Detailed Numerical Simulations Research Articles

Fractional Jacobi–Picard iteration method using Gauss–Seidel technique for solving a system of nonlinear fractional differential equations

The main objective of this study is to introduce an improvement of Picard’s method, a technique commonly used to effectively solve a set of nonlinear fractional differential equations based on Caputo’s fractional derivative. Using the Picard’s method to solve fractional differential equations is straightforward. However, dealing with the integral in each Picard’s iteration becomes tough or even impossible for nonlinear problems. Thus, we propose an iterative strategy called the fractional Jacobi–Picard iteration method, which combines Picard’s iteration method with the shifted Jacobi polynomial. The computation of the fractional integrals of the shifted Jacobi polynomials is easily achieved at each step by utilizing properties of the fractional integral and shifted Jacobi polynomial. Furthermore, this approach not only transforms the system of equations into a reversible form but also solves it using the Gauss–Seidel technique. The convergence analysis of the method has been carefully performed. We performed detailed numerical simulations to show how well our method performs compared to other methods. Our results demonstrate the effectiveness and accuracy of our approach, especially in handling problems with non-smooth solutions.

Design and Analysis of a Novel Fractional-Order System with Hidden Dynamics, Hyperchaotic Behavior and Multi-Scroll Attractors

The design of chaotic systems with complex dynamic behaviors has always been a key aspect of chaos theory in engineering applications. This study introduces a novel fractional-order system characterized by hidden dynamics, hyperchaotic behavior, and multi-scroll attractors. By employing fractional calculus, the system’s order is extended beyond integer values, providing a richer dynamic behavior. The system’s hidden dynamics are revealed through detailed numerical simulations and theoretical analysis, demonstrating complex attractors and bifurcations. The hyperchaotic nature of the system is verified through Lyapunov exponents and phase portraits, showing multiple positive exponents that indicate a higher degree of unpredictability and complexity. Additionally, the system’s multi-scroll attractors are analyzed, showcasing their potential for secure communication and encryption applications. The fractional-order approach enhances the system’s flexibility and adaptability, making it suitable for a wide range of practical uses, including secure data transmission, image encryption, and complex signal processing. Finally, based on the proposed fractional-order system, we designed a simple and efficient medical image encryption scheme and analyzed its security performance. Experimental results validate the theoretical findings, confirming the system’s robustness and effectiveness in generating complex chaotic behaviors.

Advanced Simulation and Analysis of Anisotropic Warp Fields with Positive Energy

This paper presents a comprehensive theoretical model for a warp bubble that enables faster-than-light travel using positive energy densities, an advancement over traditional models that rely on exotic negative energies. Building on the framework proposed by Eric Lentz, we introduce a non-uniform energy distribution model to enhance control and efficiency in warp field generation. The research validates the stability and feasibility of a warp bubble sustained by positive energy through detailed numerical simulations and analysis. Key findings include the discovery of anisotropic behavior in the warp bubble's structure, which allows for directional tuning of the warp field, thereby optimizing space- time manipulation and reducing energy demands. These results represent a significant step forward in the theoretical foundations of warp drive technology and its potential practical applications.

First principles insight into the study of the structural, stability, and optoelectronic properties of alkali-based single halide perovskite ZSnCl3 (Z = Na/K) materials for photovoltaic applications.

Metal halide perovskites are crystalline materials with a sharp increase in popularity and rapidly becoming a major contender for optoelectronic device applications. In this work, we provide the optoelectronic features of a possible novel candidate, ZSnCl3 (Z = Na/K) Sn-based on a detailed numerical simulation. The output of the current computations is compared to the results that are currently available, and a respectable agreement is noted. The studied compounds were cubic in nature and structurally stabe. The mechanical properties reflectthe mechanical stability and ductility of the proposed materials. The Sn-based single perovskite compounds proposed in this study are mechanically stable and ductile. The narrow direct band gap for NaSnCl3 and KSnCl3 are 1.36 eV and 1.47 eV, respectively, using the HSE06 hybrid function with the Boltztrp2 integrated in Quantum ESPRESSO (QE) software. The effective use of these compounds in perovskite solar cells and other optoelectronic applications was confirmed by optical absorption spectral measurements conducted in the photon energy range of 0-20 eV.

