Nonlinear Growth Research Articles

Aperiodic Optimal Chronotherapy in Simple Compartment Tumour Growth Models Under Circadian Drug Toxicity Conditions

Cancer cells typically divide with weaker synchronisation with the circadian clock than normal cells, with the degree of decoupling increasing with tumour maturity. Chronotherapy exploits this loss of synchronisation, using drugs with circadian-clock-dependent activity and timed infusion to balance the competing demands of reducing toxicity toward normal cells that display physiological circadian rhythms and of efficacy against the tumour. We analysed optimal chronotherapy for one-compartment nonlinear tumour growth models that were no longer synchronised with the circadian clock, minimising a cost function with a periodically driven running cost accounting for the circadian drug tolerability of normal cells. Using Pontryagin’s Minimum Principle (PMP), we show, for drugs that either increase the cell death rate or kill dividing cells, that optimal solutions are aperiodic bang–bang solutions with two switches per day, with the duration of the daily drug administration increasing as treatment progresses; for large tumours, optimal therapy can in fact switch mid treatment from aperiodic to continuous treatment. We illustrate this with tumours grown under logistic and Gompertz dynamics conditions; for logistic growth, we categorise the different types of solutions. Singular solutions can be applicable for some nonlinear tumour growth models if the per capita growth rate is convex. Direct comparison of the optimal aperiodic solution with the optimal periodic solution shows the former presents reduced toxicity whilst retaining similar efficacy against the tumour. We only found periodic solutions with a daily period in one-compartment exponential growth models, whilst models incorporating nonlinear growth had generic aperiodic solutions, and linear multi-compartments appeared to have long-period (weeks) periodic solutions. Our results suggest that chronotherapy-based optimal solutions under a harmonic running cost are not typically periodic infusion schedules with a 24 h period.

Examining Immediate and Sustained Effects of Check-In/Check-Out in Finnish Elementary Schools

Check-in/Check-out (CICO) behavioral support has been implemented in Finnish School-Wide Positive Behavior Interventions and Support (SWPBIS) schools to cater to students who require personalized behavior support beyond the universal level. Previous studies have demonstrated the effectiveness of CICO as a behavioral support method. However, further research is needed to investigate its effectiveness in a larger sample and to analyze the timeline for behavioral change. This study focused on 51 elementary school students, assessing their behavior at baseline and during the CICO intervention phase using two data collection methods: the Daily Report Card (DRC) and the School Situation Questionnaire (SSQ). Nonlinear growth modeling was employed to examine the effects of the intervention. The results indicated that CICO yielded significant positive effects on behavior within 1 week of initiating support. After the outcomes stabilized, the behavior change remained stable beyond the first week of the intervention. These effects were detected in both the target behavior measured with DRC and the problem behavior measured with SSQ. These findings suggest that CICO interventions produce rapid and sustained changes in behavior. Further, the effects of CICO were observed in various settings within the school environment, indicating distal outcomes.

Backward test particle simulation of nonlinear cyclotron wave-particle interactions in the radiation belts

Wave-particle interaction plays a crucial role in the dynamics of the Earth’s radiation belts. Cyclotron resonance between coherent whistler mode electromagnetic waves and energetic electrons of the radiation belts is often called a coherent instability. Coherent instability leads to wave amplification/generation and particle acceleration/scattering. The effect of wave on particle’s distribution function is a key component of the instability. In general, whistler wave amplitude can grow over threshold of quasi-linear (linear) diffusion theory which analytically tracks the time-evolution of a particle distribution. Thus, a numerical approach is required to model the nonlinear wave induced perturbations on particle distribution function. A backward test particle model is used to determine the energetic electrons phase space dynamics as a result of coherent whistler wave instability. The results show the formation of a phase space features with much higher resolution than is available with forward scattering models. In the nonlinear regime the formation of electron phase space holes upstream of a monochromatic wave is observed. The results validate the nonlinear phase trapping mechanism that drives nonlinear whistler mode growth. The key differences in phase-space perturbations between the linear and nonlinear scenarios are also illustrated. For the linearized equations or for low (below threshold) wave amplitudes in the nonlinear case, there is no formation of a phase-space hole and both models show features that can be characterized as linear striations or ripples in phase-space.

