Difference Method Research Articles

(Battery Student Slam 8 Award Winner) A Comparison of Different Convergence Criteria to Improve the Performance of a P2D Modelling Algorithm of a Lithium-Ion Battery

Lithium-ion batteries (LiBs) are used as the storage for electric vehicles, grid energy and consumer electronics mainly due to the LiBs’ high energy density, long cycle life, and reliable manufacturing. Effective performance and diagnostic management of LiBs is important and is implemented via Battery Management Systems (BMS) [1]. A BMS should also maximise the safety and lifetime of battery packs and therefore, needs to estimate the internal battery states including the state of charge (SoC), state of health (SoH), state of power (SoP), state of function (SoF), and state of safety (SoS) [2]. Accurate estimation of the battery SoX can be realized with the help of a battery model; an algorithm representing the electrochemical, mechanical, electrical, and thermal behaviour of the LiB cells.Cell-level battery models typically fall into three categories: (i) Empirical Models, (ii) Equivalent Circuit Models (ECM) and (iii) Physics-based Electrochemical Models (EM). Electrochemical Models represent the internal cell processes within a cell based on its governing fundamental physical and electrochemical equations [3].The Partial two-dimensional (P2D) model is considered a high-fidelity Electrochemical Model (EM), which in its most basic form, captures three major physio-chemical processes in a cell: mass transfer via reduction/oxidisation (redox) reactions, diffusion of neutral lithium in the electrodes and diffusion of lithium-ions in the electrolyte. The P2D model captures the different physio-chemical phenomena using a set of coupled Partial Differential Algebraic Equations (PDAEs) [4].Despite accuracy, P2D models are complex mathematical models with typically no analytical solution [5]. Therefore, to implement the full-order version of the P2D model, numerical-iterative solver algorithms are required. Multiple works have looked at different methods of optimizing and solving the P2D model. These methods include using different discretisation schemes, such as the finite difference method and the finite volume method, using different iterative solvers and different convergence criteria [5]. However, the different works on iterative solvers we have reviewed to date [5], haven’t investigated the effects of the different criteria on improving the performance of P2D iterative solvers.Hence, in this work, we aim to build on our previous work [6], where we proposed an algorithm to implement the P2D model using the finite volume spatial discretisation method (FVM) and Euler time integration method. We then analyse how the role of (i) the choice of convergence criteria, (ii) the choice of initial guess and (iii) the choice of root-finding method used to converge to the convergence criteria, can be varied to improve the performance of the iterative solver.Therefore, the contributions of this work can be summarised as: An algorithm that implements the isothermal P2D model of a LiB using the Finite Volume Method and Euler integration methods.An analysis of the changes in algorithm performance when the following performance factors are varied; (i) The convergence criteria, (ii) the choice of initial guess and (iii) the choice of root-finding method.An optimal configuration of performance criteria that solves the isothermal-P2D model for a 1C discharge simulation, with an average speed of 3 seconds and a root mean square error of less than 1% when compared to the commercial solver COMSOL. [1] C. P. Grey and D. S. Hall, “Prospects for lithium-ion batteries and beyond—a 2030 vision,” Nature Communications 2020 11:1, vol. 11, no. 1, pp. 1–4, Dec. 2020, doi: 10.1038/s41467-020-19991-4.[2] L. Lu, X. Han, J. Li, J. Hua, and M. Ouyang, “A review on the key issues for lithium-ion battery management in electric vehicles,” Journal of Power Sources, vol. 226. pp. 272–288, Mar. 15, 2013. doi: 10.1016/j.jpowsour.2012.10.060.[3] S. Abada, G. Marlair, A. Lecocq, M. Petit, V. Sauvant-Moynot, and F. Huet, “Safety focused modeling of lithium-ion batteries: A review,” J Power Sources, vol. 306, pp. 178–192, Feb. 2016, doi: 10.1016/J.JPOWSOUR.2015.11.100.[4] M. Doyle, T. F. Fuller, and J. Newman, “Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell,” J Electrochem Soc, vol. 140, no. 6, pp. 1526–1533, Jun. 1993, doi: 10.1149/1.2221597/XML.[5] A. M. Ramos, “On the well-posedness of a mathematical model for Lithium-ion batteries,” Appl Math Model, vol. 40, no. 1, pp. 115–125, May 2015, doi: 10.48550/arxiv.1506.00605.[6] T. Wickramanayake, M. Javadipour, and K. Mehran, “A Novel Root-Finding Algorithm to Solve the Pseudo-2D Model of a Lithium-ion Battery,” 2023 IEEE International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles and International Transportation Electrification Conference, ESARS-ITEC 2023, 2023, doi: 10.1109/ESARS-ITEC57127.2023.10114840.

