Nonlinear Growth Research Articles

Observations of co-existing rising and falling tone emissions of electromagnetic ion cyclotron waves

We report observations of co-existing rising and falling tone emissions of electromagnetic ion cyclotron (EMIC) waves by THEMIS E spacecraft. The investigation of these fine structures of the EMIC waves is essential from the point of view of understanding the connection between the proton holes and the proton hills in velocity phase-space. The wave packets of rising and falling tones are tracked by Poynting vector analysis, where we observe that the rising tones are propagating northward and the falling tones are propagating southward. The nonlinear wave growth theory supports our observations. We propose a model where the proton velocity distribution function evolves through the formation of proton holes on the negative side of the distribution function and mirrored resonant protons forming proton hills on the positive side of the distribution function, allowing us to observe the co-existing rising and falling tone EMIC waves.Graphical abstract

Zonotopic state estimation and sensor fault detection for a wastewater treatment bioprocess

AbstractIn this paper, a fault diagnosis method for the basic process of microbial growth in wastewater treatment based on interval estimation technology is proposed. First, a nonlinear microbial growth model is converted into a linear time‐varying system. A time‐varying observer is then designed for the generated system, which takes into account an performance. Furthermore, a zonotope‐based set‐membership estimation algorithm is analyzed to synchronize interval estimation operations. In addition, interval residuals are computed from the generated interval state estimation and fault diagnosis is performed for a wastewater treatment bioprocess with sensor fault signals. Finally, the feasibility of the proposed fault diagnosis strategy for the wastewater treatment bioprocess is illustrated through numerical simulations.

Long-term stress characteristics of a box culvert with a load reduction system using geogrids and EPS under high fill

Laying geogrids and compressible materials, such as expandable polystyrene (EPS), on the tops of culverts under high fill can improve the stability of the fill and reduce the earth pressure on the tops of culverts. The creep of geogrids and compressible materials under high fill affects the stress state of culvert–soil systems. However, the long-term behaviour of culverts with geogrids and EPS is not clear. This paper investigates the long-term behaviour of culvert–soil interactions under high fill, specifically focusing on the creep effects of geogrids and EPS boards. A novel mechanical model for determining the long-term stress characteristics of culverts is proposed based on limit equilibrium theory. A comparison with finite difference simulation results was conducted to validate the proposed model. The findings reveal that the vertical earth pressure on the culvert top gradually transfers to the culvert side, exhibiting a nonlinear decrease over time. Moreover, the horizontal earth pressure on the culvert sidewall exhibits nonlinear growth with time, decreasing incrementally with depth. The maximum horizontal earth pressure on the culvert sidewall increases by 12.5% postconstruction, emphasizing the importance of accounting for the creep effects of geogrids and EPS boards in engineering design to prevent structural issues.

The Sixth Organizational Maturity Level and Autonomous Digital Transformation for Nonlinear or Exponential Growth

The Sixth Organizational Maturity Level and Autonomous Digital Transformation for Nonlinear or Exponential Growth

Numerical study of the influence of electron inertial effects and electron dynamics on tearing mode instability

The tearing mode instabilities were numerically studied in two distinct models: the finite electron inertial magnetohydrodynamics (MHD) and the electron MHD (EMHD). The finite electron inertial MHD model employed a modified Hall-MHD model that incorporated the electron inertial effects in the generalized Ohm’s Law. On the other hand, the electron dynamics were described by the EMHD model. It is found that both electron inertial effects and electron dynamics significantly influence the linear and nonlinear growth of tearing mode instabilities, with electron dynamics playing a more dominant role. The dependence of the linear growth rate of tearing modes on the electron inertial length de was investigated. The results show that electron inertial effects enhance the growth rate but resemble the behavior of resistivity η. Whereas, in the EMHD model, electron inertia plays a dominant role in tearing mode instabilities. Additionally, a study on the nonlinear saturation of (2,1) tearing modes was conducted, demonstrating consistency with relevant analytical theories. The study indicates that, in both models, the magnetic island exhibits faster growth and achieves a larger saturated island width as de increases.

