Research

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22 pages, 10110 KiB

Open AccessArticle

Development and Validation of a Compressible Reacting Gas-Dynamic Flow Solver for Supersonic Combustion

by Anvar Gilmanov, Ponnuthurai Gokulakrishnan and Michael S. Klassen

Dynamics 2024, 4(1), 135-156; https://doi.org/10.3390/dynamics4010008 - 11 Feb 2024

Viewed by 767

An approach based on the OpenFOAM library has been developed to solve a high-speed, multicomponent mixture of a reacting, compressible flow. This work presents comprehensive validation of the newly developed solver, called compressibleCentralReactingFoam, with different supersonic flows, including shocks, expansion waves, and [...] Read more.

An approach based on the OpenFOAM library has been developed to solve a high-speed, multicomponent mixture of a reacting, compressible flow. This work presents comprehensive validation of the newly developed solver, called compressibleCentralReactingFoam, with different supersonic flows, including shocks, expansion waves, and turbulence–combustion interaction. The comparisons of the simulation results with experimental and computational data confirm the fidelity of this solver for problems involving multicomponent high-speed reactive flows. The gas dynamics of turbulence–chemistry interaction are modeled using a partially stirred reactor formulation and provide promising results to better understand the complex physics involved in supersonic combustors. A time-scale analysis based on local Damköhler numbers reveals different regimes of turbulent combustion. In the core of the jet flow, the Damköhler number is relatively high, indicating that the reaction time scale is smaller than the turbulent mixing time scale. This means that the combustion is controlled by turbulent mixing. In the shear layer, where the heat release rate and the scalar dissipation rate have the highest value, the flame is stabilized due to finite rate chemistry with small Damköhler numbers and a limited fraction of fine structure. This solver allows three-dimensional gas dynamic simulation of high-speed multicomponent reactive flows relevant to practical combustion applications. Full article

(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)

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17 pages, 618 KiB

Open AccessArticle

Multiplicative Renormalization of Stochastic Differential Equations for the Abelian Sandpile Model

by Dimitri Volchenkov

Dynamics 2024, 4(1), 40-56; https://doi.org/10.3390/dynamics4010003 - 04 Jan 2024

Viewed by 894

Abstract

The long-term, large-scale behavior in a problem of stochastic nonlinear dynamics corresponding to the Abelian sandpile model is studied with the use of the quantum-field theory renormalization group approach. We prove the multiplicative renormalization of the model including an infinite number of coupling [...] Read more.

The long-term, large-scale behavior in a problem of stochastic nonlinear dynamics corresponding to the Abelian sandpile model is studied with the use of the quantum-field theory renormalization group approach. We prove the multiplicative renormalization of the model including an infinite number of coupling parameters, calculate an infinite number of renormalization constants, identify a plane of fixed points in the infinite dimensional space of coupling parameters, discuss their stability and critical scaling in the model, and formulate a simple law relating the asymptotic size of an avalanche to a model exponent quantifying the time-scale separation between the slow energy injection and fast avalanche relaxation processes. Full article

(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)

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13 pages, 3140 KiB

Open AccessArticle

Thermal Hydraulics Simulation of a Water Spray System for a Cooling Fluid Catalytic Cracking (FCC) Regenerator

by Alon Davidy

Dynamics 2023, 3(4), 737-749; https://doi.org/10.3390/dynamics3040039 - 27 Oct 2023

Viewed by 1118

Abstract

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 [...] Read more.

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

(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)

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26 pages, 9336 KiB

Open AccessArticle

The Dynamics of a Turning Ship: Mathematical Analysis and Simulation Based on Free Body Diagrams and the Proposal of a Pleometric Index

by Franz Konstantin Fuss

Dynamics 2023, 3(3), 379-404; https://doi.org/10.3390/dynamics3030021 - 03 Jul 2023

Viewed by 1007

Abstract

This study attempts to shed new light on the dynamics of a turning ship using the principles of free body diagrams (FBDs). Unexpectedly, the literature gap is defined by incomplete and flawed FBDs. The method behind this new approach involves the FBD of [...] Read more.

