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Machine Learning Approaches for the Solution of the Riemann problem in Fluid Dynamics:a Case Study

Communications on Applied Mathematics and Computation 2024年第3期6卷 1832-1859页

作者： Vitaly Gyrya mikhail Shashkov Alexei Skurikhin Svetlana Tokareva Los Alamos National Laboratory Applied Mathematics and Plasma Physics(T-5)Los AlamosUSA Los Alamos National Laboratory Continuum Models and Numerical Methods(XCP-4)Los AlamosUSA Los Alamos National Laboratory Space Data Science and Systems(ISR-3)Los AlamosUSA

We present our results by using a machine learning(ML)approach for the solution of the Riemann problem for the Euler equations of fluid *** Riemann problem is an initial-value problem with piecewise-constant initial data and it represents a mathematical model of the shock *** solution of the Riemann problem is the building block for many numerical algorithms in computational fluid dynamics,such as finite-volume or discontinuous Galerkin ***,a fast and accurate approximation of the solution of the Riemann problem and construction of the associated numerical fluxes is of crucial *** exact solution of the shock tube problem is fully described by the intermediate pressure and mathematically reduces to finding a solution of a nonlinear *** to delving into the complexities of ML for the Riemann problem,we consider a much simpler formulation,yet very informative,problem of learning roots of quadratic equations based on their *** compare two approaches:(i)Gaussian process(Gp)regressions,and(ii)neural network(NN)*** these approaches,NNs prove to be more robust and efficient,although Gp can be appreciably more accurate(about 30\%).We then use our experience with the quadratic equation to apply the Gp and NN approaches to learn the exact solution of the Riemann problem from the initial data or coefficients of the gas equation of state(EOS).We compare Gp and NN approximations in both regression and classification analysis and discuss the potential benefits and drawbacks of the ML approach.

关键词： Machine learning(ML) Neural network(NN) Gaussian process(Gp) Riemann problem Numerical fluxes Finite-volume method

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Soil erosion: An important indicator for the assessment of land degradation neutrality in Russia

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International Soil and Water Conservation Research 2020年第4期8卷 418-429页

作者： petr Tsvmbarovich German Kust mikhail Kumani Valentin Golosov Olga Andreeva Institute of Geography RAS Russian Academy of SciencesMoscowRussia Lomonosov Moscow State University MoscowRussia Kursk State University KurskRussia

This review of soil erosion(SE)studies in Russia focuses on two main tasks:(i)ensuring the completeness and reliability of SE data in Russia,a large country(17.1 million km2)with a variety of natural and socio-economic causes of land degradation,(ii)assessing the possibility of including a SE indicator among the indicators of land degradation neutrality(LDN).A wide range of statistical,remote sensing,mathematical modeling *** results of scientific and field studies obtained at different levels were *** is asserted that in Russia the total area of eroded lands and those under erosion risk occupy more than 50%of all agricultural lands,whereas soil fertility of croplands decreased in Soviet time(from 1950s to 1980s)by 30-60%only due to water ***,recent scientific studies indicate a decrease in erosion rate and in the area of eroded land during the last 30-40 years as a result of abandonment of arable land and subsequent overgrown with natural *** climate change resulting in decrease of the depth of soil freezing,flow of spring runoff also adds to the decrease of soil *** SE indicator was suggested as an important complement to three global LDN *** national and subnational level,it can be interpreted through such indices as"Rate of soil loss"(ton ha-1 yr-1)and"Total soil loss"(1000 tons,in certain area during selected time period).At local level the set of indices can be wider and site-specific,including those obtained through remote sensing data by using the classifier of thematic applications of remote sensing technologies;the example was tested at the local site.

关键词： Russian Federation Soil erosion Land degradation neutrality

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Clarifying the influence of albumin on the initial stages of magnesium corrosion in Hank's balanced salt solution

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Journal of Magnesium and Alloys 2021年第3期9卷 805-817页

作者： Di Mei Cheng Wang Sviatlana V.Lamaka mikhail L.Zheludkevich Magnesium Innovation Centre-MagIC Institute of Materials ResearchHelmholtz-Zentrum GeesthachtGeesthacht 21502Germany Institute for Materials Science Faculty of EngineeringKiel UniversityKiel 24103Germany

The corrosion behavior of Mg,a promising biodegradable metallic material,in protein-containing pseudophysiological environment is still not fully *** this work,the influence of albumin on the corrosion behavior of commercially pure magnesium(Cp Mg)is investigated during short-term tests in Hank’s Balanced Salt Solution(HBSS).This work focuses on the reactions at the Mg/medium interface from the perspective of the interactions among albumin,media components and *** evolution tests demonstrate that the physiological amount of albumin(40 g L^(-1))accelerates Mg corrosion in HBSS during the first few hours but slows down the degradation *** presence of albumin decreases the concentration of free Ca^(2+)in HBSS and delays formation of protective co-precipitation products on Mg *** evolution of local pH(differs from typically monitored bulk pH)near Mg/medium interface in albumincontaining HBSS is reported for the first *** of local and bulk pH values elucidates the pH buffering effect of albumin during the immersion *** on these results,adsorption,chelating and pH buffering effects are summarized as three important aspects of albumin influence on Mg ***,constant replenishment of medium components is shown to be an influential factor during the Mg corrosion tests.

