# Seminars of the Focus Area Complex Systems

# Seminar

**Speaker:**Igor Sokolov, Universität zur Humboldt, Berlin

**Title:**Physics and Mathematics of Anomalous Diffusion * Kolloquium des Inst. f. Mathematik

**Time:**Wed, May 7, 2014, 3:30pm

**Place:**Am Neuen Palais, bldg 9, room 1.12

**Abstract:**

Particle’s motion in crowded environments often exhibits anomalous diffusion, whose nature depends on the situation at hand and is formalized within different physical models. Thus, such environments may contain traps, labyrinthine paths or macromolecular structures which the particles may be attached to. Physical assumptions are translated into mathematical models which often come with nice mathematical instruments for their description, e.g. fractional diffusion equations. We discuss the corresponding physical situations, their mathematical models, and the statistical tests which allow to distinguish between cases for which one or another model applies.

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# Seminar

**Speaker:**Igor Sokolov, Statistische Physik und Nichtlineare Dynamik, Theoretische Physik, Humboldt Universität zu Berlin

**Title:**Models of anomalous diffusion in crowded environments * Colloquium on Complex and Biological Systems

**Time:**Fri, Feb 7, 2014, 10:15am

**Place:**bldg 28, room 0.108

**Abstract:**

A particle’s motion in crowded environments often exhibits anomalous diffusion, whose nature depends on the situation at hand and is formalized within different physical models. Thus, such environments may contain traps, labyrinthine paths or macromolecular structures, which the particles may be attached to. Physical assumptions are translated into mathematical models which often come with nice mathematical instruments for their description, e.g. fractional diffusion equations. The beauty of the instrument sometimes seduces an investigator to use it without any connection to the physical model. The author hopes that the present discussion will reduce the danger of such inappropriate use. Sokolov: Soft Matter 8 (2012) 9043;

The ergodicity breaking parameter is a measure for the heterogeneity among different trajectories of one ensemble. In this report, this parameter is calculated for fractional Brownian motion with a random change of time scale, often called “subordination.” We show that this quantity is the same as the known continuous time random walks case. Thiel, Sokolov: Weak ergodicity breaking in an anomalous diffusion process of mixed origins, PRE 89, 012136 (2014);

We show that some important properties of subdiffusion of unknown origin (including ones of mixed origins) can be easily assessed when finding the “fundamental moment” of the corresponding random process, i.e., the one which is additive in time. In subordinated processes, the index of the fundamental moment is inherited from the parent process and its time dependence from the leading one. In models of a particle’s motion in disordered potentials, the index is governed by the structural part of the disorder while the time dependence is given by its energetic part. Thiel, Flegel, Sokolov: Disentangling Sources of Anomalous Diffusion, PRL 111, 010601 (2013);

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## Past NLD Seminars (1994-2007) & (2008 ...)

Students' seminar: Theoretical Physics, PIK, Modeling & TSA | Berlin-Potsdam-Colloquia: PhysGesellschaft Berlin, TU Berlin, Pro Physik, AIP, AEI, MPI-KGF, GFZ, HMI, PIK, AWI, Max Planck Institute for the History of Science, Mathematik, DPG | Disputationen, & Vorschau UP |

Udo Schwarz, Zentrum für Dynamik komplexer Systeme,

Universität Potsdam, Campus Golm Karl-Liebknecht-Str. 24, 14476 Potsdam, building 28, room 2.107

Phone: (+49-331) 977-1658, Fax : (+49-331) 977-1045

Email: Udo.Schwarz AT uni-potsdam.de