Dynamics, Volume 3, Issue 4 (December 2023) – 13 articles

We construct a fractional Laplacian spinning particle model in an external electromagnetic field that generalizes a standard relativistic spinning particle model without anti-commuting spin variables. The one-dimensional fractional Laplacian in world-line variable $\lambda$ governs the kinetic energy that is non-local in $\lambda$. The interaction between the particle’s charge and the electromagnetic four-potential is non-local in $\lambda$, while the interaction between the particle’s spin tensor and the electromagnetic field is standard. By applying the variational principle, we obtain the equations of motion for particle coordinates. We solve analytically the equations of motion in two particular cases: the constant electric and magnetic field. For more complex field configurations, the equations are, in general, non-local and non-linear. By making the assumption of a much weaker interaction term between the charge and four-potential compared with the interaction between spinning degrees of freedom and the electromagnetic field, we obtain approximate analytical solutions in the case of a quadratic electromagnetic potential. Full article

Robot manipulators possess the capability to autonomously execute complex sequences of actions. Their proficiency in handling challenging and hazardous tasks has led to their widespread adoption across diverse sectors, including industry, business, household appliances, rehabilitation, and many more. However, certain tasks prove to be challenging for individual robots, primarily due to constraints in their structure and limited degrees of freedom. Cooperative robot manipulators (CRMs) emerge as a compelling solution when dealing with large, heavy, or flexible payloads. The utilization of CRMs offers a host of benefits, including enhanced manipulation performance achieved through the synergy of sensing and actuation capabilities or by tapping into increased redundancy. Numerous techniques have been devised for the control and dynamical modeling of CRMs. Nevertheless, the field continues to present technical challenges and scientific inquiries. To inspire and facilitate further research and development in this realm, this review aims to consolidate the current body of knowledge pertaining to CRMs kinematics, dynamics modeling, and various control methodologies used for payload manipulation via CRMs. Full article

In this paper, exact analytical expressions are derived for dimensionless steady-state solutions corresponding to the modified Stokes’ problems for incompressible generalized Burgers’ fluids, considering the influence of porous and magnetic effects. Actually, these are the first exact solutions for such motions of these fluids. They can easily be particularized to give similar solutions for Newtonian, second-grade, Maxwell, Oldroyd-B and Burgers’ fluids. It is also proven that MHD motion problems of such fluids between infinite parallel plates can be investigated when shear stress is applied at the boundary. To validate the obtained results, the velocity fields are presented in two distinct forms, and their equivalence is proven through graphical representations. The obtained outcomes are utilized to determine the time required to reach a steady state and to elucidate the impacts of porous and magnetic parameters on the fluid motion. This investigation reveals that the attainment of a steady state occurs later when a porous medium or magnetic field is present. Additionally, the fluid’s flow resistance is augmented in the presence of a magnetic field or through a porous medium. Thus, as was expected, the fluid moves slower through porous media or in the presence of a magnetic field. Full article

Moving animal groups consist of many distinct individuals but can operate and function as one unit when performing different tasks. Effectively evading unexpected predator attacks is one primary task for many moving groups. The current explanation for predator evasion responses in moving animal groups require the individuals in the groups to interact via (velocity) alignment. However, experiments have shown that some animals do not use alignment. This suggests that another explanation for the predator evasion capacity in at least these species is needed. Here we establish that effective collective predator evasion does not require alignment, it can be induced via attraction and repulsion alone. We also show that speed differences between individuals that have directly observed the predator and those that have not influence evasion success and the speed of the collective evasion process, but are not required to induce the phenomenon. Our work here adds collective predator evasion to a number of phenomena previously thought to require alignment interactions that have recently been shown to emerge from attraction and repulsion alone. Based on our findings we suggest experiments and make predictions that may lead to a deeper understanding of not only collective predator evasion but also collective motion in general. Full article