INFLUENCE OF THE NANOSTRUCTURE OF TANTALUM OXIDE ON THE FLARE CHARACTER OF ITS ELECTROLUMINESCENCEWITH ANODIC-ELECTROLYSIS FORMATION IN CHEMICALLY PURE WATER

Theoretical and experimental studies were carried out to identify the reasons for the flash nature of the combustion of electroluminescence (EL) of tantalum oxide (Ta2O5), formed in chemically pure (distilled) water during high-voltage anodization of 1700 s. Nonlinear growth of the Ta2O5 film during this time was established, and a polychrome effect was discovered for its thicknesses from 150 ± 28 nm to 820 ± 80 nm. At the same time, EL ignition begins at an oxide thickness of 390 ± 74 nm, which corresponds to an anodization time of 78 ± 15 s, and from 968 ± 185 s until the end of this process, bright EL flashes are observed. Their luminosity can reach 2.8·10–3 lm/m2. It is shown that the cause of the outbreaks is explosive processes in dynamically changing Ta2O5 pores ranging in size from tens of nanometers to several micrometers and containing gas-discharge plasma from various products of electro- and plasma-chemical reactions with a temperature of the order of 12000 K, created due to Joule heating by the flowing current. It has been established that the formation of the plasma itself occurs as a result of electrical breakdown in pores, the field strength in which can reach the order of 3·108 V/m or more.

Wall modes and the transition to bulk convection in rotating Rayleigh-Bénard convection

We investigate states of rapidly rotating Rayleigh-Bénard convection in a cylindrical cell over a range of Rayleigh numbers 3×105≤Ra≤5×109 and Ekman numbers 10−6≤Ek≤10−4 for Prandtl number Pr=0.8 and aspect ratios 1/5≤Γ≤5 using direct numerical simulations. We characterize, for perfectly insulating sidewall boundary conditions, the first transition to convection via wall mode instability and the nonlinear growth and instability of the resulting wall mode states, including a secondary transition to time dependence. We show how the radial structure of the vertical velocity uz and the temperature T is captured well by the linear eigenfunctions of the wall mode instability where the radial width of uz is δuz∼Ek1/3r/H whereas δT∼e−kr (k is the wave number of a laterally infinite wall mode state). The disparity in spatial scales for Ek=10−6 means that the heat transport is dominated by the radial structure of uz since T varies slowly over the radial scale δuz. We further describe how the transition to a state of bulk convection is influenced by the presence of the wall mode states. We use temporal and spatial scales as measures of the local state of convection and the Nusselt number Nu as representative of global transport. Our results elucidate the evolution of the wall state of rotating convection and confirm that wall modes are strongly linked with the boundary zonal flow being the robust remnant of nonlinear wall mode states. We also show how the heat transport (Nu) contributions of wall modes and bulk modes are related and discuss approaches to disentangling their relative contributions. Published by the American Physical Society 2024

DeHNSSo: The Delft Harmonic Navier-Stokes Solver for nonlinear stability problems with complex geometric features

