# Phase transitions

Monday, April 28, 2014 - 11:30am - 12:20pm

Mei Yin (Brown University)

The edge-triangle exponential random graph model has been a topic of continued research interest. We review recent developments in the study of this classic model and concentrate on the phenomenon of phase transitions. We first describe the asymptotic feature of the model along general straight lines. We show that as we continuously vary the slopes of these lines, a typical graph exhibits quantized behavior, jumping from one complete multipartite structure to another, and the jumps happen precisely at the normal lines of a polyhedral set with infinitely many facets.

Wednesday, April 13, 2011 - 11:30am - 12:30pm

Malgorzata Peszynska (Oregon State University)

In the talk we describe two applications important for global climate

and energy studies: methane hydrates and coalbed methane. Methane

hydrates also known as ice that burns are present in large amounts

along continental slopes and in permafrost regions and, therefore, are

a possible source of energy and at the same time a potential

environmental hazard. Their evolution critically depends on how the

hydrate formation and dissociation affects the porescale properties.

This so far has been only modeled with ad-hoc phenomenological

and energy studies: methane hydrates and coalbed methane. Methane

hydrates also known as ice that burns are present in large amounts

along continental slopes and in permafrost regions and, therefore, are

a possible source of energy and at the same time a potential

environmental hazard. Their evolution critically depends on how the

hydrate formation and dissociation affects the porescale properties.

This so far has been only modeled with ad-hoc phenomenological

Tuesday, May 19, 2009 - 11:30am - 12:10pm

Francesco Gervasio (Eidgenössische TH Zürich)

Large scale conformational rearrangements represent both a

challenge and an opportunity for rational drug design.

Exploring the conformational space of a target protein with sufficient detail is computationally very demanding and most current docking programs are very limited in this respect.

If it were possible, however, it could open the avenue to the design of

more selective drug candidates. Here we show how atomistic molecular

dynamics together with methods developed to accelerate rare events can

challenge and an opportunity for rational drug design.

Exploring the conformational space of a target protein with sufficient detail is computationally very demanding and most current docking programs are very limited in this respect.

If it were possible, however, it could open the avenue to the design of

more selective drug candidates. Here we show how atomistic molecular

dynamics together with methods developed to accelerate rare events can

Friday, September 12, 2014 - 10:15am - 11:05am

Michael Krivelevich (Tel Aviv University)

We establish the existence of the phase transition in site percolation on pseudo-random d-regular graphs. Let G=(V,E) be an (n,d,lambda)-graph, that is, a d-regular graph on n vertices in which all eigenvalues of the adjacency matrix, but the first one, are at most lambda in their absolute values. Form a random subset R of V by putting every vertex v in V into R independently with probability p.

Friday, September 12, 2014 - 9:00am - 9:50am

Mihyun Kang (Technische Universität Graz)

The study of phase transitions in random graphs was initiated by Erdos and Renyi in 1960. They proved among other things that a uniform random graph undergoes a drastic change in the size and structure of the largest component, caused by altering a critical edge density. Since the seminal work of Erdos and Renyi, various random graph models have been introduced and studied over the last five decades. In this talk I will discuss some recent results in phase transitions in random hypergraphs. (Joint work with Oliver Cooley and Christoph Koch.)

Wednesday, May 21, 2014 - 8:40am - 9:20am

Barbara Niethammer (Rheinische Friedrich-Wilhelms-Universität Bonn)

We discuss a nonlocal Fokker-Planck equation that describes energy minimisation in a double well-potential and is driven by a time-dependent constraint. Via formal asymptotic analysis we identify different small parameter regimes that correspond to hysteretic and non-hysteretic phase transitions respectively. For the fast reaction regime that is related to Kramers-type phase transitions we also indicate how can rigorously derive a rate-independent evolution equation in a small parameter limit.

This is joint work with Michael Herrmann and Juan Velazquez.

This is joint work with Michael Herrmann and Juan Velazquez.

Monday, September 26, 2011 - 2:00pm - 3:00pm

Alfred Hero III (University of Michigan)

Random matrices are measured in many areas of engineering, social science, and natural science. When the rows of the matrix are random samples of a vector of dependent variables the sample correlations between the columns of the matrix specify a correlation graph that can be used to explore the dependency structure.

Thursday, May 19, 2011 - 10:30am - 11:30am

Shape memory alloys and other active materials undergo displacive phase transitions which change the symmetry of the crystal lattice through a diffusionless coordinated motion of atoms. A signature feature of these materials is the hysteresis they exhibit in response to cyclic loading. The dissipation is due to propagating phase boundaries that can be