Order Modeling Approach Research Articles

A fractal–fractional order modeling approach to understanding stem cell-chemotherapy combinations for cancer

The main objective of this work is to study the mathematical model that combines stem cell therapy and chemotherapy for cancer cells. We study the model using the fractal fractional derivative with the Mittag-Leffler kernel. In the analytical part, we study the existence of the solution and its uniqueness, which was studied based on the fixed point theory. The equilibrium points were also studied and discussed after stem cell therapy, and the approximate solutions for the given model were obtained using the Adam Bashford method, which depends on interpolation with Lagrange polynomials. Finally, the model was simulated using the Mathematica software, and through the figures, we found that the components of the model approach the equilibrium point, which indicates the stability of the model at the equilibrium point. Also, the result of the numerical simulation and graphic for the concentration of cells over time indicate the effects of the therapies on the decay rate of tumor cells and the growth rate of effector cells to modify the cancer patient’s immune system. It is worth noting that we simulated all the model components with different fractional orders, confirming the effect of stem cell therapy and chemotherapy on the cells and the decay of cancer cells.

The relationship between colon cancer and immune system: a fractional order modelling approach

In this paper, a new fractional-order differential equation system is developed for colon cancer to address the detailed analysis. In the model, the interaction between tumor cells, macrophage cells, dendritic cells and CD4+ T helper cells is established using Michaelis-Menten kinetics. In addition, mathematical analyses such as positivity and boundedness are also carried out. Numerical results are obtained to observe the intercellular course of colon cancer and biological interpretations are also included.

A Reduced Order Modeling Approach to Capture Transport within a Three-Electrode System Towards Fast Charge Applications

In support of GM's traction battery efforts, we derive and implement a reduced order modeling method to describe the electrochemical performance of a battery cell through the combination of a modified Newman Pseudo-2-Dimensional model and a three-electrode experimental apparatus. To assess the capability of the method, we compare the modeling results with experimental data for a lithiated graphite electrode and a lithiated nickel rich electrode system. The model is applied to simulate the electrochemical and transport processes within the battery cell to predict the negative electrode potential and positive electrode potential with respect to a lithium iron phosphate reference electrode, as well as the terminal voltage.The manufacture and set up of the three-electrode system, model development and reduction approaches, as well as a discussion of applicability to fast charge considerations to avoid lithium plating at the anode during a charging event will be presented.

Data-driven reduced order surrogate modeling for coronary in-stent restenosis

Background:The intricate process of coronary in-stent restenosis (ISR) involves the interplay between different mediators, including platelet-derived growth factor, transforming growth factor-β, extracellular matrix, smooth muscle cells, endothelial cells, and drug elution from the stent. Modeling such complex multiphysics phenomena demands extensive computational resources and time. Methods:This paper proposes a novel non-intrusive data-driven reduced order modeling approach for the underlying multiphysics time-dependent parametrized problem. In the offline phase, a 3D convolutional autoencoder, comprising an encoder and decoder, is trained to achieve dimensionality reduction. The encoder condenses the full-order solution into a lower-dimensional latent space, while the decoder facilitates the reconstruction of the full solution from the latent space. To deal with the 5D input datasets (3D geometry + time series + multiple output channels), two ingredients are explored. The first approach incorporates time as an additional parameter and applies 3D convolution on individual time steps, encoding a distinct latent variable for each parameter instance within each time step. The second approach reshapes the 3D geometry into a 2D plane along a less interactive axis and stacks all time steps in the third direction for each parameter instance. This rearrangement generates a larger and complete dataset for one parameter instance, resulting in a singular latent variable across the entire discrete time-series. In both approaches, the multiple outputs are considered automatically in the convolutions. Moreover, Gaussian process regression is applied to establish correlations between the latent variable and the input parameter. Results:The constitutive model reveals a significant acceleration in neointimal growth between 30−60 days post percutaneous coronary intervention (PCI). The surrogate models applying both approaches exhibit high accuracy in pointwise error, with the first approach showcasing smaller errors across the entire evaluation period for all outputs. The parameter study on drug dosage against ISR rates provides noteworthy insights of neointimal growth, where the nonlinear dependence of ISR rates on the peak drug flux exhibits intriguing periodic patterns. Applying the trained model, the rate of ISR is effectively evaluated, and the optimal parameter range for drug dosage is identified. Conclusion:The demonstrated non-intrusive reduced order surrogate model proves to be a powerful tool for predicting ISR outcomes. Moreover, the proposed method lays the foundation for real-time simulations and optimization of PCI parameters.