Current-vortex-sheet model of the magnetic Rayleigh-Taylor instability

This study investigates the Rayleigh-Taylor instability in the magnetic field applied parallel to the interface. The motion of the interface is described using a current-vortex-sheet model. The growth rate of the interface is obtained from a linear stability analysis of the model. The interface of a single mode k=1 is linearly stable for RA≤1, where RA denotes the Alfvén number. Further, we conduct numerical computations for the evolution of the interface from the model for both regimes of RA≤1 and RA>1. For RA≤1, the interface oscillates vertically but does not intrude into the opposite phase. The amplitude of the interface and the oscillation period decrease with decrease in RA. For 1<RA≲1.5, the interface undergoes some growth at early times and then decreases. This oscillation is repeated, and no roll-ups are observed at the interface. Therefore, the nonlinear growth of the Rayleigh-Taylor instability is stabilized by a sufficiently strong magnetic field. For RA≳3 the interface is unstable and the pattern of the interface evolution differs from the density ratio. In addition, the magnetic field is greatly amplified as RA increases. Published by the American Physical Society 2024

Allometry of human calvaria bones during development from birth to 8 years of age shows a nonlinear growth pattern

Pediatric skulls change rapidly in size and shape during development, especially for children up to 8 years of age. This project was developed to address the gap in understanding of the three-dimensional growth parameters of the human skull during this period and the impact these growth patterns have on fontanelle closure and suture formation. This study offers novel data on the dynamic changes in the anatomy of the skull with the intention of providing better guidance for pediatric surgical care. Craniometric landmarks defined on three-dimensional computed tomography reconstructions were used to map skull development in children aged 0 to 8 years old. A total of 364 datasets were analyzed and statistically representative 3D skulls with anatomical craniometric features such as head shape, bone size, suture and fontanelle closure time were generated for 17 age groups spanning birth to 8 years of age to provide a comprehensive neuroanatomical understanding of how the pediatric skull changes over time. This study indicates that the cranial bones follow a non-linear growth pattern, with the occipital and frontal bones driving the directionality of fontanelle closure and delivers a 3D visualization of the developmental characteristics of the skull providing a landmark resource for understanding the growth dynamics of the human skull. While clinical measurements remain valid approaches for the planning of surgical interventions, these 3D models may provide a more accurate planning paradigm.

A review of load forecasting technology based on artificial intelligence

Abstract. Driven by the "dual carbon" goals and the construction of new-type power systems, the importance of power load forecasting technology has become increasingly prominent. Accurate power load forecasting can not only ensure the safe and stable operation of the power system, but also promote the efficient use of clean energy and reduce carbon emissions. Traditional power load forecasting methods have become insufficient in dealing with the complexity and nonlinear growth of power systems, and the development of artificial intelligence technology has brought new possibilities for power load forecasting. Power load forecasting methods based on machine learning and deep learning have gradually become a hot topic of research due to their powerful nonlinear mapping capabilities and advantages in processing big data. These methods not only perform well in short-term forecasting, but also show potential in medium- and long-term forecasting. This paper discusses the application of different artificial intelligence technologies in power load forecasting by sorting out the development status of related technologies, and provides a reference direction for future research.

