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Groesen E., Molenaar J. — Continuum Modeling in the Physical Sciences (Monographs on Mathematical Modeling and Computation)
Groesen E., Molenaar J. — Continuum Modeling in the Physical Sciences (Monographs on Mathematical Modeling and Computation)

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Название: Continuum Modeling in the Physical Sciences (Monographs on Mathematical Modeling and Computation)

Авторы: Groesen E., Molenaar J.

Аннотация:

Mathematical modeling the ability to apply mathematical concepts and techniques to real-life systems has expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts. Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the Challenging Problems sections found at the ends of several chapters. The last chapter is devoted to elaborated case studies in polymer dynamics, fiber spinning, water waves, and waveguide optics.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 238

Добавлена в каталог: 26.09.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Action functional      153
Action principle      150 154
Admissible elements      137
Admissible states      71
Affine vector field      73
Algae dynamics      75
Asymptotic robustness      122
Asymptotic stability      107
Asymptotic structural stability      122
Atomic bomb      11
Attractor      114
Autonomous system      73
Barcelona      141
Basic laws      31
Bead-spring model      166
Bead-spring system      2
Bernoulli equation      189
Body forces      57
boundary conditions      72
Boundary layer      126
Boussinesq assumption      29
Brillouin      81
Brownian motion      174
Brusselator      18
Buckingham      5
Car flow      33
Carrier wave      100 199
Carthago      136
Catapulting      6
Catenary      139 142 152
Centrovelocity      102
Chemical reaction      18
Chill roll      178
Classical mechanics      150
Climate control      110
Collective coordinates      138
Collocation      160
Conservation principles      31
Conservative mode      99
Conservative system      154
Constitutive relations      31
Contact forces      57
Continuity equation      53
Continuous models      32
Contraction      63
Contraction of tensors      56 71
Critical states      73
Delta function      23 95
density      32
Dependent      70
Dido      136
Die      178
Diffusion equation      44
Dimensional analysis      4
Dirac      95
Directional derivative      88
Dirichlet-to-Neumann operator      195
Discrete model      32
dispersion      188
dispersion relation      98
Dispersive wave equation      102
Dissipative mode      99
distribution      32
DNA molecules      165
Domain of attraction      114
Drop tracks      12
Duality method      137
Dyadic product      57
Effective boundary conditions      209
Effective index      210
Eigenfunctions      90
Eigenvalue equations      90
Elastic behavior      46
Entangle      61
Envelope equation      201
Equation of sate      59
Equilibrium states      73
Euler equations      59 189
Euler — Lagrange equation      149 154
Extra stress tensor      57
Fading memory      80
Feasible states      71
Fermat's algorithm      146
Fermat's principle      136
Fiber spinning      178
Field      32
Finite element methods      145 160
First variation      148
Fluid potential      187
Fourier integrals      95 97
Fourier series      91 157
Fourier transform      97
Fourier's law      44
Frechet derivative      89
Free surface equation      189
frequency      98
Froude number      16
Fundamental dimensions      1
Gaudi      141
Gauss divergence theorem      58
Gauss theorem      52
Gaussian profile      144
Generalized function      96
Generalized Newtonian flow      61
Generalized Poiseuille flow      61
Geometrical optics      207
Gravitational force      31
Group velocity      101 200
Guided modes      208
Hamilton equations      155 191
Hamiltonian      151 155 191
Hanging chain      139
harmonic oscillator      2 10 70 154
Heat balance      34
Heat conduction      23 36
Heat conductivity      44 54
Heat diffusion in a rod      92
Heat diffusion in an infinitely long rod      99
Heat diffusion, equation      23
Heat equation      44
Heat flux      36
Helmholtz      205
High-dimensional modeling      144
Homogeneous boundary conditions      72
Hooke's law      46
Huygens      136
Hydrostatic pressure      56
Incompressibility condition      53
Incompressible flow      53
Independent      70