This study attempts to shed new light on the dynamics of a turning ship using the principles of free body diagrams (FBDs). Unexpectedly, the literature gap is defined by incomplete and flawed FBDs. The method behind this new approach involves the FBD of a turning ship, with all the essential forces included, namely propulsive force, sideward thruster force (producing the initial turning moment), drag force, lift force, centrifugal force, inertial force, and hydrodynamic force couple. From these forces, the force and moment equations are derived. The accelerations are calculated from the force and moment equilibria to simulate the dynamics from input parameters such as mass m, length L, draught D, and fluid density ρ. The turning dynamics are explained in terms of velocities, accelerations, forces, and moments, based on two conditions: flat and steep angles of attack (AoA) and long and short turning radii R. A critical result is the proportionality of lift and centrifugal forces, leading to the proposal of a pleometric index (m·L^–2·D^–1·ρ^–1), which is nonlinearly proportional to the product of AoA and R/L, characterising the dynamics of a turning ship. The FBD approach of this study also identified missing databases required for accurate simulation of turning dynamics, such as drag and lift coefficients of different hull geometries. Full article

(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)

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20 pages, 4863 KiB

Open AccessArticle

Uncovering the Origins of Instability in Dynamical Systems: How Can the Attention Mechanism Help?

by Nooshin Bahador and Milad Lankarany

Dynamics 2023, 3(2), 214-233; https://doi.org/10.3390/dynamics3020013 - 17 Apr 2023

Viewed by 1255

Abstract

The behavior of the network and its stability are governed by both dynamics of the individual nodes, as well as their topological interconnections. The attention mechanism as an integral part of neural network models was initially designed for natural language processing (NLP) and, [...] Read more.

The behavior of the network and its stability are governed by both dynamics of the individual nodes, as well as their topological interconnections. The attention mechanism as an integral part of neural network models was initially designed for natural language processing (NLP) and, so far, has shown excellent performance in combining the dynamics of individual nodes and the coupling strengths between them within a network. Despite the undoubted impact of the attention mechanism, it is not yet clear why some nodes of a network obtain higher attention weights. To come up with more explainable solutions, we tried to look at the problem from a stability perspective. Based on stability theory, negative connections in a network can create feedback loops or other complex structures by allowing information to flow in the opposite direction. These structures play a critical role in the dynamics of a complex system and can contribute to abnormal synchronization, amplification, or suppression. We hypothesized that those nodes that are involved in organizing such structures could push the entire network into instability modes and therefore need more attention during analysis. To test this hypothesis, the attention mechanism, along with spectral and topological stability analyses, was performed on a real-world numerical problem, i.e., a linear Multi-Input Multi-Output state-space model of a piezoelectric tube actuator. The findings of our study suggest that the attention should be directed toward the collective behavior of imbalanced structures and polarity-driven structural instabilities within the network. The results demonstrated that the nodes receiving more attention cause more instability in the system. Our study provides a proof of concept to understand why perturbing some nodes of a network may cause dramatic changes in the network dynamics. Full article

(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)

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15 pages, 665 KiB

Open AccessArticle

Search for Damped Oscillating Structures from Charged Pion Electromagnetic Form Factor Data

by Erik Bartoš, Stanislav Dubnička and Anna Zuzana Dubničková

Dynamics 2023, 3(1), 137-151; https://doi.org/10.3390/dynamics3010009 - 04 Mar 2023

Cited by 1 | Viewed by 1010

Abstract

The damped oscillating structures recently revealed by a three parametric formula from the proton “effective” form factor data extracted of the measured total cross section

σ_{t o t}^{b a r e} (e^{+} e^{-} \to p \bar{p})

[...] Read more.

