Non-homogeneous Model Research Articles

Potential climate predictability of renewable energy supply and demand for Texas given the ENSO hidden state.

Climate variability influences renewable electricity supply and demand and hence system reliability. Using the hidden states of the sea surface temperature of tropical Pacific Ocean that reflect El Niño-Southern Oscillation (ENSO) dynamics that is objectively identified by a nonhomogeneous hidden Markov model, we provide a first example of the potential predictability of monthly wind and solar energy and heating and cooling energy demand for 1 to 6 months ahead for Texas, United States, a region that has a high penetration of renewable electricity and is susceptible to disruption by climate-driven supply-demand imbalances. We find a statistically significant potential for oversupply or undersupply of energy and anomalous heating/cooling demand depending on the ENSO state and the calendar month. Implications for financial securitization and the potential application of forecasts are discussed.

Nonhomogeneous hidden semi-Markov models for toroidal data

Abstract A nonhomogeneous hidden semi-Markov model is proposed to segment bivariate time series of wind and wave directions according to a finite number of latent regimes and, simultaneously, estimate the influence of time-varying covariates on the process’ survival under each regime. The model is a mixture of toroidal densities, whose parameters depend on the evolution of a semi-Markov chain, which is in turn modulated by time-varying covariates. It includes nonhomogeneous hidden Markov models and hidden semi-Markov models as special cases. Parameter estimates are obtained using an Expectation-Maximization algorithm that relies on an efficient augmentation of the latent process. Fitted on a time series of wind and wave directions recorded in the Adriatic Sea, the model offers a clear-cut description of sea state dynamics in terms of latent regimes and captures the influence of time-varying weather conditions on the duration of such regimes.

Literature Review on Stochastic Modeling of Wet and Dry Spells

With increasing concerns about climate change and its profound implications for water resources, stochastic modeling of wet and dry spells has emerged as a critical domain within hydrology and climatology, providing insight into the temporal patterns of precipitation and drought occurrences. This review of the literature synthesizes recent advances in the modeling of wet and dry spells using stochastic methods, focusing on publications from 2000 to 2024. The review examines various modeling approaches, including Markov chain models, mixed probability models, non-homogeneous models, and time series approaches. Key findings indicate that Markov chain models are effective in simulating the sequential occurrence of wet and dry spells, with higher-order variants addressing issues of overdispersion. Mixed probability models excel at representing heterogeneity and extremes in precipitation data, especially in regions with distinct wet and dry seasons. Non-homogeneous models are valuable for understanding the temporal dynamics and irregularities of dry spells, revealing significant shifts in their frequency and duration over time. These can be complemented by time-series methods to highlight long-term trends and seasonal variations. The review underscores the importance of regional specificity in modeling approaches to accurately capture local climatic and geographical variability. Recommendations for future research include the integration of hybrid models that combine the strengths of various approaches to improve predictive precision, focusing on the impacts of climate change, and conducting cross-regional comparisons to generalize findings and enhance the robustness of the models.

Role of Multistate Models to Predict Patency, Limb Salvage, and Survival: New Concepts to Analyse Data in Peripheral Arterial Disease

In peripheral arterial disease, patency, limb salvage, and survival rates are mostly reported using Kaplan-Meier analyses. When comparing different revascularisation techniques, these methods have limitations in analysing complex patient flows over time. This study aimed to present, illustrate, and discuss new concepts based on multistate models of analysing outcome parameters in peripheral arterial disease. Previously published data from a single centre, randomised controlled trial (RCT) with 218 cases that underwent either vein bypass surgery (bypass group, n = 109) or nitinol stent angioplasty (stent group, n = 109) of long femoropopliteal lesions were re-analysed using non-homogeneous Markov models. A step by step description of the concepts of states, state space, definitions, and illustration of transition probability curves as well as the benefits of multistate models is given. The RCT was registered at ISRCTN.com (ISRCTN18315574). Transition probability curves over time showed similar patterns in the bypass and stent groups. Significant differences in the transition probabilities were found for transitions from primary patency as well as secondary patency to end of patency. The transition probability for patients with preserved primary patency at 24 months who moved to end of patency at 48 months was 19.9% in the stent group vs. 6.4% in the bypass group (p < .001). The proposed method can answer important questions, such as: Did patients after femoropopliteal stenting with preserved primary patency at two years lose their patency more quickly within the following years compared with bypass surgery? and Did stent patients after a re-intervention to maintain patency at one year lose their patency more quickly compared with bypass surgery within the following years? Completely new research questions can now be raised and answered to optimise treatment and follow up strategies; this might lead to better identification of subgroups at higher risk of clinical deterioration following revascularisation procedures.