A nonlinear Harmonic Navier-Stokes (HNS) framework is introduced for simulating instabilities in laminar spanwise-invariant shear layers, featuring sharp and smooth wall surface protuberances. While such cases play a critical role in the process of laminar-to-turbulent transition, classical stability theory analyses such as parabolized or local stability methods fail to provide (accurate) results, due to their underlying assumptions. The generalized incompressible Navier-Stokes (NS) equations are expanded in perturbed form, using a spanwise and temporal Fourier ansatz for flow perturbations. The resulting equations are discretized using spectral collocation in the wall-normal direction and finite-difference methods in the streamwise direction. The equations are then solved using a direct sparse-matrix solver. The nonlinear mode interaction terms are converged iteratively. The solution implementation makes use of a generalized domain transformation to account for geometrical smooth surface features, such as humps. No-slip conditions can be embedded in the interior domain to account for the presence of sharp surface features such as forward- or backward-facing steps. Common difficulties with Navier-Stokes solvers, such as the treatment of the outflow boundary and convergence of nonlinear terms, are considered in detail. The performance of the developed solver is evaluated against several cases of representative boundary layer instability growth, including linear and nonlinear growth of Tollmien-Schlichting waves in a Blasius boundary layer and stationary crossflow instabilities in a swept flat-plate boundary layer. The latter problem is also treated in the presence of a geometrical smooth hump and a sharp forward-facing step at the wall. HNS simulation results, such as perturbation amplitudes, growth rates, and shape functions, are compared to benchmark flow stability analysis methods such as Parabolized Stability Equations (PSE), Adaptive Harmonic Linearized Navier-Stokes (AHLNS), or Direct Numerical Simulations (DNS). Good agreement is observed in all cases. The HNS solver is subjected to a grid convergence study and a simple performance benchmark, namely memory usage and computational cost. The computational cost is found to be considerably lower than high-fidelity DNS at comparable grid resolutions. Program summaryProgram Title: DeHNSSoCPC Library link to program files:https://doi.org/10.17632/9bnms99kk2.1Developer's repository link:https://github.com/SvenWesterbeek/DeHNSSoLicensing provisions: GPLv3Programming language: MatlabSupplementary material: The supplementary material contains the code as well as a user manual.Nature of problem: Fluid flows are subject to laminar-to-turbulent transition following the growth of instabilities. To avoid computationally demanding Direct Numerical Simulations (DNS), perturbation theory is often applied to their analysis. However, classical stability methods based on the Orr-Sommerfeld equation or the Parabolized Stability Equations neglect the influence of streamwise gradients in varying degrees. The validity of these assumptions is difficult to estimate a priori.Solution method: The Delft Harmonic Navier-Stokes Solver (DeHNSSo) solves the harmonic Navier-Stokes equations nonlinearly on domains featuring sharp and smooth spanwise invariant surface features using a generalized grid approach in combination with an embedded boundary method. This allows the user to include the effects of streamwise gradients on flow at a fraction of the cost of DNS.Additional comments including restrictions and unusual features: In DeHNSSo, the equations are solved using direct matrix solvers. As such, memory is treated as a scarce resource. The problem is formulated in a mode-independent manner such that left-hand side matrices need only be computed and stored once despite incorporating nonlinear terms. Additionally, DeHNSSo offers the user the possibility to prescribe inhomogeneous boundary conditions to introduce and solve the receptivity problem or manipulate instabilities. Due to the double Fourier expansion, the solver is restricted to spanwise and temporally periodic problems.

Comparison of Nonlinear Models to Describe the Growth of Tuj and Romanov x Tuj (F1) Lambs

This study aimed to identify the most suitable model for explaining weight changes in purebred Tuj (n=35) and Romanov x Tuj (RoxTuj) (F1) (n=25) lambs using non-linear models. Single-born lambs of both breeds and genders were included in the evaluation. Five different non-linear growth models were compared: Brody, Gompertz, Logistic, Richards, and Weibull. The best model for describing growth was chosen based on four criteria: coefficient of determination (R²), mean square error (MSE), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Models with the highest R² and the lowest MSE, AIC, and BIC values were considered the best fit for the data. It was observed that the Brody model had the highest R2 and lowest MSE, AIC and BIC values for Tuj and RoxTuj (F1) female and male lambs. The Gompertz, Logistic, and Richards models exhibited similar predictive performance. In contrast, the Weibull model produced significantly different results compared to the other models when predicting weight changes. Therefore, the Brody model was identified as the most effective model for explaining growth patterns in both Tuj and RoxTuj (F1) lambs.

