Related papers: Bifurcation Analysis of Liquid Crystal Phase Trans…
Crystallization is one of the most important phase transformations of first order. In the case of metals and alloys, the liquid phase is the parent phase of materials production. The conditions of the crystallization process control the…
Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…
This study examines anomalous diffusion and dynamical phase transitions in a nonlinear bouncer model with short-range interactions leading to velocity-dependent (adiabatic) collisions. By varying a control parameter, transitions between…
We give a brief introduction to the mode-coupling theory of the glass transition, a theory which was proposed a while ago to describe the dynamics of supercooled liquids. After presenting the basic equations of the theory, we review some of…
Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to…
A number of tools have been developed to detect topological phase transitions in strongly correlated quantum systems. They apply under different conditions, but do not cover the full range of many-body models. It is hence desirable to…
We model quantum measurement of a two-level system $\mu$. Previous obstacles for understanding the measurement process are removed by basing the analysis of the interaction between $\mu$ and the measurement device on quantum field theory.…
Transition phenomena between thermodynamic branch and turbulent branch in submarginal turbulent plasma are analyzed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin equation…
We develop a Landau like theory to characterize the phase transitions in resetting systems. Restart can either accelerate or hinder the completion of a first passage process. The transition between these two phases is characterized by the…
The aim of these notes is to give a quick introduction to FK-percolation, focusing on certain recent results about the phase transition of the two dimensional model, namely its continuity or discontinuity depending on the cluster weight…
We show that finite size scaling techniques can be employed to study the glass transition. Our results follow from the postulate of a diverging correlation length at the glass transition whose physical manifestation is the presence of…
Liquid-liquid phase separation has recently emerged as an important topic in the context of cellular organization. Within this context, there are multiple poorly understood features; for instance hints of critical behavior in the plasma…
A model for two-dimensional colloids confined laterally by "structured boundaries" (i.e., ones that impose a periodicity along the slit) is studied by Monte Carlo simulations. When the distance D between the confining walls is reduced at…
We numerically investigate nucleation processes in the transient dynamics of the two-dimensional complex Ginzburg-Landau equation towards its "frozen" state with quasi-stationary spiral structures. We study the transition kinetics from…
To understand the behavior of composite fluid particles such as nucleated cells and double-emulsions in flow, we study a finite-size particle encapsulated in a deforming droplet under shear flow as a model system. In addition to its…
Using molecular dynamics simulation we examine changeovers among crystal, glass, and liquid at high density in a two dimensional binary mixture. We change the ratio between the diameters of the two components and the temperature. The…
This article introduces a dynamical Ginzburg-Landau phase transition/separation model for the mixture of liquid helium-3 and helium-4, using a unified dynamical Ginzburg-Landau model for equilibrium phase transitions. The analysis of this…
In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic…
We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…