Time Delay Parameter Research Articles

Theoretical Investigation of Rate Coefficients and Dynamical Mechanisms for N + N + N Three-Body Recombination Based on Full-Dimensional Potential Energy Surfaces

Three-body recombination reactions, in which two particles form a bound state while a third one bounces off after the collision, play significant roles in many fields, such as cold and ultracold chemistry, astrochemistry, atmospheric physics, and plasma physics. In this work, the dynamics of the recombination reaction for the N3 system over a wide temperature range (5000–20,000 K) are investigated in detail using the quasi-classical trajectory (QCT) method based on recently developed full-dimensional potential energy surfaces. The recombination products are N2(X) + N(4S) in the 14A″ state, N2(A) + N(4S) in the 24A″ state, and N2(X) + N(2D) in both the 12A″ and 22A″ states. A three-body collision recombination model involving two sets of relative translational energies and collision parameters and a time-delay parameter is adopted in the QCT calculations. The recombination process occurs after forming an intermediate with a certain lifetime, which has a great influence on the recombination probability. Recombination processes occurring through a one-step three-body collision mechanism and two distinct two-step binary collision mechanisms are found in each state. And the two-step exchange mechanism is more dominant than the two-step transfer mechanism at higher temperatures. N2(X) formed in all three related states is always the major recombination product in the temperature range from 5000 K to 20,000 K, with the relative abundance of N2(A) increasing as temperature decreases. After hyperthermal collisions, the formed N2(X/A) molecules are distributed in highly excited rotational and vibrational states, with internal energies mainly distributed near the dissociation threshold. Additionally, the rate coefficients for this three-body recombination reaction in each state are determined and exhibit a negative correlation with temperature. The dynamic insights presented in this work might be very useful to further simulate non-equilibrium dynamic processes in plasma physics involving N3 systems.

Chaotic band-gap modulation mechanism for nonlinear vibration isolation systems based on time-delay feedback control

Abstract Systems designed for nonlinear vibration isolation that incorporate chaotic states demonstrate superior capabilities in vibration attenuation, adeptly modulating the spectral constituents of vibrational noise. Yet, the challenge of eliciting low-amplitude chaotic dynamics and perpetuating these states across a diverse array of parameters remains formidable. This study proposes a pioneering strategy and technique for modulating the chaos band by incorporating a time-delayed feedback control mechanism within the framework of nonlinear vibration isolation systems.The investigation commences with an exhaustive analysis of the nonlinear dynamics, shedding light on the principles dictating the evolution of chaos. The study then advances to scrutinize the dynamics of systems with delays to elucidate the chaos-inducing processes engendered by feedback with temporal lags. Building upon the system’s responses, the chaotic performance and the effectiveness of the vibration isolation are crafted. Consequently, the time-delayed feedback control parameters are identified as pivotal design variables, which are then employed to dissect the control mechanisms influenced by the time-delayed feedback on the chaos band. Utilizing the delineated control mechanism, the nonlinear vibration isolation system is precipitously transitioned from a state of stable periodicity to one of chaos, fostering low-amplitude chaotic dynamics across an expansive parameter space, and in turn, resolving the previously stated challenge. Perhaps most significantly, the mechanism for attaining low-amplitude chaos introduced here paves the way for innovative methodologies in the active vibration isolation design of similar systems. Furthermore, it is anticipated to yield theoretical guidance for the manipulation of chaos bands and the formulation of active vibration isolation strategies within the domain of nonlinear vibration isolation systems.

Time-delay feedback control on vertical vibration of maglev train under unsteady aerodynamic force

The stability and safety of maglev trains are significantly affected by unsteady aerodynamic forces during high-speed operation. In this paper, we employ a time-delay feedback control strategy to suppress the nonlinear vertical vibrations of maglev train under periodic unsteady aerodynamic force. Firstly, the amplitude-frequency response equation of the maglev vehicle is derived using the multiple scales method, and the stability of the steady-state solutions is determined. Then, the influences of velocity feedback gain coefficient and velocity time delay on the nonlinear vibrations of the maglev vehicle are investigated. The optimal value range of the time delay is identified. The results demonstrate that the time delay feedback control can effectively suppress the nonlinear vibration of maglev vehicles and enhance their operational stability under the premise of reasonable selection of time delay parameters. The theoretical research presented in this paper can serve as a theoretical reference for the design, improvement, and optimization of control systems for high-speed maglev trains.