Groundstates for Planar Schrödinger–Poisson System Involving Convolution Nonlinearity and Critical Exponential Growth

Groundstates for Planar Schrödinger–Poisson System Involving Convolution Nonlinearity and Critical Exponential Growth

DEUCE v1.0: a neural network for probabilistic precipitation nowcasting with aleatoric and epistemic uncertainties

Abstract. Precipitation nowcasting (forecasting locally for 0–6 h) serves both public security and industries, facilitating the mitigation of losses incurred due to, e.g., flash floods and is usually done by predicting weather radar echoes, which provide better performance than numerical weather prediction (NWP) at that scale. Probabilistic nowcasts are especially useful as they provide a desirable framework for operational decision-making. Many extrapolation-based statistical nowcasting methods exist, but they all suffer from a limited ability to capture the nonlinear growth and decay of precipitation, leading to a recent paradigm shift towards deep-learning methods which are more capable of representing these patterns. Despite its potential advantages, the application of deep learning in probabilistic nowcasting has only recently started to be explored. Here we develop a novel probabilistic precipitation nowcasting method, based on Bayesian neural networks with variational inference and the U-Net architecture, named DEUCE. The method estimates the total predictive uncertainty in the precipitation by combining estimates of the epistemic (knowledge-related and reducible) and heteroscedastic aleatoric (data-dependent and irreducible) uncertainties, using them to produce an ensemble of development scenarios for the following 60 min. DEUCE is trained and verified using Finnish Meteorological Institute radar composites compared to established classical models. Our model is found to produce both skillful and reliable probabilistic nowcasts based on various evaluation criteria. It improves the receiver operating characteristic (ROC) area under the curve scores 1 %–5 % over STEPS and LINDA-P baselines and comes close to the best-performer STEPS on a continuous ranked probability score (CRPS) metric. The reliability of DEUCE is demonstrated with, e.g., having the lowest expected calibration error at 20 and 25 dBZ reflectivity thresholds and coming second at 35 dBZ. On the other hand, the deterministic performance of ensemble means is found to be worse than that of extrapolation and LINDA-D baselines. Last, the composition of the predictive uncertainty is analyzed and described, with the conclusion that aleatoric uncertainty is more significant and informative than epistemic uncertainty in the DEUCE model.

Effects of nonlinear growth, cross-diffusion and protection zone on a diffusive predation model

Effects of nonlinear growth, cross-diffusion and protection zone on a diffusive predation model

Radiofrequency ablation-Real-time visualization of lesions and their correlation with underlying parameters.

Lesion durability and transmurality are crucial for successful radiofrequency (RF) ablation. This study provides a model of real-time RF lesion visualization and insights into the role of underlying parameters, as local impedance (LI). A force-sensing, LI-sensing catheter was used for lesion creation in an ex vivo model involving cross-sections of porcine cardiac preparations. During 60 s of RF application, one measurement per second was performed regarding lesion size and available ablation parameters. In total, 1847 measurements from n=36 lesions were performed. Power (20-50W) and contact force (1-5g, 10-15g, 20-25g) were systematically alternated. Lesion formation was most prominent in the first seconds of RF application during which nonlinear lesion growth was observed (max. 1.08mm/s for lesion depth and 2.71mm/s for lesion diameter). Power levels determined the extent of lesion formation in the early phase. After 20 s, lesion size growth velocity approaches 0.1mm/s at all power levels. LI changes were also highest in the first seconds (up to - 12 Ω/s) and decreased to less than - 0.1Ω/s after prolonged application. Lesion formation in irrigated RF ablation is a nonlinear process. Final lesion size resulting from an RF application is mainly influenced by high rates of lesion growth in the first seconds of ablation. LI seems to be a good surrogate for differentiating changes in lesion formation.