Application of a non-intrusive reduced order modeling approach to magnetohydrodynamics

Magnetohydrodynamics (MHD) investigates the intricate relationship between electromagnetism and fluid dynamics, offering a complete insight into the behavior of conducting fluids under the influence of magnetic fields. This theory plays a pivotal role in the framework of magnetic confinement fusion, where it can be applied to describe both thermonuclear plasmas confined inside the vacuum vessel and operating fluids, such as liquid metals and molten salts, flowing within the blanket of future tokamaks. Currently, the state-of-the-art numerical modeling of MHD scenarios employs a multi-physics framework to examine the interplay between magnetic fields and thermal hydraulics; however, due to the complexity of the involved physics, detailed models are required, resulting in a significant computational burden. In this regard, reduced order modeling (ROM) techniques may represent a promising solution, as they enable approximating complex systems with lower-dimensional models. Indeed, ROM methodologies can significantly reduce the required computational time while maintaining accuracy in capturing the convoluted physics involved in fusion reactors, especially in the contexts of sensitivity analysis, uncertainty quantification, and control. Despite their potential, ROM methods are relatively under-explored within the MHD framework; this study applies ROM techniques to MHD scenarios, focusing on their capabilities and possible limitations. To this aim, the backward-facing step, which is well suited for exploring the effects of different magnetic fields on turbulent dynamics, is adopted as case study. In particular, this work evaluates the potentialities of the ROM approach in enhancing computational efficiency within the MHD domain. Each of the methods evaluated was effective in precisely reconstructing flow dynamics at any given time and across the full range of magnetic field values tested while significantly reducing computational costs compared to full-order simulations. Practically, this study demonstrates the feasibility to create simplified models that accurately represent the magnetohydrodynamic flows of fluids within the blanket.

Nonlinear Reduced Order Modeling of Heated Structures with Temperature-Dependent Properties

This paper focuses on extending coupled structural–thermal reduced order modeling approaches for the prediction of the nonlinear geometric response of heated structures to efficiently account for temperature-dependent structural and thermal properties. Structurally, a linear dependence of the elasticity tensor and thermal expansion coefficient is assumed consistently with typical material behavior. The resulting structural reduced order model (ROM) equations exhibit polynomials of the temperature generalized coordinates, the coefficients of which are readily identified. A different strategy is proposed for conductance and capacitance properties which typically depend nonlinearly on temperature. It relies on splitting the temperature generalized coordinates into a small set of dominant ones having a nonlinear effect on the ROM conductances and capacitances and a much larger set affecting them linearly. The inclusion of uncertainty in the structural ROM is also addressed extending earlier work limited to temperature independent properties. These strategies are exemplified on a representative hypersonic vehicle panel undergoing a full mission profile and with aero-thermal–structural coupling. The ROM predictions are observed to be very close to the full finite element ones for the mean model. Moreover, an uncertainty analysis demonstrates the strong sensitivity of the response to the structural model in the strongly nonlinear regions of the trajectory.

Investigation into hate speech dissemination dynamics in a community using fractional order modeling approach

Investigation into hate speech dissemination dynamics in a community using fractional order modeling approach

Sensitivity analysis of a dense discrete phase model for 3D simulations of a tapered fluidized bed

This study aims to conduct a sensitivity analysis of closure models and modeling parameters for the Dense Discrete Phase Modeling (DDPM) approach in order to investigate the hydrodynamics of a 3D lab-scale Tapered Fluidized Bed (TFB). The closure models and model parameters under investigation include the gas-solid drag force, viscous models, particle-particle interaction models, restitution coefficient, specularity coefficient, and rebound coefficient. The primary objective of this sensitivity analysis is to optimize the numerical model's performance. The numerical results, in terms of axial and lateral Solid Volume Fraction (SVF) profiles obtained from the sensitivity analysis, indicate that the drag force and restitution coefficient significantly influence the hydrodynamics of the TFB. Properly selecting these parameters could result in the improved performance of the numerical model. However, the sensitivity of turbulence models, particle-particle interaction models, specularity coefficient, and rebound coefficient has a lesser impact on the hydrodynamics results. This work concludes with the recommendation of a set of closure models and modeling parameters that offer the most accurate prediction of the hydrodynamics of the TFB.

