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18 Oct 2021: and. -. 𝑑. x. x. e. -. a. x. 2. =. 0. (2.24). where the second equality follows because the integrand is odd (and suitably well behaved at infinity). ... σ. ). exp. (. -. x. 2. σ. |. α. |. 2. ). =. k. 0. where, to get the final equality, we did the

11 Jun 2021: Demonstration of convergence. 24 THE BARRIERS OF DEEP LEARNING AND SMALE’S 18TH PROBLEM.

10 Sep 2021: Active Brownian motion tunable by light. J. Phys. Condens. Matter 24, 284129 (2012). ... Soft Matter 16, 4961–4968 (2020). 24. Shao, J. et al. Erythrocyte membrane modified Janus polymeric motors for thrombus therapy.

8 Sep 2021: 3Institut Universitaire de France (IUF), 75005 Paris, France. (Received 9 May 2021; accepted 24 August 2021; published 8 September 2021). ... 24). It follows that the rescaled area S = A/a2 monotonically de-creases in time,.

8 Jul 2021: of Bristol, 24 Tyndall Avenue, Bristol BS8 1TQ, UK. ... uθ = cΩ I1(κr)K1(κ) K1(κr)I1(κ)I1(κc)K1(κ) K1(κc)I1(κ), (4.24)where. α0 = cκΩ. I1(κ)I1(κc)K1(κ)

18 Oct 2021: 3 Structure Formation. 3 Structure Formation. Until now, we have discussed a universe which is perfectly homogeneous and isotropic. But that is not the universe we live in. Instead, our universe contains interesting objects which clump together,

18 Oct 2021: 5 Phase Transitions. 5 Phase Transitions. A phase transition is an abrupt, discontinuous change in the properties of a system. We’ve already seen one example of a phase transition in our discussion of Bose-Einstein condensation. In that case, we

8 Jul 2021: For larger ciliatedcells [24], or for multicellular aquatic organisms equippedwith many short flagella [25], the synchronization dynamicstakes the form of metachronal waves, akin to spectator wavesin sport stadiums. ... p = p1 O(2 ), (24). σ = σ1 O(2 ).

20 Jul 2021: RESEARCH ARTICLE. Hydrodynamics and direction change of. tumbling bacteria. Mariia DvoriashynaID, Eric LaugaID. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United. Kingdom. e.lauga@damtp.cam.ac.uk.

10 Sep 2021: coli bacteria showingchemo-attraction to self-produced autoinducers [24]. A mechanical example of taxis, viscotaxis, emerges when a cell adapts its motion in responseto viscosity gradients. ... U2 (h) = A2 D2hB2 C2h , (23). where. A2 = ξ λ′ (1 βT )R