Green micellar UPLC and complementary eco-friendly spectroscopic techniques for simultaneous analysis of anti-COVID drugs: a comprehensive evaluation of greenness, blueness, and whiteness

The development of sustainable analytical methodologies that minimize hazards, waste generation, and energy consumption has become crucial. This study introduces pioneering green‒blue-white approaches for the simultaneous quantification of montelukast sodium (MLK) and fexofenadine hydrochloride (FEX) in combination formulations. The first approach employs an ultra-performance liquid chromatographic method (UPLC) with a green micellar mobile phase of 0.02 M sodium dodecyl sulfate and 10% 1-pentanol (65:35%). The method demonstrated excellent resolution, peak symmetry, and a short analysis time, with retention times of 3.53 min for MLK and 1.67 min for FEX. The MLK and FEX linearities were 1–260 and 1.2–312 μg/mL, respectively. The second approach involves complementary built-in spectroscopic techniques (second derivative, third derivative, and ratio difference methods) using water as a solvent, providing a green, simple, low-cost alternative in laboratories where expensive chromatographic devices may not be readily available. The MLK and FEX linearities were 3–50 and 3–60 μg/mL, respectively. All methods were comprehensively validated and showed satisfactory results. The proposed methods demonstrated excellent linearity (r2 ≥ 0.9990), accuracy (recovery 98.5–101.5%), and precision (RSD ≤ 2%) across wide concentration ranges. A multifaceted evaluation was conducted to assess the environmental sustainability, real-world applicability, and economic viability of the proposed methods in comparison with previously reported techniques. This comprehensive assessment leveraged several state-of-the-art tools, including NEMI, ComplexGAPI, AGREE, ESA, BAGI, and RGB12. The suggested approaches exhibited favorable quadrant profiles in the NEMI and ComplexGAPI assessments, coupled with higher AGREE scores (0.90, 0.86) than reported (0.62, 0.74, 0.75, 0.69, 0.74, 0.74, and 0.75), in addition to higher ESA score (88, 92) than reported (75, 84, 85, 79, 82, 82, and 83), collectively affirming their environmentally friendly credentials. Moreover, we embraced the innovative notions of 'blueness' and 'whiteness' assessment by harnessing the recently formulated BAGI and RGB12 algorithms. The higher BAGI score (90, 82.5) than reported (72.5, 70, 70, 67.5, 67.5, 67.5, and 72.5), confirmed the excellent real-world applicability of the proposed methods, while the notable RGB12 indices (89.8, 88.1) than reported (67.8, 72.8, 71.5, 67.1, 73.7, 70.3, and 73.2), validated their cost-effectiveness and overall sustainability, contributing to an eco-friendly future for quality control processes.

A Comparative Study of Numerical Methods for Lithium-Ion Battery Electrochemical Modeling

Lithium-ion battery (LIB) with high specific energy density and long cycle life is one widely used energy storage technology. In order to ensure longevity and safety of the battery system, a battery management system (BMS) that relies on battery model is required. With the development of BMS technique, more attention has been given to electrochemical models that provide insights into the battery internal states. In general, battery electrochemical models consist of partial differential equations (PDEs) describing the thermodynamic and electrochemical process inside the cell, and those PDEs can only be solved numerically due to their complexity.Existing battery simulation software utilize numerical methods such as finite difference method (FDM), finite volume method (FVM), and finite element method (FEM) to solve PDEs in battery models. However, there are little discussions for the selection of a specific numerical methods. In our recent study [1], we compare two spatial discretization methods commonly used to numerically solve the governing PDEs of LIB electrochemical models, namely FDM and FVM, in terms of model accuracy and mass conservation guarantee. First, we provide the mathematical details of the spatial discretization process for both FDM and FVM to solve the battery single particle model (SPM), this result has not been shown in any publication before. Second, we propose a new Hermite extrapolation based FVM scheme leading to higher accuracy when compared to the normally used linear extrapolation based FVM scheme. Then, SPM parameters are identified using experimental data, and a comprehensive parameter sensitivity analysis is conducted under different current input profiles to study parameter identifiability. Finally, model accuracy and mass conservation analysis of the FDM and FVM schemes are presented. Our study shows that the FVM scheme with Hermite extrapolation leads to accurate and robust control-oriented battery model while guaranteeing mass conservation and high accuracy. Also, the proposed new FVM scheme can be extended to solve other battery models, such as SPM model with electrolyte and Doyle-Fuller-Newman model. Moreover, we provide findings of mass conservation analysis for FDM and FVM schemes, which we hope can facilitate BMS model selection.

