakdown. However, we demonstrate here that even in this favorable scenario, the soft dielectric is likely to first encounter the plate wrinkling phenomenon, as modeled by the onset of small-amplitude sinusoidal perturbations on its faces. We provide an explicit treatment of this incremental boundary value problem. We also derive closed-form expressions for the two limit cases of very thin membranes (with vanishing thickness) and of thick plates (with thickness comparable to or greater than the wavelength of the perturbation). We treat explicitly examples of ideal dielectric free energy functions (where the mechanical part is of the neo-Hookean, Mooney–Rivlin or Gent form) and of dielectrics exhibiting polarization saturation. In addition to the expected buckling mode coming from the purely elastic case, we discover a second mode occurring at large voltages in extension. We find that plates always wrinkle anti-symmetrically, before the symmetric modes can be reached. Finally, we make the link with the classical results of the Hessian electro-mechanical instability criterion and of Euler buckling for an elastic column.

A Synchro-Perspective-Based High-Frequency Voltage Injection Method for Position-Sensorless Vector Control of Doubly Fed Induction Machines

In this paper, a novel salient autonomous high-frequency (HF) signal injection method of sensorless drive for doubly fed induction machines (DFIM) is proposed. The HF voltage is injected into the rotor winding, and according to the concept of synchro, the rotor position can be simply extracted from the phase difference among the stator current and the rotor current regardless of machine and grid parameters. In addition, the proposed scheme is robust against the disturbance of HF stator voltage propagated from the grid. The vector phase-locked loop (PLL) technique is employed to calculate rotor position and rotor speed simultaneously, and the global stability of the PLL is mentioned. The tracking performances during acceleration and deceleration, and sinusoidal perturbation are investigated. The feasibility of the proposed concept is verified by the experimental results with a 4-kW DFIM drive. The performances of the drive system are evaluated in various operating conditions, e.g., subsynchronous, synchronous and supersynchronous speeds, voltage sag, and flying start.

Emergence of Lissajous Patterns as a Function of a Perturbation Frequency in Postural Responses to the Short Sinusoidal Translations of Varying Frequencies.

The existence of in-phase and anti-phase postural responses to sinusoidal perturbations to the base of support is well known. In this study, we investigate if such coordinated postural responses exist at 'near-sway' perturbations where the perturbation amplitudes are kept within the range of normal sway lengths in healthy adults (n=10). The postural responses are analyzed via bursts of anterior-posterior (AP) 2.5 mm horizontal sinusoidal oscillations of the base of support at sequentially varying frequencies (0.25, 0.375, 0.5, 0.625, 0.75, 1 and 1.25 Hz). The parametric plots of the perturbation signal (platform position) and the response profiles (AP Center of Pressure [APCoP]) show the emergence of elliptical Lissajous patterns as the perturbation frequency is increased from 0.25 Hz to 1.25 Hz. The presence of such characteristic pattern shows the 'lock-in' behavior of APCoP with perturbation signal. These elliptical patterns become more apparent at the center frequencies (0.375 to 0.75 Hz). At the higher frequencies (1 and 1.25 Hz), the Lissajous patterns do exist but are dominated by low-frequency drift. The area and orientation of Lissajous patterns and the phase shifts between perturbation and APCoP show a strong nonlinear decreasing trend with increasing perturbation frequency for both, young (n=5) as well as mature (n=5) adults within the study group. This may suggest that such characteristic, frequency-locked, phased shifted response of healthy posture control could be a fundamental property of a healthy posture control's response to 'near-sway' sinusoidal translations in AP direction.

Body stiffness and damping depend sensitively on the timing of muscle activation in lampreys.

Unlike most manmade machines, animals move through their world using flexible bodies and appendages, which bend due to internal muscle and body forces, and also due to forces from the environment. Fishes in particular must cope with fluid dynamic forces that not only resist their overall swimming movements but also may have unsteady flow patterns, vortices, and turbulence, many of which occur more rapidly than what the nervous system can process. Has natural selection led to mechanical properties of fish bodies and their component tissues that can respond very quickly to environmental perturbations? Here, we focus on the mechanical properties of isolated muscle tissue and of the entire intact body in the silver lamprey, Ichthyomyzon unicuspis. We developed two modified work loop protocols to determine the effect of small perturbations on the whole body and on isolated segments of muscle as a function of muscle activation and phase within the swimming cycle. First, we examined how the mechanical properties of the whole lamprey body change depending on the timing of muscle activity. Relative to passive muscle, muscle activation can modulate the effective stiffness by about two-fold and modulate the effective damping by >10-fold depending on the activation phase. Next, we performed a standard work loop test on small sections of axial musculature while adding low-amplitude sinusoidal perturbations at specific frequencies. We modeled the data using a new system identification technique based on time-periodic system analysis and harmonic transfer functions (HTFs) and used the resulting models to predict muscle function under novel conditions. We found that the effective stiffness and damping of muscle varies during the swimming cycle, and that the timing of activation can alter both the magnitude and timing of peak stiffness and damping. Moreover, the response of the isolated muscle was highly nonlinear and length dependent, but the body's response was much more linear. We applied the resulting HTFs from our experiments to explore the effect of pairs of antagonistic muscles. The results suggest that when muscles work against each other as antagonists, the combined system has weaker nonlinearities than either muscle segment alone. Together, these results begin to provide an integrative understanding of how activation timing can tune the mechanical response properties of muscles, enabling fish to swim effectively in their complex and unpredictable environment.