Symmetry in System Theory, Control and Computing

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (10 October 2023) | Viewed by 10545

Special Issue Editors

Applied Mathematics, Indian Institute of Technology (ISM), Dhanbad, India
Interests: differential equations; mathematical modeling; chaotic dynamics and dynamical system theory
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamilnadu, India
Interests: fractional calculus; mathematical control theory; stochastics differential equations

Special Issue Information

Dear Colleagues,

In several areas, including system theory, symmetry has been extensively employed to analyse and deconstruct complicated issues. In fields including mathematics, computer science, physics, and others, symmetry is a common analytical technique. Additionally, symmetry has been applied to analyse and streamline control design. Symmetries, which map the state-space matrices to themselves, are transformations of the state-space, input-space, and output-space in control theory. The state-space equations can be block-diagonalized for unconstrained symmetric linear systems. The process of representing, detecting, and reasoning about symmetries on computers is referred to as computational symmetry. Computational symmetry is important in computer science for a variety of reasons, including the fact that it appears everywhere, stimulates the mind, indicates structure and applications, and much more.

The focus of this Special Issue is to continue to advance research on topics relating to the Symmetry in System Theory, Control and Computing. Topics that are invited for submission include (but are not limited to):

  1. Symmetries of dynamic/constrained systems;
  2. Symmetry identification for linear/constrained systems;
  3. Optimal control;
  4. Model predictive control;
  5. Neural-network-based control;
  6. Stochastic control problems;
  7. Mathematical control theory;
  8. Computing applications.

Prof. Dr. Ranjit Kumar Upadhyay
Dr. Ramalingam Udhayakumar
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • symmetries of dynamic/constrained systems
  • symmetry identification for linear/constrained systems
  • optimal control
  • model predictive control
  • neural-network-based control
  • stochastic control problems
  • mathematical control theory
  • computing applications

Published Papers (9 papers)