Numerical investigation of soot formation in methane/n-heptane laminar diffusion flame doped with hydrogen at elevated pressure

The addition of hydrogen in a dual-fuel mode based on natural gas and diesel offers great potential for improving engine efficiency and reducing emissions. Therefore, detailed numerical simulations have been used to explore the effects of soot formation characteristics of natural gas-diesel dual-fuel engines doped by hydrogen at elevated pressure. Numerical simulations are compared with available experimental data, the effects of H2 addition on soot formation in laminar CH4 + n-heptane, H2 + CH4 + n-heptane, FH2 + CH4 + n-heptane diffusion flames at 2, 4, 6 and 8 atm are simulated, FH2 is added to separate the H2 chemical effects. The results show that the dilution and thermal effects of H2 inhibit soot formation, while the chemical effects of H2 promote soot formation under different pressures. The addition of H2 increases the concentration of H and OH radicals, which promotes the formation of C2H2 and benzene (A1). By simplifying the reaction path and analyzing the production rate of A1, the mechanism of H2 addition to promote A1 formation is illustrated. The concentrations of polycyclic aromatic hydrocarbon (PAH) pyrene (A4), benzo(ghi)fluoranthene (BGHIF) and benzo(a)pyrene (BAPYR) are inhibited at higher pressures that result in lower inception and condensation rates. Therefore, the increase of hydrogen abstraction acetylene addition (HACA) rate is the main reason for the increase of soot formation under chemical effects. While the O2 oxidation rate decreases and the OH oxidation rate increases, that is due to the decrease of O2 concentration and the increase of OH concentration in the soot formation area under chemical effects.

Investigate the optimum design of atomizing nozzles for coal dust suppression by using multifactor level response surface methodology

Mechanized coal extraction generates substantial dust, adversely affecting the physical and mental wellbeing of underground workers and degrading the operational environment. To address the limitations of traditional spray systems, which often suffer from poor atomization effects and limited ability to withstand wind interference, the innovative vortex atomizing nozzle has been developed specifically for dust suppression. This advanced solution was rigorously tested through detailed numerical simulations and comprehensive experimental investigations. These studies focused on examining the impact of critical parameters, including the velocity at the airflow director's exit, the angle of the exit hole, and its radius, on the efficacy of dust suppression. Findings highlighted the paramount importance of the airflow director's exit velocity in enhancing dust removal, with the exit hole's radius having the least impact. Optimal conditions for dust suppression were identified as an airflow director exit velocity of 20 m/s, an angle of 60°, and a radius of 0.6 mm. Field validations under these optimum parameters demonstrated unparalleled dust control efficiency, achieving a reduction in coal dust concentration exceeding 90 %. This apparatus offers a highly effective, user-friendly solution for comprehensive coal dust management across various mine locations.

Reduced basis method for non-symmetric eigenvalue problems: application to the multigroup neutron diffusion equations

Abstract. In this article, we propose a reduced basis method for parametrized non-symmetric eigenvalue problems arising in the loading pattern optimization of a nuclear core in neutronics. To this end, we derive a posteriori error estimates for the smallest eigenvalue which is assumed to be simple and the associated left and right eigenvectors. The practical computation of these estimators requires the estimation of a constant called prefactor, which we can express as the spectral norm of some operator. We provide some elements of theoretical analysis which illustrate the link between the expression of the prefactor we obtain here and its well-known expression in the case of symmetric eigenvalue problems, either using the notion of numerical range of the operator, or via a perturbative analysis. Lastly, we propose a practical method in order to estimate this prefactor which yields interesting numerical results on actual test cases. We provide detailed numerical simulations on two-dimensional examples including a multigroup neutron diffusion equation. 1991 Mathematics Subject Classification. 65N15, 65N25, 65N30, 82D75.

