Periodic Input Research Articles

AN OSCILLATORY MODEL FOR GLOBALLY STABLE PROTEIN TRANSCRIPTION DYNAMICS

Oscillations appear in all levels of biological organization. Oscillatory phenomena do not always possess a simple periodic nature. In this work, we analyze a gene transcriptional network in which we assume an almost periodic input that regulates gene. We use an almost periodic input [Formula: see text] since a periodic one is very restrictive. We show that the almost periodic model proposed has a unique almost periodic attractor. Numerical simulations show that the retroactivity is highly affected when an almost periodic input is used in an upstream system that is interconnected to a downstream system. By comparison of the solutions of the model, we can conclude that when the amount of protein bound to the promoter is modeled by either a periodic function or an almost periodic one, which is denoted by [Formula: see text], the amount of protein concentration [Formula: see text] can be underestimated or overestimated depending on if [Formula: see text] is modeling by a periodic or an almost periodic function. These estimation errors can lead to an error in the quantification of retroactivity which in turn can alter the coordination between an upstream system and a downstream one.

Persistence criteria for a chemostat with variable nutrient input and variable washout with delayed response in growth

We study a general single-species chemostat model with non-autonomous input and washout, and a discrete-time delay between consumption of the nutrient and growth. The goal of this article is to provide sufficient and necessary conditions for persistence. The persistence criteria obtained here extend previous works done for the autonomous model with delay and for the non-autonomous model without delay. Furthermore, in the particular case of periodic nutrient input and the same periodic washout with delayed response in growth, the persistence criteria can be expressed in terms of the average of the involved functions. We remark in no case we need to impose any restrictions on the size of the delay.

Command-Filtered Backstepping Repetitive Control for a Class of Uncertain Nonlinear Systems Based on Additive State Decomposition

This paper presents a command-filtered backstepping repetitive control (RC) method for a class of uncertain nonlinear systems with multiple disturbances, which is based on additive state decomposition (ASD) technique and active disturbance rejection approach. First, the original nonlinear system is decomposed into a linear time-invariant (LTI) primary system with periodic inputs and a nonlinear secondary system with multiple, aperiodic disturbances. The original nonlinear tracking problem is accordingly decomposed into two subproblems: RC problem for an LTI periodic system and a robust stabilization problem for a nonlinear system. By making using of the known information of the model, a linear extended state observer is constructed to estimate the matched total disturbance together with the system states and then a command-filtered backstepping control law incorporating with the estimate of the equivalent input disturbance is developed for the secondary system that ensures the robust stability and compensates for the effects of the multiple disturbances and residual nonlinearity. Stability criterion for each subsystem is established. Moreover, a particle-swarm-optimization algorithm is adopted to simultaneously optimize the controller parameters of the system. Finally, simulations and comparative experiments demonstrate the validity and superiorities of this method.

Physical and chemical processes driving remote seasonal atmospheric exposure to cyclic volatile methysiloxanes and short-chain chlorinated paraffins

Cyclic volatile methylsiloxanes (cVMS) and short-chain chlorinated paraffins (SCCPs) use has been restricted in recent years due to environmental health concerns. Both of these classes of emerging contaminants possess long range transport potential (LRTP), highlighting the need for continuous monitoring to assess effectiveness of implemented regulations. However, emission source elucidation and understanding processes affecting atmospheric transport remain challenging. Atmospheric levels of cVMSs and SCCPs were simultaneously monitored at a background monitoring site in Norway from January–July 2020. Concentrations obtained from active air samplers ranged from 49.9 to 845 (mean: 208) pg/m3 for ƩSCCPs and from 0.4 to 3.5 (mean: 1.5), 1.1–15 (mean: 5.6) and 0.1–0.9 (mean: 0.4) ng/m3 for octamethylcyclotetrasiloxane (D4), decamethylcyclopentasiloxane (D5) and dodecamethylcyclohexasiloxane (D6), respectively. As SCCPs pose several challenges to analysts, different quantification methodologies and blank handling procedures were investigated to ensure reliable environmental measurements. Simulations using a Lagrangian atmospheric transport model (FLEXPART) revealed air masses impacting sampling measurements were of Oceanic origin, but periodic emission events from Europe and Russia were also observed. Seasonal pattern in cVMS concentrations was mainly driven by atmospheric degradation via hydroxyl radical reaction, whereas SCCP concentrations were more influenced by periodic anthropogenic inputs from local and continental Europe. No clear correlation could be observed with SCCP atmospheric concentrations and temperature over the entire sampling campaign. However, increased volatilization at elevated temperatures may be important with emissions originating from local sources. Higher chlorinated homologue groups dominated during the winter season and declined towards spring and summer, whereas reverse was found for the lower and more volatile chlorinated homologue groups.

