Critical Parameter Values Research Articles

Euler–Heisenberg black hole surrounded by perfect fluid dark matter

A generation method of new metric in the case of static spherically symmetric space-time is derived. Using this approach, we construct a metric which describes Euler–Heisenberg black hole surrounded by perfect fluid dark matter and investigate its optical and thermodynamic properties. We found that radius of shadow will increase with the increase of dark matter effect, and more strong dark matter will diminish the light intensity of accretion disk generally. Moreover, in thermodynamics, when quantum electrodynamic parameter is positive, there will be a critical value of dark matter parameter, which determine the number of black hole’s critical points.

Uhlmann phase of a thermal spin-1 system with zero field splitting

We study the Uhlmann geometric phase of a spin-1 particle subjected to zero-field splitting (ZFS) interaction, modulated by a dimensionless parameter α, under the effect of an external magnetic field with a tilting angle θ. We show that the ZFS term induces a transition in the geometrical phase behavior, characterized by a critical parameter value, α=αc. For α<αc, this phase displays two critical temperatures at θ=π/2, similar to spin-1 systems without ZFS, but with a separation that varies with α. In contrast, for α>αc, the phase exhibits two singularities at a single critical temperature but at different field orientations θ≠π/2. The phase disappears for significantly large |α|, regardless of the values of the Hamiltonian parameters. This behavior clearly departs from the usual thermal Uhlmann phase observed in SU(2) systems. In addition, we analytically calculate the heat capacity, which, for θ=π/2 and nearby values, displays two different regimes according to the sign of α. For α<0, it develops two peaks associated to the multilevel nature of the system, while for α>0 only a single Schottky-anomaly like peak appears as in two level systems. Interestingly, when θ=π/2, the temperature centroids of the Uhlmann phase and the heat capacity coincide in the region between critical temperatures for a given value of α<αc. Furthermore, we demonstrate that when α=0, the Uhlmann phase, a global topological property of the system, can be expressed as a function of the thermal component of the Bures metric, a local geometric property related to the heat capacity.

Meta-heuristic algorithms for integrating manufacturing and supply chain functions

This study proposes an integrated framework that incorporates essential manufacturing and supply chain functions. These functions encompass process planning, scheduling, due-date assignment, and delivery optimization. The objective of this integrated approach is to achieve multiple benefits, including balanced workload distribution, enhanced company performance, generation of more realistic planning schedules, and ultimately, the achievement of shorter due dates. As a result, the overall efficiency of operations is substantially improved, with approximately a 50 % increase over isolated function management. Additionally, the isolated integration of the delivery function within systems comprising three integrated functions has been found to improve efficiency by 18%. The study employs various heuristic techniques, including genetic algorithms, simulated annealing, random search, hybrid search, and evolutionary strategy, to assess the optimal solution method and rules for these functions. The Taguchi technique is employed to ascertain the optimal values for critical parameters, such as population size, mutation rate, crossover points, and random search rate. Among the solution methods investigated, genetic algorithms consistently yielded superior results Additionally, the weighted slack rule consistently exhibited notable effectiveness compared to other due-date assignment rules. Similarly, the savings algorithm outperformed other delivery optimization rules. However, it is important to note that among the scheduling rules evaluated, none has emerged as dominant.

Experimental observation of topological transition in linear and nonlinear parametric oscillators.

Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is perturbed by a continuously parametrized defect. Initially in one of its stable states, the oscillator will be perturbed by the defect and finally reach another stable state, which can be its initial one or the other one. For some critical value of the defect parameter, the final state changes abruptly. We theoretically and experimentally investigate such transition both in the linear and nonlinear cases, and the effect of nonlinearities is discussed. A topological interpretation in terms of winding number is proposed, and we show that winding changes correspond to singularities in the temporal dynamics. An experimental observation of such transition is performed using parametric Faraday instability at the surface of a vibrated fluid.

Discrimination of wear performance based on surface roughness parameters arithmetic mean height (Sa) and skewness (Ssk)

Enhancing interfacial contact bearing performance typically involves minimizing the roughness parameter Sa (arithmetic mean height). Yet, exceedingly low Sa incur steep increases in processing costs, indicating that Sa-centric optimization strategies may not be universally suitable for interface performance control. Roughness parameters skewness (Ssk) and kurtosis (Sku) exert a pronounced influence on component contact wear performance. Accordingly, investigating the correlation between Ssk, Sku, and wear performance holds significant promise for enhancing wear resistance. A finite element wear calculation model for rough-surface abrasive wear employing elastic-plastic contact mechanics and the Jump-in-Cycle method. Cylindrical roller dry sliding experiments validate the model's reliability. Integrating this model, a method is proposed for wear performance discrimination based on Sa and Ssk at different loads. It enables the identification of critical roughness parameter values for improved surface wear resistance. The calculated wear model aligns with experiment trends, with predicted surface textures mirroring observed wear surface characteristics. Critical Sa and Ssk diverge under distinct loads. The study underscores the importance of moving beyond the exclusive pursuit of exceptionally low Sa and Ssk. It provides a foundation for reducing workpiece processing costs while optimizing wear performance.