The political role of middle class in China: disentangling democratic attitudes and values

ABSTRACT China's middle class is found to differ in their democratic orientations – compared to the middle class in the non-state sector, a state sector middle class is believed to show lower support for democracy. Based on data from the Asian Barometer Survey 2019, we contend that democratic attitudes and democratic values are distinct dispositions. Despite displaying weaker attitudes towards the standard Western democratic institutions - such as multiparty elections and free media - the state sector middle class exhibits equally strong democratic values as the non-state sector middle class. On the other hand, compared to other social classes, while the non-state sector middle class shows stronger democratic values, it nonetheless holds a similar level of democratic attitudes. A most similar systems design and a joint method of agreement and difference reveal how values and attitudes are shaped respectively by early existential security and the structural constraints/stimuli one faces.

Two-phase flow simulation algorithm for numerical estimation of relative phase permeability curves of porous materials

Abstract The paper presents an algorithm for three-dimensional modelling of two-phase flows on the scale of pore size order for numerical evaluation of relative phase permeability curves of porous materials. Such an evaluation is performed based on the results of numerical simulation of primary drainage with subsequent waterflooding. In this case, models of porous materials based on three-dimensional tomographic images of rocks are used. The simulation of the flow considers the Stokes equation and the Cahn–Hilliard equation for modelling phase transfer, which allows us to determine phases using the concentration function. The combination of the phase field method and finite difference method makes it possible to correctly take into account the contact angle and stably calculate surface tension forces in domains with complex topology.

Thermo-pressure coupling model for gas hydrate depressurization exploitation in South China Sea

The sediment type in the “Shenhu” sea area of the South China Sea is mud sediment, with poor reservoir physical conditions, and the seabed is loose with a small pressure window. These conditions pose heightened safety challenges for the extraction of hydrates in this region. This study develops a multiphase flow model that accounts for the endothermic decomposition of hydrates and employs the finite difference method for its solution. Utilizing this model, the multiphase flow characteristics during depressurization extraction at a specific well in the “Shenhu” area are investigated. Building on this, the study analyses the impact of varying pump rates and geothermal gradients on multiphase flow properties, hydrate yield, and engineering safety. Based on the analytical findings, recommendations are proposed to balance hydrate production with engineering safety, effectively mitigating potential engineering accidents during depressurization extraction. The outcomes of this research offer technical guidance for the commercial exploitation of hydrates in the “Shenhu” area of the South China Sea, laying a foundation for future related studies.

Numerical Investigation of Bedding Rock Slope Potential Failure Modes and Triggering Factors: A Case Study of a Bridge Anchorage Excavated Foundation Pit Slope

The analysis of slope failure modes is essential for understanding slope stability. This study investigated the failure modes and triggering factors of a rock slope using the limit equilibrium method, finite differences method, and exploratory factor analysis. First, the limit equilibrium method was used to identify potential sliding surfaces. Then, the finite differences method was employed to study deformation and failure features in a slope. Stability factors were calculated considering specific conditions such as rainfall, prestressing loss, and earthquakes using the strength reduction method. Finally, exploratory factor analysis was utilized to identify the triggering factors of each failure mode. The results revealed that failure modes were categorized into two types based on the positions of the sliding surface. The main triggering factors for Failure Mode 1 were rainfall and prestress loss, while for Failure Mode 2 they were earthquake loading and prestress loss. This study offers a comprehensive exploration of potential failure modes and their triggering factors from mechanical and statistical perspectives, enriching our understanding of potential failure modes in rock slopes.