关键词： Magnesium Corrosion Albumin Biodegradable Local pH

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Elaboration of a conceptual solution for the development of the Arctic shelf from seasonally flooded coastal areas

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International Journal of Mining Science and Technology 2022年第1期32卷 113-119页

作者： Vladimir S.Litvinenko mikhail V.Dvoynikov Vladimir L.Trushko Saint-petersburg Mining University Saint-Petersburg 199106Russia

Currently,construction of facilities in the Arctic is carried out on sand islands,but there are limitations for remote coastal *** restrictions are associated with the lack of quarries with construction sand in the immediate vicinity of the work site,as well as the risk of seasonal flooding of the *** article includes conceptual solutions for construction of modular piling in Arctic nearshore conditions,upon which drilling rigs and auxiliary equipment can be placed for the purpose of subsequent wildcatting,development and exploratory extended reach drilling wells(with measured depth about 15000 m).During the construction of the modular piling foundations,a mathematical simulation of the thermodynamic condition of the frozen ground was conducted,and the bearing capacity of the foundations was *** proposed solutions will solve these problems by constructing modular pile foundations and placing the necessary infrastructure on them,taking into account the distribution of loads during operation in seasonally flooded areas.

关键词： Drilling&drillholes Stress analysis Offshore engineering Infrastructure planning Geotechnical engineering Extended reach drilling

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Numerical Analysis of permeability of Functionally Graded Scaffolds

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Fluid Dynamics & Materials processing 2024年第7期20卷 1463-1479页

作者： Dmitry Bratsun Natalia Elenskaya Ramil Siraev mikhail Tashkinov Laboratory of Mechanics of Biocompatible Materials and Devices Perm National Research Polytechnic UniversityPerm614990Russia

In this work,we numerically study the hydrodynamic permeability of new-generation artificial porous materials used as scaffolds for cell growth in a perfusion *** consider two popular solid matrix designs based on triply periodic minimal surfaces,the Schwarz p(primitive)and D(diamond)surfaces,which enable the creation of materials with controlled porosity *** latter property is crucial for regulating the shear stress field in the pores of the scaffold,which makes it possible to control the intensity of cell *** permeability of functionally graded materials is studied within the framework of both a microscopic approach based on the Navier-Stokes equation and an averaged description of the liquid filtration through a porous medium based on the equations of the Darcy or Forchheimer *** calculate the permeability coefficients for both types of solid matrices formed by Schwarz surfaces,study their properties concerning forward and reverse fluid flows,and determine the ranges of Reynolds number for which the description within the Darcy or Forchheimer model is ***,we obtain a shear stress field that varies along the sample,demonstrating the ability to tune spatially the rate of tissue growth.

关键词： porous media ﬁltration models scaffolds functionally graded materials

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A localized Fourier collocation method for 2D and 3D elliptic partial differential equations:Theory and MATLAB code

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International Journal of Mechanical System Dynamics 2022年第4期2卷 339-351页

作者： Yan Gu Zhuojia Fu mikhail V.Golub Department of Computational Mathematics School of Mathematics and StatisticsQingdao UniversityQingdaoChina Department of Engineering Mechanics College of Mechanics and MaterialsHohai UniversityNanjingChina Department of Applied Mathematics Institute for MathematicsMechanics and InformaticsKuban State UniversityKrasnodarRussian Federation

A localized Fourier collocation method is proposed for solving certain types of elliptic boundary value *** method first discretizes the entire domain into a set of overlapping small subdomains,and then in each of the subdomains,the unknown functions and their derivatives are approximated using the pseudo-spectral Fourier collocation *** key idea of the present method is to combine the merits of the quick convergence of the pseudo-spectral method and the high sparsity of the localized discretization technique to yield a new framework that may be suitable for large-scale *** present method can be viewed as a competitive alternative for solving numerically large-scale boundary value problems with complex-shape *** numerical experiments involving poisson,Helmholtz,and modified-Helmholtz equations in both two and three dimensions are presented to demonstrate the accuracy and efficiency of the proposed method.

关键词： meshless method collocation method Fourier basis functions large-scale problem

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Second-line treatment of metastatic gastric cancer:Current options and future directions

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World Journal of Gastroenterology 2015年第41期21卷 11621-11635页

作者： Dheepak Kanagavel mikhail Fedyanin Alexey Tryakin Sergei Tjulandin Department of Clinical pharmacology andChemotherapy N. N. Blokhin Russian Cancer Research Center

Gastric cancer remains one among the leading causes of cancer-related deaths, regardless of its decreasing incidence and newly available treatment options. Most patients present at an advanced stage and are treated with upfront systemic chemotherapy. Those patients receiving first-line therapy may initially respond to treatment, but many of them relapse over time. In such condition, second-line treatment for disease progression remains the only available option. Although there exists no standard approach in the second-line setting, several phase Ⅲ trials have shown modest survival benefit in patients receiving irinotecan, taxane and ramucirumab over the best supportive care or active agents. This review analyzes the currently available treatment regimens and future directions of research in the second-line setting for metastatic gastric cancer with the best available evidence. Additionally, the prognostic factors that influence patient survival in those receiving second-line therapy are discussed.

