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Living systems may be defined as systems able to organize new, biology-specific, laws of physics and modify their parameters for specific tasks. Examples include the force-length muscle dependence mediated by the stretch reflex, and the control of movements with modification of the spatial referent coordinates for salient performance variables. Low-dimensional sets of referent coordinates at a task level are transformed to higher-dimensional sets at lower hierarchical levels in a way that ensures stability of performance. Stability of actions can be controlled independently of the actions (e.g., anticipatory synergy adjustments). Unintentional actions reflect relaxation processes leading to drifts of corresponding referent coordinates in the absence of changes in external load. Implications of this general framework for movement disorders, motor development, motor skill acquisition, and even philosophy are discussed.

Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted to admit global synchronization, a condition called Laplacian coupling. Many networks exhibit incomplete synchronization, where two or more clusters of synchronization persist, and computational group theory has recently proved to be valuable in discovering these cluster states based on the topology of the network. In the important case of Laplacian coupling, additional synchronization patterns can exist that would not be predicted from the group theory analysis alone. Understanding how and when clusters form, merge, and persist is essential for understanding collective dynamics, synchronization, and failure mechanisms of complex networks such as electric power grids, distributed control networks, and autonomous swarming vehicles. We describe a method to find and analyze all of the possible cluster synchronization patterns in a Laplacian-coupled network, by applying methods of computational group theory to dynamically equivalent networks. We present a general technique to evaluate the stability of each of the dynamically valid cluster synchronization patterns. Our results are validated in an optoelectronic experiment on a five-node network that confirms the synchronization patterns predicted by the theory.

This study examines stability by conducting a nonlinear stability analysis on the thermohaline flow of a steady, viscous, incompressible couple-stress fluid, utilizing a generalized energy method. It is observed that the linear and nonlinear thresholds are the same, and the physics of the onset of convection is fully captured. The couple-stress and solute gradient parameters are found to have a stabilizing effect on the system. [ABSTRACT FROM AUTHOR]

There is a constant demand for higher equipment parameters, such as the pressure of a sealing medium and shaft rotation speed. However, as the parameters increase, it becomes more difficult to ensure hermetization efficiency. The rotor of a multi-stage machine rotates in non-contact seals. Seals’ parameters have a great influence on vibration characteristics. Non-contact seals are considered to be hydrostatodynamic supports that can effectively dampen rotor oscillations. The force coefficients of gap seals are determined by geometric and operational parameters. A purposeful choice of these parameters can influence the vibration state of the rotor. It is shown for the first time that the initially dynamically flexible rotor, in combination with properly designed seals, can become dynamically rigid. Analytical dependencies for the computation of the dynamic characteristics are obtained. The resulting equations make it possible to calculate the radial-angular vibrations of the rotor of a centrifugal machine in the seals and construct the amplitude–frequency characteristics. By purposefully changing the parameters of non-contact seals, an initially flexible rotor can be made rigid, and its vibration resistance increases. Due to this, the environmental safety of critical pumping equipment increases.

The nonlinear Schrödinger equation is one of the most important physical model in optical fiber theory for comprehension of the fluctuations of optical bullet development. In this study, the exact bullet solutions for the (3+1)-dimensional Schrödinger equation which demonstrate the bullet behaviours in optical fibers can be accumulated through the Sardar sub-equation method and the unified method. The applied strategies may retrieve several kinds of optical bullet solutions within one frameworks as well as is quite simple and reliable. Mathematica are utilised for describing the dynamics of different wave structures as 3D, 2D, and contour visualisations for a given set of parameters. As a result, we are able to develop a variety of travelling wave structures namely the periodic, singular and V shaped soliton wave solutions. The stability analysis for the derived results is analysed efficiently while the modulation instability for the governing model has also been studied to demonstrate the reliability of the research. The approaches implemented here works perfectly and can be extended to deal with many advanced models in contemporary areas of science and engineering. The solutions attain by using these techniques are robust, unique and straight forward and has applications in different fields of physics, engineering and mathematical science. Specially physical applications of these obtain results are in the transmission of data in optical fibers. We also add the graphics for the better understanding of the attain solutions behaviour. [ABSTRACT FROM AUTHOR]

The structural, electronics, optical, and thermoelectric characteristics of BXO3(X = P, As, Sb, and Bi) perovskites are investigated within the density functional theory (DFT) framework. The full potential linearized augmented plane wave method employs various exchange–correlation potential approximations to estimate the ground state’s physical properties. The ground state stability of BXO3 perovskites was examined and all compounds have shown their cubic structure stability. The computed ground state structural parameters in the stability phase agree well with the available literature. Our results of optical properties indicated the potential use of BXO3(X = P, As, Sb, and Bi) in visible and ultraviolet zones of optoelectronic devices. The studied perovskites have indirect bandgap energy except BSbO3 has a direct bandgap. Notably, our findings show that except for BPO3 the figure of merit (ZT) values approach unity within the temperature range of 100–800 K for BSbO3 and BBiO3. In contrast, for BAsO3 the value decreases rapidly from one after 300 K. These perovskites are prospective candidates for thermoelectric applications.

Abstract Perovskite CsPbBr3 nanocrystals show excellent optical properties. However, the nanocrystals encounter a major challenge of poor stability. In this study, an effective approach is proposed for enhancing the stability of CsPbBr3 nanocrystals via a dual passivation strategy, where the dual passivation layer is composed of alumina (Al2O3) and polymer ethylene‐vinyl acetate (EVA). The Al2O3 coating on the CsPbBr3 surface is realized by in situ oxidation of trimethyl aluminum (TMA), which passivated the surface defects while blocking the intrusion of water and oxygen. The EVA film is formed by a solution method, which can further block the water and oxygen, and form the flexible composite with perovskite CsPbBr3 nanocrystals with enhanced stability toward water and heat. After soaking for 360 h and heating for 5 h, the photoluminescence (PL) intensity is higher than that without passivation. The polymer EVA packaging strategy provided CsPbBr3 with excellent extensibility and flexibility at 100% and 200% tensile rates, the PL intensity remains 91% and 88% of the initial intensity, which returns to the initial value after stretching. The unique dual‐protection structure significantly improves the water and thermal stability of the nanocrystals. The strategy might point out the direction for the future application of perovskites.

DNA origami nanostructures are promising carries for drug delivery applications. However, their limited stability under relevant conditions often presents a challenge. Herein, the structural stability of DNA origami nanostructures is investigated in a setting compatible with their application in photodynamic therapy (PDT). To this end, DNA origami triangles and six‐helix bundles (6HBs) are loaded with the clinically tested photosensitizer methylene blue, which upon irradiation with red light generates reactive oxygen species (ROS) that attack the DNA origami nanostructures. ROS‐induced structural damage is observed to depend on the ionic composition of the surrounding medium and becomes more severe at low ionic strength. Mg2+ ions can efficiently protect the DNA origami nanostructures from ROS‐induced damage and may even heal some of the damage obtained under Mg2+‐free conditions when added after irradiation. Finally, the employed DNA origami 6HBs are more resistant toward ROS‐induced structural damage than the triangles, which is attributed to their markedly different mechanical properties. These results thus provide some fundamental insights into the stabilizing role of DNA origami superstructure that may guide the selection or design of DNA origami nanocarriers with optimized stability for their application in PDT.