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Research

21 pages, 7035 KiB  
Article
Melting Heat Transfer Rheology in Bioconvection Cross Nanofluid Flow Confined by a Symmetrical Cylindrical Channel with Thermal Conductivity and Swimming Microbes
by Fuad A. Awwad, Emad A. A. Ismail, Taza Gul, Waris Khan and Ishtiaq Ali
Symmetry 2023, 15(9), 1647; https://doi.org/10.3390/sym15091647 - 25 Aug 2023
Cited by 1 | Viewed by 579
Abstract
Nonlinear thermal transport of non-Newtonian polymer flows is an increasingly important area in materials engineering. Motivated by new developments in this area which entail more refined and more mathematical frameworks, the present analysis investigates the boundary-layer approximation and heat transfer persuaded by a [...] Read more.
Nonlinear thermal transport of non-Newtonian polymer flows is an increasingly important area in materials engineering. Motivated by new developments in this area which entail more refined and more mathematical frameworks, the present analysis investigates the boundary-layer approximation and heat transfer persuaded by a symmetrical cylindrical surface positioned horizontally. To simulate thermal relaxation impacts, the bioconvection Cross nanofluid flow Buongiorno model is deployed. The study examines the magnetic field effect applied to the nanofluid using the heat generated, as well as the melting phenomenon. The nonlinear effect of thermosolutal buoyant forces is incorporated into the proposed model. The novel mathematical equations include thermophoresis and Brownian diffusion effects. Via robust transformation techniques, the primitive resulting partial equations for momentum, energy, concentration, and motile living microorganisms are rendered into nonlinear ordinary equations with convective boundary postulates. An explicit and efficient numerical solver procedure in the Mathematica 11.0 programming platform is developed to engage the nonlinear equations. The effects of multiple governing parameters on dimensionless fluid profiles is examined using plotted visuals and tables. Finally, outcomes related to the surface drag force, heat, and mass transfer coefficients for different influential parameters are presented using 3D visuals. Full article
(This article belongs to the Special Issue Symmetry in System Theory, Control and Computing)
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15 pages, 899 KiB  
Article
Balancing Tradeoffs in Network Queue Management Problem via Forward–Backward Sweeping with Finite Checkpoints
by Amr Radwan, Taghreed Ali Alenezi, Wejdan Alrashdan and Won-Joo Hwang
Symmetry 2023, 15(7), 1395; https://doi.org/10.3390/sym15071395 - 10 Jul 2023
Viewed by 727
Abstract
Network queue management can be modelled as an optimal control problem and is aimed at controlling the dropping rate, in which the state and control variables are the instantaneous queue length and the dropping rate, respectively. One way to solve it is by [...] Read more.
Network queue management can be modelled as an optimal control problem and is aimed at controlling the dropping rate, in which the state and control variables are the instantaneous queue length and the dropping rate, respectively. One way to solve it is by using an indirect method, namely forward–backward sweeping based on the Pontryagin minimum principle to derive control the trajectory of the dropping rate. However, there exists some performance balance issues in the network queue, such as memory usage versus runtime of the algorithm, or dropping rate versus network queue length. Many researchers have exploited symmetry for constrained systems, controllers, and model predictive control problems to achieve an exponential memory reduction and simple, intuitive optimal controllers. In this article, we introduce the integration of the checkpointing method into forward–backward sweeping to address such balancing issues. Specifically, we exploit the revolve algorithm in checkpointing and choose a finite number of checkpoints to reduce the complexity. Both numerical and simulation results in a popular network simulator (ns-2) are provided through two experiments: varying bandwidth and offered load, which solidify our proposal in comparison to other deployed queue management algorithms. Full article
(This article belongs to the Special Issue Symmetry in System Theory, Control and Computing)
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25 pages, 3347 KiB  
Article
Enhancing Heat Transfer in Blood Hybrid Nanofluid Flow with AgTiO2 Nanoparticles and Electrical Field in a Tilted Cylindrical W-Shape Stenosis Artery: A Finite Difference Approach
by Ebrahem A. Algehyne, N. Ameer Ahammad, Mohamed E. Elnair, Mohamed Zidan, Yasir Y. Alhusayni, Babikir Osman El-Bashir, Anwar Saeed, Ali Saleh Alshomrani and Faris Alzahrani
Symmetry 2023, 15(6), 1242; https://doi.org/10.3390/sym15061242 - 10 Jun 2023
Cited by 4 | Viewed by 1389
Abstract
The present research examines the unsteady sensitivity analysis and entropy generation of blood-based silver–titanium dioxide flow in a tilted cylindrical W-shape symmetric stenosis artery. The study considers various factors such as the electric field, joule heating, viscous dissipation, and heat source, while taking [...] Read more.