Effect of nonlinear stiffness on single link flexible joint robotic manipulator and its control

This study aims to investigate the significant dynamics of a Single Link Flexible Joint (SLFJ) Robotic Manipulator and implement chaotic control using the Adaptive Sliding Mode Control (ASMC) algorithm. The mathematical model of the system incorporates stiffness nonlinearity by introducing the function (x-x3) Various dynamical tools such as stability analysis of equilibrium points, sensitivity to initial conditions, orbit diagrams for parameter variations, Lyapunov spectrum, and frequency spectrum analysis are employed. The ASMC algorithm is utilized to suppress the chaotic behavior of the system. The equilibrium points are determined for critical parameter values, with the Jacobian matrix and corresponding eigenvalues exhibiting conjugate complex with negative real parts, indicating stability resembling a spiral saddle. Phase portraits illustrate the location and range of the chaotic attractor. Investigation of parameter ′a′ using orbit diagrams and Lyapunov spectrum reveals the transition from periodic to chaotic oscillations. The frequency spectrum confirms the chaotic nature of the system. Parameter estimation, state trajectories, and sliding surface analysis demonstrate that the ASMC scheme can effectively control the system in less than 0.3 s. Nonlinear stiffness has not been previously considered in SLFJ Robotic Manipulators, highlighting a novel aspect of this study. The results unveil new chaotic ranges for parameter variation previously undocumented. Frequency spectrum analysis is employed to distinguish between noise and chaotic oscillations, addressing a significant challenge in real-time systems. The ASMC algorithm is specifically designed to control chaotic oscillations, demonstrating its effectiveness in this context.

Impact of Short-Circuit Ratio on Control Parameter Settings of DFIG Wind Turbines

This work deals with doubly fed induction generator (DFIG) modeling and stability when connected to weak AC grids. A detailed state-space model that includes the phase-locked loop (PLL) is developed. This work aims to determine the influence of the network’s strength on DFIG stability through the short-circuit ratio (SCR). The critical values of the proportional control parameters of the grid-side and rotor-side converters (RSC and GSC), as well as PLL, which make the system unstable, are calculated for different SCR values. Finally, PSCAD/EMTDC dynamic simulations are used to validate the critical control parameters obtained by studying the eigenvalues of the DFIG state-space model regarding system stability.

The Demographic-Wealth model for cliodynamics.

Cliodynamics is a still a relatively new research area with the purpose of investigating and modelling historical processes. One of its first important mathematical models was proposed by Turchin and called "Demographic-Fiscal Model" (DFM). This DFM was one of the first and is one of a few models that link population with state dynamics. In this work, we propose a possible alternative to the classical Turchin DFM, which contributes to further model development and comparison essential for the field of cliodynamics. Our "Demographic-Wealth Model" (DWM) aims to also model link between population and state dynamics but makes different modelling assumptions, particularly about the type of possible taxation. As an important contribution, we employ tools from nonlinear dynamics, e.g., existence theory for periodic orbits as well as analytical and numerical bifurcation analysis, to analyze the DWM. We believe that these tools can also be helpful for many other current and future models in cliodynamics. One particular focus of our analysis is the occurrence of Hopf bifurcations. Therefore, a detailed analysis is developed regarding equilibria and their possible bifurcations. Especially noticeable is the behavior of the so-called coexistence point. While changing different parameters, a variety of Hopf bifurcations occur. In addition, it is indicated, what role Hopf bifurcations may play in the interplay between population and state dynamics. There are critical values of different parameters that yield periodic behavior and limit cycles when exceeded, similar to the "paradox of enrichment" known in ecology. This means that the DWM provides one possible avenue setup to explain in a simple format the existence of secular cycles, which have been observed in historical data. In summary, our model aims to balance simplicity, linking to the underlying processes and the goal to represent secular cycles.