The development of reduced models provide efficient methods that can be used to perform short term experimental data analysis or narrow down the parametric range of more sophisticated numerical approaches. Reduced models are derived by simplifying the physics description with the goal of retaining only the essential ingredients required to reproduce the phenomena under study. This is the role of the gyro-fluid code FAR3d, dedicated to analyze the linear and nonlinear stability of Alfvén Eigenmodes (AE), Energetic Particle Modes (EPM) and magnetic-hydrodynamic modes as pressure gradient driven mode (PGDM) and current driven modes (CDM) in nuclear fusion devices. Such analysis is valuable for improving the plasma heating efficiency and confinement; this can enhance the overall device performance. The present review is dedicated to a description of the most important contributions of the FAR3d code in the field of energetic particles (EP) and AE/EPM stability. FAR3d is used to model and characterize the AE/EPM activity measured in fusion devices as LHD, JET, DIII-D, EAST, TJ-II and Heliotron J. In addition, the computational efficiency of FAR3d facilitates performing massive parametric studies leading to the identification of optimization trends with respect to the AE/EPM stability. This can aid in identifying operational regimes where AE/EPM activity is avoided or minimized. This technique is applied to the analysis of optimized configurations with respect to the thermal plasma parameters, magnetic field configuration, external actuators and the effect of multiple EP populations. In addition, the AE/EPM saturation phase is analyzed, taking into account both steady-state phases and bursting activity observed in LHD and DIII-D devices. The nonlinear calculations provide: the induced EP transport, the generation of zonal structures as well as the energy transfer towards the thermal plasma and between different toroidal/helical families. Finally, FAR3d is used to forecast the AE/EPM stability in operational scenarios of future devices as ITER, CFETR, JT60SA and CFQS as well as possible approaches to optimization with respect to variations in the most important plasma parameters.

Effective exploration of the pattern dynamic behaviors of reaction–diffusion models is a popular but difficult topic. The Schnakenberg model is a famous reaction–diffusion system that has been widely used in many fields, such as physics, chemistry, and biology. Herein, we explore the stability, Turing instability, and weakly non-linear analysis of the Schnakenberg model; further, the pattern dynamics of the fractional-in-space Schnakenberg model was simulated numerically based on the Fourier spectral method. The patterns under different parameters, initial conditions, and perturbations are shown, including the target, bar, and dot patterns. It was found that the pattern not only splits and spreads from the bar to spot pattern but also forms a bar pattern from the broken connections of the dot pattern. The effects of the fractional Laplacian operator on the pattern are also shown. In most cases, the diffusion rate of the fractional model was higher than that of the integer model. By comparing with different methods in literature, it was found that the simulated patterns were consistent with the results obtained with other numerical methods in literature, indicating that the Fourier spectral method can be used to effectively explore the dynamic behaviors of the fractional Schnakenberg model. Some novel pattern dynamics behaviors of the fractional-in-space Schnakenberg model are also demonstrated.

Scientific inquiry into effective numerical methods for modelling complex physical processes has led to the investigation of fluid dynamics, mainly when non-Newtonian properties and complex heat sources are involved. This paper presents an enhanced exponential time integrator approach to dynamically simulate non-Newtonian boundary layer flow with spatially and temporally varying heat sources. We propose an explicit scheme with second-order accuracy in time, demonstrated to be stable through Fourier series analysis, for solving time-dependent partial differential equations (PDEs). Utilizing this scheme, we construct and solve dimensionless PDEs representing the flow of Williamson fluid under the influence of space- and temperature-dependent heat sources. The scheme discretizes the continuity equation of incompressible fluid and Navier–Stokes, energy, and concentration equations using the central difference in space. Our analysis illuminates how factors affect velocity, temperature, and concentration profiles. Specifically, we observe a rise in temperature profile with enhanced coefficients of space and temperature terms in the heat source. Non-Newtonian behaviours and geographical/temporal variations in heat sources are critical factors influencing overall dynamics. The novelty of our work lies in developing an explicit exponential integrator approach, offering stability and second-order accuracy, for solving time-dependent PDEs in non-Newtonian boundary layer flow with variable heat sources. Our results provide valuable quantitative insights for understanding and controlling complex fluid dynamics phenomena. By addressing these challenges, our study advances numerical techniques for modelling real-world systems with implications for various engineering and scientific applications.

The purpose of this work is to study a new mathematical model of a ring neural network with unidirectional chemical connections, which is a singularly perturbed system of differential-difference equations with delay. Methods. A combination of analytical and numerical methods is used to study the existence and stability of special periodic solutions in this system, the so-called traveling waves. Results. The proposed methods make it possible to show that the ring system under study allows the number of stable traveling waves to increase with the number of oscillators in the network. Conclusion. In this article, we rethink and refine the previously proposed method of mathematical modeling of chemical synapses. On the one hand, it was possible to fully take into account the requirement of the Volterra structure of the corresponding equations and, on the other hand, the hypothesis of saturating conductivity. This makes it possible to observe the principle of uniformity: the new mathematical model is based on the same principles as the previously proposed model of electrical synapses.

Aluminum hydride (AlH3) has attracted wide attention due to its high gravimetric and volumetric hydrogen capacity. AlH3 can easily release hydrogen when heated at relatively low temperature. Such high hydrogen density and low dehydrogenation temperature make it one of the most promising high-energy fuels for solid propellants. In particular, AlH3 as a component of solid propellants may greatly increase the specific impulse of rocket engines. However, AlH3 exhibits low chemical and thermal stability in an ambient atmosphere. In this paper, the research progress about the synthesis, dehydrogenation thermodynamics, and kinetics, the stabilization of AlH3 over the past decades are reviewed, with the aim of exploring more a economical synthesis and suitable stabilization methods for large-scale use in solid propellants. Finally, some suggestions regarding future research directions in this filed are proposed.

The purpose of this work is to investigate the effect of stochastic perturbations of the white noise type on the stability of capture into autoresonance in oscillating systems with a variable pumping amplitude and frequency such that a center–saddle bifurcation occurs in the corresponding limiting autonomous system. The another purpose is determine the dependence of the intervals of stochastic stability of the autoresonance on the noise intensity. Methods. The existence of autoresonant regimes with increasing amplitude is proved by constructing and justificating asymptotic solutions in the form of power series with constant coefficients. The stability of solutions in terms of probability with respect to noise is substantiated using stochastic Lyapunov functions. Results. The conditions are described under which the autoresonant regime is preserved and disappears when the parameters pass through bifurcation values. The dependence of the intervals of stochastic stability of autoresonance on the degree of damping of the noise intensity is found. It is shown that more stringent restrictions are required to preserve the stability of solutions for the bifurcation values of the parameters. Conclusion. At the level of differential equations describing capture into autoresonance, the effect of damped stochastic perturbations on the center–saddle bifurcation is studied. The results obtained indicate the possibility of using damped oscillating perturbations for stable control of nonlinear systems.

