Preface xi List of Symbols xv Chapter 1 Objections and Rebuttals of Current Laws 1 1.1. Discussion on the general concepts 1 1.1.1. Choosing a three-dimensional space 1 1.1.2.

Galileo''s law of free-falling bodies 2 1.1.3. Uniform rotation, a Galilean motion 2 1.1.4. Galileo and Lorentz invariants 5 1.1.

5. Distinction between velocity and celerity 6 1.1.6. Space-time or space and time? 7 1.2. Objections to the equations of classical mechanics 8 1.2.

1. Equations of mechanics 8 1.2.2. Divergence and curl operators 10 1.2.3. The Stokes relation, an erroneous assumption 11 1.

2.4. Non-relativistic equations 12 Chapter 2 A Different View of Space and Time 15 2.1. Maxwell''s local frame of reference 15 2.2. Length and time 17 2.3.

The local notion of vector in an n-dimensional space 18 2.3.1. The example of the gravity vector 20 2.3.2. Vector precession 21 2.4.

Acceleration, velocity and celerity 22 2.4.1. Velocity limits 23 2.4.2. Adding velocities 25 2.5.

Galileo and Lorentz transformations 26 2.6. The genesis of a unified law 27 2.6.1. The principle of parsimony or Ockham''s razor 27 2.6.2.

Extension of Galileo''s principle of inertia to rotation 29 2.6.3. Interpretation of the WEP 32 2.6.4. Concept of physical homology 36 2.7.

Mass or energy 36 2.7.1. Energy per unit mass 37 2.8. The quantities of a unified physics 38 2.8.1.

Historical background 38 2.8.2. From the international system to the unification of units 39 2.8.3. Unified variables 39 2.8.

4. Unified potentials 40 2.8.5. Curvature of physics potentials 43 2.9. A one-dimensional model of space and time 45 2.9.

1. Representation of space in the equations of physics 45 Chapter 3 Unified Law of Motion 49 3.1. Dynamics of accelerated motions 49 3.2. Dynamics of uniform expansion and rotational motion 50 3.3. Kinematics of motion in discrete mechanics 54 3.

3.1. Non-accelerated motion 54 3.3.2. Accelerated motion 56 3.4. Laws of conservation of compressive and rotational energy 57 3.

5. Total energy conservation law 59 3.6. Principle of inertia 62 3.6.1. The nonlinear terms of inertia 62 3.6.

2. Inertia as the curvature of the Bernoulli potential 63 3.6.3. Inertia of two superimposed motions 67 3.6.4. Example of uniform rotational motion 67 3.

7. Helmholtz-Hodge decomposition 69 3.7.1. HHD of acceleration 69 3.7.2. HHD of velocity 71 3.

7.3. Orthogonality of the decomposition 72 3.8. Properties of the law of motion 74 3.8.1. A relativistic law 74 3.

8.2. A limitless local law 75 3.8.3. Dissipation of compression and shear energies 76 3.9. Potential couplings and interaction 77 3.

9.1. Properties of media 77 3.9.2. Unified law of motion 79 3.9.3.

Law of motion and source potentials 80 Chapter 4 Consequences of the Law of Motion 83 4.1. Weak equivalence principle revisited 83 4.1.1. The example of a falling heterogeneous body 83 4.1.2.

Violation of the WEP 85 4.2. Velocity limit 89 4.2.1. Uniformly accelerated translational motion 89 4.2.2.

Uniformly accelerated rotational motion 94 4.3. Advection 95 4.4. Local primal and dual forms of Bernoulli''s law 97 4.4.1. An equation of motion for incompressible flows of viscous fluid 99 4.

5. Invariances and Noether''s theorem 101 4.6. Absence of constitutive laws 105 Chapter 5 Fluid Mechanics 107 5.1. Inertia, a concept at the heart of mechanics 107 5.1.1 Physical meaning of L = V ×∇×V 109 5.

1.2. Example of a three-dimensional space vector 111 5.1.3 Intrinsic Property V⊥∇ × V 112 5.1.4. Application of the NS equations to inertia 116 5.

1.5. The consequences 118 5.1.6. A steady solution 118 5.2. Incompressible fluid mechanics 120 5.

2.1. A unified equation of fluid motion 121 5.2.2. Poiseuille flow 123 5.2.3.

Taylor-Green vortex 125 5.2.4. Role of vortex stretching on a Taylor-Green vortex 130 5.3. Two-phase flows 133 5.3.1.

Modeling the capillary acceleration 133 5.3.2. Geometric curvature 135 5.3.3. Classical estimates of normals and curvatures 136 5.3.