Radiative dynamics of laser-driven Li@C n embedded in quantum plasma

This work considers a guest Lithium atom (Li@C n ) in an endohedral fullerene, embedded in a quantum plasma modeled by the more general exponential cosine screened Coulomb (MGECSC) potential, under the influence of a spherical confinement and laser radiation field. The system is examined in nonrelativistic form and the related wave equation is solved using the tridiagonal matrix method (TMM), thus obtaining the discrete-continuum spectrum and related wave functions. The numerical values of the relevant parameters in this process are physically accessible values. The effects of the plasma, laser field and endohedral cavity on the photoionization cross section (PCS) are analysed in detail. The shielding effect of the plasma medium and the pulsating effect of the laser field modify the effective potential energy of the system, affecting the localizations of the 2s and continuum states, causing various overlapping cases. Considering different values of the endohedral encompassement parameters, which means that different types of fullerenes are taken into account, overlapping cases occur for different spectra and wave functions. Scrutinising these overlappings, the confinement and Cooper resonances of the PCSs are analysed. This analysis provides many details for the radiative dynamics of an artificial system Li@C n . The relevant ranges and critical values of plasma, laser field, and endohedral encapsulation parameters in the formation process of these resonances and PCSs are explained, as well as the cross-section curves, resonance positions, effective photoelectron energy range, and general PCS behavior, which can be important for potential experiments in addition to other theoretical investigations.

Heat exchange under the longitudinal movement of wet steam in finning heat exchangers

The paper is devoted to the study on hydrodynamics and heat exchange of two-phase medium. While designing technological equipment, when the wet steam is used as the operating medium, the features of the interaction between liquid drops and the heat exchange surface are not considered in most cases. In full, this applies to steam turbines operating on the wet steam whose moisture content depends on the primary and secondary removal of liquid drops from the separation blocks. Purpose. Improving the method of calculation of recuperative heat exchangers, if wet steam is used as the operating medium. Methodology. It is based on the analysis of the physical model of moving the two-phase medium in the heat and mass exchange conditions, considering the design characteristics of the heat transfer surface. Findings. The correlation of critical values of two-phase flow parameters was obtained to determine the lower boundary of the process of plucking the drops from the liquid film depending on the irrigation density, geometric characteristics of the channel and physical properties of the liquid and gas. Correlations were obtained for pipes with longitudinal finning as the Π-shaped profile, based on which we recommend optimizing the geometric characteristics of longitudinal finning. Originality. Determining the limit modes of secondary removal formation during the movement of a two-phase medium in separation devices and the features of heat and mass transfer of wet steam in finning recuperative heat exchangers. Practical value. The presented results make it possible to optimize the design of recuperative heat exchangers with longitudinal Π-shaped finning.

Propagation of collisional among multi-soliton, multi-singular solition and rogue wave around the critical values in an unmagetized plasma

Progress in understanding the propagation characteristics of (i) collisional acoustic among multi-soliton and multi-singular soliton around the critical values and their corresponding phase shifts and (ii) collision between two rogue waves (RWs) propagating toward each in a plasma environment is presented. The considered plasma environment consists of mobile cold positrons, immobile positive ions and (r, q)-distributed hot positrons, and electrons. To accomplish our goal, the coupled modified Korteweg–de Vries equations (mKdVEs) and nonlinear Schrödinger equations (NLSEs) are derived from the considered plasma environment. Based on the concept of Hirota's bilinear method, the multi-soliton and multi-singular soliton solutions of the coupled mKdVEs are determined directly. In addition, the analytical unstable RWs solutions of the coupled NLSEs are determined. With the impact of physical parameters, (i) the trajectories are described for double, triple, quadruple and quintuple positron acoustic bi-directional multi-soliton and (ii) the variation of collisional RWs profiles are displayed with physical interpretation. The results described by the coupled mKdVEs also show that the scattered double-, triple-, quadruple-, and quintuple-soliton are elastic and preserved their original features oppositely after the collision around the critical value of any specific plasma parameter.

Numerical study of linear and nonlinear stability in double-diffusive Hadley-Prats flow through a horizontal porous layer with Soret and internal heat source effects

Numerical analysis is constructed to study the onset of the double-diffusion convection mechanism through an infinite parallel permeable channel with heat generation, mass flow and Soret impacts. Homogenous isotropic Darcy’s flow model is deployed to elucidate the porous features. The roll instabilities pertaining to longitudinal and transverse cases are examined through a linear and nonlinear stability analysis. The unit-less eigenvalue problem is constructed through linear and nonlinear stability assumptions and which is solved numerically using a fourth order Runge-Kutta scheme. The critical values of wave and thermal Rayleigh parameters are evaluated. Extended graphical and tabular visualization is presented to describe the onset of the convection mechanism. The results of this semi-numerical investigation may be useful in environmental, geothermal and chemical engineering processes. In addition, the critical R z value is also determined for a range of thermo-physical numbers. Significant modifications in the flow patterns are computed with mass flow parameter and vertical thermal and solutal Rayleigh number. With an increment in Soret (thermo-diffusive) parameter Sr the regime become more unstable. Based on the nonlinear stability analysis, an elevation in solutal Rayleigh number also induces earlier instability. The collective influence of the Lewis number and horizontal concentration parameter is observed to render the system more stable.