Forced Convection during Cooling of Power Supply Box using Pulsation Flow with Piezoelectric Fan

AbstractForced convection flow of air through power supply box with piezoelectric fan of nine identical electrical devices has been numerically investigated. This work simulates a practical situation in which periodic temperature is generated in an electrical device as a result of its periodic input voltage. The finite volume method has been adopted to solve the governing equations. The effects of important parameters such as pulsation flow frequencies and temperature modulation frequency on heat transfer rates were investigated in details for Re = 500 corresponding to velocity of 0.39 m/s. The piezoelectric vibration amplitude is fixed at 0.2 and frequencies are varied in the range of [0–3] corresponding to [0–287] Hz. We have found that the time averaged Nusselt number for each electrical device depends on the pulsation frequency and heat modulation, and it is always larger than that in the steady‐state case. The results show that there exists a short band of frequencies which the enhancement of heat transfer of all electrical devices is higher than 55% compared with that of steady state. In addition, the heat transfer is maximum when heated pulsation frequency in the device is set as St = 3.0 corresponding to frequency of 58.5 Hz of input voltage. The combined pulsation flow by piezoelectric fan and heated pulsation by input voltage show vigorous heat transfer through electrical devices blocks and the heat transfer enhancement was observed in relatively narrow bands of frequencies. The efficiency of piezoelectric fan is expressed by the maximum temperature of the ninth electrical device which not exceed 80°C for time‐averaged velocity of 0.556 m/s and vibration frequency of 34.75 Hz of piezoelectric fan. The pressure drop and power pumping of piezoelectric fan are obtained for different Reynolds numbers. We found that the power loss was 4.6 times higher than for the piezoelectric fan at Re = 500. Good agreement between our numerical simulations of piezoelectric fan and experimental results available from the literature is obtained. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Finite‐time stable of time‐varying delay distributed parameter systems with input saturation via periodically intermittent control

A class of time‐varying delay distributed parameter systems with input saturation is investigated in this paper. The periodic intermittent control method is adopted to make the system stable in finite time, improve the control performance of the system, and save on control cost. A periodic intermittent controller combined saturated input is designed to ensure the stability of the proposed system in finite time. Lyapunov–Krasoviskii stability theory and matrix inequality techniques are used to analyze the finite‐time stability of the system, and sufficient conditions for the system to be stable in finite time are obtained. Finally, the correctness of the theorems is verified by simulation experiments.

Shunting Inhibitory Cellular Neural Networks with Compartmental Unpredictable Coefficients and Inputs

Shunting inhibitory cellular neural networks with compartmental periodic unpredictable coefficients and inputs is the focus of this research. A new algorithm is suggested, to enlarge the set of known unpredictable functions by applying diagonalization in arguments of functions of several variables. Sufficient conditions for the existence and uniqueness of exponentially stable unpredictable and Poisson stable outputs are obtained. To attain theoretical results, the included intervals method and the contraction mapping principle are used. Appropriate examples with numerical simulations that support the theoretical results are provided. It is shown how dynamics of the neural network depend on a new numerical characteristic, the degree of periodicity.

High Frequency Response of Non-Volatile Memristors

This paper presents an analytical investigation of the transient and steady-state response of non-volatile memristors to high frequency periodic inputs, using as a case study a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textrm {TaO}_{\textrm {x}}$ </tex-math></inline-formula> -based nano-scale memristor model derived at HP Labs. For the first time, we provide a mathematical proof for the fading memory phenomenon in memristors stimulated by periodic inputs in the high frequency limit. Specifically, we demonstrate that the steady-state response of a non-volatile memristor, exhibiting asymmetric switching kinetics with respect to the polarity of the input, depends only on the amplitude of the testing signal and not on the device initial conditions. Based on the results of our analyses, we provide an alternative method for tuning the memristor state by using high-frequency AC inputs, and introduce a new system-theoretic visualization tool, namely the input-referred High-Frequency Dynamic Route Map (HF-DRM), that allows the reproduction of the memristor time-response to any high-frequency periodic input from each admissible initial condition. The purely theoretical results introduced in this paper could inspire new approaches for modulating the memory states of practical non-volatile memristors.