This study is a continuation of M. M. Preobrazhenskaya’s work “Relay System of Differential Equations with Delay as a Perceptron Model”, which aimed to combine approaches related to artificial neural networks and modeling biological neurons using differential equations with delay. The model of a single neuron was proposed, which allows for the existence of special modes called “aging” and “dying” behavior of the neuron. The study found a certain range of parameters where the “dying” mode of the neuron exists and numerically demonstrated the existence of the “aging” mode. Purpose. We will unify the concepts of “aging” and “dying” neurons into the term “freezing” neuron. For this neuron, we will analytically construct a solution and find the range of parameters for its existence and stability, which will extend the results of the reference article. Methods. To study this model, an auxiliary equation obtained by exponential substitution in the original equation is considered. Then, the method of step integration of a differential equation with delay and the introduction of additional functions are used. Results. A solution of the “freezing” neuron type for the original model is constructed, and the range of parameters for the existence and stability of this solution is described. Conclusion. The study obtained an extension of results for solutions of a special type in the model proposed by M. M. Preobrazhenskaya.

We solve two numerical experiments described by 2D nonconstant coefficient advection–diffusion equations with specified initial and boundary conditions. Three finite difference methods, namely Lax–Wendroff, Du-Fort–Frankel and a nonstandard finite difference scheme, are derived and used to solve the two problems, whereby only the first problem has an exact solution. Stability analysis is performed to obtain a range of values of the time step size at a fixed spatial step size. We obtain the rate of convergence in space when the three methods are used to solve Problem 1. Computational times of the three algorithms are computed for Problem 1. Results are displayed for the two problems using the three methods at times T=1.0T=1.0 and T=5.0T=5.0. The main novelty is the stability analysis, which is not straightforward as we are working with numerical methods discretising 2D nonconstant coefficient advection–diffusion equation where many parameters are involved. The second highlight is to determine the most efficient scheme from the three methods. Third, there are very few published studies on analysis and use of numerical methods to solve nonconstant coefficient advection–diffusion equations, and this is one of the very few rare articles treating such topics.

ABSTRACTThis concise review aims to provide a summary of the most relevant recent experimental and theoretical results for solitons, i.e. self-trapped bound states of nonlinear waves, in two- and three-dimensional (2D and 3D) media. In comparison with commonly known one-dimensional solitons, which are, normally, stable modes, a challenging problem is the propensity of 2D and 3D solitons to instability, caused by the occurrence of the critical or supercritical wave collapse (catastrophic self-compression) in the same spatial dimensions. A remarkable feature of multidimensional solitons is their ability to carry vorticity; however, 2D vortex rings and 3D vortex tori are subject to a strong splitting instability. Therefore, it is natural to categorize the basic results according to physically relevant settings which make it possible to stabilize fundamental (non-topological) and vortex solitons against the collapse and splitting, respectively. The present review is focused on schemes that were recently elaborated in terms of Bose-Einstein condensates and similar photonic setups. These are two-component systems with spin-orbit coupling, and ones stabilized by the beyond-mean-field Lee-Huang-Yang effect. The latter setting has been implemented experimentally, giving rise to stable self-trapped quasi-2D and 3D quantum droplets. Characteristic examples of stable three-dimensional solitons: a semi-vortex (top) and mixed-mode (bottom) modes in the binary Bose-Einstein condensate, stabilized by the spin-orbit coupling.

This work explores the complex interactions of magnetic fields, photothermal effects, thermoelasticity theory, and acoustic pressure in a nonlocal semiconductor medium. These numerous physical phenomena are integrated into a complete theoretical mathematical framework used to understand the dynamic behavior of wave propagation within semiconductors. Considering the spatial distribution of carriers and their interactions, the non-local character of the semiconductor material is taken into account. The physical fields as temperature, mechanical stress, displacement, carrier density, and acoustic pressure can be analytically represented mathematically using the harmonic wave approach. Numerical simulations and theoretical discussions are performed to understand the complex interactions between these fundamental physical processes. The stability analysis of the interaction between the mechanical thermal and acoustic properties of the nonlocality medium under the impact of magnetic field by add it to the physical quantities is investigation. The theoretical results are examined and graphically shown according to the nonlocal semiconductor with magnetic field.

Time-delay effect and bifurcation phenomenon are important topics in the study of reaction–diffusion equations. In this paper, we consider a three-species predator–prey system with diffusion and incubation delay for predator. The stability and Hopf bifurcation are mainly discussed. We conclude that there exists a critical value of delay, such that the internal equilibrium is stable or unstable as the delay crosses the critical value. Especially, the system emerges Hopf bifurcation phenomenon at this critical value. For bifurcation solution, the conclusions of stability, period and bifurcation direction are also presented. Additionally, numerical simulations are proceeded to support the main results. In biology, the existence of bifurcation solution means that when the delay of predator reaches to a certain extent, the predator and prey will coexist within a period of time. It turns out that the related computations and analyses are much more complicated than that of two-species time-delay systems.

Battery hybridization in hydropower plants is a hydropower flexibility enhancement technology innovation that can potentially expand hydropower's contributions to the grid, but its fundamental characteristics and influencing mechanisms are still unclear. In this paper, primary frequency regulation (PFR) performance and the mechanism of this new technology are studied. A battery hybridized hydropower plant (BH-HPP) model, based on a field-measured-data-based hydropower plant (HPP) model and a verified battery simplified model, is established. Analysis of system stability and dynamics is undertaken for three different battery control strategies by root locus and participation factor methods. Compared to conventional HPPs, analysis results theoretically reveal BH-HPP can not only accelerate system regulation rapidity but also effectively enlarge HPP stability region during PFR process. Time domain simulation verifies the results and further shows synthetic control has better performance among introduced strategies. Besides, initial design ranges of control parameters considering battery capacity and a renewable energy source scenario case are also discussed. This work could provide theoretical support for flexibility enhancement solutions for hydropower systems.

The existence of thresholdless vortex solitons trapped at the core of disclination lattices that realize higher-order topological insulators is reported. The study demonstrates the interplay between nonlinearity and higher-order topology in these systems, as the vortex state in the disclination lattice bifurcates from its linear topological counterpart, while the position of its propagation constant within the bandgap and localization can be controlled by its power. It is shown that vortex solitons are characterized by strong field confinement at the disclination core due to their topological nature, leading to enhanced stability. Simultaneously, the global discrete rotational symmetry of the disclination lattice imposes restrictions on the maximal possible topological charge of such vortex solitons. The results illustrate the strong stabilizing action that topologically nontrivial structures may exert on excited soliton states, opening new prospects for soliton-related applications.