Multiscale-mechanical analysis on self-healing microcapsules under asphalt pavement

To investigate the stress state of self-healing microcapsules in asphalt pavement during their operational phase, this study utilizes the finite difference method to establish a macroscopic structural model of asphalt pavement and a multi-scale model of representative volume elements (RVE)containing self-healing microcapsules. It systematically analyzes the effects of microcapsule content, capsule wall modulus, and wall thickness on the its mechanical performance under different asphalt pavement. Experimental findings indicate that an increase in microcapsule content initially increases and subsequently decreases the maximum principal stress and shear stress of the capsule wall, suggesting an optimal content range for achieving optimal mechanical response. Moreover, an increase in capsule wall modulus results in increased maximum principal stress, minimum principal stress, and maximum shear stress borne by the capsule wall, underscoring the importance of capsule wall modulus for the mechanical properties of microcapsules. The impact of increasing wall thickness on minimum principal stress shows an initial increase followed by a decrease, emphasizing the critical role of appropriate wall thickness selection in facilitating prompt response of microcapsules to pavement cracks. This research provides essential theoretical foundations for the design and application of microcapsules, thereby enhancing the self-healing capability of asphalt pavement.

3D modelling of ground magnetic-source airborne TEM data for anisotropic media based on the rational Krylov method

With the rapid development of the transient electromagnetic method (TEM), the numerical simulations of three-dimensional anisotropic media have garnered attention. This study used the rational Krylov method to realise the three-dimensional modelling of the ground magnetic-source airborne transient electromagnetic data for arbitrary anisotropic media. First, based on Maxwell's equations, a time-domain electromagnetic equation was derived for anisotropic media. The finite difference method was employed to discretise the equation, and the electromagnetic field was then expressed as the product of an exponential matrix and a vector related to the source. Subsequently, the rational Arnoldi algorithm was adopted to construct the rational Krylov subspace orthogonal basis vectors, and the electromagnetic fields at different times were obtained based on a model reduction strategy. The accuracy of the proposed algorithm was verified through the comparisons of its results with those of other software packages. We calculated the response for different anisotropic parameters of the typical three-dimensional anisotropic models, and analysed the influence of the anisotropic media on the ground magnetic-source airborne transient electromagnetic data. The proposed three-dimensional forward TEM algorithm provides important technical support for identifying the anisotropic geological bodies and lays the foundation for further inversion research.

Heat Transfer and Flow of Natural Convection Past a Semi-Infinite Vertical Plate

This manuscript presents a numerical investigation of the flow of an electrically conducting, incompressible, viscous fluid past a heated vertical channel with thermal radiation influence. The study uses the Rosseland approximation to describe the radiative heat flux and employs Crank Nicolson's implicit finite difference method utilizing the MATLAB programming tool for solving the non-dimensional system of equations. The results demonstrate that an increase in the thermal radiation parameter leads to a decrease in both the velocity and temperature of the fluid. The main findings of the study highlight the impact of thermal radiation on natural convection and heat transfer processes. This research is significant as it contributes to the understanding of convective heat transfer phenomena and provides valuable insights for applications in science and technology.

Modeling a poiseuille flow through a rectangular pipe in a floor slab (PSD)

This study was devoted to the modeling of a laminar fluid flow in a pipe of the rectangular section located in a floor slab. This theme was raised because of its relevance in the large business sector as well as in the areas of energy saving and storage at the residential scale. The equations of motion quantity and heat transport are the classical equations of forced convection. However, to describe the movement amount within the heating slab pipeline, Prandtl simplified model was most appropriate. In addition, this model retains the most important terms for a laminar regime flow. In addition, the modeling of fluid flow conservation in the pipeline was taken into account in the equation system. To achieve the above-mentioned objective, a numerical resolution was made for the system resolution of the Navier-Stokes equations that govern this fluid flow. These equations were discretized by an implicit finite difference method. The system of algebraic equations as well as obtained was solved by the algorithm of Gauss and the algorithm of Thomas. The results obtained such as: the evolution of the fluid velocity profile within the slab according to pipeline to the Reynolds number variation, the fluid temperature have clearly demonstrated the Poiseuille effect on fluid flow. Moreover, the stabilization of the Gauss algorithm and the Thomas algorithm in this numerical modeling was well verified against the tricks that were taken into consideration. The result of this study was that Thomas algorithm and Gauss algorithm are the best in this type of numerical modeling.