Pure Hydrogen and Methane Permeation in Carbon-Based Nanoporous Membranes: Adsorption Isotherms and Permeation Experiments.

This paper presents the results of adsorption and permeation experiments of hydrogen and methane at elevated temperatures on a carbon-based nanoporous membrane material provided by Fraunhofer IKTS. The adsorption of pure components was measured between 90 °C and 120°C and pressures up to 45 bar. The Langmuir adsorption isotherm shows the best fit for all data points. Compared to available adsorption isotherms of H2 and CH4 on carbon, the adsorption on the investigated nanoporous carbon structures is significantly lower. Single-component permeation experiments were conducted on membranes at temperatures up to 220 °C. After combining the experimental results with a Maxwell-Stefan surface diffusion model, Maxwell-Stefan surface diffusion coefficients Dis were calculated. The calculated values are in line with an empirical model and thus can be used in future multi-component modeling approaches in order to better analyze and design a membrane system. The published adsorption data fill a gap in the available adsorption data for CH4 and H2.

Hydrogen recombination continua in stellar flares

ABSTRACT An increasing interest in stellar flares stimulated various modelling approaches in order to analyse the observed flare fluxes. A particular interest was focused on photometric data obtained from Kepler and TESS satellites which detected thousands of flares on cool dwarf stars, including extremely energetic superflares. Radiation-hydrodynamical simulations, together with a rather rare broad-band spectroscopy, indicate much larger densities in the superflare chromospheres as compared to solar flares. Formation of hydrogen recombination continua under such different densities ranging from 1013 to 1015 cm−3 or more is governed by physics of optically thin to largely thick plasmas, the continuum optical thickness being within the range of four orders of magnitude. Various authors presented simple approximate methods to analyse the photometric data from Kepler or TESS under such diverse regimes of physical conditions. In this letter, we summarize the general physical approach and compute the hydrogen recombination spectra under the above range of electron densities. We show the theoretical contrast with respect to quiet-star continuum for two characteristic stars of G and dMe type. Based on that we distinguish three regimes of the continuum formation and discuss the applicability of various simple approaches.

Stochastic robustness analysis of wing-aileron flutter suppression systems

In this work a stochastic robustness analysis approach is used to compare the performances of two non-linear flutter suppression systems designed for stabilization of a wing-aileron lifting structure. A reduced order modelling approach based on an alternative aeroelastic beam finite element is presented and used for the flutter suppression systems design, which are driven by a simple adaptive controller and a sliding mode controller, respectively. A heuristic algorithm is used to determine the simple adaptive controller invariant parameters at the design point while a simple parametric study is performed to tune the sliding mode controller. The performances of each closed loop system are evaluated taking into account mass, stiffnesses, and aerodynamics uncertainties of the aeroelastic plant also considering the presence of discrete gust disturbances.

Efficient flow reconstruction between dual tidal turbines: Large eddy simulation and reduced order modeling approach

The present investigation seeks to analyze the fluid dynamics associated with tidal turbines in the context of the EU (European Union) project NEMMO (The Next Evolution in Materials and Models for Ocean Energy, nemmo.eu). A pair of counter-rotating tidal turbines is employed for propelling a ship. The separation between these turbines is approximately one rotor diameter. Consequently, the power output of the downstream turbine is adversely affected by the heightened turbulence generated by the rotation of the upstream turbine. This power imbalance poses a substantial challenge in terms of power management. Therefore, this study concentrates on conducting a flow analysis of these counter-rotating turbines. Large Eddy Simulation (LES) of a dual tidal turbine rotating in opposite directions is conducted using the actuator line method. The flow is scrutinized by employing proper orthogonal decomposition (POD). The flow field is then reconstructed using the reduced order method. It is observed that a reduced number of modes is sufficient to reconstruct the flow between the tidal turbines. However, more modes are necessary to replicate the flow beyond the downstream turbine. The utilization of fewer modes proves effective in comprehending the flow at the inlet of the downstream turbine, ultimately resulting in reduced computational power requirements through faster matrix operations and lower memory usage for the POD decomposition.