Effect of different particle sizes on combustion characteristics of DCR engines

The ramjet engine has undergone rapid development in recent decades, and the dual combustion chamber ramjet (DCR) engine was proposed in the last century. Boron, with its high volumetric and gravimetric heating values, is one of the most attractive fuel additives for ramjet engines. However, due to the problem of low combustion efficiency, boron is difficult to achieve high efficiency combustion in practical applications. In order to investigate the combustion characteristics of boron-containing gas solid phase components in DCR engines, the Realizable k-ε model, finite rate/vortex dissipation model and boron particle King model ignition combustion calculation program were written. A three-dimensional full-scale two-phase flow numerical simulation was carried out in the combustion chamber of the DCR engine to calculate the effects of different particle sizes on the combustion characteristics. Through the analysis of the simulation results, the particle size affects the ignition time of boron particles and is positively correlated with the combustion efficiency, but with a non-linear growth. A smaller particle size can promote the ignition of boron particles, improve the solid phase combustion efficiency and achieve efficient combustion.

Modelling dynamics between free-living amoebae and bacteria.

Free-living amoebae (FLA) serve as hosts for a variety of endosymbionts, which are microorganisms that reside and multiply within the FLA. Some of these endosymbionts pose a pathogenic threat to humans, animals, or both. The symbiotic relationship with FLA not only offers these microorganisms protection but also enhances their survival outside their hosts and assists in their dispersal across diverse habitats, thereby escalating disease transmission. This review is intended to offer an exhaustive overview of the existing mathematical models that have been applied to understand the dynamics of FLA, especially concerning their interactions with bacteria. An extensive literature review was conducted across Google Scholar, PubMed, and Scopus databases to identify mathematical models that describe the dynamics of interactions between FLA and bacteria, as published in peer-reviewed scientific journals. The literature search revealed several FLA-bacteria model systems, including Pseudomonas aeruginosa, Pasteurella multocida, and Legionella spp. Although the published mathematical models account for significant system dynamics such as predator-prey relationships and non-linear growth rates, they generally overlook spatial and temporal heterogeneity in environmental conditions, such as temperature, and population diversity. Future mathematical models will need to incorporate these factors to enhance our understanding of FLA-bacteria dynamics and to provide valuable insights for future risk assessment and disease control measures.

Simulations of non-integer upconversion in resonant six-wave scattering

Resonant upconversion through a sixth order relativistic nonlinearity resulting in a unique resonance was recently proposed [Malkin and Fisch, Phys. Rev. E 108, 045208 (2023)]. The high order resonance is a unique non-integer multiple of a driving pump frequency resulting in a frequency upshift by a factor of ≈3.73. We demonstrate the presence, unique requirements, and growth of this mode numerically. Through tuning waves to high amplitude, in a mildly underdense plasma, the six-photon process may grow more than other non-resonant but lower order processes. The growth of the high frequency mode remains below the nonlinear growth regime. However, extending current numerical results to more strongly coupled resonances with longer pulse propagation distances suggests a pathway to significant upconversion.

Wave–particle interactions in tokamaks

Transport consequences of the wave–particle interactions in the quasilinear plateau (QP) regime are presented. Eulerian approach is adopted to solve the drift kinetic equation that includes the physics of the nonlinear trapping (NT) and QP regimes. The localization of the perturbed distribution simplifies the test particle collision operator. It is shown that a mirror force like term responsible for the flattening of the distribution in the NT regime is subdominant in the QP regime, and controls the transition between these two regimes. Transport fluxes, flux-power relation, and nonlinear damping or growth rate are all calculated. There is no explicit collision frequency dependence in these quantities; however, the width of the resonance does. Formulas that join the asymptotic results of these two regimes to facilitate thermal and energetic particle transport, and nonlinear wave evolution of a single mode are presented.