关键词： Metastatic gastric cancer Second-line chemotherapy

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A pressure Relaxation Closure Model for One-Dimensional, Two-Material Lagrangian Hydrodynamics Based on the Riemann problem

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Communications in Computational physics 2010年第5期7卷 927-976页

作者： James R.Kamm mikhail J.Shashkov Applied physics Division Los Alamos National LaboratoryLos AlamosNM 87545USA Theoretical Division Los Alamos National LaboratoryLos AlamosNM 87545USA

Despite decades of development, Lagrangian hydrodynamics of strengthfree materials presents numerous open issues, even in one dimension. We focus on theproblem of closing a system of equations for a two-material cell under the assumptionof a single velocity model. There are several existing models and approaches, eachpossessing different levels of fidelity to the underlying physics and each exhibitingunique features in the computed solutions. We consider the case in which the changein heat in the constituent materials in the mixed cell is assumed equal. An instantaneous pressure equilibration model for a mixed cell can be cast as four equations infour unknowns, comprised of the updated values of the specific internal energy andthe specific volume for each of the two materials in the mixed cell. The unique contribution of our approach is a physics-inspired, geometry-based model in which theupdated values of the sub-cell, relaxing-toward-equilibrium constituent pressures arerelated to a local Riemann problem through an optimization principle. This approachcouples the modeling problem of assigning sub-cell pressures to the physics associated with the local, dynamic evolution. We package our approach in the frameworkof a standard predictor-corrector time integration scheme. We evaluate our model using idealized, two material problems using either ideal-gas or stiffened-gas equationsof state and compare these results to those computed with the method of Tipton andwith corresponding pure-material calculations.

关键词： Lagrangian hydrodynamics compressible flow multi-material flow pressure relaxation

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Difference in formation of plasma electrolytic oxidation coatings on MgLi alloy in comparison with pure Mg

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Journal of Magnesium and Alloys 2021年第5期9卷 1745-1760页

作者： Ting Wu Carsten Blawert Xiaopeng Lu Maria Serdechnova mikhail L.Zheludkevich Institute of Surface Science Helmholtz-Zentrum Hereon21502 GeesthachtGermany Shenyang National Laboratory for Materials Science Northeastern University110819 ShenyangChina Institute for Materials Science Faculty of EngineeringKiel UniversityKaiserstrasse 224143 KielGermany

In order to study the substrate lattice structure(Li addition)on the growth of plasma electrolytic oxidation(pEO)coatings,Mg Li alloy(11.36 wt.%of Li,cubic)and pure Mg(hexagonal)were treated under a pulsed direct pEO mode in a phosphate electrolyte for different periods of *** results revealed that the presence of Li and Li-rich phases in the cubic Mg alloy seems to be essential for the treatment result rather than the original lattice structure.A modified discharge behavior of Mg Li alloy finally led to a different microstructure of the *** unstable coatings of Mg Li alloy tended to dissolve rapidly though shared the similar composition to that of pure *** was incorporated only in the primary conversion products at the interface of coating/Mg *** spite of the advanced efficiency of energy input during processing,the more porous and thinner pEO coatings on the Mg Li alloy were less resistant to abrasion and corrosion.

关键词： plasma electrolytic oxidation Magnesium lithium alloy pure magnesium Microstructure

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Simulation of Secondary Electron and Backscattered Electron Emission in A6 Relativistic Magnetron Driven by Different Cathode

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plasma Science and Technology 2015年第1期17卷 64-70页

作者：刘美琴李博轮刘纯亮 Fuks mikhail Edl SCHAMILOGLU Key Laboratory of physical Electronics and Devices of the Ministry of Education Xi'an Jiaotong University Department of Electrical and Computer Engineering University of New Mexico

prticle-in-cell（pIC） simulations demonstrated that,when the relativistic magnetron with diffraction output（MDO） is applied with a 410 kV voltage pulse,or when the relativistic magnetron with radial output is applied with a 350 kV voltage pulse,electrons emitted from the cathode with high energy will strike the anode block *** emitted secondary electrons and backscattered electrons affect the interaction between electrons and RF fields induced by the operating modes,which decreases the output power in the radial output relativistic magnetron by about 15%（10%for the axial output relativistic magnetron）,decreases the anode current by about 5%（5%for the axial output relativistic magnetron）,and leads to a decrease of electronic efficiency by 8%（6%for the axial output relativistic magnetron）.The peak value of the current formed by secondary and backscattered current equals nearly half of the amplitude of the anode current,which may help the growth of parasitic modes when the applied magnetic field is near the critical magnetic field separating neighboring ***,mode competition becomes more serious.

关键词： secondary electron and backscattered electron emission relativistic magnetron mode competition critical magnetic field output power anode current electronic efficiency transparent cathode solid cathode

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