Reliability Prediction of Radiation Induced Failures in Semiconductor Packages

The growth and usage of semiconductor components has risen greatly due to evolution of applications in industries such as aerospace, defense, and automotive, in both the commercial and government sectors. Among the different types of components that make their way into such applications, digital logic and memory-based devices are of prime importance due to the ever-demanding need to store and compute vast amounts of data. This brings to the forefront the reliability of such components, especially in demanding applications in aerospace and defense where components are exposed to extremely harsh environments where high performance is critical. This is where we find that reliability is largely dependent on the susceptibility of semiconductor components to radiation induced effects - total ionizing dose (TID) and single event effects (SEE). Optimization in design, process, and packaging could make microelectronics more reliable to the radiation effects. Packaging material and thickness affect the incident flux of radiation on microelectronics and can help mitigate both dose and SEE effects in electronics. Additionally, packaging materials should not generate a high flux of secondary particles when exposed to environmental radiation (an example is alpha emissions from impurities in package mold compound or underfill). In this paper, the behavior of semiconductors at the component level due to radiation effects is evaluated. A reduced order model approach is presented where the analysis is performed at the functional block level then aggregated into component. The behavioral model can be used to predict the behavior across different operating, design, and process conditions.

Estimation of the Born data in inverse scattering of layered media

The first term in the Born series, as we call the Born data, is linear with the scatterers. Here we present a scheme to map the total field data to the Born data in layered media using only the single-input single-output (SISO) setup. This nonlinear mapping is based on the reduced order model (ROM) approach, which constructs ROMs of the original wave operator. Normally, the construction of ROMs requires multi-input multi-output data. By introducing fictitious sensors, we estimate the Born data with SISO data in layered media. We give a simple way of using the time-domain Green’s function to estimate the received data for other fictitious sensors without calculating the complicated Sommerfeld integral. The resulting Born data contains only the single-scattering component, which can be helpful for many imaging applications. A numerical example is given incorporating the direct imaging back-propagation method. It validates the linearity of the Born data by providing an artifact-free image without the optimization process.

High-Fidelity Reduced Order Modeling Approach for Medium Voltage Drives and Artificial Intelligence Capable Systems

High-Fidelity Reduced Order Modeling Approach for Medium Voltage Drives and Artificial Intelligence Capable Systems

Insight into the treatment strategy on pneumonia transmission with asymptotic carrier stage using fractional order modeling approach

Pneumonia remains a significant global health concern, claiming millions of lives annually. This study introduces a novel approach by developing and analyzing a Caputo fractional order pneumonia infection model that incorporates pneumonia asymptomatic carriers. Through a qualitative lens, we establish the existence and uniqueness of model solutions by applying the well-known Picard–Lindelöf criteria. Employing a next-generation approach, we compute the model's basic reproduction number, determine equilibrium points, and probe their stabilities. The main objective of this study is to investigate the transmission dynamics of pneumonia infection with a focus on asymptomatic carriers using fractional order modeling. Our findings reveal innovative outcomes as we showcase numerical simulations, providing a practical verification of the qualitative results. Notably, we explore the fractional order model solutions in-depth, examining the influence of specific model parameters and fractional orders on the dynamics of pneumonia disease transmission. The significant contributions of this study lie in advancing the theoretical foundation of infectious disease modeling, particularly in the context of pneumonia. Through rigorous analysis and numerical simulations, we provide valuable insights into the behavior of the proposed fractional order model. These findings hold practical implications for understanding and managing pneumonia transmission in real-world scenarios. Our study serves as a vital resource for researchers, policymakers, and healthcare practitioners involved in combating and preventing the spread of pneumonia, ultimately contributing to global efforts in public health.

Strong column-weak beam relationship of 3D steel joints with tubular columns: Assessment, Validation and Design proposal

The study of moment connections in steel structures subjected to cyclic loads has been extensively studied, providing a great number of requirements, including the strong column-weak beam relationship, to guarantee a satisfactory cyclic performance. However, investigations on the cyclic performance of moment connections considering the bidirectional and axial load effects simultaneously with tubular columns are limited. This study aims to assess and validate the strong column-weak beam relationship of 3D steel moment connections using reduced order models. The simplified model (reduced order model) approach was employed to extend the range of beam and column elements sizes and reduce the experimental and computational costs. These models were calibrated from full-scale experimental studies. A great number of configurations with different beam and column sizes without loss of reliability and structural representativeness of the studied phenomenon were studied. A total of 13640 simplified models were developed. Results show a cyclic behavior controlled by the strong column-weak beam relationship to modify the joint's failure mechanism. The increasing of strong column-weak beam relationship and the biaxial effect caused degradation of the strength and stiffness as well as in dissipated energy. An optimal strong column-weak beam relationship was obtained for all joint configurations analyzed. Finally, a robust design procedure is proposed, ensuring the cyclic behavior of end-plate moment connection with built-up box column including biaxial effect and axial load. Therefore, the use of this type of moment connection can be used in special and intermediate moment frames designed according to Seismic provisions.

