Distinct Initial Conditions Research Articles

Cascading Dark Energy

The standard cosmological model is in the midst of a stress test, thanks to the tension between supernova-based measurements of the Hubble constant H 0 and inferences of its values from cosmic microwave background (CMB) anisotropies. Numerous explanations for the present-day cosmic acceleration require the presence of a new fundamental scalar field, as do early dark energy solutions to the Hubble tension. This raises the possibility that multiple fields cooperatively contribute to the dark energy component in bursts throughout cosmic time due to distinct initial conditions and couplings. Here, this cascading dark energy scenario is illustrated through a realization that effectively reduces to a two-field model, with two epochs in which dark energy is cosmologically significant. The model is compared to measurements of the CMB and baryon acoustic oscillations, as well as both PANTHEON and SH0ES observations of Type Ia supernovae. Neglecting the linear perturbations, it is found that this scenario ameliorates the Hubble tension, improving over purely late-time models of dark energy and the agreement between the galaxy survey measurements of baryon acoustic oscillations.

An efficient approach for searching three-body periodic orbits passing through Eulerian configuration

A new efficient approach for searching three-body periodic equal-mass collisionless orbits passing through Eulerian configuration is presented. The approach is based on a symmetry property of the solutions at the half period. Depending on two previously established symmetry types on the shape sphere, each solution is presented by one or two distinct initial conditions (one or two points in the search domain). A numerical search based on Newton’s method on a relatively coarse search grid for solutions with relatively small scale-invariant periods T∗<70 is conducted. The linear systems at each Newton’s iteration are computed by high order high precision Taylor series method. The search produced 12,431 initial conditions (i.c.s) corresponding to 6333 distinct solutions. In addition to passing through the Eulerian configuration, 35 of the solutions are also free-fall ones. Although most of the found solutions are new, all linearly stable solutions among them (only 7) are old ones. Particular attention is paid to the details of the high precision computations and the analysis of accuracy. All i.c.s are given with 100 correct digits.

Qualitative behavior and variant soliton profiles of the generalized [formula omitted]-type equation with its sensitivity visualization

This study delves into the exploration of the dynamics of (3+1)-dimensional Painlevé integrable generalized model from different perspectives, which delineates the evolution of nonlinear phenomena in three spatial dimensions and one temporal dimension, displaying the remarkable Painlevé integrability property. The ϕ6-expansion technique is applied to extract traveling wave solutions in the form of Jacobi elliptic functions. To give physical insights of obtained solutions, we present these solutions through graphs such as 2D, 3D and contour plots. Further, to understand the planar dynamical system, we employ the concepts of bifurcation, chaos theory and sensitivity analysis. Bifurcation analysis reveals the dependence on the solution of a planar dynamical system at critical points. Additionally, the detection of chaotic movements in the perturbed dynamical system is achieved by detecting tools. Also the sensitivity analysis of the model is investigate by three distinct initial conditions. The findings are innovative, valuable and captivating for the readers in exploring this model.

Time Optimal and PID Controller for Armed Manipulator Robots

This paper is fourfold. First, three different time-optimal control problems for simulating the manipulator robots with one, two, and three arms are mathematically formulated. Corresponding to the related dynamical systems, the nonlinear system of ordinary differential equations is derived. It has been found that these problems are time-free and have distinct initial and boundary conditions, making them hard to solve. To find the minimum time with different payloads, a successful numerical method based on the finite difference and the three-stage Lobatto formula is proposed. Secondly, the related torquecontrolling problems are simulated, and then for one, two, and three armed manipulator robots, they are solved using the PID controller method. Thirdly, it is shown that, compared to the time-optimal controlling problem, the optimal PID torque controller solution takes more time to do the job than was expected. However, the solution in the PID controller method shows less oscillation than the time-optimal control problem. Fourthly, mathematical theories are used, and the numerical results for both methods and different payloads are compared.