Observational Evidence for Hot Wind Impact on Parsec Scales in Low-luminosity Active Galactic Nuclei

Supermassive black holes in galaxies spend the majority of their lifetime in the low-luminosity regime, powered by hot accretion flow. Strong winds launched from the hot accretion flow have the potential to play an important role in active galactic nuclei (AGN) feedback. Direct observational evidence for these hot winds with temperatures around 10 keV, has been obtained through the detection of highly ionized iron emission lines with Doppler shifts in two prototypical low-luminosity AGNs, namely M81* and NGC 7213. In this work, we further identify blueshifted H-like O/Ne emission lines in the soft X-ray spectra of these two sources. These lines are interpreted to be associated with additional outflowing components possessing velocity around several 103 km s−1 and lower temperature (∼0.2–0.4 keV). Blueshifted velocity and the X-ray intensity of these additional outflowing components are hard to explain by previously detected hot wind freely propagating to larger radii. Through detailed numerical simulations, we find the newly detected blueshifted emission lines would come from circumnuclear gas shock-heated by the hot wind instead. Hot wind can provide a larger ram pressure force on the clumpy circumnuclear gas than the gravitational force from the central black hole, effectively impeding the black hole accretion of gas. Our results provide strong evidence for the energy and momentum feedback by the hot AGN wind.

Choice of reaction progress variable under preferential diffusion effects in turbulent syngas combustion based on detailed chemistry direct numerical simulations

The combustion of hydrogen and carbon-monoxide mixtures, so-called syngas, plays an increasingly important role in the safety context of non-fossil energy generation, more specifically in the risk management of incidents in process engineering plants for ammonia synthesis and in nuclear power plants. In order to characterize and simulate syngas/air combustion on industrially relevant scales, subgrid modelling is required, which is often based on a reaction progress variable. To understand the influence of different fuel compositions, turbulence intensities and flame topologies on different possible definitions of reaction progress variable, detailed chemistry direct numerical simulations data of premixed, lean hydrogen/air and syngas/air flames has been considered. A reaction progress variable based on normalized molecular oxygen mass fraction has been found not to capture the augmentation of the normalized burning rate per unit flame surface area in comparison to the corresponding 1D unstretched premixed flame due to preferential diffusion effects. By contrast, reaction progress variables based on other individual species, such as hydrogen, can capture the augmentation of the rate of burning well, but exhibit a pronounced sensitivity to preferential diffusion effects, especially in response to flame curvatures. However, a reaction progress variable based on the linear combination of the main products can accurately represent the temperature evolution of the flame for different mixtures, turbulence intensities and varying local flame topology, while effectively capturing the augmentation of burning rate due to preferential diffusion effects. However, its tendency to assume values larger than 1.0 in the regions of super-adiabatic temperatures poses challenges for future modeling approaches, whereas the reaction progress variable based on hydrogen mass fraction remains bound between 0.0 and 1.0 despite showing deviations in comparison to corresponding variations obtained from the unstretched laminar flame depending on flame curvature variations.

Modeling infectious respiratory diseases considering fear effect and latent period

This paper introduces a fractional-order (FO) SEIR epidemic model for respiratory diseases considering a non-human class P(t) for pathogens to study the effects of fear and awareness programs on disease dynamics. Further, using the basic reproduction number ℛ0α, the criteria for the extinction or persistence of the disease is established. Also, the conditions for Hopf bifurcation are derived, considering both FO (α) and rate of pathogens η as the bifurcation parameters. In addition, a detailed numerical simulation is performed to substantiate our theoretical results. The study of transmission dynamics of Tuberculosis (TB), a particular example of respiratory disease, is carried out in reference to the United States (US). Finally, we have estimated model parameters with the help of actual TB data from the US and then predicted the TB dynamics and disease control. It is pointed out that the fractional order can reduce the complexity of the model and better predict the dynamics of TB in the US than the integer order.