Abstract Halide perovskites have emerged as promising materials for various optoelectronic devices because of their excellent optical and electrical properties. In particular, halide perovskite quantum dots (PQDs) have garnered considerable attention as emissive materials for light-emitting diodes (LEDs) because of their higher color purities and photoluminescence quantum yields compared to conventional inorganic quantum dots (CdSe, ZnSe, ZnS, etc.). However, PQDs exhibit poor structural stabilities in response to external stimuli (moisture, heat, etc.) owing to their inherent ionic nature. This review presents recent research trends and insights into improving the structural stabilities of PQDs. In addition, the origins of the poor structural stabilities of PQDs and various methods to overcome this drawback are discussed. The structural degradation of PQDs is mainly caused by two mechanisms: (1) defect formation on the surface of the PQDs by ligand dissociation (i.e., detachment of weakly bound ligands from the surface of PQDs), and (2) vacancy formation by halide migration in the lattices of the PQDs due to the low migration energy of halide ions. The structural stabilities of PQDs can be improved through four methods: (1) ligand modification, (2) core–shell structure, (3) crosslinking, and (4) metal doping, all of which are presented in detail herein. This review provides a comprehensive understanding of the structural stabilities and opto-electrical properties of PQDs and is expected to contribute to future research on improving the device performance of perovskite quantum dot LEDs (PeLEDs).

High Purcell enhancement structures and stable emitters are essential prerequisites for the successful development of novel fast-operating active devices. Furthermore, a uniform enhancement of the spontaneous emission rate is critical for practical applications. Despite considerable efforts being made to meet these requirements, achieving them still remains a challenging task. In this work, we demonstrate that placing stable core−shell perovskite quantum dots (PQDs) in the nanogap region of hole/sphere-based nanogap structures (HSNGs) can enhance the spontaneous emission rate by more than a thousand-fold (up to a factor of ∼1080) compared to PQDs in solution. This enhancement factor is the highest value reported using PQDs, exceeding previously reported values by two orders of magnitude. Notably, the enhancement factor of the emission rate in the HSNG maintains large values across the samples, with values ranging from ∼690 to ∼1080. Furthermore, the structural stabilities of the PQDs are remarkably enhanced with the incorporation of SiO2 shells, which is validated by monitoring the changes in photoluminescence intensities over time during continuous laser exposure. As a result, the HSNG with stable core−shell PQDs offers great potential for fast optical device applications that require high performance and long-term operational stability.

The development of electrochromic (EC) materials has paved the way for a wide range of devices, such as smart windows, color displays, optical filters, wearable camouflages, among others. However, the advancement of electrochromism faces a significant hurdle due to its poor stability and limited color options. This lack of stability is primarily attributed to the substantial alteration in the dielectric properties of EC materials during cycling. Consequently, the design of advanced plasmonic materials is a key strategy to achieve a stable EC device. In this review, we provide an overview of the current state-of-the-art designs of plasmonic-based EC materials and devices. We discuss their working principles, techniques for structure/morphology engineering, doping methods, and crystal phase design. Furthermore, we explore the integration of plasmonic materials with other EC materials to create advanced EC devices. Finally, we outline the challenges that need to be addressed and present an outlook on the development of high-performance EC devices.

The thermodynamics of black holes (BHs) and their corrections have become a hot topic in the study of gravitational physics, with significant progress made in recent decades. In this paper, we study the thermodynamics and corrections of spherically symmetric BHs in models f(R)=R+αR2 and f(R)=R+2γR+8Λ under the f(R) theory, which includes the electrodynamic field and the cosmological constant. Considering thermal fluctuations around equilibrium states, we find that, for both f(R) models, the corrected entropy is meaningful in the case of a negative cosmological constant (anti-de Sitter–RN spacetime) with Λ=−1. It is shown that when the BHs’ horizon radius is small, thermal fluctuations have a more significant effect on the corrected entropy. Using the corrected entropy, we derive expressions for the relevant corrected thermodynamic quantities (such as Helmholtz free energy, internal energy, Gibbs free energy, and specific heat) and calculate the effects of the correction terms. The results indicate that the corrections to Helmholtz free energy and Gibbs free energy, caused by thermal fluctuations, are remarkable for small BHs. In addition, we explore the stability of BHs using specific heat. The study reveals that the corrected BH thermodynamics exhibit locally stable for both models, and corrected systems undergo a Hawking–Page phase transition. Considering the requirement on the non-negative volume of BHs, we also investigate the constraint on the EH radius of BHs.

This work presents several results of the stability in steel columns subject to pure compression. A square hollow cross-section with different sizes was considered. This study presents all the analytical equations that need to be used to verify the stability of each column with different lengths and boundary conditions. A finite element program was also chosen to achieve the most critical loads (Euler and buckling resistance loads) in the calculation for each element under study, using linear and nonlinear geometric and material modeling. Steel material was used for the columns, where damage due to plasticity was included, through plastic behavior with isotropic hardening. Comparing the results allows us to conclude that the use of the finite element method is an alternative methodology to be used in other types or configurations of columns, where parameterized tests can be easily implemented and to contribute to the development of a wide-ranging database. The finite element method led to an accurate solution when compared with the analytical results with a maximum deviation of 14.7%. By increasing the column length and reducing the cross-section size, the design buckling resistance of the studied columns also decreases. These studies demonstrate that the length and size of the column cross-section can meaningfully increase the structural behavior of the columns.

This study investigated the influence of ultrasound homogenization on the physical properties of milk ice cream mixes. A frequency of 20 kHz and an exposure time of 5 min was applied during the ultrasound homogenization to conduct experiments. Stability, particle size, rheological, and microscopic analyses were performed. Moreover, chosen stabilizers were used such as iota carrageenan or its hydrolyzates in combination with locust bean gum and xanthan gum. All parameters were checked before and after maturation at 4 °C/24 h. Based on the obtained results, it was noticed that the ultrasound homogenization contributed to a lower TSI value, which means that there is better stability during the maturation of milk ice cream mixes. In all of the mentioned samples, the TSI value was around 2 or less. Another pivotal finding connected with the particle sizes showed that simultaneously after and before maturation, the values of median D50 were lower in the samples after the mechanical homogenization than after the ultrasound. The rheological properties showed that all of the samples had pseudoplastic non-Newton behavior on the grounds that the value of the n index was lower than 1. Additionally, the consistency values in samples after the ultrasound treatment were lower than in samples after the mechanical homogenization and did not exceed 0.0018 × 10−3·Pasn after 24 h of maturation.