Safety analysis of inadvertent control rods withdrawal of RSG-GAS research reactor for various initial powers

RSG-GAS is an Indonesian MTR-type multipurpose research reactor with a nominal power of 30 MW. Within the context of Design Basis Accidents (DBAs), numerous potential initiating events with the potential to lead to reactivity insertion accidents (RIA) have been identified. Among these, simultaneous inadvertent control rod withdrawal stands out as one of the most limiting scenarios for MTR-type research reactors. In these safety analyses, we employ the PARET code to simulate three distinct initial power conditions: 1 MW, 15 MW, and 30 MW during high power with forced convection cooling mode. The selection of 15 MW as an initial power level is based on the fact that the reactor predominantly operates at this power level. In addition, another safety evaluation was also performed during low power of 300 kW with natural convection cooling mode. Throughout these simulations, it was postulated that the first trip signal fails to initiate a reactor scram, and eventually, the second signal successfully scrams the reactor. This transient journey may activate various reactor protection systems, including but not limited to, period-based protection, floating limit value protection, overpower trip protection, and more. The analyses have confirmed that no single safety limit was exceeded.

High Frequency Response of Volatile Memristors

AbstractIn this theoretical study, the high‐frequency response of the electrothermal NbO2‐Mott threshold switch is focused, a real‐world electronic device, which has been proved to be relevant in several applications and is classified as a volatile memristor. Memristors of this kind, have been shown to exhibit distinctive non‐linear behaviors crucial for cutting‐edge neuromorphic circuits. In accordance with well‐established models for these devices, their resistances depend on their body temperatures, which evolve over time following Newton's Law of Cooling. Here, it is demonstrated that HP's NbO2‐Mott memristor can manifest up to three distinct steady‐state oscillatory behaviors under a suitable high‐frequency periodic voltage input, showcasing increased versatility despite its volatile nature. Additionally, when subjected to a high‐frequency periodic voltage signal, the device body temperature oscillates with a negligible peak‐to‐peak amplitude. Since the temperature remains almost constant over an input cycle, the devices under study behave as linear resistors during each input cycle. Based on these insights, this paper presents analytical equations characterizing the response of the NbO2‐Mott memristor to high‐frequency voltage inputs, demarcating regions in the state space where distinct initial conditions lead to various asymptotic oscillatory behaviors. Importantly, the mathematical methods introduced in this manuscript are applicable to any volatile electrothermal resistive switch. Additionally, this work presents analytical equations that accurately reproduce the temperature time‐waveform of the studied device during both its transient and steady‐state phases when subjected to a zero‐mean sinusoidal voltage input oscillating in the high‐frequency limit. This analytical approach not only increases the comprehension of volatile electrothermal memristors but also provides a theoretical framework to harness the enhanced dynamical capabilities of real‐world volatile memristors in practical applications.

LES of autoignition process in a turbulent droplet-laden mixing layer – impact of an evaporation model and discretisation method

This paper focuses on the numerical modelling of the autoignition process in an ethanol-air mixture within a turbulent droplet-laden temporally evolving mixing layer, utilising the Large Eddy Simulation (LES) method. We compare results obtained by implementing two notably distinct discretisation methods (second-order Total Variation Diminishing – TVD, and fifth-order Weighted Essentially Non-Oscillatory – WENO) in the species and energy transport equations. Additionally, we examine three widely recognised evaporation models (the ‘ D 2 ’ model, the Abramzon–Sirignano model, and a non-equilibrium model based on the Langmuir-Knudsen law). For modelling the combustion process, we employ the Eulerian Stochastic Field method and a laminar chemistry model. The simulations encompass two droplet diameter distributions, one with low and the other with significant diameter non-uniformity. Furthermore, nine distinct initial conditions are considered. Our findings indicate that adjusting the discretisation scheme or the evaporation model can yield simulation outcomes differing to a substantial degree, similar to the impact of modifying the actual properties of the spray droplets or their initial distribution. This is particularly pronounced in the case of sprays featuring a narrowed droplet diameter distribution. We found that the Abramzon–Sirignano model results in the most rapid autoignition. The TVD scheme contributes to a more even spatial distribution of the evaporated fuel, consequently facilitating quicker evaporation and faster autoignition. Using the WENO scheme generates higher fuel vapor gradients near the droplets, leading to less intense evaporation and slower fuel transport in space.