Effect of Water Content on Light Nonaqueous Phase Fluid Migration in Sandy Soil

Contamination from light nonaqueous phase fluids (LNAPLs) and their derivatives during mining, production, and transportation has become a concern. Scholars have extensively studied LNAPL contamination, but the role of water content variation on its migration process in the unsaturated zone has not been sufficiently researched. The specific issue addressed in this study is the impact of water content on the migration of light nonaqueous phase liquids (LNAPLs) in sandy soils, a critical yet under-researched aspect of subsurface contamination. To tackle this, we employed indoor simulated vertical, one-dimensional, multiphase flow soil column experiments, utilizing the orthogonal experimental method to systematically evaluate the effects of varying water contents on the occurrence state and migration rate of LNAPLs. The experimental results indicate the following: (1) The migration rate of LNAPL exhibits an L-shaped trend during subsurface imbibition and a nonlinear relationship with migration time. The migration rate and migration time of surface infiltration have a linear growth relationship. (2) The residual rate of LNAPL is negatively correlated with water content and positively correlated with oil content in the homogeneous non-saturated state. With the increase in the amount of leaked oil, 40% of the leaked LNAPL is sorbed within the soil. (3) When the water content of the test medium is below 14%, and the oil content is below 11%, LNAPL appears in the unsaturated zone in a solid phase. As the water content increases, the adsorption rate of the oil phase gradually decreases and eventually reaches the oil saturation point. (4) When the water content of the medium exceeds 8%, over time, LNAPL will be subject to oil–water interfacial tension, and the rate of LNAPL movement first decreases and then increases, displaying nonlinear growth. The innovation of this work lies in the comprehensive analysis of LNAPL migration under controlled laboratory conditions, providing results that enhance the understanding of LNAPL behavior in sandy soils. These quantitative insights are crucial for developing targeted remediation strategies for LNAPL-induced pollution in the unsaturated zone.

Modulation instability of whistler wave with electron loss cone distribution in magnetized plasma

Abstract The modulation instability of whistler mode waves caused by thermal electron anisotropy is studied. Based on MHD equations, the nonlinear schrödinger equation (NLSE) that describes the nonlinear modulation of whistler waves is derived by Using the Krylov-Bogoliubov-Mitropolsky (KBM) method. The condition for wave modulation instability is obtained from the loss cone distribution function of thermal electron anisotropy, revealing that the nonlinear growth of the waves tends towards electron perpendicular temperature anisotropy. By setting up continuous background waves and introducing small ion low frequency perturbations, we find that the change in the amplitude of the modulated wave is related with wave number. This finding has been validated through simulations that align with our analytical results. Additionally, we also calculate the maximum amplitude of the wave with loss cone angle and times, which revealed that the electron vertical temperature anisotropy will lead to the modulation instability of the whistler wave. This further confirms the occurrence of the modulation instability of the whistler wave in laboratory plasmas and strengthens their credibility.

Suppression of Nonlinear Chorus Wave Growth by Active Control of Gyroresonant Interactions With Electron Hole Deformation

AbstractNonlinear gyroresonant acceleration is an essential mechanism for the formation of relativistic electrons in Earth's radiation belts, yet we still have only limited knowledge of how electron motion interacts nonlinearly with plasma waves. Here we demonstrate the compelling suppression of whistler‐mode chorus emissions as a resonant wave with energetic electrons by tuning an external transmitter signal in space plasmas. Through forcible modification of electron motions via phase trapping by the external waves, the nonlinear gyroresonant current is suppressed along with the electron hole deformation. Moreover, this can decrease the population of relativistic electrons due to the lack of coherent resonant waves seen by the phase‐organized electrons. Understanding such nonlinear wave suppression effects is crucial for a potential active control of Earth's plasma environment.

Kidney growth progression patterns in autosomal dominant polycystic kidney disease

