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The present book contains the 16 papers accepted and published in the Special Issue “Mathematical Modeling and Simulation in Mechanics and Dynamic Systems” of the MDPI “Mathematics” journal, which cover a wide range of topics connected to the theory and applications of Modeling and Simulation of Dynamic Systems in different field. These topics include, among others, methods to model and simulate mechanical system in real engineering. It is hopped that the book will find interest and be useful for those working in the area of Modeling and Simulation of the Dynamic Systems, as well as for those with the proper mathematical background and willing to become familiar with recent advances in Dynamic Systems, which has nowadays entered almost all sectors of human life and activity.

Research & information: general --- Mathematics & science --- T-stress --- X-FEM --- notch --- pipe --- stress difference method (SDM) --- system of transcendental equation --- computational solutions --- code-based modelling approach --- numerical analysis --- Sine-Gordon equations --- photovoltaics --- thermophotovoltaics --- solar energy --- polymer CNTs systems --- interphase section --- percolation onset --- mechanics --- high temperature proton exchange membrane fuel cell --- exergy analysis --- ecological analysis --- ecological coefficient of performance --- SARS-CoV-2 --- COVID-19 --- SEIRD (Susceptible, Exposed, Infected and Recovered and Death) --- SDL --- Catalonia --- nanowire cantilever --- stochastic model --- double Lorentzian spectrum --- HT-PEMFC --- irreversibility --- finite time thermodynamic optimization --- power density --- thermodynamic efficiency --- geometric analogy --- similarity theory --- dimensional analysis --- model law --- heat transfer --- straight bar --- Deep Learning (DL) --- Computational Fluid Dynamics (CFD) --- Artificial Neural Network (ANN) --- Convolutional Neural Network (CNN) --- turbulent flow --- machine learning --- deep learning --- artificial neural network --- ANN --- PEM fuel cell --- modeling --- control --- differentiability --- fractal hydrodynamic regimes --- fractal Schrödinger regimes --- fractal soliton --- fractal kink --- "holographic implementations" --- cubics --- apolar transport --- harmonic mapping principle --- period doubling scenario --- state probability functions --- partial aging in standby --- Monte Carlo simulation --- qualitative and quantitative verification of simulation model --- Lagrange-d'Alembert principle --- non-conservative dynamical system --- Euler-Poincaré equation --- helicopter model --- Lie group --- extended iso-geometric analysis --- extended finite element method --- crack --- pipeline --- ABAQUS --- harmonic mapping --- complex system dynamics --- SL (2R) group --- hidden symmetries --- computer simulations --- actual systems --- transfer learning --- autonomous feature extraction --- T-stress --- X-FEM --- notch --- pipe --- stress difference method (SDM) --- system of transcendental equation --- computational solutions --- code-based modelling approach --- numerical analysis --- Sine-Gordon equations --- photovoltaics --- thermophotovoltaics --- solar energy --- polymer CNTs systems --- interphase section --- percolation onset --- mechanics --- high temperature proton exchange membrane fuel cell --- exergy analysis --- ecological analysis --- ecological coefficient of performance --- SARS-CoV-2 --- COVID-19 --- SEIRD (Susceptible, Exposed, Infected and Recovered and Death) --- SDL --- Catalonia --- nanowire cantilever --- stochastic model --- double Lorentzian spectrum --- HT-PEMFC --- irreversibility --- finite time thermodynamic optimization --- power density --- thermodynamic efficiency --- geometric analogy --- similarity theory --- dimensional analysis --- model law --- heat transfer --- straight bar --- Deep Learning (DL) --- Computational Fluid Dynamics (CFD) --- Artificial Neural Network (ANN) --- Convolutional Neural Network (CNN) --- turbulent flow --- machine learning --- deep learning --- artificial neural network --- ANN --- PEM fuel cell --- modeling --- control --- differentiability --- fractal hydrodynamic regimes --- fractal Schrödinger regimes --- fractal soliton --- fractal kink --- "holographic implementations" --- cubics --- apolar transport --- harmonic mapping principle --- period doubling scenario --- state probability functions --- partial aging in standby --- Monte Carlo simulation --- qualitative and quantitative verification of simulation model --- Lagrange-d'Alembert principle --- non-conservative dynamical system --- Euler-Poincaré equation --- helicopter model --- Lie group --- extended iso-geometric analysis --- extended finite element method --- crack --- pipeline --- ABAQUS --- harmonic mapping --- complex system dynamics --- SL (2R) group --- hidden symmetries --- computer simulations --- actual systems --- transfer learning --- autonomous feature extraction

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The fluid flow in fracture porous media plays a significant role in the assessment of deep underground reservoirs, such as through CO2 sequestration, enhanced oil recovery, and geothermal energy development. Many methods have been employed—from laboratory experimentation to theoretical analysis and numerical simulations—and allowed for many useful conclusions. This Special Issue aims to report on the current advances related to this topic. This collection of 58 papers represents a wide variety of topics, including on granite permeability investigation, grouting, coal mining, roadway, and concrete, to name but a few. We sincerely hope that the papers published in this Special Issue will be an invaluable resource for our readers.

