Search Results (31)

This article aims to clarify the applicability of He’s two-scale fractal dimension transform by replacing $t^{\mathsf{\alpha }}$ with $\mathsf{\tau }$. It demonstrates the potential to capture the influence of the fractal parameter on the system’s damping frequency, particularly when the viscoelastic term (damping) does not equal half of the fractional inertia force term. The analysis examines the elastomer materials’ dynamic fractal amplitude–time response, considering the viscohyperelastic effects related to the material’s energy dissipation capacity. To determine the amplitude of oscillations for the nonlinear equation of motion of a body supported by a viscohyperelastic elastomer subjected to uniaxial stretching, the harmonic balance perturbation method, combined with the two-scale fractal dimension transform and Ross’s formula, is employed. Numerical calculations demonstrate the effectiveness of He’s two-scale fractal transformation in capturing fractal phenomena associated with the fractional time derivative of deformation. This is due to a correlation between the fractional rate of viscoelasticity and the fractal structure of media in elastomer materials, which is reflected in the oscillation amplitude decay. Furthermore, the approach introduced by El-Dib to replace the original fractional equation of motion with an equivalent linear oscillator with integer derivatives is used to further assess the qualitative and quantitative performance of our derived solution. The proposed approach elucidates the applicability of He’s two-scale fractal calculus for determining the amplitude of oscillations in viscohyperelastic systems, where the fractal derivative order of the inertia and damping terms varies. Full article

Experimental and numerical investigations are conducted on a rotating disk from the perspective of convective heat transfer to understand the effect of heating on the stability of flow. A non-invasive approach with a thermal camera is employed to determine local Nusselt numbers for different rotational rates and perturbation parameters, i.e., the strength of the heat transfer. A novel transient temperature data extraction over the disk radius and an evaluation method are developed and applied for the first time for the air on a rotating disk. The evaluation method utilizes the lumped capacitance approach with a constant heat flux input. Nusselt number distributions from this experimental study show that there is a good agreement with the previous experimental correlations and linear stability analysis on the subject. A significant result of this approach is that by using the experimental setup and developed approach, it is possible to qualitatively show that instability in the flow starts earlier, i.e., an earlier departure from laminar behavior is observed at lower rotational Reynolds numbers with an increasing perturbation parameter, which is due to the strength of heating. Two experimental setups are modeled and simulated using a validated in-house Python code, featuring a three-dimensional thermal model of the disk. The thermal code was developed for the rotating disks and brake disks with a simplified geometry. Experimentally evaluated heat transfer coefficients are implemented and used as convective boundary conditions in the thermal code. Radial temperature distributions are compared with the experimental data, and there is good agreement between the experiment and the model. The model was used to evaluate the effect of radial conduction, which is neglected when using the lumped capacitance approach to determine heat transfer coefficients. It was observed that the radial conduction has a slight effect. The methodology and approach used in this experimental study, combined with the numerical model, can be used for further investigations on the subject. Full article

L-tryptophan is an essential amino acid widely used in the pharmaceutical and feed industries. Enhancing its production in microorganisms necessitates activating and inactivating specific genes to direct more resources toward its synthesis. In this study, we developed a classification model based on Qualitative Perturbation Analysis and Machine Learning (QPAML). The model uses pFBA to obtain optimal reactions for tryptophan production and FSEOF to introduce perturbations on fluxes of the optima reactions while registering all changes over the iML1515a Genome-Scale Metabolic Network model. The altered reaction fluxes and their relationship with tryptophan and biomass production are translated to qualitative variables classified with GBDT. In the end, groups of enzymatic reactions are predicted to be deleted, overexpressed, or attenuated for tryptophan and 30 other metabolites in E. coli with a 92.34% F1-Score. The QPAML model can integrate diverse data types, promising improved predictions and the discovery of complex patterns in microbial metabolic engineering. It has broad potential applications and offers valuable insights for optimizing microbial production in biotechnology. Full article