Comparison and Determination of the Content of Mosapride Citrate by Different qNMR Methods.

As a salt-type compound, mosapride citrate's metabolism and side effects are correlated with its salt-forming ratio. Several techniques were developed in this work to compare various quantitative nuclear magnetic resonance (qNMR) methodologies and to quantitatively examine the content of raw materials. Among the qNMR techniques, methods for 1H NMR and 19F NMR were developed. Appropriate solvents were chosen, and temperature, number of scans, acquisition time, and relaxation delay parameter settings were optimized. Maleic acid was chosen as the internal standard in 1H NMR, and the respective characteristic signals of mosapride and citrate were selected as quantitative peaks. The internal standard in 19F NMR analysis was 4,4'-difluoro diphenylmethanone, and the distinctive signal peak at -116.15 ppm was utilized to quantify mosapride citrate. The precision, repeatability, linearity, stability, accuracy, and robustness of the qNMR methods were all validated according to the ICH guidelines. By contrasting the outcomes with those from high-performance liquid chromatography (HPLC), the accuracy of qNMR was assessed. As a result, we created a quicker and easier qNMR approach to measure the amount of mosapride citrate and evaluated several qNMR techniques to establish a foundation for choosing quantitative peaks for the qNMR method. Concurrently, it is anticipated that various selections of distinct quantitative objects will yield the mosapride citrate salt-forming ratio.

Time-delay feedback control of nonlinear forced vibration of graphene/piezoelectric sandwich nanoplates under a mechanical shock

In this study, the nonlinear forced vibration of graphene/piezoelectric sandwich nanosheets under mechanical impact was investigated. For the first time, linear (displacement and velocity) and nonlinear (displacement) time-delay proportional derivative (PD) controllers were applied to graphene/piezoelectric sandwich nanosheets, and the primary/secondary resonance under different time-delay parameters were analyzed. An approximate analytical solution for the nonlinear forced vibration control equation was obtained using the multiple scale perturbation method, and the stability of graphene/piezoelectric sandwich nanosheets under primary/secondary resonance conditions was discussed using the Ross Herwitz theorem. Finally, the results of this study were compared with those of other studies. The feasibility of the research methodology was demonstrated. On this basis, the research results indicate that linear displacement delay, nonlinear displacement delay, and velocity delay parameters can suppress the unsteady vibration characteristics of the main system. And comparing the linear and nonlinear displacement time-delay, it is found that the nonlinear displacement time-delay has a greater effect on the system. Specifically, the presence of nonlinear displacement time-delay changes the vibration characteristics of the curve from hard spring characteristics to soft spring characteristics. Comparison of displacement time-delay and velocity time-delay reveals that velocity time-delay gives better control over the system. In addition, the results show that the excitation amplitude, nonlocal parameters, and external voltage enhance the nonlinear characteristics of the system under the main and superharmonic resonance conditions before the time-delay control. Subharmonic resonance conditions, the system parameters make the vibration range wider. After the time-delay control, the influence of these three factors on the system vibration is significantly reduced for the three resonance conditions, especially for the non-local parameters. The results of the study can provide guidance for active control of time delay in different types of nanodevices for engineering applications.

Exact discrete-time stability analysis of multi-DOF haptic rendering: Impact of multi-rate, time-delay, and mechanical parameters

Previous studies on the stability analysis of haptic devices have predominantly focused on single-DOF devices, thereby limiting attention to multi-DOF devices, particularly those employing multi-rate sampling schemes. In this paper, we introduce a formulation for the coupled dynamics between the haptic device and the virtual environment for a multi-DOF haptic device controlled using a dual-rate sampling scheme. Subsequently, we analyze its stability through the application of a dynamic decoupling strategy within an exact discrete-time state-space framework while the device is engaged in rendering a virtual wall along one of its operational space coordinates. Furthermore, we explore how the combined influence of the dual-rate sampling approach, time delay, and the mechanical design affects the stability boundaries of the multi-DOF haptic device at a fixed workspace location as well as within the entire usable workspace. Additionally, we utilize a model-order reduction (MOR) framework to simplify the determination of the device’s stability limits, irrespective of the specific combinations of time delay and sampling rates employed.

