Author: Roberto Monaco
Publisher: World Scientific
ISBN: 9812568042
Category : Science
Languages : en
Pages : 582
Book Description
The book contains recent contributions in the field of waves propagation and stability in continuous media. In particular, the contributions consider discontinuity and shock waves, stability in fluid dynamics, small parameter problems, kinetic theories towards continuum models, non-equilibrium thermodynamics, and numerical applications.The volume is the fourth in a series published by World Scientific since 1999. The following distinguished authors contribute to the present book: S Bianchini, R Caflish, C Cercignani, Y Choquet-Bruhat, C Dafermos, L Desvillettes, V Giovangigli, H Gouin, I Muller, D Parker, B Straughan, M Sugiyama and W Weiss.
Proceedings, "WASCOM 2003"
Author: Roberto Monaco
Publisher: World Scientific
ISBN: 9789812702937
Category : Mathematics
Languages : en
Pages : 600
Book Description
This book contains about 20 invited papers and 40 contributed papers in the research areas of theoretical continuum mechanics, kinetic theory and numerical applications of continuum mechanics. Collectively these papers give a good overview of the activities and developments in these fields in the last few years. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences. Contents: Chaos in Some Linear Kinetic Models (J Banasiak); Inverse Problems in Photon Transport. Part I: Determination of Physical and Geometrical Features of an Interstellar Cloud (A Belleni-Morante et al.); Inverse Problems in Photon Transport. Part II: Features of a Source Inside an Interstellar Cloud (A Belleni-Morante & R Riganti); The Riemann Problem for a Binary Non-Reacting Mixture of Euler Fluids (F Brini & T Ruggeri); Rate of Convergence toward the Equilibrium in Degenerate Settings (L Desvillettes & C Villani); Asymptotic and Other Properties of Positive Definite Integral Measures for Nonlinear Diffusion (J N Flavin); Thermocapillary Fluid and Adiabatic Waves Near its Critical Point (H Gouin); Constitutive Models for Atactic Elastomers (C O Horgan & G Saccomandi); Considerations about the Gibbs Paradox (I Mller); Transport Coefficients in Stochastic Models of the Revised Enskog and Square-Well Kinetic Theories (J Polewczak & G Stell); Some Recent Mathematical Results in Mixtures Theory of Euler Fluids (T Ruggeri); From Kinetic Systems to Diffusion Equations (F Salvarani & J L Vizquez); Non-Boussinesq Convection in Porous Media (B Straughan); and other papers. Readership: Researchers, academics and graduate students working in the fields of continuum mechanics, wave propagation, stability in fluids, kinetic theory and computational fluid dynamics."
Publisher: World Scientific
ISBN: 9789812702937
Category : Mathematics
Languages : en
Pages : 600
Book Description
This book contains about 20 invited papers and 40 contributed papers in the research areas of theoretical continuum mechanics, kinetic theory and numerical applications of continuum mechanics. Collectively these papers give a good overview of the activities and developments in these fields in the last few years. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences. Contents: Chaos in Some Linear Kinetic Models (J Banasiak); Inverse Problems in Photon Transport. Part I: Determination of Physical and Geometrical Features of an Interstellar Cloud (A Belleni-Morante et al.); Inverse Problems in Photon Transport. Part II: Features of a Source Inside an Interstellar Cloud (A Belleni-Morante & R Riganti); The Riemann Problem for a Binary Non-Reacting Mixture of Euler Fluids (F Brini & T Ruggeri); Rate of Convergence toward the Equilibrium in Degenerate Settings (L Desvillettes & C Villani); Asymptotic and Other Properties of Positive Definite Integral Measures for Nonlinear Diffusion (J N Flavin); Thermocapillary Fluid and Adiabatic Waves Near its Critical Point (H Gouin); Constitutive Models for Atactic Elastomers (C O Horgan & G Saccomandi); Considerations about the Gibbs Paradox (I Mller); Transport Coefficients in Stochastic Models of the Revised Enskog and Square-Well Kinetic Theories (J Polewczak & G Stell); Some Recent Mathematical Results in Mixtures Theory of Euler Fluids (T Ruggeri); From Kinetic Systems to Diffusion Equations (F Salvarani & J L Vizquez); Non-Boussinesq Convection in Porous Media (B Straughan); and other papers. Readership: Researchers, academics and graduate students working in the fields of continuum mechanics, wave propagation, stability in fluids, kinetic theory and computational fluid dynamics."
