Presentation on theme: "Metody opisu dyfuzji wielu składników, unifikacja metody dyfuzji wzajemnej i termodynamiki procesów nieodwracalnych Marek Danielewski Interdisciplinary."— Presentation transcript:
Metody opisu dyfuzji wielu składników, unifikacja metody dyfuzji wzajemnej i termodynamiki procesów nieodwracalnych Marek Danielewski Interdisciplinary Centre for Materials Modeling AGH Univ. of Sci. & Technology, Cracow, Poland Będlewo, Czerwiec 2013
The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1997: "for a new method to determine… the value of derivatives" Robert C. Merton Harvard University Myron S. Scholes Long Term Capital Management Greenwich, CT, USA
Economy & diffusion… But…. money is not conserved!!! Merton & Sholes Nobel price „helped in”… …grand failure in 2008!!!
Öttinger (2005): „something is missing” 19 th century : Cauchy, Navier, Lam é … Stephenson (1988): drift & m up to 2007: only m Brenner (2006): Fluid Mechanics Revisited… Cracow (1994): v d & drift
Brenner in „Fluid Mechanics Revisited” (Physica A, 2006) 1. Complemented: volume fixed RF 2. Was polite to not notice: conflict between RF’s … in our papers
150 years of diffusion equation: Defects „everywhere & always”… (1918 Frenkel) Nonstoichiometry is a rule… (1933 Schottky & Wagner) Lattice sites are not conserved (1948 Kirkendall & Darken) Diffusion velocity… (~1900 Nernst & Planck) Darken problem has a unique solution (2008 Holly, Danielewski & Krzyżański) Darken problem is self-consistent with LIT (ActaMat 2010, Danielewski & Wierzba)
150 years of diffusion: Number of laws decreases… Complexity increases… Do we „stay with”: m, ρυ, q, U only ?
Dynamics & diffusion? Does x m depend on time, i.e., x m (t) or x m = const?
Brenner 2009, Danielewski & Wierzba 2010: Entropy production term is always positive Bi-velecity method is consistent with LIT
. Fulfill the fundamental conditions: acceleration does not depend on internal energy, centre of mass is not affected by diffusion, drift velocity is the unique frame of reference diffusion fluxes generate Darken’s drift.
Conservation laws in material reference frame Bi-velocity vs. LIT Diffusion, stress, reactions & more Planck-Kleinert Crystal
Reactions & Interdiffusion: Multiples T= 150, 180, 200 o C t = 3h, 30h, 100h, 7days, 14days… Experiment: Cu-Sn-Ag Cu-Ag-Sn-Ni Fabrication and vacuum annealing: Cu Ag Ni Sn M. Pawełkiewicz, EMPA & AGH
International PhD School Switzerland – Poland Fabrication Sectioning
International PhD School Switzerland – Poland after heat treatment: t=4h and T=180 C Sn Cu
Oliver Heaviside (1850-1925) Impedance Complex numbers Heaviside function Maxwell reformulated "Mathematics is an experimental science, and definitions do not come first, but later on." "I do not refuse my dinner simply because I do not understand the process of digestion."
Planck-Kleinert Crystal M. Danielewski, “The Planck-Kleinert Crystal”, Z. Naturforsch. 62a, 564-568 (2007).
„ The assumption, therefore, that gravitation arises from the action of the surrounding medium in the way pointed out, leads to the conclusion that every part of this medium possesses, when undisturbed, an enormous intrinsic energy, and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction. As I am unable to understand in what way a medium can possess such properties, I cannot go any further in this direction in searching for the cause of gravitation.”
Physics Today  → “The persistence of ether” Statistical mechanics  → dimensions become large quantum properties emerge. Quantum space  → analogous to crystal... Kleinert  → Einstein gravity from a defect model  F. Wilczek, Phys. Today 52, 11 (1999).  J. L. Lebowitz, Rev. of Modern Phys. 71, S347-S357 (1999).  M. Bojowald, Nature 436, 920-921 (2005).  H. Kleinert, Ann. Phys. 44, 117 (1987). Vacuum… No! → “There is no information without representation”  W. Żurek, Nature, 453, (2008), 23.