Finite element mesh transition for local–global modeling of composite structures

This study presents an automatic mesh generation algorithm designed to address computational challenges in simulating small-scale defects within large composite structures. The algorithm seamlessly transitions from a coarse mesh, corresponding to the global structure, to a highly refined mesh in targeted local regions of interest. The transition element number and shape can be adjusted by the specified parameters. Tailored to complement this method for non-homogeneous composite models, which include multiple materials such as cohesive layers representing interlayer properties, a volume fraction calculator is integrated to automatically assign the mixture material property in each transition element. Entire processes are fully automated using a MATLAB script, eliminating the need to open the FEA software interface. The validation studies of the reconstructed two-dimensional models, assembled with the wrinkle-defect model, demonstrate their feasibility. The performance of the model is examined in terms of strain and displacement at the connecting boundaries, load–displacement curve, and interlayer failure prediction. The mesh transition model achieves agreeable results compared to a fully fine mesh model, and a 92% reduction in computational time in stress analysis, showing the efficiency of the mesh transition for local–global modeling of composite structures.

Non-homogeneous model for studying femur bone implants with considering defects

ABSTRACT In this article, the natural frequencies of the femur in the presence and absence of defects have been calculated. For this purpose, two approaches to bone modeling have been considered: one for the homogeneous case and the other for the non-homogeneous case, which more closely reflects the reality of the femur bone. In the next step, in order to identify suitable materials for femur bone implants, two materials AZ31 and CP Ti have been selected, and the natural frequencies of the femur made with these two materials have been calculated and compared with the results of the natural femur. From the obtained results, it can be concluded that although these two materials are attractive for bone implants from other aspects, they are not approved from the point of view of vibrations, although material AZ31 is a little better. It is also observed that the selected defect in the femur has little effect on the natural frequencies.

Properties and Model of Pore-Scale Methane Displacing Water in Hydrate-Bearing Sediments

The flow characteristics of methane and water in sedimentary layers are important factors that affect the beneficial exploitation of marine hydrates. To study the influencing factors of methane drive-off water processes in porous media, we constructed nonhomogeneous geometric models using MATLAB 2020a random distribution functions. We developed a mathematical model of gas–water two-phase flow based on the Navier–Stokes equation. The gas-driven water processes in porous media were described using the level-set method and solved through the finite element method. We investigated the effects of the nonhomogeneous structure of pore media, wettability, and repulsion rate on gas-driven water channeling. The nonhomogeneity of the pore medium is the most critical factor influencing the flow. The size of the throat within the hydrophilic environment determines the level of difficulty of gas-driven water flow. In regions with a high concentration of narrow passages, the formation of extensive air-locked areas is more likely, leading to a decrease in the efficiency of the flow channel. In the gas–water drive process, water saturation changes over time according to a negative exponential function relationship. The more hydrophilic the pore medium, the more difficult the gas-phase drive becomes, and this correlation is particularly noticeable at higher drive rates. The significant pressure differentials caused by the high drive-off velocities lead to quicker methane breakthroughs. Instantaneous flow rates at narrow throats can be up to two orders of magnitude higher than average. Additionally, there is a susceptibility to vortex flow in the area where the throat connects to the orifice. The results of this study can enhance our understanding of gas–water two-phase flow in porous media and help commercialize the exploitation of clean energy in the deep ocean.

Shape optimization study for heat and mass transport of magnetic fluid in a closed domain using a nonhomogeneous dynamic model

The current study deeply investigates nanofluid's heat and mass transport in a staggered-shaped enclosure with wavy walls. A nonhomogeneous mathematical model with thermophoresis and Brownian diffusion is considered in our study. The finite element method is implemented to solve the set of governing equations. Impacts of magnetic field (B0) and its orientation (γ), undulation number (N), amplitude (A) and nanoparticle types are examined for heat and mass flow. Investigations show that the most demoting trend is obtained when the inclination of B0 is either vertical or horizontal. It is concluded that mean Nusselt (Nuavg) and Sherwood number (Shavg) are increasing functions of Ra. When Ra is changed from 103 to 107, the Shavg value is increased up to six times. The impacts of wall shape show that as we increase A, the Nuavg decreases while the maximum can be obtained for the flat boundary. For small N, Shavg is an increasing function. Shape optimization revealed that there exists a critical point between Shavg and N after which it declines. Investigations further show that this point can be changed. Some critical points have been calculated that can be counted as novel results.