Squeezing hydromagnetic nanofluid flow between two parallel plates with joule heating effects and induced magnetic field

Over the years, cooling high energy devices has become a major challenge to most industries. Thus, squeezing hydromagnetic nanofluid flow between two parallel plates has garnered alot of attention. In the present study, an unsteady, incompressible, hydromagnetic gold and water nanofluid flow squeezed between two parallel plates with Joule heating and a magnetic field that is induced is considered. The model considers the impacts of Joule heating,Viscous dissipation and induced magnetic field. In contrast with other studies which may have focussed on only one or two of these aspects this comprehensive approach provides a more accurate depiction of the flow pattern. Employing the finite difference method, the flow's non-linear differential equations are numerically solved and then implemented in MATLAB. The effect of changing various parameters on flow variables such as velocity, magnetic induction and thermal profiles are determined and the results obtained are presented graphically. Increasing magnetic parameter and Prandtl magnetic number caused a decline in temperature,velocity and magnetic induction profiles. Further, increasing the Eckert number and Joule heating parameter lead to an increase in temperature profiles. This findings have a direct impact on high-energy cooling devices which frequently experience heat dissipation. Additionally, engineers can ensure optimal performance and the longevity of plate heat exchangers in industries.

Unlocking the benefits of montessori-based reading activities in nursing home: A multiple baseline study on groups of individuals with severe dementia.

Group activities are commonly offered to residents of nursing homes, and increasingly with a person-centred care approach. The aim of this study is to compare the impacts of a Montessori-based reading activity with a more traditional reading activity. A multiple baseline design was used, with 3 groups of 5 older adults with moderate to severe dementia. All sessions were videorecorded and analysed by independent judges, blinded to our hypotheses and conditions. Impacts of the type of activity (storytelling or Montessori-based reading) on verbal interactions, engagement level, affect and behavioural aspects were estimated with both visual analyses and statistical analyses using the between-case standardised mean differences method. Significant differences were found in favour of the Montessori-based activities with regard to the number of verbal interactions, constructive and passive engagement and positive affect expressed, with moderate to large effect size (from 0.46 to 1.66). The Montessori-based reading group activity really seems to be preferable to a more traditional storytelling activity, with multiple benefits for residents. Depending on the preserved abilities and interests of the participants, it can also be aimed at people with severe dementia.

Numerical Analysis of Low-Enthalpy Deep Geothermal Energy Extraction Using a Novel Gravity Heat Pipe Design

Geothermal energy, derived from the Earth’s internal heat, can be harnessed due to the geothermal gradient between the Earth’s interior and its surface. This heat, sustained by radiogenic decay, varies across regions, and is highest near volcanic areas. In 2020, 108 countries utilised geothermal energy, with an installed capacity of 15,950 MWe for electricity and 107,727 MWt for direct use in 2019. Low-enthalpy sources require binary systems for power production. Open-loop systems face issues like scaling, difficult water treatment, and potential seismicity, while closed-loop systems, using abandoned petroleum or gas wells, reduce costs and environmental impacts greatly. The novel geothermal gravity heat pipe (GGHP) design eliminates parasitic power consumption by using hydrostatic pressure for fluid circulation. Implemented in an abandoned well in north-east (NE) Slovenia, the GGHP uses a numerical finite difference method to model heat flow. The system vaporises the working fluid in the borehole, condenses it at the surface, and uses gravitational flow for circulation, maintaining efficient heat extraction. The model predicts that continuous maximum capacity extraction depletes usable heat rapidly. Future work will explore sustainable heat extraction and potential discontinuous operation for improved efficiency.