The combined Lyapunov functionals method for stability analysis of neutral Cohen–Grossberg neural networks with multiple delays

This research article will employ the combined Lyapunov functionals method to deal with stability analysis of a more general type of Cohen–Grossberg neural networks which simultaneously involve constant time and neutral delay parameters. By utilizing some combinations of various Lyapunov functionals, we determine novel criteria ensuring global stability of such a model of neural systems that employ Lipschitz continuous activation functions. These proposed results are totally stated independently of delay terms and they can be completely characterized by the constants parameters involved in the neural system. By making some detailed analytical comparisons between the stability results derived in this research article and the existing corresponding stability criteria obtained in the past literature, we prove that our proposed stability results lead to establishing some sets of stability conditions and these conditions may be evaluated as different alternative results to the previously reported corresponding stability criteria. A numerical example is also presented to show the applicability of the proposed stability results.

Gaussian and Lévy noises excited delayed tumor growth model: first-passage behavior and stochastic resonance

In this paper, we analyze the dynamical behavior of a delayed tumor growth model under the joint effect of Gaussian white noise and Lévy noise by studying the mean first passage time (MFPT) and stochastic resonance (SR). Firstly, the tumor growth model under the joint effect of Gaussian white noise, Lévy noise and time delay is introduced. Then, the Lévy noise sequence is simulated by Janicki-Weron algorithm, and the MFPT and signal-to-noise ratio(SNR) of the system are simulated by using fourth-order stochastic Runge–Kutta algorithm. The effects of noise parameters, time delay and periodic signal parameters on MFPT, SR are discussed in detail, respectively. In addition, we find the phenomenon of noise enhanced stability. The results of the study can help to select the optimal regulatory parameters in the tumor growth model and promote the treatment of tumors.

Stochastic response and stability analysis of nonlinear vehicle energy-regenerative suspension system with time delay

With the rapid development of new energy vehicles, a novel vehicle energy-regenerative suspension for simultaneous vibration suppression and energy harvesting has become one of the key development directions of the next generation of vehicle design. In order to improve the performance of suspension system, the time-delayed feedback control is applied to the novel suspension system subjected to different external excitation. At the same time, there are few studies related to the stochastic dynamics of nonlinear vehicle energy-regenerative suspension system with time delay. This paper studies stochastic response and stability of nonlinear vehicle energy-regenerative suspension with time-delayed feedback control under the excitation of Gaussian white noise. First of all, a stochastic dynamic model of the nonlinear vehicle energy-regenerative suspension with time delay system is established. Secondly, using the stochastic averaging method based on generalized harmonic function, the steady-state probability density function (PDF) of amplitude is obtained. The accuracy of the presented approach is verified through the comparison of analytical and numerical solutions. In addition, through combining the stochastic averaging method with the Khasminskii method, the top Lyapunov exponent (TLE) of the system is obtained, and then the influence of time delay and system parameters on the asymptotic Lyapunov stability is discussed. Finally, the effects of time delay and system parameters on system performance are also studied.

Pattern formation and delay-induced instability in a Leslie–Gower type prey–predator system with Smith growth function

In this article, we have investigated the spatiotemporal dynamics and delay-induced instability of a Leslie–Gower type prey–predator model under the influence of environmental toxicants with Smith growth function. This growth function is more realistic than logistic growth as it better describes the growth of the biological population. It has been used where the growth limitations are based on the proportion of available resources not utilized. A few works of Smith’s growth models are reported in the literature. Therefore, spatiotemporal dynamics and pattern formation with delay effect remain an exciting area of research, which motivates the present work. This work has studied two types of dynamical systems: (i) an ordinary differential temporal system with time delay and (ii) a reaction–diffusion system with time delay. The existence of equilibrium points and their stability conditions are discussed. Hopf bifurcation emerges in both proposed systems with respect to delay parameter. The stability and direction of Hopf bifurcation and delay–diffusion-driven instability have been investigated for the reaction–diffusion system. Numerical simulation is performed to support the analytical results and theorems. Moreover, the existence of Hopf and delay-induced instability are proved numerically. Interesting one-dimensional regular and irregular stripe patterns are obtained for increased values of the time delay parameter. Also, the presence of natural toxicants has a negative impact on the growth of prey–predator species.