A Nonlinear Megastable System with Diamond-Shaped Oscillators

Benefiting from trigonometric and hyperbolic functions, a nonlinear megastable chaotic system is reported in this paper. Its nonlinear equations without linear terms make the system dynamics much more complex. Its coexisting attractors’ shape is diamond-like; thus, this system is said to have diamond-shaped oscillators. State space and time series plots show the existence of coexisting chaotic attractors. The autonomous version of this system was studied previously. Inspired by the former work and applying a forcing term to this system, its dynamics are studied. All forcing term parameters’ impacts are investigated alongside the initial condition-dependent behaviors to confirm the system’s megastability. The dynamical analysis utilizes one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents, Kaplan–Yorke dimension, and attraction basin. Because of this system’s megastability, the one-dimensional bifurcation diagrams and Kaplan–Yorke dimension are plotted with three distinct initial conditions. Its analog circuit is simulated in the OrCAD environment to confirm the numerical simulations’ correctness.

Optical solitons, qualitative analysis and multistability response to study the dynamical behaviour of light wave promulgation

Our aim is to explore novel optical solitons within the context of an extended higher-order nonlinear Schrödinger equation that governs the behaviour of propagating light waves. Primarily, this research finds abundant types of solitons, such as singular, kink and trigonometric functions subject to certain constraint conditions. We have utilized G ′ / ( b G ′ + G + a ) -expansion method, which has proved effective in retrieving these solitons and presenting them for further analysis. The model's dynamic behaviour is then investigated through bifurcation, quasi-periodic oscillations, chaotic behaviour, and sensitivity. These include methods like phase portrait rendering, time series scrutiny, Lyapunov exponents calculation, and the assessment of multi-stability. Finally, sensitivity analysis is conducted at three distinct initial conditions, revealing that the model displays a high level of sensitivity, with substantial alterations occurring in response to minor changes in the initial conditions. The results of this study are revolutionary, intriguing, and possess crucial theoretical importance in evolution disruptions.

Parametric fractional-order analysis of Arneodo chaotic system and microcontroller-based secure communication implementation

Chaotic systems are often used in cryptology applications thanks to their complex dynamic structures. By increasing the dynamic diversity of chaotic systems through fractional-order analysis, more complex systems for data security can be obtained. In this study, fractional calculus analyses of the Arneodo chaotic jerk system with cubic nonlinearity and its microcontroller-based chaotic masking application are presented. Numerical analyses such as bifurcation diagrams, spectral entropy complexity, and Lyapunov spectra are performed to examine the dynamic characteristics of the fractional-order system. The parametric analysis indicates the presence of chaotic states in the system for nearly all fractional-order values ranging from 0.55 to 1. In this manner, the study focuses on investigating the minimum applicable fractional-order value for use in secure communication applications, constituting the main contribution of this research. Consequently, the dynamic diversity and unpredictability of the cubic system are greatly increased. Moreover, two fractional-order Arneodo chaotic (FOAC) systems with distinct initial conditions are synchronized using a single-state fractional-order sliding mode controller (FOSMC). Finally, an innovative secure communication system based on a microcontroller is designed and implemented by employing the chaotic masking method. As anticipated, the voltage outputs of the microcontroller-based secure communication application demonstrated good agreement with the numerical simulations.

Analysis of a mathematical model of the aggregation process of cellular slime mold within the frame of fractional calculus

ABSTRACT The pivotal aim of the present study is to find the solution for a nonlinear system describing the aggregation process of cellular slime mold by using -homotopy analysis transform method. The coupled system is considered within the frame of the Caputo fractional operator. We examine three different cases with distinct values of sensitivity function , and to exemplify the efficiency and applicability of the considered scheme. We capture the nature of the obtained results with respect to the fractional order, with distinct initial conditions, and illustrate them using 2D and 3D plots for particular values of the parameters. The considered scheme offers parameters, which help to adjust the convergence region, and we plotted the ℏ-curves to dissipate the effect in the present framework. Moreover, some simulating and important behavior of the considered model using attained results shows the prominence of the hired operator while analyzing the coupled equations and confirms the competence of the projected scheme.

Spatially extended radiant heat fire model.