Entanglement and Chaos near critical point in strongly coupled Gauge theory

We perform a holographic study of the high and low temperature behaviours of logarithmic negativity (LN) and entanglement wedge cross section (EWCS) in a large N strongly coupled thermal field theory with critical point, having a well defined gravity dual known as 1RC black hole. The bulk theory accommodates a dimensionless parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}, proportional to the charge of the 1RC black hole. Holographically, ξ→2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi \\rightarrow 2$$\\end{document} limit ensures an existence of a critical point in the dual boundary theory. We show that the logarithmic negativity in low and high temperature limits enhances with increasing ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. We analytically compute the EWCS in low and high temperature limits and find an agreement with the previously reported numerical results. We holographically explore the correlation between two identical copies of thermal field theory with critical point forming a thermofield double state (TFD) by computing the thermo mutual information (TMI). TMI shows an increasing behaviour with respect to the width of the boundary region. Furthermore, we study the chaotic behaviour of the field theory by analyzing a shock wave in the dual eternal 1 RC black hole and then estimate the degradation of TMI. The rate of such disruption of TMI slows down as the value of critical parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document} takes higher values.

Stability and bifurcation analysis of fractional‐order tumor–macrophages interaction model with multi‐delays

In the realm of modeling biological systems with memory, particularly those involving intricate interactions like tumor‐immune responses, the utilization of multiple time delays and Caputo‐type fractional‐order derivatives represents a cutting‐edge approach. In this research paper, we introduce a novel fractional‐order model to investigate the dynamic interplay between tumors and macrophages, a key component of the immune system, while incorporating multiple time delays into our framework. Our proposed model comprises a system of three Caputo‐type fractional‐order differential equations, each representing distinct cell populations: tumor cells, anti‐tumor cells (specifically ‐type macrophages with pro‐inflammatory properties), and pro‐tumor cells ( ‐type macrophages with immune‐suppressive characteristics). The stability of equilibria is discussed by analyzing the characteristic equations for each case, and the existence conditions for the Hopf bifurcation are obtained according to the critical values of delay parameters. Furthermore, numerical simulations are presented in order to verify the analytical results obtained for stability and Hopf‐bifurcation with respect to the two‐time delay parameters and . The analysis shows the rich dynamics of the model according to the fractional‐order parameter and the time delay parameters.

Asymptotics of multivariate sequences in the presence of a lacuna

We explain a discontinuous drop in the exponential growth rate for certain multivariate generating functions at a critical parameter value in even dimensions d \geq 4 . This result depends on computations in the homology of the algebraic variety where the generating function has a pole. These computations are similar to, and inspired by, a thread of research in applications of complex algebraic geometry to hyperbolic PDEs, going back to Leray, Petrowski, Atiyah, Bott and Gårding. As a consequence, we give a topological explanation for certain asymptotic phenomena appearing in the combinatorics and number theory literature. Furthermore, we show how to combine topological methods with symbolic algebraic computation to determine explicitly the dominant asymptotics for such multivariate generating functions, giving a significant new tool to attack the so-called connection problem for asymptotics of P-recursive sequences. This in turn enables the rigorous determination of integer coefficients in the Morse–Smale complex, which are difficult to determine using direct geometric methods.

Seismic pounding of adjacent buildings considering torsional effects

This study aims to evaluate pounding effects in fixed-base models by considering torsional irregularity. For this purpose, 8 different adjacent building combinations were created by using 3-dimensional 5- and 9-story building models. In adjacent building models, the most critical situation was determined by evaluating the gap distance, different sequences of the same building models and regular or irregular plan view and if the structures are irregular, their eccentricity cases relative to each other. Nonlinear behavior of structural elements was taken into account for examine the change in the seismic behavior of structural elements due to pounding and torsion effects. The nonlinear time history analysis of the adjacent models was performed for 11 pairs of spectrum compatible ground motion recordings in the SAP2000 program. The results of 176 different analyzes show that the displacement demand, interstory drift ratio, damage ratio and torsional irregularity coefficient values tend to increase in general with the combined effects of pounding and torsion. The absolute maximum and most critical values of the relevant parameters were calculated in irregular structures with pounding where the eccentricity of buildings is in the same direction and same side. In addition, the large standard deviation of the result values according to the ground motion records indicates that care should be taken in choosing the number of ground motion records.