This study explores the application of random matrices to track chaotic dynamics within the Chirikov standard map. Our findings highlight the potential of matrices exhibiting Wishart-like characteristics, combined with statistical insights from their eigenvalue density, as a promising avenue for chaos monitoring. Inspired by a technique originally designed for detecting phase transitions in spin systems, we successfully adapted and applied it to identify analogous transformative patterns in the context of the Chirikov standard map. Leveraging the precision previously demonstrated in localizing critical points within magnetic systems in our prior research, our method accurately pinpoints the Chirikov resonance overlap criterion for the chaos boundary at $K\approx 2.43$, reinforcing its effectiveness. Additionally, we verified our findings by employing a combined approach that incorporates Lyapunov exponents and bifurcation diagrams. Lastly, we demonstrate the adaptability of our technique to other maps, establishing its capability to capture the transition to chaos, as evidenced in the logistic map. Full article

The essence of the stochastic processes behind the empirical data on infection and fatality during pandemics is the complex interdependence between biological and social factors. Their balance can be checked on the data of new virus outbreaks, where the population is unprepared to fight the viral biology and social measures and healthcare systems adjust with a delay. Using a complex systems perspective, we combine network mapping with K-means clustering and multifractal detrended fluctuations analysis to identify typical trends in fatality rate data. We analyse global data of (normalised) fatality time series recorded during the first two years of the recent pandemic caused by the severe acute respiratory syndrome coronavirus 2 as an appropriate example. Our results reveal six clusters with robust patterns of mortality progression that represent specific adaptations to prevailing biological factors. They make up two significant groups that coincide with the topological communities of the correlation network, with stabilising (group g1) and continuously increasing rates (group g2). Strong cyclic trends and multifractal small-scale fluctuations around them characterise these patterns. The rigorous analysis and the proposed methodology shed more light on the complex nonlinear shapes of the pandemic’s main characteristic curves, which have been discussed extensively in the literature regarding the global infectious diseases that have affected humanity throughout its history. In addition to better pandemic preparedness in the future, the presented methodology can also help to differentiate and predict other trends in pandemics, such as fatality rates, caused simultaneously by different viruses in particular geographic locations. Full article

Effectively identifying and characterizing the various dynamics present in complex and chaotic systems is fundamental for chaos control, chaos classification, and behavior-transition forecasting, among others. It is a complicated task that becomes increasingly difficult as systems involve more dimensions and parameters. Here, we extend methods inspired in ordinal patterns to analyze 2D iterative maps to unveil underlying approximate symmetries of their dynamics. We distinguish different families of chaos within the systems, find similarities among chaotic maps, identify approximate temporal and dynamical symmetries, and anticipate sharp transitions in dynamics. We show how this methodology displays the evolution of the spatial correlations in a dynamical system as the control parameter varies. We prove the power of these techniques, which involve simple quantifiers as well as combinations of them, in extracting relevant information from the complex dynamics of 2D systems, where other techniques are less informative or more computationally demanding. Full article

Olefins are crucial building blocks for petrochemical industry, serving as raw materials for the production of various products such as plastics, synthetic fibers, detergents, solvents, and other chemicals. In FCC, heavy petroleum feedstocks are injected into a catalytic cracking unit, where they are mixed with a catalyst. The catalyst aids in breaking down the large hydrocarbon molecules into smaller fragments, including olefins like Propylene and Ethylene. These polymerization reactions occur at high temperatures. They demand that heat removal occurs as quickly as possible in order to control the reactor temperature and to avoid “hot spots” in the Regenerator or localized oxidation reactions (and to avoid creep rupture of the regenerator steel cladding). The cooling of the regenerator cladding surface can be achieved by impinging water droplets (spray), ejected from a spray nozzle. Spray cooling can provide uniform cooling and handle high heat fluxes in both a single phase and two phases. This research provides a thermal hydraulic design of regenerator spray cooling systems. In the framework of this research, Fire Dynamics Simulator (FDS) software was applied in order to simulate the temperature field and the water vapor mass fraction. A COMSOL Multiphysics finite element code was used in order to calculate the temperature field inside the regenerator cladding. The calculated surface temperatures and heat transfer convective coefficient, obtained using FDS software, were validated successfully against COMSOL numerical results and previous results in the literature. The numerical simulations were carried out for two cases. The first case was carried out at a distance of 0.5 m, and the second case was carried out at a distance of 0.2 m. A grid sensitivity study was carried out on the FDS model. Numerical integrations were carried out over time in order to calculate the average temperatures. The difference between these four average temperatures, calculated by applying different grids, is less than 7.4%. The calculated surface temperatures and heat transfer convective coefficient were validated successfully against COMSOL numerical results and previous research. It was shown that the calculated temperatures decrease in the second case. The water spray system managed to cool the steel wall more effectively as the water spray system approaches the steel cladding. Full article