Inertia force      2
Inhomogeneous boundary conditions      72
Inner product      52
Instability      107 116
Integrated optics      205
Irrotational flow      187
Jacobi conditions      192
KdV equation      26 199
Kelvin model      47
Kinematic relation      66
Korteweg — de Vries equation      26
Kramer      81
Lagrange multiplier      147
Lagrange, lemma of      35 52
Lagrangian      151 154
Laminar flow      61
Landslide      187
Laplace equation      189
Laplace operator      54
Least squares method      137
Leibniz      146
Light propagation      81
Lindstedt's method      132
Linear model      73
Linear vector field      73
Linearization      79 117
Linearization of PDE      89
Long wave approximation      197
Low-dimensional modeling      144
Luke's variational principle      188
Lyapunov stability      107
Mass balance      34
Mass flux      34
Mass matrix      154
Matched asymptotic expansions      126
Material time derivative      53
Mathematical model      1
Mathematical swing      8
Matrix-vector product      56
Maupertuis      136
Maxwell equations      31 205
Maxwell model      47 61
Memory      50 51
Modes      98
Modulation      101
Momentum equation      58
Monochromatic modes      98
Monomers      165
Natural boundary condition      135 151
Navier — Stokes equation      59
Newton cooling law of      44
Newton equation      154
Newton second law of      2 31
Newtonian flow      58 181
Normal stress      55
Optics      204
Optimality      136
Orbital stability      115
Orbital stability, asymptotic      115
Osborne — Reynolds      14
Parameters      1 70
Particular solution      78
Pendulum of varying length      82
Period      98 114
Periodic boundary conditions      95
Phase boundaries      38
Phase shift      115
phase velocity      98
Pi theorem of Buckingham      5
Plane waves      97
Poiseuille flow      60
Poiseuille velocity profile      61
Poisson system      192
Pollution of water      129
Polymer dynamics      171
Polymer melts      57
Polymer solutions      61
Polymers      165
Population dynamics      131
Poynting identity      214
Prandtl — Blasius problem      20
Principle of minimal potential energy      138
Profile      32
Projecting out      93
Propagation constant      210
Rate of deformation tensor      59
Rayleigh quotient      158
Reduced equation      125
Refractive index      205
Relaxation time      47
Resonance      110
Rest states      73
Reynolds number      14
Ritz — Galerkin method      157
Robustness      105 120 122
Rouse model      166
Sagrada Familia      141
Scaling      17
Sedimentation      39
Self-adjoint      90
Separation of variables      93
Shallow water equations      66 197
Shear rate      21 61
Shear stress      55
Shear thinning      61
Ship modeling      16
Shock fronts      37
Shock wave      12
Single integral problems      150
Singular perturbation      125
Singular states      73
Slow variations      81
Snell's law      136 207
Solitons      152
Sparsity      163
Spectrum      91
Stability      106 113
State      70
State space      71
Stationary states      73
Steady states      73
strain      46
streamline      53
Stress tensor      55
Stretched region      127
Strong formulation      149
Structural stability      122
Structural unstability      122
Sturm — Liouville problems      151 158 162
Swinging pendulum      8
Tapered waveguide      213
Taylor, G.I.      11
Tectonic plate      187
Tent functions      146
thermal conductivity      23 44 54
Thermodynamics, second law of      43
Total time derivative      53
traffic flow      130
Traffic jam      40
Train speed      12
Transient solution      108
Transition region      126
Translation equation      28 42
Transparent influx boundary conditions      216
Transport theorem      51 52
Tsunami      187
Variables      1 70
Variation of constants formula      78
Variational accuracy      158
Variational derivative      88 148
Variational structure      150
Vector field      73
Vibrating string      171
Viscoelastic behavior      47
viscosity      13 20 47 59 182
Viscous behavior      46
Water waves      25 186
Wave equation      67 75
Wave group      199
Wave length      98
wave number      98
Wave package      101
Wavegroup      101
Waveguide optics      207
Weak formulation      149
Weather forecasting      1
Wentzel      81
William Froude      16
WKB (Wentzel — Kramer — Brillouin) method      81 213
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