Enhancing energy recovery in automotive suspension systems by utilizing time-delay

This study introduces time-delay active control technology to with the aim of enhancing the system's energy harvesting potential and ride smoothness. The time-delay active suspension represents a nonlinear, multivariable system, and stability analysis in this context is intricate. The mainly challenge lies in effectively leveraging time delay to augment the system's energy collection potential while harmonizing the vehicle's ride comfort and energy efficiency. Addressing this issue, our study proposes enhancing the suspension's energy recovery capability through time-delay control. Initially, the impact of time-delay control parameters on energy collection ability under various operational conditions was analyzed, establishing that appropriate time-delay parameters can enhance energy harvesting capacity. Subsequently, to balance the relationship between vehicle comfort and energy efficiency, the research introduces a method for constructing an optimized objective function based on linear equivalent excitation, thereby quantifying the relationship between system time-domain vibrational response, time-delay control parameters, and external excitations. This approach enables the comprehensive optimization of the suspension system's comfort, safety, and energy efficiency. The control system's stability was analyzed using cluster treatment of characteristic roots method. Finally, simulations and experiments were conducted to evaluate the effectiveness of time-delay active across different scenarios, confirming the efficacy of the proposed control methodology.

Research on a Sound Source Localization Method for UAV Detection Based on Improved Empirical Mode Decomposition.

To address the challenge of accurately locating unmanned aerial vehicles (UAVs) in situations where radar tracking is not feasible and visual observation is difficult, this paper proposes an innovative acoustic source localization method based on improved Empirical Mode Decomposition (EMD) within an adaptive frequency window. In this study, the collected flight signals of UAVs undergo smoothing filtering. Additionally, Robust Empirical Mode Decomposition (REMD) is applied to decompose the signals into Intrinsic Mode Function (IMF) components for spectrum analysis. We introduce a sliding frequency window with adjustable bandwidth, which is automatically determined using a Grey Wolf Optimizer (GWO) with a sliding index. This window is used to lock and extract specific frequencies from the IMFs. Based on predefined criteria, the extracted IMF components are reconstructed, and trigger signal times are analyzed and recorded from these reconstructed IMFs. The time differences between sensor receptions are then calculated. Furthermore, this study introduces the Chan-Taylor localization algorithm based on weighted least squares. This advanced algorithm takes sensor time delay parameters as input and solves a set of nonlinear equations to determine the target's location. Simulations and real-world signal tests are used to validate the robustness and performance of the proposed method. The results indicate that the localization error remains below 5% within a 15 m × 15 m measurement area. This provides an efficient and real-time method for detecting the location of small UAVs.

Stability Analysis and Hopf Bifurcation for the Brusselator Reaction–Diffusion System with Gene Expression Time Delay

This paper investigates the effect of a gene expression time delay on the Brusselator model with reaction and diffusion terms in one dimension. We obtain ODE systems analytically by using the Galerkin method. We determine a condition that assists in showing the existence of theoretical results. Full maps of the Hopf bifurcation regions of the stability analysis are studied numerically and theoretically. The influences of two different sources of diffusion coefficients and gene expression time delay parameters on the bifurcation diagram are examined and plotted. In addition, the effect of delay and diffusion values on all other free parameters in this system is shown. They can significantly affect the stability regions for both control parameter concentrations through the reaction process. As a result, as the gene expression time delay increases, both control concentration values increase, while the Hopf points for both diffusion coefficient parameters decrease. These values can impact solutions in the bifurcation regions, causing the region of instability to grow. In addition, the Hopf bifurcation points for the diffusive and non-diffusive cases as well as delay and non-delay cases are studied for both control parameter concentrations. Finally, various examples and bifurcation diagrams, periodic oscillations, and 2D phase planes are provided. There is close agreement between the theoretical and numerical solutions in all cases.