The present research was carried out in stands of Scots pine and black pine, pure or mixed with deciduous trees, installed on degraded lands from the Curvature Subcarpathian area, Romania, in a representative network of permanent research plots and followed the analysis of the structural diversity and stability indicators of these stands at different ages and in different conditions of degraded lands. The relationships between the quantitative variables with reference to the structure were established by analyzing the significance of the Pearson correlation coefficient (r) and also including datasets of slenderness indexes, which were classed into three domains of vulnerability to abiotic factors (like wind and snow). The compositional diversity of pine stands (pure or mixed with deciduous ones) is different in relation to age and is correlated with the structural diversity. The obtained correlation coefficients (r Pearson) express very strong and significant relationships between biometric parameters (h x Dbh, h x Lc%, Dc x Dbh, and Lc% x Dbh) of the structural diversity (r = 0.800–0.930), which is important for the analysis of the stability and vulnerability of pine forests. The strong correlation between the analyzed variables expresses a weak vulnerability to the action of harmful abiotic factors and the increase in the stability and resilience of the studied stands, especially of over 50 years old. In the old pine stands, the low-vulnerability domain (I < 0.80) is the best represented one, with an average of 64.01% from the total number of trees. At this age, trees with DBH > 22 cm fall into the low-vulnerability category. The explanation is that the stands were affected in their youth by the action of snow and wind, which, combined with the silvotechnical works performed, led to their compositional and structural diversification and increased stability. The young (0.8) and even-aged structure are the most vulnerable to abiotic factors due to the fact that a large number of trees are passing gradually into the higher cenotic classes.

Geosynthetic-reinforced embankments are subject to two primary failure mechanisms: bond failure and rupture. Bond failure occurs when the critical slip surface extends beyond the reinforced zone, while rupture occurs when the slip surface intersects the reinforcement. For a specified factor of safety and reinforcement length, there exists a minimum tensile strength of the reinforcement required to ensure bond failure only. Increasing the tensile strength beyond this minimum does not alter the failure mechanism or the factor of safety. Conversely, extending the reinforcement length while keeping the tensile strength below this critical value may lead to rupture failure at the same factor of safety. This study utilizes Monte Carlo simulation to perform a probabilistic stability analysis of these failure mechanisms in embankments with varying soil types and slope angles. The analysis evaluates safety margins in terms of the factor of safety and probability of failure. Furthermore, this study investigates the impact of cross-correlation between soil strength parameters, demonstrating that realistic values of the correlation coefficient can reduce the probability of failure for both failure mechanisms.

In daily routine movement, the ankle joint plays a crucial role in stability and mobility, especially when different types of terrain are involved. However, the simple task of standing can become a biomechanical difficulty when performed on a slope since demands that have to be accommodated are made on the complex structure of the ankle joint. The purpose of this study is to develop finite element (FE) models of the ankle joint with different inclined foot postures and to analyse the stress distributions on the ankle joint while standing on an inclined or declined surface. In this study, the FE model of the foot was developed, and von Mises stress distribution at the ankle joint was explored. The results show that the bone, cartilage, and ligament of the ankle experienced a different von Mises stress distribution pattern during flat standing in comparison with slope standing. In addition, this study found that the maximum von Mises stress distribution at the component of the ankle joint is higher during slope standing than flat standing. Taken together, these results suggest that slope standing, both inclined and declined, with more than 10° inclination, might contribute to a higher risk of injury as a higher maximum stress was observed. Therefore, to maintain proper body posture, it is suggested that weight be evenly distributed at both feet, since this can reduce stress at the ankle.

Abstract The ability to transfer microdroplets between fluid phases offers numerous advantages in various fields. This study focuses on the stability and morphology of a sessile oil microdropletduring the transfer from underwater to air. A distinct transition in microdroplet dynamics is observed, characterized by a shift from a scenario dominated by Marangoni forces to one dominated by capillary forces. In the former regime, the oil microdroplets spread in response to the contact between the water‐air interface and the water‐oil interface. The spreading distance follows a power law relationship of t3/4, reflecting the balance between Marangoni forces and viscous forces. On the other hand, in the capillarity‐dominated regime, the oil microdroplets remain stable at the contact line and after being transferred into the air. The crossover between these two regimes is identified in the parameter space defined by three factors: the approaching velocity of the solid‐water‐air contact line (vcl), the radius of the oil microdroplet (ro), and the radius of the water drop (rw). Furthermore, how to use the four‐phase contact line for shaping oil microdroplets is demonstrated using a full liquid process by the contact line lithography.

A novel stochastic numerical scheme is introduced to solve stochastic differential equations. The development of the scheme is based on two different parts. One part finds the solution for the deterministic equation, and the second part is the numerical approximation for the integral part of the Wiener process term in the stochastic partial differential equation. The scheme’s stability and consistency in the mean square sense are also ensured. Additionally, a respective mathematical model of the boundary layer flow of Casson fluid on a flat and oscillatory plate is formulated. Wiener process terms perturb the model to be studied. This scheme will be solved in contexts including deterministic and stochastic. The influence of different parameters on velocity, temperature, and concentration profiles is demonstrated in various graphical representations. The main objective of this study is to present a reliable numerical approach that surpasses the limitations of traditional numerical methods to analyze non-Newtonian mixed convective fluid flows with varying transport parameters. Our objective is to demonstrate the capabilities of the new stochastic finite difference scheme in enhancing our comprehension of stochastic fluid flow phenomena. This will be achieved by comprehensively examining its mathematical foundations and computer execution. Our objective is to develop a revolutionary method that will serve as a valuable resource for scientists and engineers studying the modeling and understanding of stochastic unstable non-Newtonian mixed convective fluid flow. This method will address the challenges posed by the fluid’s changing thermal conductivity and mass diffusivity.

Measles is a highly communicable viral infection that mostly affects children aged 5 years and below. Maternal antibodies in neonates help protect them from infectious diseases, including measles. However, maternal antibodies disappear a few months after birth, necessitating vaccination against measles. A mathematical model of measles, incorporating maternal antibodies and a double-dose vaccination, was proposed. Whenever ℛ0

Background and Objectives: Cellular labeling with fluorescent molecules appears to be one of the key methods of cell biology that continues to evolve with the advent of new fluorescent probes possessing unique properties. Ternary AgInS2/ZnS quantum dots occupy a special position comparedto other fluorescentmolecules duetotheir size-adjustable photoluminescence combined with broadband excitation and long emission lifetime. For the use of quantum dots of AgInS2/ZnS composition as a fluorescent probe in in vitro applications, they should have low physiological toxicity and good stability in physiological pH range. The objective of this work is therefore to evaluate the change of photoluminescent properties of AgInS2/ZnS quantum dots with changing pH of the medium and ionic strength. Materials and Methods: To evaluate the effect of pH and ionic strength on the photoluminescence properties of AgInS2/ZnS quantum dots, a size-selective precipitation procedure was carried out and the photoluminescence and absorption spectra of the quantum dot fractions were analyzed. Results: Ternary photoluminescent AgInS2/ZnS quantum dots stabilized in water by thioglycolic acid have been obtained by direct synthesis. Size-selective precipitation allowed to discriminate of 11 AgInS2/ZnS quantum dots fractions from the initial ensemble, revealing distinctly various optical properties. The effect of different pH and ionic strengths on the photoluminescent properties of AgInS2/ZnS quantum dots fractions has been studied. While in strong acidic and basic media the dramatic changes have been observed, the pH and ionic strength range corresponding to the biological fluids has shown no significant influence on the photoluminescent properties of all quantum dots fractions. Conclusion: This indicates the potential application of these nanoobjects as photoluminescent probes in various bioapplications.