BackgroundPrognosis for autosomal dominant polycystic kidney disease (ADPKD), the main inherited cause of kidney failure, relies on estimating cystic growth using linear formulas derived from height-adjusted total kidney volume (Ht-TKV). However, nonlinear renal growth patterns may occur in typical ADPKD. AimsTo determine kidney outcomes of subjects diagnosed with typical ADPKD exhibiting nonlinear, and unpredictable cystic growth during follow-up. MethodsRetrospective cohort study. We categorized TKV changes in individuals with typical ADPKD according to observed kidney growth trajectories. Ht-TKV was calculated from consecutive CT or MRI using the ellipsoid method. We compared estimated glomerular filtration rate (eGFR) trajectories with linear mixed models. ResultsWe included 83 individuals with ADPKD (67% women; age 47 ± 12 years; follow-up 5.2 years [IQR 2.8–9.0]). Three kidney growth patterns were observed: slow progression (24%, <3%/year linear increase), fast progression (39%, ≥3%/year linear increase), and atypical progression (37%, nonlinear growth). Adjusted ht-TKV change in mL/m/year was +1.4 (IQR –4.5 to +10.0), +40.3 (+16.9 to +89.3), and +32.8 (+15.9 to +85.9) for slow, fast, and atypical progressors, respectively (p <0.001). Atypical progressors exhibited a significantly greater decline in eGFR in mL/min/m²/year (–7.9, 95% CI –6.5, –3.9) compared to slow (–0.5, 95% CI –3.1 to +0.5) and fast progressors (–3.4, 95% CI –7.9, –2.0; between-group p <0.001). Atypical progressors had a higher proportion of acute complications, including hemorrhages, infections, and urolithiasis (84%), compared to slow (20%) and fast progressors (31%) (p <0.001). ConclusionIn typical ADPKD, nonlinear, abrupt, and unpredictable cyst growth occurs frequently, leading to a higher risk of acute complications and kidney function decline.

Finite element modeling for cohesive/adhesive failure of adhesive structures with a thermosetting resin

In this study, we established a novel method based on the finite element method (FEM) for predicting the strength of adhesive structures. Viscoplasticity, void growth, and cohesive zone model were introduced into the FEM to create a nonlinear damage growth (NDG) model. This model was used to comprehensively analyze the process zones within the adhesive layer. Furthermore, the embedded process zone approach was used to develop an interface constitutive law that averages the mechanical response of the adhesive layer. This modified Ma–Kishimoto (MMK) model can accurately represent the adhesive layer as an interface element and is computationally efficient. Furthermore, the study obtained the necessary interface properties for the MMK model from the NDG model, creating a numerical material test that can approximate the effect of the process zone. To validate the proposed method, single-lap shear tests were performed, and the accuracy of the predicted strength and deformation field was evaluated. The damage evolution in the NDG model and the MMK model were compared, and the scope of application of the MMK model was discussed. The results of this study can be used as a reference for the failure mechanism of thermosetting adhesives and establishment of design indices for adhesive structural strength.

Temporal Precipitation Variation and Leaf Stoichiometric Changes Mediate the Dynamics of Tree Growth Responses to Nitrogen Addition Over Time

AbstractNitrogen (N) addition can stimulate tree growth; however, the strength of this growth effect usually changes over time and the factors underlying these responses are not fully understood. Based on a decade‐long N addition experiment (by adding 0, 20, 50, and 100 kg N ha−1 yr−1) in a boreal forest, we studied responses of tree growth to N addition over time and explored the potential role of temporal precipitation variation and plant stoichiometric changes in mediating this. We found positive growth responses to N addition but this effect changed nonlinearly over time. Annual precipitation was positively related to growth under high‐level N addition; hence, a hump‐shape temporal pattern in precipitation contributed to the nonlinear tree growth responses. After precipitation effects were accounted for, the positive growth responses to N addition peaked in the seventh year and then declined for all levels of N. Later reductions in growth responses could partly be attributed to increased leaf N:phosphorus (P) ratio over time, especially at higher N addition rates. We also found an increase in soil acid phosphatase, the ratio of labile to occluded soil P fraction, and a decreased ratio in leaf N to P resorption efficiency with increasing N addition rates during the late stage of this experiment, suggesting increased P demand. Collectively, our results imply that changes in plant nutrient stoichiometry with cumulative N input may limit the N stimulation on tree growth over time, while temporal precipitation variation appears unlikely to modulate this effect under the atmospheric N deposition.

A Stochastic SIR Epidemic with Nonlinear Power Functions and Logistic Growth

This research conducts a comprehensive analytical investigation into a stochastic SIR epidemic model that integrates nonlinear power functions and logistic growth dynamics. We examine the intricacies of model behavior, demonstrating its capability to produce a positive global solution. Utilizing precisely defined Lyapunov functions, we demonstrate the essential prerequisites for establishing the ergodicity of this particular model. Furthermore, the research deduces adequate criteria for predicting the eventual eradication of infectious diseases within this theoretical framework. Ultimately, we supplement the study with numerical simulations to elucidate and substantiate the analytical findings. This work contributes to comprehending epidemic systems with nuanced growth patterns and intricate disease transmission mechanisms, offering insights into real-world epidemic potential behaviors and outcomes.

Latitudinal Mapping of Chorus Waves Growth Rates Based on Multi‐Spacecraft Wave and Plasma Measurements

AbstractWhistler mode chorus waves are one of the most intense and important electromagnetic emissions in the Earth's radiation belt, where these waves are responsible for electron acceleration to relativistic energies and for energetic electron precipitation into the Earth's atmosphere. This study reports a unique multi‐spacecraft observation event that allowed for the first time to verify theoretical models of chorus wave generation. The growth rates derived from the multi‐spacecraft observations of chorus waves Cluster WBD electric field waveforms collected during the crossing of the equatorial source region were compared to the theoretical linear and nonlinear growth rates calculated using simultaneous PEACE electron measurements. We have revealed that the growth rate estimated from wave measurements is substantially higher than the estimated linear growth rate but is quite close to the estimated nonlinear growth rate. A notable wave amplification is found up to 5 degrees of magnetic latitude and higher.

Mass scaling relations for dark halos from an analytic universal outer density profile

Context. The average matter density within the turnaround scale, which demarcates where galaxies shift from clustering around a structure to joining the expansion of the Universe, is an important cosmological probe. However, a measurement of the mass enclosed by the turnaround radius is difficult. Analyses of the turnaround scale in simulated galaxy clusters place the turnaround radius at about three times the virial radius in a ΛCDM universe and at a (present-day) density contrast with the background matter density of the Universe of δ ~ 11. Assessing the mass at such extended distances from a cluster’s center is a challenge for current mass measurement techniques. Consequently, there is a need to develop and validate new mass-scaling relations, to connect observable masses at cluster interiors with masses at greater distances. Aims. Our research aims to establish an analytical framework for the most probable mass profile of galaxy clusters, leading to novel mass scaling relations, allowing us to estimate masses at larger scales. We derive such analytical mass profiles and compare them with those from cosmological simulations. Methods. We used excursion set theory, which provides a statistical framework for the density and local environment of dark matter halos, and complement it with the spherical collapse model to follow the non-linear growth of these halos. Results. The profile we developed analytically showed good agreement (better than 30%, and dependent on halo mass) with the mass profiles of simulated galaxy clusters. Mass scaling relations were obtained from the analytical profile with offset better than 15% from the simulated ones. This level of precision highlights the potential of our model for probing structure formation dynamics at the outskirts of galaxy clusters.

Efficient approximation of global population dynamic models through statistical inference using local data

Biological growth curves are pivotal in predicting natural growth across disciplines, typically analyzed using nonlinear least squares or maximum likelihood methods. Bhowmick et al. (2014) introduced the interval-specific rate of parameters (ISRP) for growth equations, improving the estimation of relative growth rate (RGR) and model selection accuracy. Despite its effectiveness, computing these model-specific RGR estimates involves complex calculations and lacks explicit expressions for many nonlinear models. Also, for highly nonlinear models and non-monotonic data where the parameters are non-linearly related, the computation of interval estimates is almost impossible and may suffer from significant approximation errors. So, the need for a more efficient computation method for ISRP remains a significant challenge in growth studies. In this article, we propose a computational approach to obtain interval estimates of parameters based on the maximum likelihood estimation method. The likelihood function is maximized using the data on smaller intervals. Our study underscores the importance of an efficient ISRP computation technique, providing a more stable, unbiased, and normally distributed estimator. The most important advantage is that it can be implemented using existing optimizers in software packages efficiently, therefore, giving more accessibility to the practitioners. Both simulation studies and real data analysis have been carried out to validate the proposed estimation process. Additionally, its applicability to non-monotonic growth profiles and its robustness in handling highly non-linear growth equations highlight its versatility. We also developed a web application GpEM-R which is freely available for researchers and practitioners to analyze growth data.

Psychometric Analysis of the Hip Disability and Osteoarthritis Outcome Score (HOOS).

Hip Disability and Osteoarthritis Outcome Survey (HOOS) was developed as a region- and disease-specific outcome to assess hip disability. Despite the use of the HOOS in clinical practice and research, psychometric analyses of the scale in a large dataset of patients have not been performed. As such, the purposes of this study were to assess the structural validity of the HOOS in patients who underwent a total hip arthroplasty. Data were obtained from the Surgical Outcome System (SOS) global registry. Confirmatory factor analysis (CFA) was conducted to assess the scale structure of the 40-item HOOS and exploratory factor analysis (EFA) was conducted to identify a parsimonious scale structure. The parsimonious model identified was subjected to multi-group and longitudinal invariance testing and LGC modeling. The original five-factor, 40-item HOOS did not meet recommended model fit indices values (CFI = 0.822, TLI = 0.809, IFI = 0.822, RMSEA = 0.085). Alternate model generation identified an alternative model (i.e., HOOS-9). Sound model fit was identified for the HOOS-9 (CFI = 0.974, TLI = 0.961, RMSEA = 0.046). Invariance testing criteria were also met between groups (i.e., age and sex) and across time. Lastly, a nonlinear growth trajectory was identified in responses pertaining to hip disability. The original scale structure of the 40-item HOOS was not supported. The HOOS-9 met contemporary model fit recommendations, along with multi-group and longitudinal invariance testing. Our findings support the preliminary use of the HOOS-9 to assess hip function and disability in research and clinical practice.

Dynamics of an amensalism system with strong Allee effect and nonlinear growth rate in deterministic and fluctuating environment

Dynamics of an amensalism system with strong Allee effect and nonlinear growth rate in deterministic and fluctuating environment

Evaluations of storm tide hazard along the coast of China using synthetic dynamic tropical cyclone events

Concurring with high astronomical tides, storm surges have caused devastating damage in low-lying areas along the Chinese coastal regions. However, accurately calculating tropical cyclone (TC) storm tide hazards, especially those with long return periods, has proven challenging due to limited temporal and spatial information on TCs. In this study, we adopt the Synthetic Dynamic TC Method (SDTM), which enables a more robust estimation of storm tide hazards by generating a large number of synthetic TCs based on historical best track data and ocean-atmosphere environmental data. Within the SDTM framework, synthetic TCs corresponding to 10,000 years are validated using several statistical metrics, and the associated storm tides are simulated. For comparison, we employ the Historical Storm Method (HSM) to simulate storm tides for historical TCs from 1950 to 2019. Storm tide hazard curves are calculated and compared using these two methods. Our results demonstrate that the SDTM can robustly estimate storm tide hazards for both short and long return periods, whereas the HSM performs well for short return periods but struggles to reliably assess storm tide hazards for long return periods. Notably, within the SDTM, storm tide height exhibits nonlinear growth with increasing return periods in the Gumbel plot, a phenomenon not observed in the HSM due to the limited time span of TC records. With sufficient TC data, the spatial storm tide hazard maps obtained from the SDTM can serve as a robust foundation for developing disaster prevention and mitigation policies.

Nonlinear transient disturbance growth analysis for the compressible external flow and application to a flow around circular cylinder

The property of nonlinear optimal perturbation (NLOP) analysis for the flow around the circular cylinder was investigated with a comparison with the linear optimal perturbation analysis (LOP). Our analysis revealed that NLOP is highly dependent on the initial disturbance norm and highlighted the limitation of linear prediction in triggering instability in the flow field. This NLOP shows an asymmetric and deformed vortex structure on the cylinder wall, with the angle of the maximum wall vorticity shifting in relation to the initial disturbance norm. We also observed that the circulation and disturbance vorticity at the shear layer in boundary layer efficiently contributed to larger disturbance growth of the separation vortex behind the cylinder compared with the LOP.