Bifurcation Regulations Induced by Joint Noise in a Tri-Rhythmic Van Der Pol System

Tri-rhythmical nature has attracted extensive attention from scholars in describing the dynamical behaviors of self-sustained systems. In this paper, we consider a tri-rhythmic van der Pol system and give a bifurcation analysis of a stochastic tri-rhythmic self-sustained system under joint noise perturbation. Based on an approximate approach, we give the stationary probability density function of amplitudes, and we find that the noise and time-delay feedback, regulating the velocity time-delay feedback strength parameter, may not cause transitions among unimodal, bimodal and trimodal in the tri-rhythmic system. More stochastic bifurcations appear by regulating the time delay in this system. The system, surprisingly, undergoes five times of stochastic bifurcations when the time delay is monotonically increased. It is shown that the time delay is more sensitive to the tri-rhythmic system and a much stronger dependence on the system. From a biological point of view, the reaction rate of biological molecules can be enhanced or diminished by the change of the noise intensity or correlation time of Gaussian colored noise. More surprisingly, an increase in displacement feedback will delay the reaction rate; however, the effect of an increase in velocity feedback on the reaction rate depends on the time delay. A detailed research on the parameter space indicates that time delay and colored noise parameters can effectively control the multirhythmicity of the system. Finally, this paper verifies the effectiveness of the theoretical solution through the numerical results of Monte Carlo simulation of the original system. These results may help to further explore forking bifurcations in real-world applications. This research provides new insight into the understanding of nontrivial effects of joint noise on the tri-rhythmic system.

Bifurcation analysis of a delayed stochastic HBV epidemic model: Cell-to-cell transmission

In the present study, we develop a model for hepatitis B virus (HBV) that integrates cell-to-cell transmission of the virus, CTL immunological response, delay effects, and the effect of fluctuating environmental noise. The inheritance randomness of the system shifting the system from a deterministic to another system consists of stochastic differential equations (SDEs). After model formulation, the dynamical aspects of the model are investigated by using the key threshold quantity R0. If the threshold value R0 is assumed less than unity, then it is proven that the solution trajectories are fluctuating around the disease-free state (DFS) of the associated deterministic model. The fluctuation of the trajectories around the DFS explains the phenomenon of extinction of the stochastic models. It is also proved that the trajectories of the SDE model oscillate around the endemic state of the underlying ODE system when R0s>1 explains the sure persistence theory of the proposed model. One notable finding of the present manuscript is the positive association between the fluctuating amplitude and the intensities of the white noises. This understanding can provide useful control tools for managing the worst dynamic(s) of the infection. The exact value of the parameter for time delay determines the stability of the model under consideration. By analyzing the time-delayed parameter, it was identified that the model is stable by keeping the value of the parameter below the crucial value that causes the Hopf bifurcation. This conclusion is supported by the numerical examples having epidemiological significance. Furthermore, the findings suggest that stochastic environmental disturbance can impact the spread of infectious illnesses. Notably, the high levels of noise can help to slow down the spread of epidemics in the population.

Inverter and Universal Gates Implementation Using Novel Core Insulator Double Gate (CIDG) MOSFETs

The Core Insulator Double Gate (CIDG) MOSFET has been explored for digital applications in which the presence of core insulator diminishes the bulk conduction and reduces the off state current. The drain currents of n- and p-type CIDG MOSFETs are matched by tuning gate work functions to deliver the symmetrical pull-up and pull-down characteristics. The inverter and universal logic gates (NAND and NOR) have been designed and implemented to show the usability of the CIDG MOSFETs for digital applications. The DC and transient characteristic of the inverter along with Static Noise Margin (SNM) and time delay parameters have been examined. The designed Inverter shows steeper voltage transfer characteristics, reduced short circuit power dissipation and improved noise immunity. The CIDG MOSFET based NAND and NOR gate implementation and validation by transient analysis have been shown for the first time to the best knowledge of the authors. Also, the rise and fall times of the inverter, NAND and NOR gates have been found to be improved as compared to the DG MOSFET counterparts. The present analysis establishes that CIDG MOSFETs are useful in designing digital circuits with improved performance.

Stability and bifurcation analysis of fractional‐order tumor–macrophages interaction model with multi‐delays

In the realm of modeling biological systems with memory, particularly those involving intricate interactions like tumor‐immune responses, the utilization of multiple time delays and Caputo‐type fractional‐order derivatives represents a cutting‐edge approach. In this research paper, we introduce a novel fractional‐order model to investigate the dynamic interplay between tumors and macrophages, a key component of the immune system, while incorporating multiple time delays into our framework. Our proposed model comprises a system of three Caputo‐type fractional‐order differential equations, each representing distinct cell populations: tumor cells, anti‐tumor cells (specifically ‐type macrophages with pro‐inflammatory properties), and pro‐tumor cells ( ‐type macrophages with immune‐suppressive characteristics). The stability of equilibria is discussed by analyzing the characteristic equations for each case, and the existence conditions for the Hopf bifurcation are obtained according to the critical values of delay parameters. Furthermore, numerical simulations are presented in order to verify the analytical results obtained for stability and Hopf‐bifurcation with respect to the two‐time delay parameters and . The analysis shows the rich dynamics of the model according to the fractional‐order parameter and the time delay parameters.