Proceedings, "WASCOM 2005"
Author: Roberto Monaco
Publisher: World Scientific
ISBN: 9812773614
Category : Science
Languages : en
Pages : 582
Book Description
The book contains recent contributions in the field of waves propagation and stability in continuous media. In particular, the contributions consider discontinuity and shock waves, stability in fluid dynamics, small parameter problems, kinetic theories towards continuum models, non-equilibrium thermodynamics, and numerical applications. The volume is the fourth in a series published by World Scientific since 1999. The following distinguished authors contribute to the present book: S Bianchini, R Caflish, C Cercignani, Y Choquet-Bruhat, C Dafermos, L Desvillettes, V Giovangigli, H Gouin, I Muller, D Parker, B Straughan, M Sugiyama and W Weiss. Contents: On Whitham Equations for Camassa-Holm (S Abenda et al.); An Operational Description of Stock Markets (F Bagarello); Vortex Layers in the Small Viscosity Limit (R E Caflisch & M Sammartino); Integration of Partially Integrable Equations (R Conte); Waves and Vibrations in a Solid of Second Grade (M Destrade & G Saccomandi); Multicomponent Reactive Flows (V Giovangigli); Singularities for Prandtl''s Equations (G Lo Bosco et al.); Stability of Solitons of the ZakharovOCoRubenchik Equation (F Oliveira); Plain Waves and Vibrations in the Elastic Mixtures (M Svanadze); Extended Thermodynamics with Consistent Order (W Weiss); and other papers. Readership: Academics, researchers and post-graduates in mathematics and physics."
Publisher: World Scientific
ISBN: 9812773614
Category : Science
Languages : en
Pages : 582
Book Description
The book contains recent contributions in the field of waves propagation and stability in continuous media. In particular, the contributions consider discontinuity and shock waves, stability in fluid dynamics, small parameter problems, kinetic theories towards continuum models, non-equilibrium thermodynamics, and numerical applications. The volume is the fourth in a series published by World Scientific since 1999. The following distinguished authors contribute to the present book: S Bianchini, R Caflish, C Cercignani, Y Choquet-Bruhat, C Dafermos, L Desvillettes, V Giovangigli, H Gouin, I Muller, D Parker, B Straughan, M Sugiyama and W Weiss. Contents: On Whitham Equations for Camassa-Holm (S Abenda et al.); An Operational Description of Stock Markets (F Bagarello); Vortex Layers in the Small Viscosity Limit (R E Caflisch & M Sammartino); Integration of Partially Integrable Equations (R Conte); Waves and Vibrations in a Solid of Second Grade (M Destrade & G Saccomandi); Multicomponent Reactive Flows (V Giovangigli); Singularities for Prandtl''s Equations (G Lo Bosco et al.); Stability of Solitons of the ZakharovOCoRubenchik Equation (F Oliveira); Plain Waves and Vibrations in the Elastic Mixtures (M Svanadze); Extended Thermodynamics with Consistent Order (W Weiss); and other papers. Readership: Academics, researchers and post-graduates in mathematics and physics."