An Inverse Matrix Eigenvalue Problem for Constructing a Vibrating Rod

Abstract The free longitudinal vibrations of a rod are described by a differential equation of the form ( P ( x ) y ′ ) ′ + λ P ( x ) y ( x ) = 0 {(P(x)y\prime)^{\prime}+\lambda P(x)y(x)=0} , where P ⁢ ( x ) {P(x)} is the cross section area at point x and λ is an eigenvalue parameter. In this paper, first we discretize this differential equation by using the finite difference method to obtain a matrix eigenvalue problem of the form 𝐀 ⁢ Y = Λ ⁢ 𝐁 ⁢ Y {\mathbf{A}Y=\Lambda\mathbf{B}Y} , where 𝐀 {\mathbf{A}} and 𝐁 {\mathbf{B}} are Jacobi and diagonal matrices dependent to cross section P ⁢ ( x ) {P(x)} , respectively. Then we estimate the eigenvalues of the rod equation by correcting the eigenvalues of the resulting matrix eigenvalue problem. We give a method based on a correction idea to construct the cross section P ⁢ ( x ) {P(x)} by solving an inverse matrix eigenvalue problem. We give some numerical examples to illustrate the efficiency of the proposed method. The results show that the convergence order of the method is O ⁢ ( h 2 ) {O(h^{2})} .

Numerical simulation for an initial-boundary value problem of time-fractional Klein-Gordon equations

This paper mainly presents numerical solutions to an initial-boundary value problem of the time-fractional Klein-Gordon equations. We developed a numerical scheme with the help of the finite difference methods and the predictor-corrector methods to find numerical solutions of the considered problems. The proposed scheme is based on discretizing the considered problems with respect to spatial and temporal domains. Numerical results are derived for some illustrative problems, and the outputs are compared with the exact solution in the integer order case. The solution behavior and 3D graphics of the discussed problems are demonstrated using the proposed scheme. Finally, the proposed scheme, which does not require solving large systems of linear equations, can be extended and modified to handle other classes of time-fractional PDEs.

Direct position determination of moving targets based on DOA

AbstractCompared with the traditional two‐step localization methods, the direct position determination (DPD) method is more robust at low signal‐to‐noise ratio. However, to guarantee the optimal location result, the computational complexity of DPD with grid search is too high, especially for moving targets. Therefore, a new DPD method is proposed for moving targets with low computational complexity. First, using a proposed cost function, the position information is obtained from the received array signals directly, which enhances the accuracy of localization. Second, utilizing the method of successional difference the velocity is extracted, which avoid the multi‐dimensional grid search and reduces the computational complexity. Simulation results demonstrate that the proposed method reduces the computational complexity greatly and outperforms the conventional methods.

The extraction method of the time difference in the output angle of MLS

The extraction method of the time difference in the output angle of MLS

China's Low-carbon city policy and manufacturing firms' servitization: Do environmental regulations matterʔ

Manufacturing servitization is an effective way to improve both environmental performance and economic benefits in developing countries. In this paper, we first propose the firm-level manufacturing servitization (FMS) measurement method. Then, based on Chinese firm-level data for 2000–2015, we take low-carbon city pilot (LCCP) policy implementation as a quasi-natural experiment to investigate the effect of low-carbon city governance on FMS. The propensity score matching-difference-in-differences (PSM-DID) model results indicate that the construction of LCCP policy could significantly improve FMS. In addition, we explain the promoting effect of low-carbon city governance on FMS by enhancing innovation intensity and promoting pollution factor substitution. Specifically, low-carbon city governance increases the innovation intensity of enterprises and promotes service factors as substitutes for other pollution production factors, changing the service factor input structure. Furthermore, by dynamically decomposing aggregate FMS growth, we found that LCCP policy generates a positive within-firm effect for surviving enterprises. However, the role of the resource reallocation effect has not been fully explored. Based on the findings, this study offers more theoretical backing and empirical substantiation for developing countries' pursuit of simultaneously achieving sustainability and economic growth under environmental regulations.

Analyzing the exothermic reactions of [formula omitted] nanoparticles with the Dufour effect and the influence of the heat generation and permeability past a porous moving surface

The heat and mass concept is analyzed through the properties of the Dufour number, chemical reactions, and the heat generation parameters on MHD incompressible nanofluids flow. The MATLAB software with the finite difference method (FDM) was employed to find and graphically present the system’s numerical solutions. This study finds an increased Dufour number enhancing the flow speed and hotness of the nanofluid. The chemical reactions released heat energy to the surrounding environment, escalating the nanofluid’s temperature and decreasing the concentration of the nanoparticles. The rate of permeability strengthens the flow velocity by improving the flow network. The increased heat generation parameter influenced the increase in nanofluids’ velocity and temperature. This study can be considered in some applications, such as designing heat exchangers, solar cells, climate changes, and separation process industries.