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Deep bed filtration model for cake filtration and erosion

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applied mathematics and Mechanics(English Edition) 2024年第2期45卷 355-372页

作者： L.I.KUZMINA Y.V.OSIPOV A.R.PESTEREV Department of applied mathematics HSE UniversityMoscow 101000Russia Department of computer science and applied mathematics Moscow State University of Civil EngineeringMoscow 129337Russia

Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media. Two main types of particle deposition,namely, cake filtration at the inlet and deep bed filtration throughout the entire porous medium, are studied by different models. A unified approach for the transport and deposition of particles based on the deep bed filtration model is proposed. A variable suspension flow rate, proportional to the number of free pores at the inlet of the porous medium, is considered. To model cake filtration, this flow rate is introduced into the mass balance equation of deep bed filtration. For the cake filtration without deposit erosion,the suspension flow rate decreases to zero, and the suspension does not penetrate deep into the porous medium. In the case of the cake filtration with erosion, the suspension flow rate is nonzero, and the deposit is distributed throughout the entire porous medium. An exact solution is obtained for a constant filtration function. The method of characteristics is used to construct the asymptotics of the concentration front of suspended and retained particles for a filtration function in a general form. Explicit formulae are obtained for a linear filtration function. The properties of these solutions are studied in detail.

关键词： deep bed filtration cake filtration porous medium particle deposition and erosion analytical solution concentration front

One-dimensional monotone nonautonomous dynamical systems

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science China mathematics 2024年第2期67卷 281-314页

作者： David Cheban Faculty of mathematics and computer science Laboratory of Fundamental and Applied MathematicsMoldova State UniversityChisinau 2009Moldova

This work is devoted to the study of the dynamics of one-dimensional monotone nonautonomous(cocycle) dynamical systems. A description of the structures of their invariant sets, omega limit sets,Bohr/Levitan almost periodic and almost automorphic motions, global attractors, and pinched and minimalsets is given. An application of our general results is given to scalar differential and difference equations.

关键词： one-dimensional dynamics pinched and minimal sets global attractors monotone nonautonomous cocycle almost periodic solutions scalar differential/difference equations

Context-aware reinforcement learning for cooling operation of data centers with an Aquifer Thermal Energy Storage

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Energy and AI 2024年第3期17卷 233-246页

作者： Lukas Leindals Peter Grønning Dominik Franjo Dominković Rune Grønborg Junker Department of applied mathematics and computer science Technical University of DenmarkDenmark

Data centers are often equipped with multiple cooling units. Here, an aquifer thermal energy storage (ATES) system has shown to be efficient. However, the usage of hot and cold-water wells in the ATES must be balanced for legal and environmental reasons. Reinforcement Learning has been proven to be a useful tool for optimizing the cooling operation at data centers. Nonetheless, since cooling demand changes continuously, balancing the ATES usage on a yearly basis imposes an additional challenge in the form of a delayed reward. To overcome this, we formulate a return decomposition, Cool-RUDDER, which relies on simple domain knowledge and needs no training. We trained a proximal policy optimization agent to keep server temperatures steady while minimizing operational costs. Comparing the Cool-RUDDER reward signal to other ATES-associated rewards, all models kept the server temperatures steady at around 30 °C. An optimal ATES balance was defined to be 0% and a yearly imbalance of −4.9% with a confidence interval of [−6.2, −3.8]% was achieved for the Cool 2.0 reward. This outperformed a baseline ATES-associated reward of 0 at −16.3% with a confidence interval of [−17.1, −15.4]% and all other ATES-associated rewards. However, the improved ATES balance comes with a higher energy consumption cost of 12.5% when comparing the relative cost of the Cool 2.0 reward to the zero reward, resulting in a trade-off. Moreover, the method comes with limited requirements and is applicable to any long-term problem satisfying a linear state-transition system.

关键词： Data centers ATES Smart energy systems Reinforcement learning Delayed rewards

EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation

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National science Review 2024年第7期11卷 135-147页

作者： Yue Zhao Wei Zhang Tiejun Li Center for Data science Peking University Zuse institute Berlin Department of mathematics and computer science Freie Universit?t Berlin Laboratory of mathematics and applied mathematics(LMAM)and School of Mathematical sciences Peking University Center for Machine Learning Research Peking University

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state ***-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product ***, our loss function has an intimate connection with the steady entropy production rate(EPR),enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional(8D)limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

关键词： high-dimensional potential landscape non-equilibrium system entropy production rate dimensionality reduction deep learning

Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

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computer Modeling in Engineering & sciences 2024年第3期138卷 2471-2495页

作者： Wimonmas Bamrungsetthapong Pramote Charongrattanasakul Division of applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiPathum Thani12110Thailand Division of mathematics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology KrungthepBangkok10120Thailand