The damped oscillating structures recently revealed by a three parametric formula from the proton “effective” form factor data extracted of the measured total cross section

σ_{t o t}^{b a r e} (e^{+} e^{-} \to p \bar{p})

still seem to have an unknown origin. The conjectures of their direct manifestation of the quark-gluon structure of the proton indicate that they are not specific only of the proton and neutron, but they have to be one’s own, similar to other hadrons. Therefore, the oscillatory structures from the charged pion electromagnetic form factor timelike data, extracted of the process

e^{+} e^{-} \to π^{+} π^{-}

are investigated by using the same procedure as in the case of the proton. The analysis shows the appearance of the oscillating structures in the description of the charged pion electromagnetic form factor timelike data by three parametric formula with a rather large value of

χ^{2} / n d f

, while the description of the data by the physically well-founded Unitary and Analytic model has not revealed any damped oscillating structures. From the obtained result on the most simple object of strong interactions, one can conclude that damped oscillating structures received from the “effective” proton form factor data are probably generated by a utilization of the improper three parametric formula which does not describe these data with sufficient precision. Full article

(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)

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19 pages, 1518 KiB

Open AccessArticle

An Energy-Based Complex Brain Network Model—Part 1: Local Electrophysiological Dynamics

by Chun-Lin Yang, Nandan Shettigar and C. Steve Suh

Dynamics 2023, 3(1), 96-114; https://doi.org/10.3390/dynamics3010007 - 20 Feb 2023

Cited by 1 | Viewed by 1309

Abstract

The human brain is a complex network of connected neurons whose dynamics are difficult to describe. Brain dynamics are the global manifestation of individual neuron dynamics and the synaptic coupling between neurons. Membrane potential is a function of synaptic dynamics and electrophysiological coupling, [...] Read more.

The human brain is a complex network of connected neurons whose dynamics are difficult to describe. Brain dynamics are the global manifestation of individual neuron dynamics and the synaptic coupling between neurons. Membrane potential is a function of synaptic dynamics and electrophysiological coupling, with the parameters of postsynaptic potential, action potential, and ion pump dynamics. By modelling synaptic dynamics using physical laws and the time evolution of membrane potential using energy, neuron dynamics can be described. This local depiction can be scaled up to describe mesoscopic and macroscopic hierarchical complexity in the brain. Modelling results are favorably compared with physiological observation and physically acquired action potential profiles as reported in the literature. Full article

(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)

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0 pages, 2174 KiB

Open AccessCommunication

Beyond the Light-Cone Propagation of Relativistic Wavefunctions: Numerical Results

by Xabier Gutierrez de la Cal and Alex Matzkin

Dynamics 2023, 3(1), 60-70; https://doi.org/10.3390/dynamics3010005 - 06 Feb 2023

Cited by 1 | Viewed by 1422

Abstract

It is known that relativistic wavefunctions formally propagate beyond the light cone when the propagator is limited to the positive energy sector. By construction, this is the case for solutions of the Salpeter (or relativistic Schrödinger) equation or for Klein–Gordon and Dirac wavefunctions [...] Read more.

It is known that relativistic wavefunctions formally propagate beyond the light cone when the propagator is limited to the positive energy sector. By construction, this is the case for solutions of the Salpeter (or relativistic Schrödinger) equation or for Klein–Gordon and Dirac wavefunctions defined in the Foldy–Wouthuysen representation. In this work, we quantitatively investigate the degree of non-causality for free propagation for different types of wavepackets that all initially have a compact spatial support. In the studied examples, we find that non-causality appears as a small transient effect that can in most cases be neglected. We display several numerical results and discuss the fundamental and practical consequences of our findings concerning this peculiar dynamical feature. Full article

(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)

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14 pages, 306 KiB

Open AccessArticle

Dynamical Invariant for Dissipative Systems via Complex Quantum Hydrodynamics

by Dieter Schuch and Moise Bonilla-Licea

Dynamics 2023, 3(1), 18-31; https://doi.org/10.3390/dynamics3010002 - 16 Jan 2023

Viewed by 1320

Abstract

For Hamiltonian systems with time-dependent potential, the Hamiltonian, and thus the energy, is no longer a constant of motion. However, for such systems as the parametric oscillator, i.e., an oscillator with time-dependent frequency

ω (t)

, still, a dynamical invariant can [...] Read more.