Waves And Stability In Continuous Media - Proceedings Of The 12th Conference On Wascom 2003
Author: Roberto Monaco
Publisher: World Scientific
ISBN: 981448329X
Category : Science
Languages : en
Pages : 590
Book Description
This book contains about 20 invited papers and 40 contributed papers in the research areas of theoretical continuum mechanics, kinetic theory and numerical applications of continuum mechanics. Collectively these papers give a good overview of the activities and developments in these fields in the last few years.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Publisher: World Scientific
ISBN: 981448329X
Category : Science
Languages : en
Pages : 590
Book Description
This book contains about 20 invited papers and 40 contributed papers in the research areas of theoretical continuum mechanics, kinetic theory and numerical applications of continuum mechanics. Collectively these papers give a good overview of the activities and developments in these fields in the last few years.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Proceedings, "WASCOM 2007"
Author: Natale Manganaro
Publisher: World Scientific
ISBN: 9812772359
Category : Science
Languages : en
Pages : 619
Book Description
This volume is the fifth in a series of proceedings which started in 1999. The contributions include the latest results on the theory of wave propagation, extended thermodynamics, and the stability of the solutions to partial differential equations. Sample Chapter(s). Chapter 1: Reciprocal Transformations and Integrable Hamiltonian Hydrodynamic Type Systems (334 KB). Contents: Quantitative Estimates for the Large Time Behavior of a Reaction-Diffusion Equation with Rational Reaction Term (M Bisi et al.); Linearized Euler''s Variational Equations in Lagrangian Coordinates (G Boillat & Y J Peng); Restabilizing Forcing for a Diffusive Prey-Predator Model (B Buonomo & S Rionero); Fluid Dynamical Features of the Weak KAM Theory (F Cardin); Ricci Flow Deformation of Cosmological Initial Data Sets (M Carfora & T Buchert); Fuchsian Partial Differential Equations (Y Choquet-Bruhat); Analytic Structure of the Four-Wave Mixing Model in Photoreactive Material (R Conte & S Bugaychuk); A Note about Waves in Dissipative and Dispersive Solids (M Destrade & G Saccomandi); Exponential and Algebraic Relaxation in Kinetic Models for Wealth Distribution (B Dring et al.); Solitary Waves in Dispersive Materials (J Engelbrecht et al.); A GinzburgOCoLandau Model for the Ice-Water and Liquid-Vapor Phase Transitions (M Fabrizio); Stability Considerations for Reaction-Diffusion Systems (J N Flavin); A Mechanical Model for Liquid Nanolayers (H Gouin); A Particle Method for a Lotka-Volterra System with Nonlinear Cross and Self-Diffusion (M Groppi & M Sammartino); Transport Properties of Chemically Reacting Gas Mixtures (G M Kremer); Navier-Stokes in Aperture Domains: Existence with Bounded Flux and Qualitative Properties (P Maremonti); On Two-Pulse Interaction in a Class of Model Elastic Materials (A Mentrelli et al.); On a Particle-Size Segregation Equation (C Mineo & M Torrisi); Problems of Stability and Waves in Biological Systems (G Mulone); Multiple Cold and Hot Second Sound Shocks in HE II (A Muracchini & L Seccia); Differential Equations and Lie Symmetries (F Oliveri et al.); Bifurcation Analysis of Equilibria in Competitive Logistic Networks with Adaptation (A Raimondi & C Tebaldi); Poiseuille Flow of a Fluid Overlying a Porous Media (B Straughan); Analysis of Heat Conduction Phenomena in a One-Dimensional Hard-Point Gas by Extended Thermodynamics (S Tanigushi et al.); On Waves in Weakly Nonlinear Poroelastic Materials Modeling Impacts of Meteorites (K Wilmanski et al.); and other papers. Readership: Researchers in mathematics, physics, chemistry and engineering."