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull *** control chart developed supports the examination of the mean lifespan variation for a particular product in the process of *** control limit levels are used:the warning control limit,inner control limit,and outer control ***,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control *** control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control ***,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

关键词： Modified DS np chart generalizedmultiple dependent state sampling time truncated life test Weibull distribution average run length average sample size

Ionization Potential Depression Model for Warm/Hot and Dense Plasmas

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Chinese Physics Letters 2024年第8期41卷 45-57页

作者： Chensheng Wu Fuyang Zhou Jun Yan Xiang Gao Yong Wu Chunhua Zeng Jianguo Wang institute of applied Physics and Computational mathematics Beijing 100088China Faculty of science Kunming University of Science and TechnologyKunming 650500China

For warm/hot and dense plasmas(WDPs),ionization potential depression(IPD)plays a crucial role in determining its ionization balance and understanding the resultant microscopic plasma properties.A sophisticated and unified IPD model is necessary to resolve those existing discrepancies between theoretical and experimental ***,the applicability of those widely used IPD models nowadays is limited,especially for the nonlocal thermodynamic equilibrium(non-LTE)dense plasma produced by short-pulse *** this work,we propose an IPD model that considers inelastic atomic processes,in which three-body recombination and collision ionization processes are found to play a crucial role in determining the electron distribution and IPD for a *** IPD model is validated by reproducing latest experimental results of Al plasmas with a wide-range condition of 70 eV–700 eV temperature and 0.2–3 times solid density,as well as a typical non-LTE system of hollow Al *** is demonstrated that the present IPD model has a significant temperature dependence due to the consideration of the inelastic collision *** a lower computational cost and wider application range of plasma conditions,the proposed model is expected to provide a promising tool to study the ionization balance and the atomic processes,as well as the related radiation and particle transports properties of the WDP.

关键词： properties. collision determining

Exploration of microscopic physical processes of Z-pinch by a modified electrostatic direct implicit particle-in-cell algorithm

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Chinese Physics B 2024年第9期33卷 433-442页

作者： Kaixuan Li Cheng Ning Ye Dong Chuang Xue institute of applied Physics and Computational mathematics Beijing 100088China

For investigating efficiently the stagnation kinetic-process of Z-pinch,we develop a novel modified electrostatic implicit particle-in-cell algorithm in radial one-dimension for Z-pinch simulation in which a small-angle cumulative binary collision algorithm is *** our algorithm,the electric field in z-direction is solved by a parallel electrode-plate model,the azimuthal magnetic field is obtained by Ampere’s law,and the term for charged particle gyromotion is approximated by the cross product of the averaged velocity and magnetic *** simulation results of 2 MA deuterium plasma shell Zpinch,the mass-center implosion trajectory agrees generally with that obtained by one-dimensional MHD simulation,and the plasma current also closely aligns with the external *** phase space diagrams and radial-velocity probability distributions of ions and electrons are *** main kinetic characteristic of electron motion is thermal equilibrium and oscillation,which should be oscillated around the ions,while that of ion motion is implosion *** the region of stagnation radius,the radial-velocity probability distribution of ions transits from the non-equilibrium to equilibrium state with the current increasing,while of electrons is basically the equilibrium *** the initial ion density and current peak are not high enough,the ions may not reach their thermal equilibrium state through collisions even in its stagnation phase.

关键词： Z-pinch particle-in-cell ion heating charged particle collisions

Radial solution of the Logarithmic Laplacian system

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applied mathematics(A Journal of Chinese Universities) 2024年第1期39卷 114-124页

作者： ZHANG Li-hong NIE Xiao-feng WANG Guo-tao Bashir Ahmad School of mathematics and computer science Shanxi Normal UniversityLinfen 041004China Nonlinear Analysis and applied mathematics(NAAM)Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityJeddah 21589Saudi Arabia.

The paper generalizes the direct method of moving planes to the Logarithmic Laplacian ***,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at ***,the radial symmetry of th... 详细信息

关键词： the Logarithmic Laplacian system radial symmetry the direct method of moving planes

Irrational-Behavior-Proof Conditions for Stochastic Games over Event Trees

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Journal of the Operations Research Society of China 2024年第1期12卷 243-263页

作者： Lei Wang Cui Liu Hong-Wei Gao Chong Lin School of Automation Institute of Complexity ScienceQingdao UniversityQingdao 266071ShandongChina School of mathematics and Statistics Institute of Applied Mathematics of ShandongQingdao UniversityQingdao 266071ShandongChina

In this paper,the irrational-behavior-proof conditions in a class of stochastic dynamic games over event trees are *** kinds of irrational-behavior-proof conditions are proposed by the imputation distribution procedure,and their relationships are *** specific properties for the general transformation of characteristic functions are developed,based on which,the irrational-behavior-proof conditions are proved to be true in a transformed cooperative game.

关键词： Dynamic cooperative game Event tree Irrational-behavior-proof condition Imputation distribution procedure Transformation of characteristic function