deformation feature --- minerals --- microstructure --- mixing --- permeability --- gas concentration --- water–rock interaction --- loose gangue backfill material --- unified pipe-network method --- fracture --- roof-cutting resistance --- crack --- similar-material --- movable fluid --- gob-side entry retaining (GER) --- rock-soil mechanics --- bed separation --- orthogonal tests --- charge separation --- water soaked height --- fluid flow in reclaimed soil --- laboratory experiment --- longwall mining --- grading broken gangue --- MIP --- elastic modulus --- effective stress --- permeability coefficient --- mixer --- naturally fracture --- SEM --- microstructure characteristics --- artificial joint rock --- fractured rock --- strata movement --- conservative solute --- particle velocity --- dry-wet cycles --- hydraulic fractures --- numerical calculation --- mechanical behaviors --- normalized conductivity-influence function --- fractured porous rock mass --- PPCZ --- segmented grouting --- non-aqueous phase liquid --- intelligent torque rheometer --- numerical analysis --- temperature --- unsaturated soil --- uniaxial compressive strength --- mine shaft --- coalbed methane (CBM) --- nonlinear flow in fractured porous media --- similar simulation --- forecasting --- tight sandstones --- oriented perforation --- hydro-mechanical coupling --- constant normal stiffness conditions --- cohesive soils --- layered progressive grouting --- chemical grouts --- grain size of sand --- Darcy’s law --- soft coal masses --- hydro-power --- cyclic heating and cooling --- cohesive element method --- cement-based paste discharge --- tectonically deformed coal --- split grouting --- fault water inrush --- filtration effects --- T-stress --- particle flow modeling --- new cementitious material --- strength --- stabilization --- fractured porous medium --- brine concentration --- initial water contained in sand --- XRD --- fracture criteria --- hydraulic conductivity --- roadway deformation --- backfill mining --- adsorption/desorption properties --- pore pressure --- roughness --- cement–silicate grout --- compressive stress --- discrete element method --- dynamic characteristics --- strain-based percolation model --- thermal-hydrological-chemical interactions --- pore distribution characteristics --- transversely isotropic rocks --- nitric acid modification --- disaster-causing mechanism --- CH4 seepage --- crack distribution characteristics --- micro-CT --- relief excavation --- Darcy flow --- hydraulic fracturing --- mixed-form formulation --- propagation --- scanning electron microscope (SEM) images --- propagation pattern --- consolidation process --- rheological deformation --- gas adsorption --- soft filling medium --- ground pressure --- orthogonal ratio test --- rock fracture --- coal seams --- high-steep slope --- interface --- orthogonal test --- stress interference --- physical and mechanical parameters --- fracture propagation --- fluid–solid coupling theory --- coupling model --- surface characteristics --- numerical manifold method --- gas --- lignite --- water inrush prevention --- coupled THM model --- hard and thick magmatic rocks --- Ordos Basin --- porosity --- damage mechanics --- seepage --- degradation mechanism --- high temperature --- visualization system --- bentonite-sand mixtures --- contamination --- conductivity-influence function --- water-rock interaction --- deterioration --- seepage pressure --- glutenite --- adhesion efficiency --- mechanical behavior transition --- bedding plane orientation --- n/a --- enhanced gas recovery --- debris-resisting barriers --- reinforcement mechanism --- on-site monitoring --- geophysical prospecting --- cyclic wetting-drying --- scoops3D --- semi-analytical solution --- enhanced permeability --- management period --- seepage control --- deformation --- Yellow River Embankment --- impeded drainage boundary --- rheological test --- circular closed reservoir --- grout penetration --- viscoelastic fluid --- coal-like material --- paste-like slurry --- floor failure depth --- supercritical CO2 --- gravel --- numerical model --- fractal --- gas-bearing coal --- shear-flow coupled test --- rheological limit strain --- CO2 flooding --- flotation --- goaf --- slope stability --- damage --- coal and gas outburst --- hydraulic fracture --- anisotropy --- high-order --- effluents --- FLAC --- limestone roof --- sandstone --- TG/DTG --- Xinjiang --- two-phase flow --- model experiment --- coal particle --- volumetric strain --- failure mode --- land reclamation --- sandstone and mudstone particles --- contiguous seams --- CO2 geological storage --- numerical simulation --- geogrid --- stress relief --- optimum proportioning --- roadside backfill body (RBB) --- pervious concrete --- mudstone --- hydraulic fracture network --- grouted sand --- fractal pore characteristics --- refraction law --- segmented rheological model --- ductile failure --- heterogeneity --- flow law --- fracture closure --- coal measures sandstone --- tight sandstone gas reservoirs --- gob behaviors --- water-dripping roadway --- creep characteristics --- internal erosion --- warning levels of fault water inrush --- hydraulic aperture --- bolt support --- discontinuous natural fracture --- microscopic morphology --- critical hydraulic gradient --- mixed mode fracture resistance --- differential settlement --- alternate strata --- finite element method --- crushing ratio --- chloride --- glauberite cavern for storing oil &amp --- macroscopic mechanical behaviors --- collision angle --- adsorption performance --- failure mechanism --- mechanical properties --- transmissivity --- damage evolution --- gas fracturing --- multitude parameters --- deviatoric stress --- Jiaohe --- coal --- soil properties --- acoustic emission --- pore structure --- grouting experiment --- concrete --- confining pressures --- green mining --- gas drainage --- fluid viscosity --- compression deformation --- Unsaturation --- adsorption–desorption --- seepage-creep --- constitutive model --- soil particle size --- Pseudo Steady-State (PPS) constant --- soil–structure interface --- debris flow --- fracture grouting --- initial settlement position --- regression equation --- electrical potential --- secondary fracture --- surrounding rock --- solid backfill coal mining --- time variation --- excess pore-pressures --- finite-conductivity fracture --- permeability characteristics --- rainfall-unstable soil coupling mechanism(R-USCM) --- shaft lining --- Darcy's law --- cement-silicate grout --- fluid-solid coupling theory --- adsorption-desorption --- soil-structure interface