4. Curvature in DM 138 5.3.5. Surface energy 141 5.3.6. An anisotropic intrinsic superficial tension 142 5.

3.7. An equation of motion based on capillary acceleration 144 5.3.8. Capillary rise between two planar surfaces 146 5.4. Compressible flows 152 5.

4.1. Analysis of redundancies in Euler''s equations 152 5.4.2. Proposition for an alternative to Euler''s equations 155 5.4.3.

Rankine-Hugoniot conditions 158 5.4.4. Surface and shock discontinuities 159 5.4.5. Some elementary test cases 161 5.4.

6. Propagation of a surface discontinuity 161 Chapter 6 Fluid-Structure Interactions and Porous Media 175 6.1. Equation of motion for a solid 176 6.2. Connection conditions 179 6.3. Some examples 182 6.

3.1. Fluid-solid monolithic interaction on a simple example 182 6.3.2. Periodic shear in a fluid-solid layer 184 6.4. Other constitutive laws 187 6.

4.1. Compression-related properties 187 6.4.2. Non-deformable solid 188 6.4.3.

Viscoelastic model 189 6.4.4. Threshold fluid 190 6.5. Porous media 190 6.5.1.

Physical description of flows in porous media 190 6.5.2. Discrete approach to flows in porous media 192 6.5.3. Darcy''s law 195 6.5.

4. An examination of media anisotropy 198 6.5.5. Darcy-Forchheimer''s law 198 6.5.6. Flow in a variable cross-section channel 201 Chapter 7 Heat Transfer 203 7.

1. Introduction 203 7.2. Analysis of the heat transfer equations 204 7.3. An alternative law of heat propagation 208 7.3.1.

Maxwell''s local frame of reference 208 7.3.2. Modeling radiative transfer 210 7.3.3. Modeling diffusion transfer 213 7.4.

A law of discrete transfer 215 7.4.1. Equivalence of discrete distributions 215 7.4.2. A unified law of motion 217 7.4.

3. Advection 219 7.4.4. Anisotropy and polarization 220 7.4.5. Phase change 222 7.

4.6. A relativistic equation 224 7.4.7. A reduction in the number of variables 225 7.5. Test cases 226 7.

5.1. Radiative transfer between two cylinders 226 7.5.2. Heat transfer by diffusion in conductive media 228 7.5.3.

The Stefan problem for a melting-type phase change 230 7.5.4. Simulation of melting in discrete formulation 233 7.5.5. Condensation in an undercooled cavity 235 7.5.

6. Condensation with imposed temperature 236 7.5.7. Condensation in an anisothermic system 237 Chapter 8 Electromagnetism 241 8.1. Introduction 241 8.2.

A few remarks about Maxwell''s equations 242 8.2.1. Maxwell''s model 242 8.2.2. Maxwell''s equations in terms of potentials 244 8.2.

3. Non-existence of monopoles 245 8.3. An alternative law of propagation of electromagnetic waves 245 8.3.1. Maxwell''s local frame of reference 246 8.3.

2. Modeling currents 247 8.3.3. The discrete law of motion 253 8.3.4. Inertia and Lorentz acceleration 255 8.

3.5. Conservation of charges 256 8.3.6. Equations in terms of potential 258 8.3.7.

A relativistic equation 259 8.3.8. The potential existence of monopoles 260 8.3.9. A drastic reduction in the number of variables 262 8.3.

10. Differences and convergences 263 8.4. Some examples 265 8.4.1. Magnetic field created by a wire of infinite length 265 8.4.

2. Magnetic field around a permanent magnet 266 8.4.3. Induced currents in a cylindrical conductor 267 8.4.4. Electromagnet coil 270 8.

4.5. An example of electromagnetic levitation 271 8.5. Propagation of light 275 8.5.1. Light propagation equation 275 8.

5.2. Interference produced from two coherent point sources 276 8.5.3. Refraction of a polarized monochromatic wave 278 Chapter 9 Relativity, Gravitation 281 9.1. An alternative to the theory of relativity 281 9.

1.1. Alternative relativistic equation 282 9.2. Wave-energy duality 283 9.3. Photon velocity 286 9.3.

1. Photon energy in theory of relativity 286 9.3.2. Photon energy in discrete mechanics 288 9.4. Gravitation 291 9.4.

1. Physical principles revisited 291 9.4.2. Universal law of the fall of bodies with or without mass 293 9.4.3. Creation of the energy of bodies 295 9.

4.4. The mechanism of star accretion 298 9.5. Two typical examples 301 9.5.1. Gravitational acceleration as a source term 301 9.

5.2. Gravitational lensing 301 9.6. Gravitational redshift 303 9.7. Quantification 309 9.7.

1. Notion of spin 309 9.7.2. A potential unification 311 References 315 Index 327.