Anúncios · Física Estatística Complementar
https://fenix.ciencias.ulisboa.pt/courses/fec-1128979398395671/sumarios/announcement
Anúncios · Física Estatística Complementarpt-PTFaculdade de Ciências (FenixEdu)FenixEdu CMS v3.3.0-FORKhttp://blogs.law.harvard.edu/tech/rss601st set of homework<p>1. Solve one dimensional, -\infty <x< +\infty, Fokker-Planck equation for a free Brownian particle, i.e., external potential V = 0. Assume that at time t=0 the particle was at x=0. Plot the result as a function of x for several values of t. Calculate moments <x<sup>n</sup>><sup> </sup> and compare with the results of Langevin equation approach (<...> denotes the ensemble average).</p><p><br /></p><p>2. Solve one dimensional, -\infty <x< +\infty, Fokker-Planck equation for a Brownian particle in the external potential V(x) = mg x, m is the particle mass, and g is the gravitation acceleration. Assume that at time t=0 the particle was at x=x<sub>0</sub>. Plot the result as a function of x for several values of t, choose some value for x<sub>0</sub>.</p><p><br /></p><p>3. For a free one dimensional Brownian motion of a particle starting at time t = 0 from x = 0, determine the probability density P<sub>x</sub>(t) that the particle will reach for the first time a given point x at a moment of time in the interval (t, t + dt). </p><p>[Remark: P<sub>x</sub>(t) dt is the probability that the particle for the first time will get from x=0 to the point x in time from the interval (t, t+dt)].</p>
https://fenix.ciencias.ulisboa.pt/courses/fec-1128979398395671/ver-artigo/1st-set-of-homework
mtasinkevych@fc.ul.pt (Mykola Tasinkevych)https://fenix.ciencias.ulisboa.pt/courses/fec-1128979398395671/ver-artigo/1st-set-of-homework#2252590087673394AnúnciosFri, 28 Sep 2018 15:10:50 +0100