Partial Derivatives of Gompertz, Logistic, and Weibull Non-Linear Growth Models on Confirmed COVID-19 Cases

. The epidemiological picture of COVID-19 is still unknown, and the number of confirmed cases of COVID-19 varies every day. Researchers have studied COVID-19 a lot, and many of them have used statistical models to estimate the growth of the outbreak. Non-linear statistical models can be used to describe growth behavior, as it varies in time. The aim of this research is to analyze, compare, and find the best model from the Gompertz, Logistic, and Weibull non-linear models. Daily cumulative data on confirmed COVID-19 viruses in Indonesia for 2020-2021 will be used in this research. The results obtained by the Logistic model proved to be very effective in describing the COVID-19 epidemic curve and estimating epidemiological parameters. The Logistic Model provides the best results compared to other growth models applied by Gompertz and Weibull. The R-Square of the logistic model is 0.9990, meaning that the model is able to explain or predict 99.90% of the data and 0.10% is explained by other factors. However, this research cannot explain the turning point of the curve, because there are many factors other than the model. One of them is the nature of the virus carrier from one place to another, then the behavior of the carrier who has not fully implemented the health protocol rules.

Using multiomics to explore the weight differences between genders in Muscovy ducks

Sexual dimorphism in poultry, especially in Muscovy ducks, is a proven phenomenon characterized by significant differences in body weight, growth patterns, and gene expression between male and female individuals. However, there is a dearth of research on the candidate genes and mechanisms underlying these weight differences. We selected 301 Muscovy ducks and recorded their weekly body weights from birth. We utilized 3 non-linear growth models (Logistic, Bertalanffy, and Gompertz) to fit the growth curve of Muscovy ducks, it was found that the logistic model was the most suitable model for describing the growth curve of Muscovy ducks. The results from the logistic model showed that the inflection point of male Muscovy ducks occurred at a later age, and they had a heavier mature body weight than female Muscovy ducks. At 10 wk of age, we collected Muscovy duck breast muscle tissues for transcriptome sequencing (RNA-seq). To exclude the impact of weight difference, 185 differentially expressed genes (DEGs), such as PPAR, FABP3, PLIN1, and FOXO1, were screened. These DEGs were predominantly enriched in terms related to mitochondria, lipids, and nucleic acids. In addition, the gut microbiota has the ability to influence host physiology through the regulation of multiple processes, including playing a crucial role in host muscle growth and development. We randomly selected male and female Muscovy ducks for 16S rRNA sequencing analysis of their cecal microbiota. The results showed that there were significant differences in the composition of cecal microbiota between male and female Muscovy ducks. At the genus level, the relative abundance of Enterenecus and CAG_269 were lower in males compared to females, while Lawsonibacter, Parabacteroides_B, Streptococcus, UBA2658, Caccousia, and Butyricimonas were higher in males than in females. In summary, this study provides a scientific theoretical basis for revealing the different growth patterns of male and female Muscovy ducks, and offers explanations from both the molecular level and microbiological perspectives.

Emulating Power Spectra for Prereconstructed and Postreconstructed Galaxy Samples

The small-scale linear information in galaxy samples typically lost during nonlinear growth can be restored to a certain level by the density field reconstruction, which has been demonstrated for improving the precision of the baryon acoustic oscillation (BAO) measurements. As proposed in the literature, a joint analysis of the power spectrum before and after the reconstruction enables an efficient extraction of information carried by high-order statistics. However, the statistics of the postreconstruction density field are difficult to model. In this work, we circumvent this issue by developing an accurate emulator for the prereconstructed, postreconstructed, and cross-power spectra ( Ppre , P post, P cross) up to k = 0.5 h Mpc−1 based on the Dark Quest N-body simulations. The accuracy of the emulator is at the percent level; namely, the error of the emulated monopole and quadrupole of the power spectra is less than 1% and 10% of the ground truth, respectively. A fit to an example power spectrum using the emulator shows that the constraints on cosmological parameters get largely improved using Ppre +P post+P cross with kmax=0.25hMpc−1 , compared to that derived from Ppre alone; namely, the constraints on (Ω m , H 0, σ 8) are tightened by ∼41%–55%, and the uncertainties of the derived BAO and RSD parameters (α ⊥, α ∣∣, f σ 8) shrink by ∼28%–54%, respectively. This highlights the complementarity among Ppre , P post, and P cross, which demonstrates the efficiency and practicability of a joint Ppre , P post, and P cross analysis for cosmological implications.