Related papers: Dynamic Landau Theory for Supramolecular Self-Asse…
Understanding the continuum limit of a theory of discrete random geometries is a beautiful but difficult challenge. In this optic, we review here the insights that can be obtained for Causal Dynamical Triangulations (CDT) by employing the…
In this study, we present theoretical investigations of phase transitions and critical phenomena in materials through the lens of second-order Ginzburg-Landau theory, in conjunction with considerations of symmetry groups and thermal…
We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…
The classical kinetic theory of one-component self-interacting scalar fields is formulated in the broken symmetry phase and applied to the phenomenon of Landau damping. The domain of validity of the classical approach is found by comparing…
We have developed a theory of polymer entanglement using an extended Cahn-Hilliard functional, with two extra terms. One is a nonlocal attractive term, operating over mesoscales, which is interpreted as giving rise to entanglement, and the…
Transition from bending-dominated to stretching-dominated elastic response in semi-flexible fibrous networks plays an important role in the mechanical behavior of cells and tissues. It is induced by changes in network connectivity and…
By constructing a Landau-like energy functional, we investigate the molecular organization of a three-component mixture in cell membranes. In the strongly interacting limit, we model the interaction between molecules using pseudospin…
Protein aggregation is of great importance in biology, e.g., in amyloid fibrillation. The aggregation processes that occur at the cellular scale must be highly stochastic in nature because of the statistical number fluctuations that arise…
We make a connection between quantum phase transitions in condensed matter systems, and supersymmetric gauge theories that are of interest in the particle physics literature. In particular, we point out interesting effects of the…
Protein collapse can be viewed as a dynamical phase transition, during which new scales and collective variables become excited while the old ones recede and fade away. This causes formidable computational bottle-necks in approaches that…
Several field theoretical approaches to the superconducting phase transition are discussed. Emphasis is given to theories of scaling and renormalization group in the context of the Ginzburg-Landau theory and its variants. Also discussed is…
The Landau theory of phase transitions has been re-examined under the framework of a modified mean field theory in ferroelectrics. By doing so, one can see that there are two atomic movements involved in the ferroelectric phase transition;…
Supermodeling is a modern, model-ensembling paradigm that integrates several self-synchronized imperfect sub-models by controlling a few meta-parameters to generate more accurate predictions of complex systems' dynamics. Continual…
The Landau paradigm has been a powerful framework for understanding phase transitions involving spontaneous symmetry breaking. In contrast, phase transitions between two symmetric phases, where neither phase breaks any symmetry, remain less…
Landau damping is a key mechanism to preserve the stability of particle beams under the influence of various collective forces that would otherwise spoil its quality through beam instabilities. We describe its root cause as well as ways to…
We show that nonlinear continuum elasticity can be effective in modeling plastic flows in crystals if it is viewed as Landau theory with an infinite number of equivalent energy wells whose configuration is dictated by the symmetry group…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
Several sub-diffusive stochastic processes in nature, e.g., motion of tagged monomer in polymers, height fluctuation of interfaces and particle dynamics in single-file diffusion etc. can be described rigorously or approximately by the…
Amorphous particulate matter constitutes a wide range of natural and synthetic materials. Despite this ubiquity, the way in which these systems' disordered microstructure couples to their often subtle and complex dynamical behavior is not…
The gauge dependence of the renormalization group functions of the Ginzburg-Landau model is investigated. The analysis is done by means of the Ward-Takahashi identities. After defining the local superconducting order parameter, it is shown…