End-to-end simulations of exoplanet detection with multiplexed volume Bragg gratings

Context. Direct imaging of exoplanets greatly enhances our ability to spectroscopically detect molecules in their atmospheres, but requires both excellent angular and spectral resolution. A highly promising approach uses multiplexed transmission gratings to achieve compressed sensing, but the published theoretical calculations are not realistic enough to determine whether the approach is feasible. Aims. We aim to determine the performance of recovering exoplanet signals of an instrument with multiplexed volume Bragg gratings in a full, detailed numerical simulation, specifically examining any effects caused by multiplexing several gratings. Methods. Our end-to-end simulation includes realistic stellar and planetary spectra, a closed-loop adaptive optics simulation, and rigorous coupled wave analysis to model the multiplexed gratings. We chose 20 passbands around expected methane absorption features that were optically combined using 20 gratings. Results. We find that exoplanet signals can be recovered down to contrasts of 10−6−10−7, without the addition of a coronagraph. Multiplexing a larger number of gratings improves the deepest recovered contrast, if photon noise is the dominant noise source. When residuals from our simple post-processing approach are the largest noise source, a larger number of multiplexed gratings decreases the performance, due to the stacking of the PSFs at different wavelengths. This is an artifact of our data reduction approach. Conclusions. We conclude that multiplexed Bragg gratings are a viable method to look for exoplanets with a compressed sensing approach, and additional gains may be made in post-processing.

Analyzing the impact of sinusoidal wavy rib geometric parameters on turbine blade thermal and fluid dynamics

The wavy rib is a spoiler structure designed to improve flow and heat transfer within turbine blade cooling channels, offering valuable insights for efficient cooling design in aerospace applications. This study employs a blend of experimental validation and detailed numerical simulations to investigate how rib height, amplitude, and discontinuity size collectively impact heat transfer enhancement and flow resistance in wavy ribs. By integrating TSP temperature field measurements with SST k-ω numerical calculations across 8 rib heights, 7 amplitudes, and 9 discontinuities at Reynolds numbers ranging from 10000 to 40000, the research reveals intricate relationships between these parameters. Studies have shown that there is a strong interaction between amplitude and rib height, as well as amplitude and discontinuity. Under small amplitude, Nu/Nu0 increases monotonously with the increase of rib height, but increases first and then decreases under large amplitude. When the discontinuity is small, the dimensionless Nusselt number (Nu/Nu0) of the ribbed wall increases first and then decreases with the increase of rib height, while it increases monotonously when the discontinuity is large. In contrast, the interaction between amplitude and discontinuity is weak. The ribbed wall with the greatest heat transfer improvement has Nu/Nu0 nearly 80 % higher than the reference wavy rib scheme, but it also has the highest corresponding pressure loss. The best overall thermal performance is 20 % higher than the reference structure, and the ribbed wall Nu/Nu0 is also increased by 24 %. The change of Reynolds number at the inlet of the channel has little effect on the wall Nu/Nu0 and pressure loss of the wavy rib channel.

Simulating electromagnetic cascades with Lorentz invariance violation

Lorentz invariance violation (LIV) is a phenomenon featuring in various quantum gravity models whereby Lorentz symmetry is broken at high energies, potentially impacting the behaviour of particles and their interactions. Here we investigate the phenomenology of LIV within the context of gamma-ray–induced electromagnetic cascades. We conduct detailed numerical simulations to explore the expected manifestations of LIV on gamma-ray fluxes, taking into account relevant effects such as pair production and inverse Compton scattering. Additionally, we consider processes forbidden in the standard model, namely vacuum Cherenkov emission and photon decay. Our analysis reveals that these modifications result in distinct characteristics within the measured particle fluxes at Earth, which have the potential to be observed in high-energy gamma-ray observations.