Modeling and analysis of demand-supply dynamics with a collectability factor using delay differential equations in economic growth via the Caputo operator

&lt;abstract&gt; &lt;p&gt;In this paper, to investigate the dynamic interplay between supply and demand, with a focus on collectability, a novel mathematical model was introduced via conformable operator. This model considers the possibility that operating expenses or a lack of raw materials causes a manufacturing delay than the supply of goods instantly matching demand. This maturation (delay) is represented by the delay factor $ \left(\tau \right) $. Stability analysis revolves around the equilibrium point other than zero. Chaotic behavior emerges through Hopf bifurcation at the critical delay parameter value. If this delay parameter is even slightly perturbed, oscillatory limit cycles can be induced in the market dynamics, leading to equilibrium with brisk market expansion, frequent recessions, and sudden collapses. We conducted sensitivity and directional analysis on a number of factors while also examining the stability and duration of the Hopf bifurcation. Numerical findings were validated using MATLAB. Additionally, the Caputo operator was used to examine the fractional of demand and supply dynamics. Importantly, we assumed a pivotal role in advancing fair labor practices and fostering economic growth on a national scale.&lt;/p&gt; &lt;/abstract&gt;

Experimental Observation of Extreme Events in the Shimizu Morioka Oscillator

In this study, we investigate the occurrence of dragon-king extreme events in a three-dimensional autonomous Shimizu–Morioka oscillator. We observe that the bounded chaotic oscillations transition into large amplitude extreme events at a critical value of the system control parameter triggered by an interior crisis. These extreme events exhibit a unique distribution characterized by the probability distribution function. We performed laboratory experiments and conducted rigorous numerical simulations on the Shimizu–Morioka oscillator to validate our findings. The results from both approaches are in excellent agreement and confirm extreme behavior in this autonomous system. Our study represents the first comprehensive investigation of extreme events in the Shimizu–Morioka oscillator, integrating experimental observations and numerical simulations. Also, we observed the dragon-king extreme events in both experimental and numerical studies. These findings enhance our understanding of extreme events and their potential applications in chaos-based dynamical systems, contributing to advancing this field.

Analyzing the impact of geosynthetic reinforcement on Sinkhole: A numerical investigation with Machine Learning approach

The present study describes the results of numerical investigations with implementation of Machine Learning approach to prevent the event of sinkhole formation into the ground by using geosynthetic reinforcement. A series of 2D finite-element analysis were carried out with emphasis on the effects of geosynthetics reinforcement parameters such as geogrid length, stiffness and spacing between the geogrid layers to evaluate the behavior of ground over the sinkhole. Moreover, a database was also generated from the simulations for the application of Machine Learning techniques to predict the behavior as well. The hyperparameters of the Machine Learning models were optimized using Bayesian optimization to enhance the prediction accuracy. The critical values of geogrid reinforcement parameters for maximum reinforcing effect are also suggested. The results indicate the effectiveness of geosynthetic reinforcement to significantly reduce the sinkhole deformations and also the potential of Machine Learning to predict ground subsidence.

Mass and efficiency optimization of a He-Xe Brayton cycle for mobile, land-based nuclear microreactors

Nuclear microreactors represent an option for distributed power generation, which can be deployed in military installations, remote off-grid villages, and locations recovering from natural disasters. Small system mass is necessary to achieve their mobility. In this study, a He-Xe gas-cooled reactor coupled with a Closed Brayton cycle (CBC) is optimized in terms of system mass and thermal efficiency. A single-channel model is developed for the reactor to predict the minimum mass according to the thermal–hydraulic limitations. Masses of the heat exchanger and turbo-machines are calculated based on empirical curves. The simple regenerative and intercooling cycles are considered. A parametric study is conducted to investigate the influence of key parameters on system mass and to explore the tradeoffs between different components that satisfy the power requirements of 8 MWe. Furthermore, the Non-dominated Sorting Genetic Algorithm (NSGA-II) is used to optimize the system mass and thermal efficiency. Optimal values of critical parameters on the Pareto Frontier are presented and discussed. Results show that the masses of the reactor core and coolers dominate the total mass in most cases, and increasing the height of the reactor core can help reduce the system mass by allowing a smaller core radius. The Pareto Frontier shows that at thermal efficiencies around 40% or below, the system mass is depressed by using large CPR, molecular weight of the mixture, height of the reactor core, and small recuperator effectiveness. Increasing the recuperator's effectiveness from about 90% is required for higher thermal efficiency design, but its mass increases dramatically and can surpass the mass share of other components. The current analysis can provide a guide for detailed system and component design.