+ stationary, traveling & their combinations! Processes: 1.Transverse wave 2.Longitudinal wave 3. lattice deformation (Kleinert 2003) 4. P i diffusion (mass) 5. Heat transfer…
Physical QuantityUnitSymbol for unitValue in SI unitsSI unitReference Lattice parameterPlanck lengthlPlP 1.61624(12)·10 -35 mNIST Poisson ratio in ideal fcc crystal0.25- Cauchy & Poisson Mass of particlePlanck massmPmP 2.17645(16)·10 -8 kgNIST Frequency of the internal process Inverse of the Planck time f P = 1/t P 1.85486(98)·10 43 s -1 NIST Lamé constantEnergy density1.853237194·10 114 kgm -1 s -2 This work Number of particles in unit cell4This work National Institute of Standards and Technology, Reference on Constants, Units and Uncertainty, http://physics.nist.gov (2006).http://physics.nist.gov The physical constants (ideal regular fcc lattice)
The energy of volume deformation field: The energy of the torsion field:.
Mass conservation: Energy conservation: Volume continuity: Gravity:
4. The “dark energy” → energy of the DIPP’s. 1.The Diffusing Interstitial Planck Particles (DIPP’s) = WIMP’s 2. DIPP’s create the gravitational interaction between matter. 3. The “dark matter” → DIPP’s
Full set Maxwell eqs. in vacuum: analogous simple transformations...
Other Maxwell “empty lattice” and low deformation. From noncompressible flow follows:. The charged particles are not considered differentiating equation for E : The identity. The Maxwell system in vacuum.
Mass conservation: Energy Conservation: and… Quantum mechanics:
1.The deformation, its velocity and diffusion of defects are now assumed to be negligible
The energy flux: 1.The process that governs de Broglie waves is the fast internal process. 2.We analyze the case when the driving force of the transport (the collective Planck mass movement, i.e., the movement of a complex of particles showing an energy E and mass M = E c -2 ), is controlled by the imaginary part of mechanical potential
The physical constants at the Planck scale and... four time scales! Physical QuantityValue in SI unitsSI unitReference Volume of PC cell4.222 002 828·10 -105 m3m3 This work & NIST Planck density2.062 008 662·10 97 kg m -3 This work & NIST Young modulus4.633 092 986·10 114 kg m -1 s -2 This work Planck mass mobility5.391 213 982·10 -44 sThis work Defects self-diffusion coefficient2.422 685 816·10 -27 m 2 s -1 This work Planck constant 6.626 069 311·10 -34 6.626 069 3(11)·10 -34 kg m 2 s -1 This work NIST Gravitational constant 6.6742(10)·10 -11 6.674176·10 -11 m 3 kg -1 s -2 NIST This work Speed of longitudinal wave519 255 240m s -1 This work Speed of transverse wave 299 792 153 299 792 458 m s -1 This work NIST
Physical reality at the Planck scale: Faster than light velocity of longitudinal wave… Kleinert: "fine-tuning" to make all “sound speeds” equal or… consider: The different velocities are related to specific force field → a real quantities that mark different time-scales. The Diffusing Interstitial Planck Particles (DIPP’s) → gravity The collective behavior of the Planck particles → the particle: Schrödinger equation follows.
Transverse wave ≡ electromagnetic wave DIPP’s → Dark Matter → Dark Energy Waves involving temperature ≡ “the second sound” described by Landau and Lifschitz, etc…
Physical QuantityUnitSymbol for unitValue in SI unitsSI unitReference Lattice parameterPlanck lengthlPlP 1.61624(12)·10 -35 mNIST Poisson ratio in PKC0.25-Poisson Mass of particlePlanck massmPmP 2.17645(16)·10 -8 kgNIST Frequency of the internal process Inverse of the Planck time f P = 1/t P 1.85486(98)·10 43 s -1 NIST Lamé constant Energy density 1.853237194·10 114 kgm -1 s -2 This work Number of particles in unit cell4This work National Institute of Standards and Technology, Reference on Constants, Units and Uncertainty, http://physics.nist.gov (2006).http://physics.nist.gov The physical constants in Planck-Kleinert Crystal
The collective movement (“the particle like” behavior): - in fluids (e.g., vortex, soliton, etc.), - in solids (e.g., complex defects and standing waves*. The particle wave → E = M c 2 The particle is a complex → by analogy its mobility, B M : *J. Giannoulis and A. Mielke, Nonlinearity 17, 551-565 (2004).
Fundamentals I Euler - the volume & molar volume: … homogeneous of the 1 st degree in the variables n 1,…, n r
The volume and molar volume: N i = c i /c is molar ratio … homogeneous of the 1 st degree in the variables N 1,…, N r
Maxwell equations in vacuum → assume: - the rotation of the deformation vector = -E - the mass flux due to deformation = B. Multiply both sides by: