Stationary Model Research Articles

Simplified Whittle Estimators for Spectral Parameters of Stationary Linear Models with Tapered Data

Simplified Whittle Estimators for Spectral Parameters of Stationary Linear Models with Tapered Data

Dynamic evolutions of Bohm sheaths and pre-sheaths

The time evolutions of the Bohm sheath and the related pre-sheath are analyzed as an initial value problem. The standard classical fluid model of a collisionless plasma is used with cold ions and Boltzmann distributed electrons. Numerical solutions of the basic equations show that a stationary plasma sheath itself is established within a few ion plasma periods. It is demonstrated analytically that for infinitely extended homogeneous plasmas in one spatial dimension, the only possible pre-sheath solution is dynamic, giving a steady expansion: no stationary solution exists for this one-dimensional case. The potential and density drops along the dynamic pre-sheath differ notably from the values found for stationary models suggested in the literature. Collisions give only formal changes to the collisionless results, and their substance remains the same in one spatial dimension. Cylindrical and spherical geometries, on the other hand, allow for physically acceptable, fully nonlinear, stationary solutions with analytical results given. These are supported by numerical solutions.

Investigation on wave-induced responses of heterogeneous seabed around a buried pipeline based on nonstationary random field model

The instability of the seabed poses a threat to the structural integrity and functionality of submarine pipelines. This numerical study investigates wave-induced responses in a heterogeneous seabed around a buried pipeline, considering spatial variability in soil properties through nonstationary random field models. Three scenarios of spatial variability for soil parameters changing with depth are simulated using both stationary and nonstationary random field models via the Karhunen-Loève expansion method. The discrete random fields are validated in terms of correlation structures and statistical characteristics. The stochastic finite element method, incorporating random fields and a poroelastic seabed model through a LiveLink code, is employed to examine probabilistic outcomes of dynamic soil responses and liquefaction zone distributions within a probabilistic framework. Contrastive analyses are conducted for seabed models with different random field scenarios, in addition to deterministic analyses. The results of the stochastic analysis show that the increasing trend of soil strength with depth has significant effects on the seabed responses and transient liquefaction characteristics around a pipeline.

Anodic dissolution model with diffusion–migration transport for simulating localized corrosion

A one-dimensional model for simulating localized corrosion is developed, incorporating a time-dependent diffusion–migration transport and a moving interface. The model is applied to iron with the Butler–Volmer formula as the dissolution law, and both crevice and pit configurations are simulated. The mathematical procedure for solving this strongly coupled differential equations system and the numerical development for simulations are detailed. A finite-difference ALE scheme is used for the numerical computation of the solutions of this free boundary problem. The results show that the dissolution rate increases with chloride concentration and metal potential, and migration plays, most of the time, a significant role in species transport for both crevice and pit configurations. The evolution of the repassivation potential with pit depth is computed and is in good agreement with experimental results. The time-dependent model under consideration provides more accurate quantitative results for concentration profile and crevice depth than stationary models.

Implementing Non-Poissonian Forecasts of Distributed Seismicity into the 2022 Aotearoa New Zealand National Seismic Hazard Model

ABSTRACT Seismicity usually exhibits a non-Poisson spatiotemporal distribution and could undergo nonstationary processes. However, the Poisson assumption is still deeply rooted in current probabilistic seismic hazard analysis models, especially when input catalogs must be declustered to obtain a Poisson background rate. In addition, nonstationary behavior and scarce earthquake records in regions of low seismicity can bias hazard estimates that use stationary or spatially precise forecasts. In this work, we implement hazard formulations using forecasts that trade-off spatial precision to account for overdispersion and nonstationarity of seismicity in the form of uniform rate zones (URZs), which describe rate variability using non-Poisson probabilistic distributions of earthquake numbers. The impact of these forecasts in the hazard space is investigated by implementing a negative-binomial formulation in the OpenQuake hazard software suite, which is adopted by the 2022 Aotearoa New Zealand National Seismic Hazard Model. For a 10% exceedance probability of peak ground acceleration (PGA) in 50 yr, forecasts that only reduce the spatial precision, that is, stationary Poisson URZ models, cause up to a twofold increase in hazard for low-seismicity regions compared to spatially precise forecasts. Furthermore, the inclusion of non-Poisson temporal processes in URZ models increases the expected PGA by up to three times in low-seismicity regions, whereas the effect on high-seismicity is minimal (∼5%). The hazard estimates presented here highlight the relevance, as well as the feasibility, of incorporating analytical formulations of seismicity that go beyond the inadequate stationary Poisson description of seismicity.

Influence of large-scale climate indices and regional meteorological elements on drought characteristics in the Luanhe River Basin

Frequent drought disasters have significant impacts on socio-economic and ecosystems, and it is crucial to explore the propagation characteristics of drought for disaster prevention and mitigation. In this paper, based on 0.25° × 0.25° grid-point Meteorological hydrological and large-scale climate factor data, the start-to-start, peak-to-peak, and end-to-end drought propagation times, and the periods and rates of drought development and recovery were estimated for 11 regions in the Luanhe River Basin under stationary and non-stationary conditions. The Generalized Additive Model for Location, Scale and Shape (GAMLSS) framework was used to construct stationary and non-stationary models to capture the stationary and non-stationary drought characteristics respectively, and then the drought development and recovery patterns, and drought propagation times were assessed. The results showed that under the influence of climate factors, severe drought events occurred in most study areas, the duration of meteorological drought was prolonged by 0.1–0.6 months, and the peak intensity was increased by about 0.05. The severity of hydrological drought increased by 0.2–0.8, and the peak intensity decreased by 0.1–0.2. The rate of development and recovery of hydrological drought was accelerated by 0.1–0.2 per month. The propagation time of start-to-start was shortened by 0.2 months, and the propagation time of end-to-end was extended by 1–2 months. These mean that water resource control authorities need to propose responses to droughts more quickly.

Syntrichia ruralis as a suitable bioindicator for urban areas – the case study of Tallinn city

Environmental pollution is one of the most important problems in urban environment. Mosses are good indicatorsof air pollution. In Estonia, heavy metals have been measured from Pleurozium schreberi and Hylocomium splendens, whichdo not grow in areas of Tallinn with a higher pollution load. In the present study, Cu, Fe and Cd were measured from fivemoss species growing in contaminated as well less polluted areas of Tallinn. Based on stationary and street pollution sourceinventory and air pollution dispersion modelling, the long-term average concentrations of fine particles (PM10) and nitrogenoxides (NOx) in air were estimated. The work revealed that it is possible to find a moss species that is common in Tallinnand grows in both polluted and less polluted areas – Syntrichia ruralis, which is the most suitable species for bioindicationbased on this work. Moss species Ceratodon purpureus accumulated the most Cd, Cu, and Fe, then Brachytheciumrutabulum/Sciuro-hypnum curtum, and Rhytidiadelphus squarrosus the least. Statistically significant higher Fe concentrationswere in the Syntrichia ruralis, compared to the Sciuro-hypnum curtum and Rhytidiadelphus squarrosus. The Syntrichia ruralisalso had significantly higher Cd content compared to the Brachythecium rutabulum/Sciuro-hypnum curtum. The results ofthe GLM analysis showed that the content of various heavy metals depends on the moss species and the degree of fine particlesin the environment, and it didn't depend on whether the moss grows on the soil or a hard substrate such as concrete, stoneor asphalt.

The New Model of Atom

In this paper the new mathematical model of atom was derived. This model contributes quantum theory of atom. The nonstationay model and stationary model were defined. The derived model contributes atom’s stability. The comparison of all models of atoms was discussed and underline. Early atomic models and latest atomic models were analyzed. Phylosopy and theory of atom were disscused. Kinetic theory of nobles gases and periodicity of properties of the elements were considered.

Reliability Assessment of Distribution Stations Considering Spare Transformer Sharing

A reliability study has been performed recently at Hydro One to evaluate the reliability of groups of distribution stations involved in a spare transformer sharing policy. The groups may include distribution utilities stations and distribution customer own stations. The study used a probabilistic method based on stationary Markov models and two performance criteria namely the group availability criterion and the total cost criterion in the evaluation. The study results demonstrate that the number of spare transformers required for the groups involved in the spare transformer sharing policy will be reduced while maintaining almost the same reliability levels of individual groups. The purpose of this paper is to describe the study, its reliability assessment method and to illustrate it using a sample system.

Predictive Analytics on Indian Pharmaceutical Sector Through the Application of ARIMA and GARCH

A company acquiring an ownership through transfer of resources and technical know-how is essential for a sustainable growth and to face competition in the existing industry. The aim is to study the effect of CAGR on Foreign Direct Investment (FDI) inflows into Indian Pharmaceutical sector, secondly to regress the stock prices of top listed Indian Pharmaceutical sector and finally to analyse the Generalised Auto Regressive Conditional Heteroskedasticity (GARCH) effect on the Stock prices of selected Pharmaceutical sector. The research methodology applied is descriptive, analytical and univariate analysis. Time series tool of Auto Regressive Integrated Moving Averages (ARIMA) and GARCH is applied for generating the output and the major findings from the study is Apollo Hospitals Enterprise Limited, Cipla Ltd and Dr. Reddy’s Laboratories Limited Lab are stationary and optimum model as per information criteria is at ARIMA, (1, 1, 0) for Apollo Hospitals Enterprise Limited and ARIMA (0, 1, 1) for Cipla Limited and Dr. Reddy’s Laboratories Limited Lab.

Applying Stationary and Nonstationary Generalized Extreme Value Distributions in Modeling Annual Extreme Temperature Patterns

This study applies both stationary and nonstationary generalized extreme value (GEV) models to analyze annual extreme temperature patterns in four stations of Southern Highlands region of Tanzania: Iringa, Mbeya, Rukwa, and Ruvuma over a 30‐year period. Parameter estimates reveal varied distribution characteristics, with the location parameter μ ranging from 28.98 to 33.44, and shape parameter ξ indicating both bounded and heavy‐tailed distributions. These results highlight the potential for extreme temperature conditions, such as heatwaves and droughts, particularly in regions with heavy‐tailed distributions. Return level estimates show increasing temperature extremes, with 100‐year return levels reaching 33.95 °C in Ruvuma. Nonstationary models that incorporate time‐varying location and scale parameters significantly improve model fit, particularly in Mbeya, where such a model outperforms the stationary model (p value = 0.0092). Trend analyses identify significant temperature trends in Mbeya (p value = 0.0123) and Ruvuma (p value = 0.0015), emphasizing the need for adaptive climate strategies. These findings underscore the importance of accounting for nonstationarity in climate models to better understand and predict temperature extremes.

Assesment of rheological properties of drilling fluids based on rotational viscometry data

The model of interpretation of rotational viscometry data is described using a strict solution of the Couette flow equation and considering the information resulting from the experiments. Using the example of common rheological models of drilling muds, the influence of the radii ratio and rheological properties on the accuracy of their estimation was studied using the dependence of the Newtonian fluid shear rate gradient. Comparative results of the rheological properties assessment for drilling muds in industrial conditions are given. Keywords: bi-viscous fluid; Couette flow; maximum likelihood principle; rheologically stationary models.

Non-equilibrium Onsager–Machlup theory

This paper proposes a simple mathematical model of non-stationary and non-linear stochastic dynamics, which approximates a (globally) non-stationary and non-linear stochastic process by its locally (or ‘piecewise’) stationary version. Profiting from the elegance and simplicity of both, the exact mathematical model referred to as the Ornstein–Uhlenbeck stochastic process (which is globally stationary, Markov and Gaussian) and of the Lyapunov criterion associated with the stability of stationarity, we show that the proposed non-linear non-stationary model provides a natural extension of the Onsager–Machlup theory of equilibrium thermal fluctuations, to the realm of non-stationary, non-linear and non-equilibrium processes. As an illustrative application, we then apply the extended non-equilibrium Onsager–Machlup theory, to the description of thermal fluctuations and irreversible relaxation processes in liquids, leading to the main exact equations employed to construct the non-equilibrium self-consistent generalised Langevin equation (NE-SCGLE) theory of irreversible processes in liquids. This generic theory has demonstrated that the most intriguing and long-unsolved questions of the glass and gel transitions are understood as a natural consequence of the second law of thermodynamics, enunciated in terms of the proposed piecewise stationary stochastic mathematical model.

Optimizing Mass Transfer in Multiphase Fermentation: The Role of Drag Models and Physical Conditions

Detailed knowledge of the flow characteristics, bubble movement, and mass transfer is a prerequisite for the proper design of multiphase bioreactors. Often, mechanistic spatiotemporal models and computational fluid dynamics, which intrinsically require computationally demanding analysis of local interfacial forces, are applied. Typically, such approaches use volumetric mass-transfer coefficient (kLa) models, which have demonstrated their predictive power in water systems. However, are the related results transferrable to multiphase fermentations with different physicochemical properties? This is crucial for the proper design of biotechnological processes. Accordingly, this study investigated a given set of mass transfer data to characterize the fermentation conditions. To prevent time-consuming simulations, computational efforts were reduced using a force balance stationary 0-dimension model. Therefore, a competing set of drag models covering different mechanistic assumptions could be evaluated. The simplified approach of disregarding fluid movement provided reliable results and outlined the need to identify the liquid diffusion coefficients in fermentation media. To predict the rising bubble velocities uB, the models considering the Morton number (Mo) showed superiority. The mass transfer coefficient kL was best described using the well-known Higbie approach. Taken together, the gas hold-up, specific surface area, and integral mass transfer could be accurately predicted.

Testing for coefficient distortion due to outliers with an application to the economic impacts of climate change

Outlying observations can bias regression estimates, requiring the use of outlier-robust estimators. Comparing robust estimates to those obtained using ordinary least squares (OLS) is a common robustness check, however, such comparisons have been mostly informal due to the lack of available tests. Here we introduce a formal test for coefficient distortion due to outliers in regression models. Our proposed test is based on the difference between OLS and robust estimates obtained using a class of Huber-skip M-type estimators (such as Impulse Indicator Saturation or Robustified Least Squares). We show that our distortion test has an asymptotic chi-squared distribution by establishing the asymptotics of the corresponding Huber-skip M-estimators using an empirical process Central Limit Theorem recently developed in the literature. The test is valid for cross-sectional, as well as panel, and stationary or deterministically-trending time series models. To improve finite sample performance and to alleviate concerns on distributional assumptions, we explore several bootstrap testing schemes. We apply our outlier distortion test to estimates of the macro-economic impacts of climate change allowing for adaptation.

Non-Stationary Modeling of Annual Flood Peak Heights of Mahanadi River Basin with the q-Generalized Extreme Value Distribution

In recent years, due to climate change, catastrophic events are increased largely in India. Hence researchers are forced to consider non-stationary flood frequency analysis as an improved method. In this paper, non-stationarity of annual daily maximum flood heights were studied at 12 sites of Mahanadi River Basin (MRB) by analyzing the flood frequency of a stationary model and 4 non-stationary models using time dependent q-GEV model by considering trend as a linear function of its location and scale parameters. The q-GEV distribution is utilized in this study because of its flexibility and accuracy than GEV distribution in modeling extreme flood heights. The results found that there is strong evidence of a linear trend existence for both the location and scale parameters at the Kesinga site; for the location parameter at Pathardi and Simga sites; for the scale parameter at Dharmajagarh, Kotni and Seorinarayan, and no linear trend exists for both location and scale parameters at Alipingal, Bomnidhi, Manendragarh, Mohana, Rajim and Sundargarh, there may be exists other form of trend at these sites. The findings also indicate that nonstationarity is present in the MRB due to climate change, which help to water practitioner for taking precautions against adverse effect of extreme floods.

Evaluating Non-Stationarity in Precipitation Intensity-Duration-Frequency Curves for the Dallas–Fort Worth Metroplex, Texas, USA

Extreme precipitation has become more frequent and intense with time and space. Infrastructure design tools such as Intensity-Duration-Frequency (IDF) curves still rely on historical precipitation and stationary assumptions, risking current and future urban infrastructure. This study developed IDF curves by incorporating non-stationarity trends in precipitation annual maximum series (AMS) for Dallas–Fort Worth, the fourth-largest metropolitan region in the United States. A Pro-NEVA tool was used to develop non-stationary IDF curves, taking historical precipitation AMS for seven stations that showed a non-stationary trend with time as a covariate. Four statistical indices—the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Root Mean Square Error (RMSE), and Nash–Sutcliffe Efficiency (NSE)—were used as the model goodness of fit evaluation. The lower AIC, BIC, and RMSE values and higher NSE values for non-stationary models indicated a better performance compared to the stationary models. Compared to the traditional stationary assumption, the non-stationary IDF curves showed an increase (up to 75%) in the 24 h precipitation intensity for the 100-year return period. Using the climate change adaptive non-stationary IDF tool for the DFW metroplex and similar urban regions could enable decision makers to make climate-informed choices about infrastructure investments, emergency preparedness measures, and long-term urban development and water resource management planning.

Unsupervised learning of stationary and switching dynamical system models from Poisson observations

Objective. Investigating neural population dynamics underlying behavior requires learning accurate models of the recorded spiking activity, which can be modeled with a Poisson observation distribution. Switching dynamical system models can offer both explanatory power and interpretability by piecing together successive regimes of simpler dynamics to capture more complex ones. However, in many cases, reliable regime labels are not available, thus demanding accurate unsupervised learning methods for Poisson observations. Existing learning methods, however, rely on inference of latent states in neural activity using the Laplace approximation, which may not capture the broader properties of densities and may lead to inaccurate learning. Thus, there is a need for new inference methods that can enable accurate model learning. Approach. To achieve accurate model learning, we derive a novel inference method based on deterministic sampling for Poisson observations called the Poisson Cubature Filter (PCF) and embed it in an unsupervised learning framework. This method takes a minimum mean squared error approach to estimation. Terms that are difficult to find analytically for Poisson observations are approximated in a novel way with deterministic sampling based on numerical integration and cubature rules. Main results. PCF enabled accurate unsupervised learning in both stationary and switching dynamical systems and largely outperformed prior Laplace approximation-based learning methods in both simulations and motor cortical spiking data recorded during a reaching task. These improvements were larger for smaller data sizes, showing that PCF-based learning was more data efficient and enabled more reliable regime identification. In experimental data and unsupervised with respect to behavior, PCF-based learning uncovered interpretable behavior-relevant regimes unlike prior learning methods. Significance. The developed unsupervised learning methods for switching dynamical systems can accurately uncover latent regimes and states in population spiking activity, with important applications in both basic neuroscience and neurotechnology.

Stationary Model of Quantum Tunneling Through Composite Layers

Stationary Model of Quantum Tunneling Through Composite Layers

Probabilistic stationary subspace regression model for soft sensing of nonstationary industrial processes

AbstractBenefitting from the development of industrial intelligence, data‐driven soft sensors have been widely applied in industrial processes in recent years. Driven by fluctuations in raw material quality, varying loads, and uncertain disturbances, industrial processes are often characterized by nonstationary properties. However, the nonstationary characteristics of the process are not considered in traditional data‐driven methods, leading to the poor prediction performance of soft sensors. Meanwhile, numerous nonstationary modelling methods have been proposed for process monitoring, with probabilistic stationary subspace analysis (PSSA) showing significant application potential. Unfortunately, PSSA has not yet been used to develop effective soft sensors for nonstationary processes. Therefore, the PSSA model is extended to the regression form (PSSR), and a corresponding soft sensing model is developed in this paper. Unlike previous approaches, the proposed PSSR can offer a suitable description of nonstationary processes and fully capture the mathematical correlation between input and output variables. Finally, the prediction performance of PSSR is verified through case studies on a numerical example and penicillin fermentation process. The experimental results indicate that PSSR can provide a superior solution for soft sensing modelling of nonstationary industrial processes.