Frequency diversity of modal dispersion in mode-division multiplexing systems from strong to weak coupling regimes

Based on a statistical model applicable to all mode-coupling regimes and a trace covariance function of the group-delay matrix for characterizing the modal-dispersion correlation, we study the frequency diversity of modal dispersion in randomly-perturbed mode-division multiplexing optical communication systems. Particularly, we conduct detailed numerical simulation and analysis on the statistical properties of the modal dispersion in a 6-mode fiber under random perturbation. The results show that, at two frequencies of sufficiently large difference, while the modal dispersion eventually gets uncorrelated in the strong coupling regime, there remains a significant amount of “residual” correlation in the weak coupling regime. Also, we find that, although the typically-assumed frequency-domain ergodicity is reasonably valid in the strong coupling regime, it clearly fails in the weak coupling regime. The crossover from the strong to weak coupling regimes is also quantitatively investigated.

Effects of joint invasion: How co-invaders affect each other's success in model food webs?

While there has been considerable research on the interactions between invasive and native species, and on the impact of invasive species on the resident community, there has been less focus on exploring the relationship and interactions among invasive species themselves. Nevertheless, it is widely recognised that invasive species can have either positive or negative effects on each other, as well as neutral outcomes. In the present theoretical study, we compared the success of two invasive non-native species in two scenarios: when they invaded the resident food web separately and simultaneously. We examined the correlations between their direct and indirect ecological relationships and their topological positions in the food web, with the varying outcomes of joint invasion. Using the Allometric Bioenergetic Model (ABM) for dynamic simulations, we determined the success of invasion (presence or absence of invaders) and, in the case of successful co-invasion, the direction of their biomass change, comparing separate and simultaneous invasion scenarios. We studied the relationships between these variables after detailed numerical simulations with variable key parameters of the model.We found that direct and indirect ecological relationships between the two invaders can significantly modifiy the outcomes of the invasion scenarios. For example, their predator-prey relationship increases the probability of invasion success for both invaders, but at the same time the equilibrium biomass of at least one of them is likely to be reduced compared to its separate invasion. Trophic cascade or competitive relationship between them during simultaneous invasion also affects their success rate, with the former having a positive effect and the latter a negative one, as they can hinder each other's spread. Further, we found that higher trophic level and lower betweenness centralities of the invaders reduces the likelihood of invasion success regardless of the presence or absence of another invasive species. The results of the study can be tested experimentally in micro- and mesocosms.

Numerical vibrational acoustics and sound quality assessment of pipa strings

This study harmonizes subjective auditory and psychological elements related to plucked strings with objective physical attributes through spectrum analysis and numerical simulation, confirming the congruity between objective assessment systems and subjective perceptions in evaluating pipa string sound quality. The research combines experimental investigation of plucked pipa string vibrations with detailed numerical simulations of vibrational acoustic fields using a specified 3 N input force. Results demonstrate that as frequency increases (from A4: 440 Hz to E6: 1320 Hz), more pronounced vibrations emerge along the pipa body, leading to heightened overall sound pressure within the vibrational acoustic fields. The sound pressure distribution analysis reveals that the rosewood pipa exhibits significantly lower standard deviations of 41.8% and 41.9% compared to the tung wood pipa, and 24.6% and 32.2% lower than the white wood pipa at 440 Hz and 1320 Hz, respectively, highlighting the rosewood pipa’s superior sound pressure uniformity. Additionally, an assessment of the A4 signal’s Power Spectral Density (PSD) distribution underscores even spectral energy dispersion in the rosewood pipa’s A4 sound signal, with minor resonance peaks in higher-order overtones beyond 5000 Hz, further substantiating the superior sound quality of the rosewood pipa, in line with expert reviews.