Grey modelling and real-time forecasting for the approximate non-homogeneous white exponential law BDS clock bias sequences

Precise forecasting of satellite clock bias is crucial for ensuring service quality and enhancing the efficiency of real-time precise point positioning (PPP).The grey model with many benefits is an excellent choice for predicting real-time clock bias. However, the absolute prediction error of a small number of satellites is very high in actual forecasting process. In order to address this issue, a non-homogeneous white exponential law grey model has been constructed specifically for predicting clock bias sequences with non-homogeneous class ratio approximating constants. Considering that any model is difficult to apply to different kinds of satellite clocks and clock bias signals, an adaptive selection strategy for forecast model is proposed to ensure more excellent prediction accuracy. Afterwards, a prediction scenario based on the observed products of the BeiDou satellite navigation system (BDS) is created to demonstrate the effectiveness of the approach described in this article. The outcomes of the method are then compared with those of a single grey model and the ultra-rapid predicted products. The outcomes demonstrate that this strategy’s prediction accuracy is less than 1 ns/day and that its prediction uncertainty is much decreased, which may improve data selection for real-time applications like real-time kinematics (RTK) and PPP.

The analysis of asthma control using Markov models: MOSAR study (Multicenter Observational Study of Asthma in Rabat-Morocco)

Background This study aimed to analyze the probabilities of transitioning between controlled, uncontrolled, and partially controlled states of asthma patients and investigate the influence of age, smoking, dust allergy, and obesity on these probabilities. Methods This study aimed to analyze the probabilities of transitioning between controlled, uncontrolled, and partially controlled states of asthma patients and investigate the influence of age, smoking, dust allergy, and obesity on these probabilities. Results Results showed that controlled patients were more likely to remain in that state, with approximately 79 out of 100 patients expected to stay in optimal control in the long term. A discrete nonhomogeneous time Markov Model with the stationarity criterion was used to examine the factors affecting patient states and transitions. Patients seen during the spring and summer seasons were more likely to move into a controlled state compared with those seen in the fall and winter seasons. Patients with dust allergies and obesity significantly impacted asthma exacerbation, with overweight patients more likely to transition into a controlled state. The study estimated the transition intensities matrix under certain conditions, assuming the regularity of patients. In the long term, the probability of an asthmatic patient being in a controlled state was approximately 0.8. Conclusion This study provided insights into the probabilities and factors influencing asthma progression in Morocco. Dust allergy and obesity were identified as significant contributors to asthma exacerbation, emphasizing the need for effective management strategies.

A Reliability Assessment Method for Complex Systems Based on Non-Homogeneous Markov Processes.

The Markov method is a common reliability assessment method. It is often used to describe the dynamic characteristics of a system, such as its repairability, fault sequence and multiple degradation states. However, the "curse of dimensionality", which refers to the exponential growth of the system state space with the increase in system complexity, presents a challenge to reliability assessments for complex systems based on the Markov method. In response to this challenge, a novel reliability assessment method for complex systems based on non-homogeneous Markov processes is proposed. This method entails the decomposition of a complex system into multilevel subsystems, each with a relatively small state space, in accordance with the system function. The homogeneous Markov model or the non-homogeneous Markov model is established for each subsystem/system from bottom to top. In order to utilize the outcomes of the lower-level subsystem models as inputs to the upper-level subsystem model, an algorithm is proposed for converting the unavailability curve of a subsystem into its corresponding 2×2 dynamic state transition probability matrix (STPM). The STPM is then employed as an input to the upper-level system's non-homogeneous Markov model. A case study is presented using the reliability assessment of the Reactor Protection System (RPS) based on the proposed method, which is then compared with the models based on the other two contrast methods. This comparison verifies the effectiveness and accuracy of the proposed method.