The present research examines the unsteady sensitivity analysis and entropy generation of blood-based silver–titanium dioxide flow in a tilted cylindrical W-shape symmetric stenosis artery. The study considers various factors such as the electric field, joule heating, viscous dissipation, and heat source, while taking into account a two-dimensional pulsatile blood flow and periodic body acceleration. The finite difference method is employed to solve the governing equations due to the highly nonlinear nature of the flow equations, which requires a robust numerical technique. The utilization of the response surface methodology is commonly observed in optimization procedures. Drawing inspiration from drug delivery techniques used in cardiovascular therapies, it has been proposed to infuse blood with a uniform distribution of biocompatible nanoparticles. The figures depict the effects of significant parameters on the flow field, such as the electric field, Hartmann number, nanoparticle volume fraction, body acceleration amplitude, Reynolds number, Grashof number, and thermal radiation, on velocity, temperature (nondimensional), entropy generation, flow rate, resistance to flow, wall shear stress, and Nusselt number. The velocity and temperature profiles improve with higher values of the wall slip parameter. The flow rate profiles increase with an increment in wall velocity but decrease with the Womersley number. Increasing the intensity of radiation and decreasing magnetic fields both result in a decrease in the rate of heat transfer. The blood temperature is higher with the inclusion of hybrid nanoparticles than the unitary nanoparticles. The total entropy generation profiles increase for higher values of the Brickman number and temperature difference parameters. Unitary nanoparticles exhibit a slightly higher total entropy generation than hybrid nanoparticles, particularly when positioned slightly away from the center of the artery. The total entropy production decreases by 17.97% when the thermal radiation is increased from absence to 3. In contrast, increasing the amplitude of body acceleration from 0.5 to 2 results in a significant enhancement of 76.14% in the total entropy production. Full article
(This article belongs to the Special Issue Symmetry in System Theory, Control and Computing)
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15 pages, 3494 KiB  
Article
Heat and Mass Transport in Casson Nanofluid Flow over a 3-D Riga Plate with Cattaneo-Christov Double Flux: A Computational Modeling through Analytical Method
by Karuppusamy Loganathan, S. Eswaramoorthi, P. Chinnasamy, Reema Jain, Ramkumar Sivasakthivel, Rifaqat Ali and N. Nithya Devi
Symmetry 2023, 15(3), 725; https://doi.org/10.3390/sym15030725 - 14 Mar 2023
Cited by 4 | Viewed by 1072
Abstract
This work examines the non-Newtonian Cassonnanofluid’s three-dimensional flow and heat and mass transmission properties over a Riga plate. The Buongiorno nanofluid model, which is included in the present model, includes thermo-migration and random movement of nanoparticles. It also took into account the Cattaneo–Christov [...] Read more.
This work examines the non-Newtonian Cassonnanofluid’s three-dimensional flow and heat and mass transmission properties over a Riga plate. The Buongiorno nanofluid model, which is included in the present model, includes thermo-migration and random movement of nanoparticles. It also took into account the Cattaneo–Christov double flux processes in the mass and heat equations. The non-Newtonian Casson fluid model and the boundary layer approximation are included in the modeling of nonlinear partial differential systems. The homotopy technique was used to analytically solve the system’s governing equations. To examine the impact of dimensionless parameters on velocities, concentrations, temperatures, local Nusselt number, skin friction, and local Sherwood number, a parametric analysis was carried out. The velocity profile is augmented in this study as the size of the modified Hartmann number increases. The greater thermal radiative enhances the heat transport rate. When the mass relaxation parameter is used, the mass flux values start to decrease. Full article
(This article belongs to the Special Issue Symmetry in System Theory, Control and Computing)
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21 pages, 2056 KiB  
Article
The Impact of Heat Source and Temperature Gradient on Brinkman–Bènard Triple-Diffusive Magneto-Marangoni Convection in a Two-Layer System
by Yellamma, Manjunatha Narayanappa, Ramalingam Udhayakumar, Barakah Almarri, Sumithra Ramakrishna and Ahmed M. Elshenhab
Symmetry 2023, 15(3), 644; https://doi.org/10.3390/sym15030644 - 03 Mar 2023
Cited by 3 | Viewed by 1112
Abstract
The effect of a heat source and temperature gradient on Brinkman–Bènard Triple-Diffusive magneto-Marangoni (BBTDMM) convection in a two-layer system is investigated. The two-layer system is horizontally infinite and is surrounded on all sides by adiabatic boundaries. It is exposed to basic uniform and [...] Read more.