Publisher: World Scientific
ISBN: 9812772359
Category : Science
Languages : en
Pages : 619
Book Description
This volume is the fifth in a series of proceedings which started in 1999. The contributions include the latest results on the theory of wave propagation, extended thermodynamics, and the stability of the solutions to partial differential equations. Sample Chapter(s). Chapter 1: Reciprocal Transformations and Integrable Hamiltonian Hydrodynamic Type Systems (334 KB). Contents: Quantitative Estimates for the Large Time Behavior of a Reaction-Diffusion Equation with Rational Reaction Term (M Bisi et al.); Linearized Euler''s Variational Equations in Lagrangian Coordinates (G Boillat & Y J Peng); Restabilizing Forcing for a Diffusive Prey-Predator Model (B Buonomo & S Rionero); Fluid Dynamical Features of the Weak KAM Theory (F Cardin); Ricci Flow Deformation of Cosmological Initial Data Sets (M Carfora & T Buchert); Fuchsian Partial Differential Equations (Y Choquet-Bruhat); Analytic Structure of the Four-Wave Mixing Model in Photoreactive Material (R Conte & S Bugaychuk); A Note about Waves in Dissipative and Dispersive Solids (M Destrade & G Saccomandi); Exponential and Algebraic Relaxation in Kinetic Models for Wealth Distribution (B Dring et al.); Solitary Waves in Dispersive Materials (J Engelbrecht et al.); A GinzburgOCoLandau Model for the Ice-Water and Liquid-Vapor Phase Transitions (M Fabrizio); Stability Considerations for Reaction-Diffusion Systems (J N Flavin); A Mechanical Model for Liquid Nanolayers (H Gouin); A Particle Method for a Lotka-Volterra System with Nonlinear Cross and Self-Diffusion (M Groppi & M Sammartino); Transport Properties of Chemically Reacting Gas Mixtures (G M Kremer); Navier-Stokes in Aperture Domains: Existence with Bounded Flux and Qualitative Properties (P Maremonti); On Two-Pulse Interaction in a Class of Model Elastic Materials (A Mentrelli et al.); On a Particle-Size Segregation Equation (C Mineo & M Torrisi); Problems of Stability and Waves in Biological Systems (G Mulone); Multiple Cold and Hot Second Sound Shocks in HE II (A Muracchini & L Seccia); Differential Equations and Lie Symmetries (F Oliveri et al.); Bifurcation Analysis of Equilibria in Competitive Logistic Networks with Adaptation (A Raimondi & C Tebaldi); Poiseuille Flow of a Fluid Overlying a Porous Media (B Straughan); Analysis of Heat Conduction Phenomena in a One-Dimensional Hard-Point Gas by Extended Thermodynamics (S Tanigushi et al.); On Waves in Weakly Nonlinear Poroelastic Materials Modeling Impacts of Meteorites (K Wilmanski et al.); and other papers. Readership: Researchers in mathematics, physics, chemistry and engineering."
Waves And Stability In Continuous Media - Proceedings Of The 13th Conference On Wascom 2005
Author: Roberto Monaco
Publisher: World Scientific
ISBN: 9814478032
Category : Science
Languages : en
Pages : 582
Book Description
The book contains recent contributions in the field of waves propagation and stability in continuous media. In particular, the contributions consider discontinuity and shock waves, stability in fluid dynamics, small parameter problems, kinetic theories towards continuum models, non-equilibrium thermodynamics, and numerical applications.The volume is the fourth in a series published by World Scientific since 1999. The following distinguished authors contribute to the present book: S Bianchini, R Caflish, C Cercignani, Y Choquet-Bruhat, C Dafermos, L Desvillettes, V Giovangigli, H Gouin, I Muller, D Parker, B Straughan, M Sugiyama and W Weiss.
Publisher: World Scientific
ISBN: 9814478032
Category : Science
Languages : en
Pages : 582
Book Description
The book contains recent contributions in the field of waves propagation and stability in continuous media. In particular, the contributions consider discontinuity and shock waves, stability in fluid dynamics, small parameter problems, kinetic theories towards continuum models, non-equilibrium thermodynamics, and numerical applications.The volume is the fourth in a series published by World Scientific since 1999. The following distinguished authors contribute to the present book: S Bianchini, R Caflish, C Cercignani, Y Choquet-Bruhat, C Dafermos, L Desvillettes, V Giovangigli, H Gouin, I Muller, D Parker, B Straughan, M Sugiyama and W Weiss.
Waves And Stability In Continuous Media - Proceedings Of The 14th Conference On Wascom 2007
Author: Roberto Monaco
Publisher: World Scientific
ISBN: 9814474002
Category : Science
Languages : en
Pages : 619
Book Description
This volume is the fifth in a series of proceedings which started in 1999. The contributions include the latest results on the theory of wave propagation, extended thermodynamics, and the stability of the solutions to partial differential equations.
Publisher: World Scientific
ISBN: 9814474002
Category : Science
Languages : en
Pages : 619
Book Description
This volume is the fifth in a series of proceedings which started in 1999. The contributions include the latest results on the theory of wave propagation, extended thermodynamics, and the stability of the solutions to partial differential equations.