Correction to “The predictability of daily rainfall during rainy season over East Asia by a Bayesian nonhomogeneous hidden Markov model”

Correction to “The predictability of daily rainfall during rainy season over East Asia by a Bayesian nonhomogeneous hidden Markov model”

A predictor-informed multi-subject bayesian approach for dynamic functional connectivity.

Dynamic functional connectivity investigates how the interactions among brain regions vary over the course of an fMRI experiment. Such transitions between different individual connectivity states can be modulated by changes in underlying physiological mechanisms that drive functional network dynamics, e.g., changes in attention or cognitive effort. In this paper, we develop a multi-subject Bayesian framework where the estimation of dynamic functional networks is informed by time-varying exogenous physiological covariates that are simultaneously recorded in each subject during the fMRI experiment. More specifically, we consider a dynamic Gaussian graphical model approach where a non-homogeneous hidden Markov model is employed to classify the fMRI time series into latent neurological states. We assume the state-transition probabilities to vary over time and across subjects as a function of the underlying covariates, allowing for the estimation of recurrent connectivity patterns and the sharing of networks among the subjects. We further assume sparsity in the network structures via shrinkage priors, and achieve edge selection in the estimated graph structures by introducing a multi-comparison procedure for shrinkage-based inferences with Bayesian false discovery rate control. We evaluate the performances of our method vs alternative approaches on synthetic data. We apply our modeling framework on a resting-state experiment where fMRI data have been collected concurrently with pupillometry measurements, as a proxy of cognitive processing, and assess the heterogeneity of the effects of changes in pupil dilation on the subjects' propensity to change connectivity states. The heterogeneity of state occupancy across subjects provides an understanding of the relationship between increased pupil dilation and transitions toward different cognitive states.

A global space–time Trefftz DG scheme for the time-dependent isotropic elastic wave equations

In this paper we are concerned with Trefftz discretizations of the time-dependent linear elastic wave equation in arbitrary space dimensional domains Ω⊂Rd(d∈N). We propose a Trefftz discontinuous Galerkin method, construct Trefftz basis functions and prove that the corresponding approximate solutions possess optimal-order error estimates with respect to the meshwidth. A space–time domain decomposition preconditioner is introduced for the system generated by the proposed variational formula. Besides, we propose the global Trefftz DG method combined with local DG methods to solve the nonhomogeneous model. The numerical results verify the validity of the theoretical results, and show that the resulting approximate solutions possess high accuracy, and the proposed preconditioner is effective.

Experimental and numerical investigation on the heat and mass transfer performance of tar rich coal in-situ pyrolysis

On ground experiments are conducted firstly to simulate the multi-physics underground pyrolysis of tar rich coal and find out the kinetic parameters of the reaction. And then multi-physics simulation is performed by coupling heat transfer, fluid flow and chemical reactions. Three pyrolysis models are compared and it’s found that the convective flow of heat carrier in coal seam plays an important role in heat transfer although the flow velocity is low. Then the effects of permeability, inlet mass flow rate on heat and mass transfer are investigated for two geometric models with homogeneous and inhomogeneous permeability. It’s found that increasing the permeability is beneficial for fast production of tar. For the homogeneous permeability model, the pyrolysis reaction can be completed in only 140 days when the permeability is 1000 md while for the non-homogeneous permeability model, increasing the inlet mass flow rate can improve the heat and mass transfer performance only in the early stage when the pyrolysis occurs mainly in the fractured zone with higher permeability. The pyrolysis reaction time when the inlet mass flow rate is 0.174 kg/s is 22 days shorter than that of 0.054 kg/s. But in the later stage the inlet mass flow rate has little effect on the reaction rate and brings about a higher pressure drop. The pyrolysis under different well patterns is also compared and the results indicate that four-well heating and six-well heating modes can improve the uniformity and the reaction conversion rate with the same total inlet mass flow rate during the same time. For the six-well heating mode, the pyrolysis reaction can be completed in about 100 days, which is 60 days shorter than the single-well heating mode.