A continuous iron ore pellet feed system for a direct reduction ironmaking furnace is reportedly jamming in a hopper above the furnace, where a counterflowing gas seals off the furnace flue gas. The conditions that result in jamming are not well understood. The system is computationally modeled utilizing the coupled discrete element method (DEM) and computational fluid dynamics (CFD) technique. The technique is computationally expensive; therefore, the pellet sizing is modified while preserving the key metrics important in jamming. The model is used to study the impact of pellet moisture, heating, and ice formation between pellets in relation to the jamming event. The results indicate that the influence of moisture alone on the bulk shear rate is unlikely to jam the system and that insufficient heat is supplied by the counterflowing gas to raise the temperature of the pellets, which suggests freezing conditions can exist within the hopper. Particle bonding is implemented to replicate wet and icy pellets freezing and breaking up. The results indicate that the system jams in winter conditions when the hopper is charged with a minimum of 15% icy pellets, or 10% icy with 5% wet pellets. These results agree with industry reports of jamming during winter operations. Full article

We develop a new formalism for constructing probabilities associated with the causal ordering of events in quantum theory, where an event is defined as the emergence of a measurement record on a detector. We start with constructing probabilities for the causal ordering events in classical physics, where events are defined in terms of worldline coincidences. Then, we show how these notions generalize to quantum systems, where there exists no fundamental notion of trajectory. The probabilities constructed here are experimentally accessible, at least in principle. Our analysis here clarifies that the existence of quantum orderings of events do not require quantum gravity effects: it is a consequence of the quantum dynamics of matter, and it appears in the presence of a fixed background spacetime. Full article

In this paper, we analyse the classical action as a tool to reveal the phase space structure of Hamiltonian systems simply and intuitively. We construct a scalar field using the values of the action along the trajectories to analyse the phase space. The different behaviours of the trajectories around important geometrical objects like normally hyperbolic invariant manifolds, their stable and unstable manifolds, and KAM structures generate characteristic patterns in the scalar field generated by the action. Also, we present a simple argument based on the conservation of energy and the behaviour of the trajectories to understand the origin of the patterns in this scalar field. As examples, we study the phase space of open Hamiltonian systems with two and three degrees of freedom. Full article

This article aims to develop a new Adaptive Proportional Integral Derivative (PID) Nonsingular Dual Terminal Sliding Mode Control, designed for tracking the position of robot manipulators under disturbances and uncertainties. Compared with existing PID Nonsingular Fast Terminal Sliding Mode (PIDNFTSM) controllers, this work effectively avoids singularity problems in control while significantly enhancing the convergence speed of errors. An adaptive reaching law is proposed to estimate the bound information of the first derivative of lumped disturbance by regulating itself based on sliding variables. The overall system stability is proven by using the Lyapunov approach. Subsequent simulation results verify the effectiveness of the proposed controller regarding tracking error reduction, energy efficiency enhancements, and singularity avoidance. Full article

Computational fluid dynamics (CFD)-based simulation has been the traditional way to model complex industrial systems and processes. One very large and complex industrial system that has benefited from CFD-based simulations is the steel blast furnace system. The problem with the CFD-based simulation approach is that it tends to be very slow for generating data. The CFD-only approach may not be fast enough for use in real-time decisionmaking. To address this issue, in this work, the authors propose the use of machine learning techniques to train and test models based on data generated via CFD simulation. Regression models based on neural networks are compared with tree-boosting models. In particular, several areas (tuyere, raceway, and shaft) of the blast furnace are modeled using these approaches. The results of the model training and testing are presented and discussed. The obtained $R^2$ metrics are, in general, very high. The results appear promising and may help to improve the efficiency of operator and process engineer decisionmaking when running a blast furnace. Full article