Practical approaches for evaluating radiative heat from high pressure hydrogen flame

As the construction of hydrogen stations and other hydrogen-related facilities progresses, it becomes increasingly crucial for safety designs to account for scenarios where leaked hydrogen might ignite. Since a hydrogen flame is usually invisible, detection must rely on radiative heat or temperature. While it is possible to predict accurate radiative heat flux from a high pressure hydrogen jet flame through detailed numerical calculations of hydrogen combustion with its radiation, the objective of this study is to provide a simpler and more accurate prediction method. Previous experimental data of radiative heat flux, Qr from high pressure hydrogen jet flames were compiled, and a simple experimental equation Qr=1463.3(Lo/Lf)−2.32 was derived, where Lf and Lo represent the flame length and the distance perpendicular to the flame axis from the midpoint of the flame length to the observer, respectively. Radiative heat fluxes were computed through detailed numerical simulations using three types of water vapor radiation models: Goody's narrow random band model, the exponential broad band model by Edward and Elsasser's narrow regular band model. The temperature and water vapor partial pressure distributions obtained from numerical simulations were used as input conditions. The results were found to be in good agreement with the experimental equation. Moreover, a simple diagram representing the radiative heat flux from a hydrogen flame was derived using the method of cylinder-like approximation. The results of this study show that if the hydrogen pressure and leakage aperture diameter are given, the radiative heat flux at a certain distance can be predicted with high accuracy. Additionally, the average value of emissivity for the hydrogen diffusion flame was found to be on the order of 0.03.

Automatic Detection of Nuclear Spins at Arbitrary Magnetic Fields via Signal-to-Image AI Model.

Quantum sensors leverage matter's quantum properties to enable measurements with unprecedented spatial and spectral resolution. Among these sensors, those utilizing nitrogen-vacancy (NV) centers in diamond offer the distinct advantage of operating at room temperature. Nevertheless, signals received from NV centers are often complex, making interpretation challenging. This is especially relevant in low magnetic field scenarios, where standard approximations for modeling the system fail. Additionally, NV signals feature a prominent noise component. In this Letter, we present a signal-to-image deep learning model capable of automatically inferring the number of nuclear spins surrounding a NV sensor and the hyperfine couplings between the sensor and the nuclear spins. Our model is trained to operate effectively across various magnetic field scenarios, requires no prior knowledge of the involved nuclei, and is designed to handle noisy signals, leading to fast characterization of nuclear environments in real experimental conditions. With detailed numerical simulations, we test the performance of our model in scenarios involving varying numbers of nuclei, achieving an average error of less than 2kHz in the estimated hyperfine constants.

Modelling the adverse impacts of urbanization on human health

Abstract Urbanization has been a growing trend for decades, but the Coronavirus disease 2019 (COVID-19) pandemic has accelerated this trend in several ways. In many countries, the pandemic has prompted significant investments in urban health infrastructure, including hospitals, clinics, and public health facilities. Also, there are many studies suggesting that COVID-19, urbanization, and chronic diseases are interconnected in several ways, and addressing one aspect requires a comprehensive approach that considers the interconnectedness of these factors. To date, there are no studies depicting COVID-19 as a cause of emerging chronic diseases within the urban population. To address this sensitive issue, we propose a mathematical model in which we divide the total human population into three compartments: susceptible, diseased, and recovered. We have obtained the equilibrium points of the model and the conditions for their local stabilities. A suitable Lyapunov function has been used to derive the condition for the global stability of the nontrivial equilibrium point. A detailed numerical simulation of the model has been carried out, which is followed by sensitivity analysis of the model system.

Direct Evidence of Klein and Anti-Klein Tunneling of Graphitic Electrons in a Corbino Geometry.

Transport measurement of electron optics in monolayer graphene p-n junction devices has been traditionally studied with negative refraction and chiral transmission experiments in Hall bar magnetic focusing setups. We show direct signatures of Klein (monolayer) and anti-Klein (bilayer) tunneling with a circular "edgeless" Corbino geometry made out of gated graphene p-n junctions. Noticeable in particular is the appearance of angular sweet spots (Brewster angles) in the magnetoconductance data of bilayer graphene, which minimizes head-on transmission, contrary to conventional Fresnel optics or monolayer graphene which show instead a sharpened collimation of transmission paths. The local maxima on the bilayer magnetoconductance plots migrate to higher fields with increasing doping density. These experimental results are in good agreement with detailed numerical simulations and analytical predictions.