Direction and stability of Hopf bifurcation in an eco-epidemic model with disease in prey and predator gestation delay using Crowley-Martin functional response

<p>In this work, we have studied an eco-epidemic model using the Crowley-Martin functional response that includes disease in prey and gestation delay in the predator population. The model possesses three equilibria, namely the disease-free, Predator-free, and the interior equilibrium point. In addition, we examined the stability of the equilibrium points varying the infection rate and time delay parameter. Detailed analysis of Hopf bifurcation of the interior equilibrium point contains two situations: with delay and without delay. Moreover, we have studied the direction of the Hopf bifurcation and the stability of periodic solutions utilizing normal form theory and the center manifold theorem. It is emphasized that Hopf bifurcation occurs when the time delay exceeds the critical value and that the critical value of the delay is strongly impacted by the infection rate in prey. A detailed numerical simulation is provided to verify the analytical results.</p>

No Combined Effect of Caffeinated Chewing Gum and Priming Exercise on Oxygen Uptake and Muscle Near-Infrared Spectroscopy-Derived Kinetics: A Double-Blind Randomized Crossover Placebo-Controlled Trial in Cyclists.

This study aimed to investigate the effects of caffeine ingestion by chewing gum (GUMCAF) combined with priming exercise on pulmonary oxygen uptake (V˙O2) and near-infrared spectroscopy-derived muscle oxygen extraction (HHb + Mb) kinetics during cycling performed in a severe-intensity domain. Fifteen trained cyclists completed four visits: two under a placebo gum (GUMPLA) and two under GUMCAF ingestion. Each visit consisted of two square-wave cycling bouts at Δ70 intensity (70% of difference between the V˙O2 at first ventilatory threshold and V˙O2max) with duration of 6min each and 5min of passive rest between the bouts. The GUMPLA or GUMCAF (400mg) was chewed for 5min, 12min before the first Δ70 bout in a randomized double-blind procedure. The fundamental phase and slow component of HHb + Mb and V˙O2 kinetics were evaluated. For HHb + Mb kinetics, regardless of ingested gum, priming exercise effects occurred on the time constant (GUMCAF 16.0 ± 4.0 vs. 13.9 ± 2.9s; GUMPLA 15.7 ± 6.1 vs. 13.2 ± 2.5s), amplitude, slow component, time delay, and mean response time parameters (p ≤ .032). For V˙O2 kinetics, there were significant effects of bouts on the amplitude, slow component, end V˙O2, and the gain kinetics parameters (p < .017). Baseline V˙O2 was higher during GUMCAF than GUMPLA (p = .020). No significant effects occurred for the interaction between gum and bout in any parameter of V˙O2 or HHb + Mb kinetics. Therefore, unlike the priming exercise in severe-intensity exercise, GUMCAF is not an effective strategy for improving V˙O2 or HHb + Mb kinetics acceleration.

Distributionally robust parameter estimation for nonlinear fed-batch switched time-delay system with moment constraints of uncertain measured output data

&lt;p&gt;In this paper, we investigated a nonlinear continuous-time switched time-delay (NCTSTD) system for glycerol fed-batch bioconversion to 1, 3-propanediol with unknown time-delay and system parameters. The measured output data was uncertain, while the first moment information about its distribution was available. Our goal was to identify these unknown quantities under the environment of uncertain measurement output data. A distributionally robust parameter estimation problem (i.e., a bi-level parameter estimation (BLPE) problem) subject to the NCTSTD system was presented, where the expectation of the discrepancy between the output of the NCTSTD system and the uncertain measured output data with respect to its probability distributions was included in the cost functional. By applying the duality theory, the BLPE problem was transformed into a single-level parameter estimation (SLPE) problem with non-smooth term approximated by a smoothing technique and its error analysis was given. Then, the gradients of the cost function of the SLPE problem were derived. A hybrid optimization algorithm was proposed for solving the SLPE problem. The paper concluded by presenting the simulation results.&lt;/p&gt;