Closed-Loop Frequency Analysis of Reset Control Systems

This article introduces a closed-loop frequency analysis tool for reset control systems. To begin with sufficient conditions for the existence of the steady-state response for a closed-loop system with a reset element and driven by periodic references are provided. It is then shown that, under specific conditions, such a steady-state response for periodic inputs is periodic with the same period as the input. Furthermore, a framework to obtain the steady-state response and to define a notion of closed-loop frequency response, including high order harmonics, is presented. Finally, pseudosensitivities for reset control systems are defined. These simplify the analysis of this class of systems and allow a direct software implementation of the analysis tool. This methods gives deeper insight into the performance of the system than that achieved with the describing function method.

A new method for calculation of closed‐form response of linear time‐invariant systems to periodic input signals

AbstractA new method for finding closed‐form time‐domain solutions of linear time‐invariant (LTI) systems with arbitrary periodic input signals is presented. These solutions, unlike those obtained based on the conventional Fourier‐phasor method, have a finite number of terms in one period. To implement the proposed method, the following steps are carried out: (1) For a given system, represented by a transfer function, an impulse response, a block diagram etc., the governing differential equation relating the output of the system, , to its input, , is obtained. (2) An auxiliary differential equation is formed by simply replacing with and equating the input side to alone. The auxiliary differential equation is solved for each time segment of the input signal in one period, leaving the constant coefficients associated with the homogeneous solutions as unknowns. For an nth‐order system with an input signal consisting of q segments in one period, there are such unknown coefficients. (3) Continuity of and its derivatives, at the connection points of successive segments and the periodicity conditions for the beginning and end points of the period are implemented. (4) The outcome of step 3 is a system of equations in terms of unknown coefficients described in step 2. Solving this system of equations, the solution for in one period is obtained. (5) Finally, using the linearity and differentiation properties of the system and the coefficients of the input side of the differential equation of the system, the total response, , in one period is constructed in terms of and its derivatives. For stable LTI systems, the proposed method can be used without any limitations.

Formation of a nontrivial finite-time stable attractor in a class of polyhedral sweeping processes with periodic input

We consider a differential inclusion known as a polyhedral sweeping process. The general sweeping process was introduced by J.-J. Moreau as a modeling framework for quasistatic deformations of elastoplastic bodies, and a polyhedral sweeping process is typically used to model stresses in a network of elastoplastic springs. Krejčí’s theorem states that a sweeping process with periodic input has a global attractor which consists of periodic solutions, and all such periodic solutions follow the same trajectory up to a parallel translation. We show that in the case of polyhedral sweeping process with periodic input the attractor has to be a convex polyhedron χ of a fixed shape. We provide examples of elastoplastic spring models leading to structurally stable situations where χ is a one- or two- dimensional polyhedron. In general, an attractor of a polyhedral sweeping process may be either exponentially stable or finite-time stable and the main result of the paper consists of sufficient conditions for finite-time stability of the attractor, with upper estimates for the settling time. The results have implications for the shakedown theory.

Observer-Based Output Feedback Tracking Consensus for Multi-Agent Systems With Periodic Intermittent Communication and Input Saturation

Observer-Based Output Feedback Tracking Consensus for Multi-Agent Systems With Periodic Intermittent Communication and Input Saturation

Microbial communities associated with kelp detritus in temperate and subantarctic intertidal sediments.

Kelp forests, among the most productive ecosystems on Earth, cover large areas of the South Atlantic coast. Sediment heterotrophic bacteria have a pivotal role in the degradation of kelp biomass, however, the response of sediment microbial communities to periodic kelp biomass inputs is mostly unknown. Here, we show that kelp biomass induced rapid changes in overlying water chemistry and shifts in sediment microbial communities, which differed in the experimental systems containing Macrocystis pyrifera (M) and Undaria pinnatifida (U) with sediments of the respective regions. We observed results compatible with the degradation of labile, high molecular weight compounds into smaller and more refractory compounds towards the end of the incubations. The capability of microbial communities to degrade alginate, the major component of kelp cell walls, significantly increased with respect to controls after kelp biomass addition (Absorbance at 235 nm 1.2 ± 0.3 and 1.0 ± 0.2 for M and U, respectively, controls <0.2, t = 4 days). Shifts in microbial community structure (based on 16S rRNA gene amplicon sequencing) were tightly related to the kelp treatment and, to a lesser extent, to the sediment provenance (Principal Coordinates Analysis, 80 % of variation explained in the first two axes). Dissolved oxygen, pH, salinity, alginolytic potential, Absorbance at 235 and 600 nm, total N, total C, and SUVA index correlated significantly with community structure. Differentially abundant populations between kelp-amended treatments and controls included members of the Flavobacteriia class (Algibacter and Polaribacter), and Gammaproteobacteria (Psychromonas and Marinomonas), among others. Metagenomes of M and U-amended sediments contained sequences from 18 of the 19 enzyme families related to alginate or fucoidan degradation. Specific taxonomic groups were associated with enzyme classes targeting different substrates, suggesting niche differentiation. This work expands our knowledge on the patterns of microbial assemblages from intertidal sediments in response to kelp biomass inputs.