Continuous Media with Microstructure
Author: Bettina Albers
Publisher: Springer Science & Business Media
ISBN: 3642114458
Category : Science
Languages : en
Pages : 384
Book Description
This book discusses the extension of classical continuum models. To the first class addressed belong various thermodynamic models of multicomponent systems, and to the second class belong primarily microstructures created by phase transformations.
Publisher: Springer Science & Business Media
ISBN: 3642114458
Category : Science
Languages : en
Pages : 384
Book Description
This book discusses the extension of classical continuum models. To the first class addressed belong various thermodynamic models of multicomponent systems, and to the second class belong primarily microstructures created by phase transformations.
Rational Extended Thermodynamics beyond the Monatomic Gas
Author: Tommaso Ruggeri
Publisher: Springer
ISBN: 3319133411
Category : Mathematics
Languages : en
Pages : 381
Book Description
This book is dedicated to the recent developments in RET with the aim to explore polyatomic gas, dense gas and mixture of gases in non-equilibrium. In particular we present the theory of dense gases with 14 fields, which reduces to the Navier-Stokes Fourier classical theory in the parabolic limit. Molecular RET with an arbitrary number of field-variables for polyatomic gases is also discussed and the theory is proved to be perfectly compatible with the kinetic theory in which the distribution function depends on an extra variable that takes into account a molecule’s internal degrees of freedom. Recent results on mixtures of gases with multi-temperature are presented together with a natural definition of the average temperature. The qualitative analysis and in particular, the existence of the global smooth solution and the convergence to equilibrium are also studied by taking into account the fact that the differential systems are symmetric hyperbolic. Applications to shock and sound waves are analyzed together with light scattering and heat conduction and the results are compared with experimental data. Rational extended thermodynamics (RET) is a thermodynamic theory that is applicable to non-equilibrium phenomena. It is described by differential hyperbolic systems of balance laws with local constitutive equations. As RET has been strictly related to the kinetic theory through the closure method of moment hierarchy associated to the Boltzmann equation, the applicability range of the theory has been restricted within rarefied monatomic gases. The book represents a valuable resource for applied mathematicians, physicists and engineers, offering powerful models for potential applications like satellites reentering the atmosphere, semiconductors and nano-scale phenomena.
Publisher: Springer
ISBN: 3319133411
Category : Mathematics
Languages : en
Pages : 381
Book Description
This book is dedicated to the recent developments in RET with the aim to explore polyatomic gas, dense gas and mixture of gases in non-equilibrium. In particular we present the theory of dense gases with 14 fields, which reduces to the Navier-Stokes Fourier classical theory in the parabolic limit. Molecular RET with an arbitrary number of field-variables for polyatomic gases is also discussed and the theory is proved to be perfectly compatible with the kinetic theory in which the distribution function depends on an extra variable that takes into account a molecule’s internal degrees of freedom. Recent results on mixtures of gases with multi-temperature are presented together with a natural definition of the average temperature. The qualitative analysis and in particular, the existence of the global smooth solution and the convergence to equilibrium are also studied by taking into account the fact that the differential systems are symmetric hyperbolic. Applications to shock and sound waves are analyzed together with light scattering and heat conduction and the results are compared with experimental data. Rational extended thermodynamics (RET) is a thermodynamic theory that is applicable to non-equilibrium phenomena. It is described by differential hyperbolic systems of balance laws with local constitutive equations. As RET has been strictly related to the kinetic theory through the closure method of moment hierarchy associated to the Boltzmann equation, the applicability range of the theory has been restricted within rarefied monatomic gases. The book represents a valuable resource for applied mathematicians, physicists and engineers, offering powerful models for potential applications like satellites reentering the atmosphere, semiconductors and nano-scale phenomena.