Proximity or opportunity? Spatial and market determinants of private individuals’ buy-to-let investments

This paper contributes to the debate on the liquidity of real estate investment in the context of financialisation. Using microdata built from tax registers, we analyse the geography of rental housing purchases by private individuals from three French cities. We develop a modelling approach in order to better understand the respective roles of space and market characteristics in determining buy-to-let investment flows. Considering the distribution of the data and our objective of integrating both intra- and intercity housing investments in a single model, we use an adaptive zoning approach. This approach allows high spatial resolution where interactions are strong to be kept and the aggregation of more distant, less populated areas. We demonstrate that geographical proximity is highly determinant in explaining flows of buy-to-let investments from private individuals. We also uncover striking facts related to the geography of rental investments, such as the convergence of investments from rich suburbs toward the centre of agglomerations and preferential flows from the Paris region to southern and coastal cities. Finally, we find that investors tend to buy in upmarket areas and in places that are more expensive than their market of residence. Our results indicate that geographical proximity and safety of investments are key factors in housing wealth accumulation by private individuals.

Reduced order modeling of structural problems with damage and plasticity

AbstractModel order reduction (MOR) techniques are used across the engineering sciences to reduce the computational complexity of high‐fidelity simulations. MOR methods reduce the computation time by representing the problem using a lower number of degrees of freedom (DOF). The use of reduced order models (ROM) in the analysis of structural problems with damage and plasticity has the potential to significantly reduce computational time and increase efficiency. Of course, the approximation of a problem in a lower dimensional space introduces an approximation error that needs to be kept small enough so that the results of the ROM maintain their validity. One well‐known reduced order modeling approach is the proper orthogonal decomposition (POD). POD is used to extract the dominant modes of the structure, which are then used to solve a problem in the smaller dimensional subspace. To overcome the limitations of the POD regarding nonlinear problems, the discrete empirical interpolation method (DEIM) is employed. An exemplary uncertainty quantification application is used to investigate the methodology. The investigation shows that the POD‐based DEIM can significantly reduce the computational effort of highly nonlinear structural simulations incorporating damage while maintaining a high approximation accuracy.

Comparison of the ozone formation mechanisms and VOCs apportionment in different ozone pollution episodes in urban Beijing in 2019 and 2020: Insights for ozone pollution control strategies

Ground-level ozone (O3) pollution has been a tough issue in urban areas of China in the past decade. Clarifying the formation mechanisms of O3 and the sources of its precursors is necessary for the effective prevention of O3 pollution. In this study, a comparative analysis of O3 formation mechanisms and VOCs apportionment for five O3 pollution episodes was carried out at two urban sites (CRAES and CGZ) in Beijing in 2019 and 2020 by applying an observation-based modeling approach in order to obtain insights into O3 pollution control strategies. Results indicated that O3 pollution levels were generally more severe in 2019 than in 2020 during the observation periods. O3 formation at the two sites was both VOCs-limited on O3 polluted days and non-O3 polluted days. Stronger atmospheric oxidation capacity and ROx radicals cycling processes were found on O3 polluted days which could accelerate the local production of O3, and local photochemical production dominated the observed O3 concentrations at the two sites even on non-O3 polluted days. Emission reduction of VOCs should be a priority for mitigating O3 pollution, and alkenes and biogenic VOCs was the priority species at the CRAES and CGZ sites, respectively. Additionally, the reduction of oxygenated VOCs should also be important for the ozone control. Gasoline exhaust at the CRAES site, and solvent utilization and fuel evaporation at the CGZ site were main anthropogenic sources of VOCs. Therefore, local control measures should be further strengthened and differentiated control strategies of VOCs in the aspects of area, time, sources and species should be adopted in urban Beijing in the future. Overall, the findings of this study could provide a scientific understanding of the causes of O3 pollution and significant guidelines for formulating O3 control strategies from the perspective of different ozone pollution episodes in urban Beijing.