Numerical investigation for the fractional model of pollution for a system of lakes using the SCM based on the Appell type Changhee polynomials

&lt;abstract&gt;&lt;p&gt;This article proposed a useful simulation to investigate the Liouville-Caputo fractional order pollution model's solution behavior for a network of three lakes connected by channels. A supposedly new approximation technique using the Appell type Changhee polynomials (ACPs) was used to treat the periodic and linear input models. This work employs the spectral collocation method based on the properties of the ACPs. The given technique creates a system of algebraic equations from the studied model. We verified the efficiency of the suggested technique by computing the residual error function. We compared the results to those obtained by the fourth-order Runge-Kutta method (RK4). Our findings confirmed that the technique used provides a straightforward and efficient tool to solve such problems. The key benefit of the suggested method is that it only requires a few easy steps, doesn't produce secular terms and doesn't rely on a perturbation parameter.&lt;/p&gt;&lt;/abstract&gt;

Analysis of a fractional pollution model in a system of three interconnecting lakes

&lt;abstract&gt; &lt;p&gt;Water pollution is a critical global concern that demands ongoing scrutiny and revision of water resource policies at all levels to safeguard a healthy living environment. In this study, we focus on examining the dynamics of a fractional-order model involving three interconnected lakes, utilizing the Caputo differential operator. The aim is to investigate the issue of lake pollution by analyzing a system of linear equations that represent the interconnecting waterways. To numerically solve the model, we employ two methods: The Laplace transform with the Adomian decomposition method (LADM) and the Homotopy perturbation method (HPM). We compare the obtained numerical solutions from both methods and present the results. The study encompasses three variations of the model: the periodic input model, the exponentially decaying input model, and the linear input model. MATLAB is employed to conduct numerical simulations for the proposed scheme, considering various fractional orders. The numerical results are further supported by informative graphical illustrations. Through simulation, we validate the suitability of the proposed model for addressing the issue at hand. The outcomes of this research contribute to the understanding and management of water pollution, aiding policymakers and researchers in formulating effective strategies for maintaining water quality and protecting our environment.&lt;/p&gt; &lt;/abstract&gt;

Phase Synchronization for Helix Enhanced Wake Mixing in Downstream Wind Turbines

Wind farm controllers such as the Helix approach have shown potential in increasing plant power production through wake mixing. The concept suggests that actuating the upstream turbines’ blade pitching with a specific periodic signal can induce a helix-shaped wake, thereby alleviating wind velocity deficit on downstream turbines. Wake mixing initiation by downstream turbines may also be shown advantageous for power production; however, little to no attention has been given to such an approach. Similar wake mixing is expected to be achievable at lower control costs if the downstream turbine can benefit from the periodic component already present in the wake of the upstream turbine. Such a hypothesis is studied in this work by designing a minimal control scheme where the wake acting on the downstream turbine is simulated by a periodic input disturbance. A Kalman filter is proposed for incoming input disturbance phase estimation using SCADA data. The reconstructed phase information allows synchronization of the downstream control action with the periodic input disturbance by means of a phase synchronization wake mixing controller. The periodic component was estimated with a minimal root-mean-square error and the resulting control action was in phase with the input disturbance and demonstrated satisfactory performance even with a small phase perturbation. Future work will include applications in a high-fidelity wind turbine model and wind tunnel studies.

Model-free continuation of periodic orbits in certain nonlinear systems using continuous-time adaptive control

This paper generalizes recent results by the authors on noninvasive model-reference adaptive control designs for control-based continuation of periodic orbits in periodically excited linear systems with matched uncertainties to a larger class of periodically excited nonlinear systems with matched uncertainties and known structure. A candidate adaptive feedback design is also proposed in the case of scalar problems with unmodeled nonlinearities. In the former case, rigorous analysis shows guaranteed performance bounds for the associated prediction and estimation errors. Together with an assumption of persistent excitation, there follows asymptotic convergence to periodic responses determined uniquely by an a priori unknown periodic reference input and independent of initial conditions, as required by the control-based continuation paradigm. In particular, when the reference input equals the sought periodic response, the steady-state control input vanishes. Identical conclusions follow for the case of scalar dynamics with unmodeled nonlinearities, albeit with slow rates of convergence. Numerical simulations validate the theoretical predictions for individual parameter values. Integration with the software package coco demonstrates successful continuation along families of stable and unstable periodic orbits with a minimum of parameter tuning. The results expand the envelope of known noninvasive feedback strategies for use in experimental model validation and engineering design.