This paper examines a time delay in position and velocity to minimize the nonlinear vibration of an excited Duffing oscillator (DO). This model is highly beneficial for capturing the nonlinear characteristics of many different applications in engineering. To achieve an estimated uniform solution to the problem under consideration, a modified homotopy perturbation method (HPM) is utilized. This adaptation produces a more accurate precise approximation with a numerical solution (NS). This is obtained by employing Mathematica software 12 (MS) in comparison with the analytical solution (AS). The comparison signifies a good match between the two methodologies. The comparison is made with the aid of the NS. Consequently, the work allows for a qualitative assessment of the results of a representative analytical approximation approach. A promising stability analysis for the unforced system is performed. The time history of the accomplished results is illustrated in light of a diverse range of physical frequency and time-delay aspects. The outcomes are theoretically discussed and numerically explained with a set of graphs. The nonlinear structured prototype is examined via the multiple-scale procedure. It investigates how various controlling limits affect the organization of vibration performances. As a key assumption, according to cubic nonlinearity, two significant examples of resonance, sub-harmonic and super-harmonic, are explored. The obtained modulation equations, in these situations, are quantitatively investigated with regard to the influence of the applied backgrounds. Full article

This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model’s intricate dynamics. Full article

A mathematical justification of some basic structural properties of stochastically perturbed gene regulatory networks, including those with autoregulation and delay, is offered in this paper. By using the theory of stochastic differential equations, it is, in particular, shown how to control the asymptotic behavior of the diffusion terms in order to not destroy certain qualitative features of the networks, for instance, their sliding modes. The results also confirm that the level of randomness is gradually reduced if the gene activation times become much smaller than the time of interaction of genes. Finally, the suggested analysis explains why the deterministic numerical schemes based on replacing smooth, steep response functions by the simpler yet discontinuous Heaviside function, the well-known simplification algorithm, are robust with respect to uncertainties in data. The main technical difficulties of the analysis are handled by applying the uniform version of the stochastic Tikhonov theorem in singular perturbation analysis suggested by Yu. Kabanov and S. Pergamentshchikov. Full article

Ground triplet 4,6-bis(trifluoromethyl)-1,3-phenylene bis(tert-butyl nitroxide) (TF2PBN) reacted with [Y(hfac)₃(H₂O)₂] (hfac = 1,1,1,5,5,5-hexafluoropentane-2,4-dionate), affording a doubly hydrogen-bonded adduct [Y(hfac)₃(H₂O)₂(TF2PBN)]. The biradical was recovered from the adduct through recrystallization. Crystallographic analysis indicates that the torsion angles (|θ| ≤ 90°) between the benzene ring and nitroxide groups were 74.9 and 84.8° in the adduct, which are larger than those of the starting material TF2PBN. Steric congestion due to o-trifluoromethyl groups gives rise to the reduction of π-conjugation. Two hydrogen bonds enhance this deformation. Susceptometry of the adduct indicates a ground singlet with 2J/k_B = −128(2) K, where 2J corresponds to the singlet–triplet gap. The observed magneto-structure relation is qualitatively consistent with Rajca’s pioneering work. A density functional theory calculation at the UB3LYP/6-311+G(2d,p) level using the atomic coordinates determined provided a result of 2J/k_B = −162.3 K for the adduct, whilst the corresponding calculation on intact TF2PBN provided +87.2 K. After a comparison among a few known compounds, the 2J vs. |θ| plot shows a negative slope with a critical torsion of 65(3)°. The ferro- and antiferromagnetic coupling contributions are balanced in TF2PBN, being responsible for ground-state interconversion by means of small structural perturbation like hydrogen bonds. Full article