This study investigates the effectiveness of positive position feedback (PPF) in reducing vibration amplitudes in an electric vehicle generator, specifically at super harmonic resonance (SHR) with 1:1 Internal Resonance (IR). Here is a breakdown. Simplified Model: The study uses a simplified nonlinear dynamic model (one degree of freedom, up to fifth-order nonlinear components) with external force, analyzed using the Multiple Time Scales Method (MTSM) with a first-order approximation. Focus on Resonance: The primary focus is on understanding the system’s behavior at SHR with 1:1 IR and how PPF can mitigate vibrations in this specific scenario. Frequency Response and Controller Influence: Frequency response functions are used to analyze the system’s stability with PPF, examining how different controller parameters affect the main system’s dynamics. Validation: Numerical solutions, obtained using the fourth-order Runge–Kutta method (‘RK-4’), are used to demonstrate and evaluate the system’s amplitude with and without PPF. The analytical and numerical results show strong agreement, validating the model’s accuracy. In essence, the research explores using PPF as a vibration control strategy in a specific resonance condition within an electric vehicle generator, using a combination of analytical and numerical methods for analysis and validation.

Investigating the influence of varying shaft steelwork stiffness on the stability of horizontal mass displacements, which are crucial elements of a conveyance-shaft steelwork system, is a significant step in evaluating the risk of parametric vibrations in steel constructions. While the Rayleigh method is limited to the first approximation in the solution to this analysis, it still provides valuable insights. Our examination indicates that the impact of a varying shaft steelwork system may not be noticeable in practical applications. This is a significant finding, as it suggests that the impact of varying stiffness in real working objects may be ignored, because the increase in the parametric resonance effects is negligible. This underscores the importance of our research in understanding the stability of steel constructions. This research, which involves theoretical analysis, simplifies the dynamic analysis of the conveyance-shaft steelwork system’s behavior. The result of the performed analysis is a valuable equation for predicting stable work in real hoist installations.

Yield and stability are desirable characteristics that crops need to have high agronomic value; sugarcane stands out globally due to its diverse range of products and by-products. However, genotype-environment (G × E) interactions can affect the overall performance of a crop. The objective of this study is to identify genotypes with the highest yield and stability, as well as to understand their independent and interactive effects. A collection of 10 sugarcane varieties was evaluated, including Colombian, Dominican, Ecuadorian lines, and a group of clones planted across five different locations from 2018 to 2020. A two-way ANOVA along with the GGE biplot technique were used to analyze yield and stability. The ANOVA model shows highly significant effects in all cases (p < 0.001) except for the genotype by year and sector interaction (G × Y × S); however, the decomposition by sectors reveals a significant triple interaction in sector 04 (p < 0.05). The GGE biplot model accounted for up to 74.77% of the total variance explained in its PC1 and PC2 components. It also highlighted the group of clones as having the highest yield and environmental instability, and the Ecuadorian varieties EC-07 and EC-08 as having the best yield-stability relationship. We conclude that the combined results of the ANOVA and GGE biplot models provide a more synergistic and effective evaluation of sugarcane varieties, offering theoretical and practical bases for decision-making in the selection of specific varieties.

Investigating the significant “roles” within financial complex networks and their stability is of great importance for preventing financial risks. On one hand, this paper initially constructs a complex network model of the stock market based on mutual information theory and threshold methods, combined with the closing price returns of stocks. It then analyzes the basic topological characteristics of this network and examines its stability under random and targeted attacks by varying the threshold values. On the other hand, using systemic risk entropy as a metric to quantify the stability of the stock market, this paper validates the impact of the COVID-19 pandemic as a widespread, unexpected event on network stability. The research results indicate that this complex network exhibits small-world characteristics but cannot be strictly classified as a scale-free network. In this network, key roles are played by the industrial sector, media and information services, pharmaceuticals and healthcare, transportation, and utilities. Upon reducing the threshold, the network’s resilience to random attacks is correspondingly strengthened. Dynamically, from 2000 to 2022, systemic risk in significant industrial share markets significantly increased. From a static perspective, the period around 2019, affected by the COVID-19 pandemic, experienced the most drastic fluctuations. Compared to the year 2000, systemic risk entropy in 2022 increased nearly sixtyfold, further indicating an increasing instability within this complex network.

Back-Support Industrial Exoskeletons (BSIEs) are designed to reduce muscle effort during repetitive tasks that involve trunk bending. We recruited twelve participants to perform 30 cycles of 45° trunk bending with/without the assistance of BSIEs and with/without postural asymmetry, first without any back fatigue, and then at the medium–high level of perceived back fatigue. To study the benefits of BSIEs, the effects of being in a fatigued state were assessed by comparing the muscle demands, kinematics, and stability measures during bending, retraction, and their transition portions per cycle across the study conditions. Overall, the BSIEs caused a minimal decrease in the lower-back activity (0–1.8%), caused by the increased demands during the retraction portion. A substantial decrease in leg activity was observed (10–18%). Asymmetry increased the right-lower-back and leg demands. Medium–high fatigue caused an increase in the lower-back activity (8–12%) during bending and retraction. The BSIEs caused slower movements and improved the stability by lowering the maximum distance of the Center of Pressure (COP) during the transition portion, as well as by lowering the mean velocity of the COP during the bending/retraction portions. This controlled study demonstrated the use of a cyclic trunk flexion–extension paradigm to study the effects of BSIEs, and the outcomes can help with understanding the temporal effects of using BSIEs on physiological measures, ultimately benefiting their proper implementation.

A battery track engineering vehicle faces challenges such as derailment and other safety concerns when navigating an R20m minimum radius curve, primarily owing to its low vertical and horizontal stabilities. To address these issues, a methodology integrating genetic optimization algorithms with a rigid and flexible coupled multi-body dynamics simulation is proposed to optimize the primary suspensions of the bogie of the vehicle. Initially, a multi-objective optimization model combining rigid and flexible coupled multi-body dynamics of battery track engineering vehicles with a genetic optimization algorithm was formulated. Subsequently, the optimal Latin hypercube design was applied to analyze the sensitivity of vertical and horizontal stability to various suspension parameters. Finally, a non-dominated sorting genetic algorithm (NSGA-II) and an archive-based micro genetic algorithm (AMGA) were applied to optimize the primary suspensions to enhance stability. Consequently, a set of optimal suspension parameter combinations was obtained. A notable enhancement was observed in the lateral stability of the optimized battery track engineering vehicles by 23.33% and in the vertical stability by 3.5% when traversing the R20m minimum radius curve, thereby establishing a theoretical foundation for further improving the running safety of railway vehicles and resolving the shortcomings of less research on the smallest radius curve.