Analytical modelling of heat accumulation in laser based additive manufacturing processes of metals

The flexibility of additive manufacturing processes results from the principle of subsequently adding small amounts of material in individual layers or beads on top of each other. The periodic input of energy required to melt the material can lead to an accumulation of heat, which increases the temperature of the part and changes the local temperature distribution in the melt pool. This heat accumulation results in local shape deviations of the part and can lead to inhomogeneous solidification conditions coinciding with inhomogeneous grain structures and potentially inhomogeneous mechanical properties or build failures. To produce high quality parts with homogeneous properties and to reduce unproductive dwell times, a comprehensive knowledge of the heat accumulation phenomena is required. The present work considers an explicit analytical description of the heat accumulation effect, which allows for a mathematical analysis of the influence of all contributing process parameters on the temperature increase of the part. The analytical equations were derived from simplified heat conduction equations and validated by comparison with temperature measurements from literature. The calculated temperature increase shows a good agreement with measurements observed during additive manufacturing of different materials and alloys in case of cladding or building volumes with direct energy deposition (DED) and laser powder bed fusion (LPBF). Finally, the obtained analytical solution is used to derive optimization strategies aiming to reduce heat accumulation while simultaneously increasing productivity. • Analytical equations for the prediction of the temperature increase. • Analytical description of the heat accumulation in cladding and volume building with DED and LPBF • Validation for titanium-, inconel-, steel-, and aluminum-alloys • Identification of conditions that lead to a convergence of heat accumulation • Mathematical identification of the key factors, which influence heat accumulation. • Derivation of optimization strategies to increase productivity

Analytical non‐Fourier solution of linear time‐invariant circuits with periodic inputs

SummaryA systematic approach for solving linear time‐invariant electric circuits with periodic input signals is presented. The method involves the following steps: (1) The governing differential equation for the desired output is solved for each time segment of the input signal in one period, leaving the constant coefficients of the homogeneous parts of the solution as unknowns. For an nth‐order circuit with a source consisting of q segments in one period, there are such unknown coefficients. (2) Using the solution obtained in step 1, the voltage of each capacitor and the current of each inductor are determined. (3) Transition conditions for the voltages and currents found in step 2 at the transition points of successive segments and also periodicity conditions for the beginning and end points of the period are applied. (4) Implementation of step 3 results in a system of equations in terms of the unknown coefficients described in step 1. Solving this system of equations, the circuit response in one period becomes readily available.

Direct-seeded rice reduces methane emissions by improving root physiological characteristics through affecting the water status of paddy fields

Both direct-seeded rice (DSR) and water-saving irrigation effectively reduce methane (CH4) emissions from paddy fields. However, little is known about the effects of water-saving irrigation with DSR on root growth and CH4 emissions in paddy fields. In this study, a field experiment was conducted with three treatments including transplanted flooded rice (TFR), direct-seeded flooded (DSF), and direct-seeded alternate wetting and drying (DSA), and root morphological and physiological traits and CH4 emissions were determined. Compared to TFR, DSR (DSF and DSA) significantly decreased CH4 emissions at all growth stages and reduced total CH4 emissions by 85.6–96.8%. Root morphological traits were significantly and positively correlated with total CH4 emissions, whereas root oxidation activity (ROA); root oxygen loss (ROL); and root organic acids malic acid (MA), succinic acid (SA) and citric acid (CA) were significantly and negatively correlated with total CH4 emissions. The flooding depth (FD), flooding period (FP), and total water input (TWI) were 34.1%, 17.8%, and 22.1% lower for DSF and 79.5%, 88.2%, and 53.7% lower for DSA, respectively, compared with those of TFR, which showed a significant positive correlation with CH4 emissions. These results suggest that DSF and DSA improve the root physiological traits of rice by regulating the water status of paddy fields, which in turn lead to CH4 reduction. The results of this study are essential for developing sustainable management practices for paddy soils and reducing greenhouse gas emissions.