For Hamiltonian systems with time-dependent potential, the Hamiltonian, and thus the energy, is no longer a constant of motion. However, for such systems as the parametric oscillator, i.e., an oscillator with time-dependent frequency

ω (t)

, still, a dynamical invariant can be found that now has the dimension of action. The question, if such an invariant still exists after the addition of a dissipative friction force is analyzed for the classical as well as for the quantum mechanical case from different perspectives, particularly from that of a complex hydrodynamic formulation of quantum mechanics. Full article

(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)

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17 pages, 1214 KiB

Open AccessArticle

Non-Equilibrium ϕ⁴ Theory in a Hierarchy: Towards Manipulating Holograms in Quantum Brain Dynamics

by Akihiro Nishiyama, Shigenori Tanaka and Jack A. Tuszynski

Dynamics 2023, 3(1), 1-17; https://doi.org/10.3390/dynamics3010001 - 04 Jan 2023

Cited by 7 | Viewed by 1755

Abstract

We describe non-equilibrium

ϕ^{4}

theory in a hierarchical manner to develop a method for manipulating coherent fields as a toy model of introducing control into Quantum Field Theory (QFT) of the brain, which is called Quantum Brain Dynamics (QBD). We begin with [...] Read more.

We describe non-equilibrium

ϕ^{4}

theory in a hierarchical manner to develop a method for manipulating coherent fields as a toy model of introducing control into Quantum Field Theory (QFT) of the brain, which is called Quantum Brain Dynamics (QBD). We begin with the Lagrangian density of

ϕ^{4}

model, where we adopt 2-Particle-Irreducible (2PI) effective action, and derive the Klein–Gordon equation of coherent fields with a damping term as an input–output equation proposed in areas of morphological computation or reservoir computing. Our analysis is extended to QFT in a hierarchy representing multiple layers covering cortex in a brain. We find that the desired target function is achieved via time-evolution in the Klein–Gordon equations in a hierarchy of numerical simulations when a signal in both the input and output prevails over noise in the intermediate layers. Our approach will be applied to control coherent fields in the systems (in a hierarchy) described in the QFT framework, with potential applications allowing the manipulation of quantum fields, especially holograms in QBD. We could then provide realistic physical degrees of freedom of a light–matter system in the contexts of quantum cognition and the associated free-energy principle. Full article

(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)

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Review

Jump to: Research

25 pages, 535 KiB

Open AccessReview

Dark Energy as a Natural Property of Cosmic Polytropes—A Tutorial

by Kostas Kleidis and Nikolaos K. Spyrou

Dynamics 2023, 3(1), 71-95; https://doi.org/10.3390/dynamics3010006 - 15 Feb 2023

Viewed by 1679

Abstract

A conventional approach to the dark energy (DE) concept is reviewed and discussed. According to it, there is absolutely no need for a novel DE component in the universe, provided that its matter–energy content is represented by a perfect fluid whose volume elements [...] Read more.

A conventional approach to the dark energy (DE) concept is reviewed and discussed. According to it, there is absolutely no need for a novel DE component in the universe, provided that its matter–energy content is represented by a perfect fluid whose volume elements perform polytropic flows. When the (thermodynamic) energy of the associated internal motions is taken into account as an additional source of the universal gravitational field, it compensates the DE needed to compromise spatial flatness in an accelerating universe. The unified model which is driven by a polytropic fluid not only interprets the observations associated with universe expansion but successfully confronts all the current issues of cosmological significance, thus arising as a viable alternative to the

Λ

CDM model. Full article

(This article belongs to the Special Issue Recent Advances in Dynamic Phenomena)

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