Segmentation methods based on convolutional neural networks (CNN) have achieved remarkable results in the field of medical image segmentation due to their powerful representation capabilities. However, for brain-tumor segmentation, owing to the significant variations in shape, texture, and location, traditional convolutional neural networks (CNNs) with limited convolutional kernel-receptive fields struggle to model explicit long-range (global) dependencies, thereby restricting segmentation accuracy and making it difficult to accurately identify tumor boundaries in medical imaging. As a result, researchers have introduced the Swin Transformer, which has the capability to model long-distance dependencies, into the field of brain-tumor segmentation, offering unique advantages in the global modeling and semantic interaction of remote information. However, due to the high computational complexity of the Swin Transformer and its reliance on large-scale pretraining, it faces constraints when processing large-scale medical images. Therefore, this study addresses this issue by proposing a smaller network, consisting of a dual-encoder network, which also resolves the instability issue that arises in the training process of large-scale visual models with the Swin Transformer, where activation values of residual units accumulate layer by layer, leading to a significant increase in differences in activation amplitudes across layers and causing model instability. The results of the experimental validation using real data show that our dual-encoder network has achieved significant performance improvements, and it also demonstrates a strong appeal in reducing computational complexity.

In this article, a one-dimensional kinetic model is used to obtain space charge solitary waves in a beam of hot charged particles into a transmission channel with a resistance wall of radius rw. The axial electric field is obtained as , where and are geometric constants. In addition, due to the resistance of the wall, an electric field appears. The moments of the Vlasov equation for the water bag distribution function are converted into fluid equations and these fluid equations are reduced to the kdv equation using the reduced perturbation method. The shape of the fast and slow space charge solitary waves caused by the beam of hot charged particles in the presence of wall resistance is obtained by numerically examining the KdV equation at different times. Finally, it is revealed that with the increase of the wall resistance, the growth(attenuation) rate of the relative amplitude of the slow (fast) space charge soliton waves caused by the beams of charged particles increases.

A dose Calibrator is one of the dosimeters used to measure radionuclide activity before being given to patients. In order to function as a radiation dosimeter, the dose calibrator must have several good dosimeter properties, such as precision and stability. To test the dose calibrator, a source used by the hospital is required. The dose calibrator used in Instalasi Kedokteran Nuklir RSUD A. W. Sjahranie Samarinda is Capintec 25R. Two of the isotopes are widely used in nuclear medicine, namely Tc-99m and Co-57. The first step of this research was the elution performed by radiopharmaceuticals, then measured background activity. Then, Tc-99m and Co-57 activity were measured. Then, Tc-99m and Co-57 activity were measured for precision and stability tests, finally, graphs were made and evaluated. Based on the research results on the precision test, it was found that the measurement results for the Tc-99m source were obtained at 0.305%, while the result for measuring the activity of the standard Co-57 source was obtained at 0.307%. In the stability test, the result of measuring the Tc-99m source obtained a value of 0.563%, while the result of measuring the activity of the standard Co-57 source obtained a value of 0.437%. It can be concluded that the Capintec CRC 25R in RSUD A. W. Sjahranie Samarinda has good characteristics and performance so the measurement results can be trusted.

The subject of this work is the study of local dynamics of full-coupled chains of a great number of oscillators with a large delay in couplings. From a discrete model describing the dynamics of a great number of coupled oscillators, a transition has been made to a nonlinear integro-differential equation, continuously depending on time and space variable. A class of full-coupled systems has been considered. The main assumption is that the amount of delay in the couplings is large enough. This assumption opens the way to the use of special asymptotic methods of study. The parameters under which the critical case is realized in the problem of the equilibrium state stability have been distinguished. It is shown that they have infinite dimension. The analogues of normal forms — nonlinear boundary value problems of Ginzburg–Landau type have been constructed. In some cases, these boundary value problems contain integral components too. Their nonlocal dynamics describes the behavior of all solutions of the original equations in the balance state neighbourhood. Methods. As applied to the considered problems, methods of constructing quasinormal forms on central manifolds are developed. An algorithm for constructing the asymptotics of solutions based on the use of quasinormal forms for determining slowly varying amplitudes has been created. Results. Quasinormal forms that determine the dynamics of the original boundary value problem have been constructed. The dominant terms of asymptotic approximations for solutions of the considered chains have been obtained. On the basis of the given statements, a number of interesting dynamical effects have been revealed. For example, an infinite alternation of direct and reverse bifurcations when the delay coefficient increases. Their distinguishing feature is that they have two or three spatial variables.

Ecotourism is a form of tourism involving responsible travel to natural areas, conserving the environment, and improving the well-being of the local people. Its purpose may be to educate the traveler, to provide funds for ecological censervation, to directly benifit the economic development, and political empowerment of local communities. Ecotourism has come up as an important conservation strategy in the tropical areas where diversity of species and habitats are threatened because of the traditional forms of development. This study deals with a non-linear mathematical model with a novel idea for sustainable development of biomass with ecotourism which is imperative in the present scenario. Stability and bifurcation analysis of the model is done and it is observed from our study that the system predicts unstability and exhibits bifurcation if ecotourism goes beyond a threshold value.

Highly reliable atomic layer deposition (ALD)‐derived In‐Ga‐Zn‐O thin‐film transistors with high field‐effect mobility (μFE) and hydrogen (H) resistivity are crucial for the semiconductor industry. Herein, a hybrid Al2O3 gate insulator (GI) is proposed that is designed by controlling the plasma‐enhanced ALD and thermal ALD processes in situ to demonstrate robust characteristics. A hybrid GI is applied to the top‐gate geometry of an In0.71Ga0.08Zn0.21O active layer. The optimal device exhibits exceptional electrical characteristics, including a threshold voltage of 0.37 V, μFE of 150.7 cm2 V s−1, subthreshold swing of 64.0 mV decade−1, and hysteresis of 0.02 V. It demonstrates high resistance to H annealing and reliable positive bias temperature stress, as well as changes in VTH shifts of −0.43 and 0.00 V, respectively. The excellent electrical characteristics and high robustness of the device can be attributed to the precise control of H, oxygen, and carbon species within the upper region of the hybrid GI. The achievement of robust device characteristics enables the design of a novel vertical complementary metal‐oxide‐semiconductor inverter that exhibits a voltage gain of 44.7 V V−1 and a noise margin of 87.5% at a 10 V supply voltage.