Recent wildfire prevalence and destruction have led to new initiatives in the search for better land management techniques and prescriptions for controlled burns. With limited data on low-intensity prescribed burns, finding models that can represent fire behavior is of great importance to learning how to control fires with more accuracy while also maintaining the purpose for the burn, be it reducing fuels or managing the ecosystem. Here we use a data set of infrared temperatures collected in the New Jersey Pine Barrens from 2017 through 2020 to develop a model for very fine-scale fire behavior (≈0.05m^{2}). The model uses distributions from the data set to define five stages in fire behavior in a cellular automata framework. For each cell, the transition between each stage is probabilistically driven based on the radiant temperature values of the cell and its immediate neighbors in a coupled map lattice. With five distinct initial conditions, we performed 100 simulations and used the parameters derived from the data set to develop metrics for model verification. To validate the model, we also expanded it to include variables not in the data set that are important for fire behavior, e.g., fuel moisture levels and spotting ignitions. The model matches several metrics compared to the observational data set and exhibits behavioral characteristics expected from low-intensity wildfire behavior including a long and varied burn time for each cell after initial ignition, and lingering embers in the burn zone.

Emerging Spiral Waves and Coexisting Attractors in Memductance-Based Tabu Learning Neurons

Understanding neuron function may aid in determining the complex collective behavior of brain systems. To delineate the collective behavior of the neural network, we consider modified tabu learning neurons (MTLN) with magnetic flux. Primarily, we explore the rest points and stability of the isolated MTLN, as well as its dynamical characteristics using maximal Lyapunov exponents. Surprisingly, we discover that for a given set of parameter values with distinct initial conditions, the periodic and the chaotic attractors may coexist. In addition, experimental analysis is carried out using a microcontroller-based implementation technique to support the observed complex behavior of the MTLN. We demonstrate that the observed numerical results are in good agreement with the experimental verification. Eventually, the collective behaviors of the considered MTLN are investigated by extending them to the network of the lattice array. We discover that when the magnetic flux coupling coefficient is varied in the presence of an external stimulus, the transition from spiral waves to traveling plane waves occurs. Finally, we manifest the formation of spiral waves in the absence of an external stimulus in contrast to previous observations.

Design and analysis of recurrent neural networks for ultrafast optical pulse nonlinear propagation.

In this work, we analyze different types of recurrent neural networks (RNNs) working under several different parameters to best model the nonlinear optical dynamics of pulse propagation. Here we studied the propagation of picosecond and femtosecond pulses under distinct initial conditions going through 13 m of a highly nonlinear fiber and demonstrated the application of two RNNs returning error metrics such as normalized root mean squared error (NRMSE) as low as 9%. Those results were further extended for a dataset outside the initial pulse conditions used on the RNN training, and the best-proposed network was still able to achieve a NRMSE below 14%. We believe that this study can contribute to a better understanding of building RNNs employed for modeling nonlinear optical pulse propagation and of how the peak power and nonlinearity affect the prediction error.

New Types of Distance Padovan Sequences via Decomposition Technique

In this paper, we introduce new kinds of generalized Padovan sequences and study their properties using number decomposition techniques. In particular, we consider three types of generalized Padovan sequences defined by the same recurrence equation with distinct initial conditions which follows from special number decomposition. Using the number decomposition method, we give their mutual relations and direct binomial formulas for considered sequences. Moreover, we give some combinatorial properties of these sequences and also define their matrix generators.

Analysis of local fractional Klein-Gordon equations arising in relativistic fractal quantum mechanics

In this paper, we present the implementation of a local fractional homotopy perturbation method pertaining to the local fractional natural transform (LFNT) operator for local fractional Klein-Gordon equations (LFKGEs) under distinct fractal initial conditions. The Klein-Gordon equation is a relativistic wave equation which estimates the nature and movement of zero spin particles at high velocities and energies resembling the lightspeed. This equation admits the laws of special relativity and describes zero spin particles with relativistic energy. This work also examines uniqueness and convergence analyses of the obtained solution for a general local fractional partial differential equation via applied method. The numerical simulations are presented for each LFKG equation on the Cantor set. The computational process ensures that the copulation of local fractional homotopy perturbation method and LFNT operator provides series solutions in closed form with fast convergence for local fractional Klein-Gordon equation in a very lucid way. Furthermore, the results have also been compared with solutions obtained by other methods.

