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20 Oct 2022: atom. It is another thing to solve it! No exact solutions of (3.24) are known for. ... in (3.24). In this case, the Hamiltonian reduces to N copies of.

9 Nov 2022: Newtonian fluids, includingboth short-range and long-range hydrodynamic interactions,direct collisions, and Brownian motion (24, 28, 29, 31, 32,43, 44). ... 24) forNewtonian fluids to predict the size of the radius of curvatureusing the distribution of

3 Dec 2022: 2. Zd3r0 r0 J(r0) (3.24). Just as in the electric case, the multipole expansion continues to higher terms. ... 3.24),. B(r) =µ04. 3(m1 r̂)r̂ m1. r3. (3.30). Now we’ll consider how this aects the second dipole m = m2.

27 Mar 2022: Expand out all 24 terms and watch them cancel one by one.

25 Aug 2022: 24. Conclusions: mechanisms. I Visco-elastic Oldroyd-B predicts a reduction in pressure drop compared with a Newtonian.

24 Jul 2022: walls, but somewhat beyond the scope of these lectures.). – 24 –. 2.2.1 R-Symmetry. We started this section by noting that all internal symmetries must commute with the. ... e. iQ̄̇ (2.24). This U(1) symmetry is known as an R-symmetry and is

16 Jun 2022: Û(t) = exp(itĤ) (24). which is sensibly called the time evolution operator.

10 May 2022: 2.24). Notably, this expression can be simplified into. s0 =sb(rc) r s(.

18 Nov 2022: mpEDMD: First convergent Galerkin method! 24/34. Numerical examples. 25/34. Lorenz system: scalar-valued spec measሶ𝑥1 = 10 𝑥2 𝑥1 , ሶ𝑥2 = 𝑥1 28 𝑥3 𝑥2, ሶ𝑥3 = 𝑥1𝑥2.

21 Oct 2022: 2.4.1 Noether’s Theorem 24. 2.5 Applications 26. 2.5.1 Bead on a Rotating Hoop 26. ... kinetic energy,. T(t2) T(t1) =i. Fexti dri. i 6=j. Fij dri (1.24).