The effect of a heat source and temperature gradient on Brinkman–Bènard Triple-Diffusive magneto-Marangoni (BBTDMM) convection in a two-layer system is investigated. The two-layer system is horizontally infinite and is surrounded on all sides by adiabatic boundaries. It is exposed to basic uniform and non-uniform temperature profiles and heat sources. The appropriate eigenvalues and thermal Marangoni numbers (TMNs), which depend on temperature and concentration, are obtained for the temperature profiles (TPs) for lower rigid and higher free boundaries with surface tension. The transformed system of ordinary differential equations is solved by using an exact technique. For all three TPs, the impact of significant relevant parameters on these eigenvalues, and hence on BBTDMM convection, are investigated versus the thermal ratio. It is observed that, by increasing the values of the modified internal Rayleigh number for the fluid layer and the solute Marangoni numbers, the Darcy number, and the viscosity ratio for the set of physical parameters chosen in the study, one can postpone BBTDMM convection. Higher values of the modified internal Rayleigh numbers for the porous layer augment BBTDMM convection. Full article
(This article belongs to the Special Issue Symmetry in System Theory, Control and Computing)
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16 pages, 4072 KiB  
Article
Computational Modeling of Thermodynamical Pulsatile Flow with Uncertain Pressure in Hydrocephalus
by Hemalatha Balasundaram, Nazek Alessa, Karuppusamy Loganathan, V. Vijayalakshmi and Nayani Uday Ranjan Goud
Symmetry 2023, 15(2), 534; https://doi.org/10.3390/sym15020534 - 16 Feb 2023
Cited by 2 | Viewed by 1182
Abstract
The watery cerebrospinal fluid that flows in the subarachnoid space (SAS) surrounds the entire central nervous system via symmetrical thermo-solute flow. The significance of this study was to present a flexible simulation based on theoretical vivo inputs onto a mathematical framework to describe [...] Read more.
The watery cerebrospinal fluid that flows in the subarachnoid space (SAS) surrounds the entire central nervous system via symmetrical thermo-solute flow. The significance of this study was to present a flexible simulation based on theoretical vivo inputs onto a mathematical framework to describe the interaction of cerebrospinal fluid circulation restricted to a pathological disorder. The pathophysiology disorder hydrocephalus is caused by an enormous excess of asymmetric fluid flow in the ventricular region. This fluid imposition increases the void space of its boundary wall (Pia mater). As a result, the dumping effect affects an inertial force in brain tissues. A mathematical model was developed to impose the thermal dynamics of hydrocephalus, in which solute transport constitutes the excess watery CSF fluid caused by hydrocephalus, in order to demonstrate perspective changes in ventricular spaces. This paper investigated brain porous spaces in order to strengthen the acceleration and thermal requirements in the CNS mechanism. To characterize neurological activities, a unique mathematical model that includes hydrodynamics and nutrient transport diffusivity was used. We present the analytical results based on physical experiments that use the novel Laplace method to determine the nutrients transported through permeable pia (brain) parenchyma with suitable pulsatile boundary conditions. This causes high CSF pressure and brain damage due to heat flux over the SAS boundary wall. As a result of the increased Schmidt number, the analysis of the hydrocephalus problem revealed an increase in permeability and drop in solute transport. A high-velocity profile caused a rise in thermal buoyancy (Grashof number). When the CSF velocity reached an extreme level, it indicated a higher Womersley number. Additionally, the present study compared a number of clinical studies for CSF amplitude and pressure. We validated the results by providing a decent justification with the clinical studies by appropriate field references. Full article
(This article belongs to the Special Issue Symmetry in System Theory, Control and Computing)
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28 pages, 4044 KiB  
Article
Chaos Control of a Delayed Tri-Trophic Food Chain Model with Fear and Its Carry Over Effects
by Sivasamy Ramasamy, David Banjerdpongchai and PooGyeon Park
Symmetry 2023, 15(2), 484; https://doi.org/10.3390/sym15020484 - 12 Feb 2023
Cited by 3 | Viewed by 1191
Abstract
One of the main objectives of theoretical ecologists involves finding mechanisms to control the chaos in ecological models to maintain positive densities of the species. Numerous researchers have suggested that, apart from the direct killing in the prey–predator relationship, there are some indirect [...] Read more.