Next-generation antivirus endowed with web-server Sandbox applied to audit fileless attack

Almost all malwares running on web-server are php codes. Then, the present paper creates a next generation antivirus (NGAV) expert in auditing threats web-based, specifically from php files, in real time. In our methodology, the malicious behaviors, of the personal computer, serve as input attributes of the statistical learning machines. In all, our dynamic feature extraction monitors 11,777 behaviors that the web fileless attack can do when launched directly from a malicious web-server to a listening service in a personal computer. Our NGAV achieves an average 99.95% accuracy in the distinction between benign and malware web scripts. Distinct initial conditions and kernels of neural networks classifiers are investigated in order to maximize the accuracy of our NGAV. Our NGAV can supply the limitations of the commercial antiviruses as for the detection of Web fileless attack. In opposition of analysis of individual events, our engine employs authorial Web-server Sandbox, machine learning, and artificial intelligence in order to identify malicious Web-sites.

Voltage-driven multistability and chaos in magnetic films

The control of magnetization dynamics has allowed numerous technological applications. Magnetization dynamics can be excited by, e.g., alternating magnetic fields, charge and spin currents, and a voltage-induced control of interfacial properties. An example of the last mechanism is the voltage-controlled magnetic anisotropy effect, which can induce magnetization precessions and switchings with low-power consumption. Time-dependent voltage-controlled magnetic anisotropy can induce complex dynamic behaviors for magnetization. This work studies the magnetization dynamics of a single magnetic nano-oscillator forced with a time-dependent voltage-controlled magnetic anisotropy. Unexpectedly, the oscillator displays multistable regimes, i.e., distinct initial conditions evolve towards different oscillatory states. When voltage is changed the oscillatory state exhibits period-doubling route to chaos. The chaotic behavior is numerically demonstrated by the determination of the largest Lyapunov exponent.

Analysis and dynamics of the Ivancevic option pricing model with a novel fractional calculus approach

The aim of the current study is to capture the complex behavior of the Ivancevic option pricing (IOP) model using the -homotopy analysis transform method (-HATM) with novel fractional operator. The generalization of the Black-Scholes model with the nonlinear Schrödinger equation plays a pivotal role in financial mathematics in studying the option-pricing wave function associated with two parameters. Based on adaptive market potential and volatility constant with distinct initial situations, we hired three distinct cases to exemplify the ability of -HATM. The considered method is elegant unification of the -homotopy analysis and Laplace transform algorithms. The derivative of fractional order is projected with the Atangana-Baleanu (AB) operator. The fixed-point theorem is used to present the existence and uniqueness of the attained result for the considered model, and we hire five distinct initial conditions. The hired scheme is highly methodical and exact to analyze the insights of the complex system with integer and fractional order exemplifying associated areas of science, which can be observed using plots and table.

Observing and modelling the young solar analogue EK Draconis: starspot distribution, elemental abundances, and evolutionary status

ABSTRACT Observations and modelling of stars with near-solar masses in their early phases of evolution are critical for a better understanding of how dynamos of solar-type stars evolve. We examine the chemical composition and the spot distribution of the pre-main-sequence solar analogue EK Dra. Using spectra from the HERMES Spectrograph (La Palma), we obtain the abundances of 23 elements with respect to the solar ones, which lead to a [Fe/H] = 0.03, with significant overabundance of Li and Ba. The s-process elements Sr, Y, and Ce are marginally overabundant, while Co, Ni, Cu, Zn are marginally deficient compared to solar abundances. The overabundance of Ba is most likely due to the assumption of depth-independent microturbulent velocity. Li abundance is consistent with the age and the other abundances may indicate distinct initial conditions of the pre-stellar nebula. We estimate a mass of 1.04 M⊙ and an age of $27^{+11}_{-8}$ Myr using various spectroscopic and photometric indicators. We study the surface distribution of dark spots, using 17 spectra collected during 15 nights using the CAFE Spectrograph (Calar Alto). We also conduct flux emergence and transport (FEAT) simulations for EK Dra’s parameters and produce 15-d-averaged synoptic maps of the likely starspot distributions. Using Doppler imaging, we reconstruct the surface brightness distributions for the observed spectra and FEAT simulations, which show overall agreement for polar and mid-latitude spots, while in the simulations there is a lack of low-latitude spots compared to the observed image. We find indications that cross-equatorial extensions of mid-latitude spots can be artefacts of the less visible southern-hemisphere activity.