Ecosystem modeling is a complex and multidisciplinary modeling problem which emerged in the 1950s. It takes advantage of the computational turn in sciences to better understand anthropogenic impacts and improve ecosystem management. For that purpose, ecosystem simulation models based on difference or differential equations were built. These models were relevant for studying dynamical phenomena and still are. However, they face important limitations in data-poor situations. As a response, several formal and non-formal qualitative dynamical modeling approaches were independently developed to overcome some limitations of the existing methods. Qualitative approaches allow studying qualitative dynamics as relevant abstractions of those provided by quantitative models (e.g., response to press perturbations). Each modeling framework can be viewed as a different assemblage of properties (e.g., determinism, stochasticity or synchronous update of variable values) designed to satisfy some scientific objectives. Based on four stated objectives commonly found in complex environmental sciences ((1) grasping qualitative dynamics, (2) making as few assumptions as possible about parameter values, (3) being explanatory and (4) being predictive), our objectives were guided by the wish to model complex and multidisciplinary issues commonly found in ecosystem modeling. We then discussed the relevance of existing modeling approaches and proposed the ecological discrete-event networks (EDEN) modeling framework for this purpose. The EDEN models propose a qualitative, discrete-event, partially synchronous and possibilistic view of ecosystem dynamics. We discussed each of these properties through ecological examples and existing analysis techniques for such models and showed how relevant they are for environmental science studies. Full article

In this work, a new method for constructing the infinite-dimensional Ornstein–Uhlenbeck stochastic process is introduced. The constructed process is used to perturb the harmonic system in order to model anomalously fast heat transport in one-dimensional nanomaterials. The introduced method made it possible to obtain a transition probability function that allows for a different approach to the analysis of equations with such a disturbance. This creates the opportunity to relax assumptions about temporal correlations for such a process, which may lead to a qualitatively different model of energy transport through vibrations of the crystal lattice and, as a result, to obtain the superdiffusion equation on a macroscopic scale with an order of the fractional Laplacian different from the value of 3/4 obtained so far in stochastic models. Simulations confirming these predictions are presented and discussed. Full article

Cropland ecosystem functioning may be affected by human perturbations transmitted from adjacent ecosystems, such as freshwater systems. However, our limited knowledge of the ecological interactions within cropland–freshwater networks hinders projecting the consequences of anthropogenic pressures. We reviewed the information from freshwater and cropland communities in the Mediterranean zone of Chile and constructed an ecological metanetwork for characterizing the structure and projecting responses of this system facing environmental pressures. We performed a semi-qualitative analysis to identify the nodes that strongly influence other network components and (or) could significantly affect the transmission of effects within the system. Our analyses show that omnivore fish, amphibians, annual pollinated crops, and deciduous orchards are the most important groups. Although we expected that amphibious predators were the most important groups in transmitting perturbations between ecosystems, we also found groups of plants and pollinators performing this function. We stress that the fate of crop systems facing environmental disturbances should be assessed in a broader context rather than as an isolated system. Full article

Climate change, one of the severest environmental threats to humankind, disproportionately affects low-income, developing countries in the Global South. Having no feasible mitigation alternatives, these countries resort to adaptation efforts to address climate perturbations. Climate change adaptation (or resilience) is primarily a localized course of action that depends on individuals, social networks, economies, ecologies, political structures, and the capabilities of all those to work collectively to absorb, learn from, and transform in the face of new realities. With a view to controlling the floods that shattered the life and economy of the then East Pakistan, which is now Bangladesh, during the mid-twentieth century, the coastal embankment project (CEP) was instituted as an adaptation strategy to natural disasters in Southwestern Bangladesh. Based on a qualitative analysis of primary and secondary data, this paper seeks to critically evaluate the efficacy of the CEP in terms of the space for feasible action and ecological modernization. The findings of this research indicate that the CEP has become an unrealistic venture that hinders the growing economic activity of shrimp aquaculture in the area. This paper is expected to contribute to generating further theoretical and empirical discourse on the evaluation of similar development projects around the globe. Full article