One of the main objectives of theoretical ecologists involves finding mechanisms to control the chaos in ecological models to maintain positive densities of the species. Numerous researchers have suggested that, apart from the direct killing in the prey–predator relationship, there are some indirect effects, such as fear of predation. Induced fear can lead to slowing down the growth rate of the prey species, and this non-chemical strategy can be carried over to successive seasons or upcoming generations. In this work, we explore the impact of fear due to predation and its carry-over effect (COE) in a delayed tri-trophic food chain model, whereas the Holling type-II functional response is used to determine the interference among the species. The proposed model is an asymmetric interaction food chain model since the species in this model only kills other species. The growth rate of prey and middle predators is affected due to the respective fear of predation by middle and special predators. The non-delayed model considered in this paper generalizes the models developed by Hastings–Powell and Panday et al. The gestation delay in the special predator’s growth term is incorporated into the proposed model. We determined the essential conditions for the existence of ecologically feasible equilibrium points and their local and global stability. Furthermore, we developed the conditions for the occurrence of the Hopf bifurcation around an interior equilibrium to seek periodic behaviors of delayed and non-delayed models. Numerical examples were performed to justify the proposed theoretical findings and to show the impacts of fear and its COE parameters on the system dynamics through phase portraits, the time series of solutions, and bifurcation diagrams. We discovered that the chaotic behavior of the food chain model can be controlled by using the fear effect and its COE parameters. The dynamics of the delayed food chain model with the fear effect and its COEs are further explored in our findings. Our theoretical findings clearly provide a mechanism to protect and control species populations in ecological systems. It is also essential for developing optimized harvesting strategies in fisheries and pest management in agriculture. Full article
(This article belongs to the Special Issue Symmetry in System Theory, Control and Computing)
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16 pages, 751 KiB  
Article
Comparative Analysis of Darcy–Forchheimer Radiative Flow of a Water-Based Al2O3-Ag/TiO2 Hybrid Nanofluid over a Riga Plate with Heat Sink/Source
by R. Sindhu, Nazek Alessa, S. Eswaramoorthi and Karuppusamy Loganathan
Symmetry 2023, 15(1), 199; https://doi.org/10.3390/sym15010199 - 09 Jan 2023
Cited by 3 | Viewed by 1170
Abstract
The behavior of the Darcy–Forchheimer flow of a double-hybrid nanofluid toward a Riga plate with radiation and heat source/sink effects is investigated. The two different hybrid nanofluids, (Al2O3 and Ag) and (Al2O3 and TiO2) with [...] Read more.
The behavior of the Darcy–Forchheimer flow of a double-hybrid nanofluid toward a Riga plate with radiation and heat source/sink effects is investigated. The two different hybrid nanofluids, (Al2O3 and Ag) and (Al2O3 and TiO2) with a base fluid (H2O), are considered. The governing flow models with accompanying boundary constraints are reshaped into non-linear ODEs by applying the symmetry variables. The reshaped ODEs are numerically computed using Bvp4c in Matlab and the ND solver in Mathematica. The impact of the emerging parameters on the heat transfer, surface shear stress, temperature and velocity profile is scrutinized and expressed in a tabular and graphical structure. It is noticed that the upsurge of the Hartmann number leads to an improvement in the velocity profile. The velocity declines when enriching the porosity parameter. The radiation and Biot number lead to strengthening the temperature profile. The surface shear stress exalts due to a larger modified Hartman number. The radiation and unsteady parameters are downturns in the heat transfer gradient. Full article
(This article belongs to the Special Issue Symmetry in System Theory, Control and Computing)
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18 pages, 374 KiB  
Article
Optimal Control Problems for Hilfer Fractional Neutral Stochastic Evolution Hemivariational Inequalities
by Sivajiganesan Sivasankar, Ramalingam Udhayakumar, Velmurugan Subramanian, Ghada AlNemer and Ahmed M. Elshenhab
Symmetry 2023, 15(1), 18; https://doi.org/10.3390/sym15010018 - 21 Dec 2022
Cited by 3 | Viewed by 825
Abstract
In this paper, we concentrate on a control system with a non-local condition that is governed by a Hilfer fractional neutral stochastic evolution hemivariational inequality (HFNSEHVI). By using concepts of the generalized Clarke sub-differential and a fixed point theorem for multivalued maps, we [...] Read more.
In this paper, we concentrate on a control system with a non-local condition that is governed by a Hilfer fractional neutral stochastic evolution hemivariational inequality (HFNSEHVI). By using concepts of the generalized Clarke sub-differential and a fixed point theorem for multivalued maps, we first demonstrate adequate requirements for the existence of mild solutions to the concerned control system. Then, using limited Lagrange optimal systems, we demonstrate the existence of optimal state-control pairs that are regulated by an HFNSEHVI with a non-local condition. In order to demonstrate the existence of fixed points, the symmetric structure of the spaces and operators that we create is essential. Without considering the uniqueness of the control system’s solutions, the best control results are established. Lastly, an illustration is used to demonstrate the major result. Full article
(This article belongs to the Special Issue Symmetry in System Theory, Control and Computing)
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