Abstract Organic–inorganic halide perovskite solar cells (PVSCs) are considered a promising emerging photovoltaic technology that offer exceptional optoelectronic properties and the potential for economic solar energy conversion. Additive engineering‐based fabrication processes can achieve highly efficient and stable PVSCs that feature well‐controlled perovskite layers with a dense, uniform, “black” α‐phase crystal structure, as well as large grains and few defects. In this study, several hydroxylamine derivatives are introduced as additives to FAPbI3 precursor solutions to investigate their effects on the performance of PVSCs. The addition of hydroxylamine derivatives suppresses the formation of the unwanted δ‐phase and lead iodide, while the α‐phase cubic structure is preferentially formed without changing the bandgap of FAPbI3. Additionally, the additive‐treated perovskite films show improved stability compared with those without additives. Moreover, using X‐ray diffraction and X‐ray photoelectron spectroscopy analyses, it is discovered that the hydroxylamine‐based additives are not incorporated in the crystal lattices but rather resided on the surface or grain boundaries. Notably, the inverted PVSCs added with N‐methylhydroxylamine exhibit an improved power conversion efficiency, higher stability, and minimal hysteresis.

The mathematical model for monkeypox infection using the ψ–Hilfer fractional derivative is presented in this study. The integer order formulation is extended to the fractional order system by employing the ψ–Hilfer fractional derivative. The fractional order model analysis is provided. We investigate the model’s local asymptotical stability when R01, the global asymptotical stability result is displayed. We parameterize the model using recently reported cases of monkeypox infection in the United States. We calculated the basic reproduction using the estimated data and found it to be R0≈0.7121. We investigate the sensitivity of the monkeypox infection model and find the parameters that are sensitive R0. In general, we offer a numerical approach, and then for the monkeypox model, we present detailed findings. Some graphical outcomes for disease control in the United States are shown.

Complex systems, as interwoven miscellaneous interacting entities that emerge and evolve through self-organization in a myriad of spiraling contexts, exhibit subtleties on global scale besides steering the way to understand complexity which has been under evolutionary processes with unfolding cumulative nature wherein order is viewed as the unifying framework. Indicating the striking feature of non-separability in components, a complex system cannot be understood in terms of the individual isolated constituents' properties per se, it can rather be comprehended as a way to multilevel approach systems behavior with systems whose emergent behavior and pattern transcend the characteristics of ubiquitous units composing the system itself. This observation specifies a change of scientific paradigm, presenting that a reductionist perspective does not by any means imply a constructionist view; and in that vein, complex systems science, associated with multiscale problems, is regarded as ascendancy of emergence over reductionism and level of mechanistic insight evolving into complex system. While evolvability being related to the species and humans owing their existence to their ancestors' capability with regards to adapting, emerging and evolving besides the relation between complexity of models, designs, visualization and optimality, a horizon that can take into account the subtleties making their own means of solutions applicable is to be entailed by complexity. Such views attach their germane importance to the future science of complexity which may probably be best regarded as a minimal history congruent with observable variations, namely the most parallelizable or symmetric process which can turn random inputs into regular outputs. Interestingly enough, chaos and nonlinear systems come into this picture as cousins of complexity which with tons of its components are involved in a hectic interaction with one another in a nonlinear fashion amongst the other related systems and fields. Relation, in mathematics, is a way of connecting two or more things, which is to say numbers, sets or other mathematical objects, and it is a relation that describes the way the things are interrelated to facilitate making sense of complex mathematical systems. Accordingly, mathematical modeling and scientific computing are proven principal tools toward the solution of problems arising in complex systems' exploration with sound, stimulating and innovative aspects attributed to data science as a tailored-made discipline to enable making sense out of voluminous (-big) data. Regarding the computation of the complexity of any mathematical model, conducting the analyses over the run time is related to the sort of data determined and employed along with the methods. This enables the possibility of examining the data applied in the study, which is dependent on the capacity of the computer at work. Besides these, varying capacities of the computers have impact on the results; nevertheless, the application of the method on the code step by step must be taken into consideration. In this sense, the definition of complexity evaluated over different data lends a broader applicability range with more realism and convenience since the process is dependent on concrete mathematical foundations. All of these indicate that the methods need to be investigated based on their mathematical foundation together with the methods. In that way, it can become foreseeable what level of complexity will emerge for any data desired to be employed. With relation to fractals, fractal theory and analysis are geared toward assessing the fractal characteristics of data, several methods being at stake to assign fractal dimensions to the datasets, and within that perspective, fractal analysis provides expansion of knowledge regarding the functions and structures of complex systems while acting as a potential means to evaluate the novel areas of research and to capture the roughness of objects, their nonlinearity, randomness, and so on. The idea of fractional-order integration and differentiation as well as the inverse relationship between them lends fractional calculus applications in various fields spanning across science, medicine and engineering, amongst the others. The approach of fractional calculus, within mathematics-informed frameworks employed to enable reliable comprehension into complex processes which encompass an array of temporal and spatial scales notably provides the novel applicable models through fractional-order calculus to optimization methods. Computational science and modeling, notwithstanding, are oriented toward the simulation and investigation of complex systems through the use of computers by making use of domains ranging from mathematics to physics as well as computer science. A computational model consisting of numerous variables that characterize the system under consideration allows the performing of many simulated experiments via computerized means. Furthermore, Artificial Intelligence (AI) techniques whether combined or not with fractal, fractional analysis as well as mathematical models have enabled various applications including the prediction of mechanisms ranging extensively from living organisms to other interactions across incredible spectra besides providing solutions to real-world complex problems both on local and global scale. While enabling model accuracy maximization, AI can also ensure the minimization of functions such as computational burden. Relatedly, level of complexity, often employed in computer science for decision-making and problem-solving processes, aims to evaluate the difficulty of algorithms, and by so doing, it helps to determine the number of required resources and time for task completion. Computational (-algorithmic) complexity, referring to the measure of the amount of computing resources (memory and storage) which a specific algorithm consumes when it is run, essentially signifies the complexity of an algorithm, yielding an approximate sense of the volume of computing resources and seeking to prove the input data with different values and sizes. Computational complexity, with search algorithms and solution landscapes, eventually points toward reductions vis à vis universality to explore varying degrees of problems with different ranges of predictability. Taken together, this line of sophisticated and computer-assisted proof approach can fulfill the requirements of accuracy, interpretability, predictability and reliance on mathematical sciences with the assistance of AI and machine learning being at the plinth of and at the intersection with different domains among many other related points in line with the concurrent technical analyses, computing processes, computational foundations and mathematical modeling. Consequently, as distinctive from the other ones, our special issue series provides a novel direction for stimulating, refreshing and innovative interdisciplinary, multidisciplinary and transdisciplinary understanding and research in model-based, data-driven modes to be able to obtain feasible accurate solutions, designed simulations, optimization processes, among many more. Hence, we address the theoretical reflections on how all these processes are modeled, merging all together the advanced methods, mathematical analyses, computational technologies, quantum means elaborating and exhibiting the implications of applicable approaches in real-world systems and other related domains. [ABSTRACT FROM AUTHOR]