We consider a problem of hydrodynamic stability of the liquid displacement by gas in a porous medium in the case when a light gas is located above the liquid. The onset of instability and the evolution of the small shortwave perturbations are investigated. We show that when using the Darcy filtration law, the onset of instability may take place at an infinitely large wavenumber when the normal modes method is inapplicable. The results of numerical simulation of the nonlinear problem indicate that the anomalous growth of the amplitude of shortwave small perturbations persists, but the growth rate of amplitude decreases significantly compared to the results of linear analysis. An analysis of the stability of the gas/liquid interface is also carried out using a network model of a porous medium. It is shown that the results of surface evolution calculations obtained using the network model are in qualitative agreement with the results of the continual approach, but the continual model predicts a higher velocity of the interfacial surfaces in the capillaries. The growth rate of perturbations in the network model also increases with decreasing perturbation wavelength at a constant amplitude. Full article

Background: Despite extensive literature regarding laboratory-based balance perturbations, there is no up-to-date systematic review of methods. This systematic review aimed to assess current perturbation methods and outcome variables used to report participant biomechanical responses during walking. Methods: Web of Science, CINAHL, and PubMed online databases were searched, for records from 2015, the last search was on 30th of May 2022. Studies were included where participants were 18+ years, with or without clinical conditions, conducted in non-hospital settings. Reviews were excluded. Participant descriptive, perturbation method, outcome variables and results were extracted and summarised. Bias was assessed using the Appraisal tool for Cross-sectional Studies risk of bias assessment tool. Qualitative analysis was performed as the review aimed to investigate methods used to apply perturbations. Results: 644 records were identified and 33 studies were included, totaling 779 participants. The most frequent method of balance perturbation during gait was by means of a treadmill translation. The most frequent outcome variable collected was participant step width, closely followed by step length. Most studies reported at least one spatiotemporal outcome variable. All included studies showed some risk of bias, generally related to reporting of sampling approaches. Large variations in perturbation type, duration and intensity and outcome variables were reported. Conclusions: This review shows the wide variety of published laboratory perturbation methods. Moreover, it demonstrates the significant impact on outcome measures of a study based on the type of perturbation used. Registration: PROSPERO ID: CRD42020211876. Full article

This paper studies synchronization of a class of even pairs and symmetrically distributed eccentric rotors in a vibration system of a single mass body. A vibration system driven by four ERs with circular distribution structure and the same rotating direction is adopted as the dynamic model. The motion differential equations of the system are established based on Lagrange equation. The angular velocity and the phase of each rotor are perturbed by the average value of the synchronous velocity. The state equation of the system is obtained by applying the averaging method. According to the necessary condition of the steady-state motion, the synchronization condition and the dimensionless coupling torques of the system are deduced. The stability condition of the synchronous motion is derived by applying Lyapunov indirect method. The distribution law of the steady-state phase difference is discussed qualitatively by the numerical analysis of the theoretical results. Then combined with the numerical results, five sets of experiments are carried out on the experimental machine, which includes the sub-resonant state and the super-resonant state. The experimental results show that this vibration system has two super-resonant motion states and one sub-resonant motion state. The experiment proves the correctness of the theory, which can provide theoretical guidance for the design of this kind of vibration machine. Full article

In this paper, a new hybrid TSA-PSO algorithm is proposed that combines tunicate swarm algorithm (TSA) with the particle swarm optimization (PSO) technique for efficient maximum power extraction from a photovoltaic (PV) system subjected to partial shading conditions (PSCs). The performance of the proposed algorithm was enhanced by incorporating the PSO algorithm, which improves the exploitation capability of TSA. The response of the proposed TSA-PSO-based MPPT was investigated by performing a detailed comparative study with other recently published MPPT algorithms, such as tunicate swarm algorithm (TSA), particle swarm optimization (PSO), grey wolf optimization (GWO), flower pollination algorithm (FPA), and perturb and observe (P&O). A quantitative and qualitative analysis was carried out based on three distinct partial shading conditions. It was observed that the proposed TSA-PSO technique had remarkable success in locating the maximum power point and had quick convergence at the global maximum power point. The presented TSA-PSO MPPT algorithm achieved a PV tracking efficiency of 97.64%. Furthermore, two nonparametric tests, Friedman ranking and Wilcoxon rank-sum, were also employed to validate the effectiveness of the proposed TSA-PSO MPPT method. Full article