Constitutive Models for Rubber IV
Author: Per-Erik Austrell
Publisher: Routledge
ISBN: 1351458272
Category : Technology & Engineering
Languages : en
Pages : 646
Book Description
The unique properties of elastomeric materials offer numerous advantages in many engineering applications. Elastomeric units are used as couplings or mountings between rigid components, for example in shock absorbers, vibration insulators, flexible joints, seals and suspensions, etc. However, the complicated nature of the behaviour of such material makes it difficult to accurately predict the performance of these units using finite element modelling, for example. It is imperative that constitutive models accurately capture relevant aspects of mechanical behaviour. The latest developments concerning constitutive modelling of rubber is collected in these Proceedings. Topics included in this volume are, Hyperelastic models, Strength, fracture & fatigue, Dynamic properties & the Fletcher-Gent effect, Micro-mechanical & statistical approaches, Stress softening, iscoelasticity, Filler reinforcement, and Tyres, fibre & cord reinforced rubber.
Publisher: Routledge
ISBN: 1351458272
Category : Technology & Engineering
Languages : en
Pages : 646
Book Description
The unique properties of elastomeric materials offer numerous advantages in many engineering applications. Elastomeric units are used as couplings or mountings between rigid components, for example in shock absorbers, vibration insulators, flexible joints, seals and suspensions, etc. However, the complicated nature of the behaviour of such material makes it difficult to accurately predict the performance of these units using finite element modelling, for example. It is imperative that constitutive models accurately capture relevant aspects of mechanical behaviour. The latest developments concerning constitutive modelling of rubber is collected in these Proceedings. Topics included in this volume are, Hyperelastic models, Strength, fracture & fatigue, Dynamic properties & the Fletcher-Gent effect, Micro-mechanical & statistical approaches, Stress softening, iscoelasticity, Filler reinforcement, and Tyres, fibre & cord reinforced rubber.
Classical and Relativistic Rational Extended Thermodynamics of Gases
Author: Tommaso Ruggeri
Publisher: Springer Nature
ISBN: 3030591441
Category : Mathematics
Languages : en
Pages : 675
Book Description
Rational extended thermodynamics (RET) is the theory that is applicable to nonequilibrium phenomena out of local equilibrium. It is expressed by the hyperbolic system of field equations with local constitutive equations and is strictly related to the kinetic theory with the closure method of the hierarchies of moment equations. The book intends to present, in a systematic way, new results obtained by RET of gases in both classical and relativistic cases, and it is a natural continuation of the book "Rational Extended Thermodynamics beyond the Monatomic Gas" by the same authors published in 2015. However, this book addresses much wider topics than those of the previous book. Its contents are as follows: RET of rarefied monatomic gases and of polyatomic gases; a simplified RET theory with 6 fields being valid far from equilibrium; RET where both molecular rotational and vibrational modes exist; mixture of gases with multi-temperature. The theory is applied to several typical topics (sound waves, shock waves, etc.) and is compared with experimental data. From a mathematical point of view, RET can be regarded as a theory of hyperbolic symmetric systems, of which it is possible to conduct a qualitative analysis. The book represents a valuable resource for applied mathematicians, physicists, and engineers, offering powerful models for many potential applications such as reentering satellites into the atmosphere, semiconductors, and nanoscale phenomena.
Publisher: Springer Nature
ISBN: 3030591441
Category : Mathematics
Languages : en
Pages : 675
Book Description
Rational extended thermodynamics (RET) is the theory that is applicable to nonequilibrium phenomena out of local equilibrium. It is expressed by the hyperbolic system of field equations with local constitutive equations and is strictly related to the kinetic theory with the closure method of the hierarchies of moment equations. The book intends to present, in a systematic way, new results obtained by RET of gases in both classical and relativistic cases, and it is a natural continuation of the book "Rational Extended Thermodynamics beyond the Monatomic Gas" by the same authors published in 2015. However, this book addresses much wider topics than those of the previous book. Its contents are as follows: RET of rarefied monatomic gases and of polyatomic gases; a simplified RET theory with 6 fields being valid far from equilibrium; RET where both molecular rotational and vibrational modes exist; mixture of gases with multi-temperature. The theory is applied to several typical topics (sound waves, shock waves, etc.) and is compared with experimental data. From a mathematical point of view, RET can be regarded as a theory of hyperbolic symmetric systems, of which it is possible to conduct a qualitative analysis. The book represents a valuable resource for applied mathematicians, physicists, and engineers, offering powerful models for many potential applications such as reentering satellites into the atmosphere, semiconductors, and nanoscale phenomena.