Cost Evaluation for Capacity Planning Based on Patients’ Pathways via Semi-Markov Reward Modelling

In the present paper, we develop a non-homogeneous semi-Markov reward model, deriving expressions for a healthcare system’s expected structure along with the expected costs generated by medical services and patients’ holding times in the states. We provide a novel definition and investigation for states’ availability, which is critical for capacity planning based on service demand in an environment of limited resources. The study is based on patients’ mobility through hospital care, where each patient spends an amount of time in every state of the hospital (emergency room, short-term acute care, hospitalization, surgery room, and intensive care unit). Multiple outcomes, such as discharge or death, can also be taken into account. We envisage a situation where any discharges are immediately replaced by a number of new admissions that carry on the pathways of the patients who exit. By assuming an expanding system, the new idea of states’ inflows is considered due to new patients who create pathways through hospital care, along with internal entrances. The theoretical results are illustrated numerically with simulated hospital data informed by aggregated public data of the Greek public health sector. The framework can be used for both strategic planning and cost evaluation purposes for hospital resources.

Effect of the impeller blade outlet setting angle on the performance of the helical axial-flow multiphase pump

Effect of the impeller blade outlet setting angle on the performance of the helical axial-flow multiphase pump

Couple-stress nanofluid flow comprising gyrotactic microbes subject to convective boundary conditions: Numerical solution

Couple-stress nanofluids have multiple potential applications in numerous industrial and engineering sectors, such as energy production, medical diagnostics, thermal control systems, and the aerospace industry. Couple-stress nanofluids have the ability to improve the heat exchange properties and elevate the performance of nuclear power plants, solar panels, and other renewable energy sources. Therefore, in the current analysis, a non-homogeneous nanofluid model is considered to examine the non-Newtonian Casson nanofluid flow across a prolonging sheet. The flow has been studied under the significance of generalized Fourier’s and Fick’s laws, convective boundary conditions, and the heat source/sink. The modeled equations are simplified into a dimensionless lowest-order system of ordinary differential equations by using similarity transformation. The numerical outcomes are achieved by using the “ND-Solve” approach. It has been noticed that the energy field decreases because of the Prandtl number’s impacts, whereas it increases with the increase in the heat radiation parameter. The couple-stress nanoliquid’s velocity decreases vs increasing values of the magnetic field and mixed convection parameter. The influence of thermal relaxation and couple-stress parameters falls off the energy field. Furthermore, the intensifying effect of Rayleigh number and buoyancy ratio increases the fluid temperature.

On some computational aspects for electromagnetic-thermal dosimetry of mm waves

This work is on the use of a state-of-the-art hybrid boundary element method/finite element method (BEM/FEM) for electromagnetic (EM) dosimetry and the coupled thermal dosimetry model based on the Pennes’ heat transfer equation (PHE) for biological tissue solved by means of FEM. The distribution of the induced electric field obtained in both homogeneous and non-homogeneous human head models using EM model is used as a distributed heat source in the piecewise homogeneous human head thermal dosimetry model. As the penetration depth is inversely proportional to the frequency of incident EM wave, we consider the heating depth in several human head models, to illuminate whether homogeneous models in the EM part of the model are pertinent in the thermal dosimetry part. If confirmed, the results could be found useful in standardisation efforts related to the assessment of human exposure to EM fields in the high frequency range.

Insight into the dynamics of bioconvective Walter’s-B nanofluid flow subjected to Cattaneo–Christov heat flux and activation energy

In order to study the implementation of the generalized magnetohydrodynamic (MHD) bioconvective aspects of the Walter’s-B fluid flows over a convectively heated stretched sheet in the presence of activation energy and numerous boundary conditions, the non-homogeneous nanofluid flow model is used. Here, the nonlinear differential equations illustrating the current nanofluid flow model of non-Newtonian fluid explicitly include the concentration of both motile microbes and solid nanoparticles. Furthermore, the associated temperature, impact of thermal radiation and the Cattaneo–Christov heat flux model are discussed. The similarity transformations are formally displayed to transfer the consequential reduction in the mathematical complexity of the existing physical situation by converting partial differential equations (PDEs) into a nonlinear associated framework of ordinary differential equations (ODEs). Furthermore, the homotopy analysis method (HAM) through the MATLAB tool is used to numerically solve the dimensionless similarity equations. The results are extremely well demonstrated. In this manner, the significant engineering procedures are more accurately and entirely estimated before being reported. The results of the fixed physical factors of velocity, temperature, concentration, and microbe concentration profiles are effectively demonstrated through multiple types of illustrations and comprehensive explanations. The principal assumption is that the greater significance of the bioconvection Lewis and Peclet numbers can lead to a drop in the microbe concentration profile. It is observed that the concentration profile is reduced with the greater value of the concentration relaxation parameter.