Related papers: Dynamic Landau Theory for Supramolecular Self-Asse…
We explore a supersymmetric (SUSY) theory that arises in the Landau level problem with disorder. Charged particles in a strong magnetic field and a local potential are described by small excitations around the ground state, the lowest…
The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order…
The simulated self-assembly of molecular building blocks into functional complexes is a key area of study in computational biology and materials science. Self-assembly simulations of proteins using physically-motivated potentials for…
The coexistence of the superconductivity and magnetism in the Ho$_{1-x}$Dy$_x$Ni$_2$B$_2$C is studied by using Ginzburg-Landau theory. This alloy shows the coexistence and complex interplay of superconducting and magnetic order. We propose…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
Reconstruction of a dynamical system from a time series requires the selection of two parameters, the embedding dimension $d_e$ and the embedding lag $\tau$. Many competing criteria to select these parameters exist, and all are heuristic.…
Spontaneous self-assembly in molecular systems is a fundamental route to both biological and engineered soft matter. Simple micellisation, emulsion formation, and polymer mixing principles are well understood. However, the principles behind…
With exquisite precision and reproducibility, cells orchestrate the cooperative action of thousands of nanometer-sized molecular motors to carry out mechanical tasks at much larger length scales, such as cell motility, division and…
Dynamical processes on networks are currently being considered in different domains of cross-disciplinary interest. Reaction-diffusion systems hosted on directed graphs are in particular relevant for their widespread applications, from…
Bimetric theory describes a massless and a massive spin-2 field with fully non-linear (self-)interactions. It has a rich phenomenology and has been successfully tested with several data sets. However, the observational constraints have not…
The supersymmetry method has proven to be a very powerful tool of study of the statistical properties of energy levels and eigenfunctions in disordered and chaotic systems. The aim of these lectures is to present a tutorial introduction to…
We have mapped the physics of a system of semi-flexible inextensible polymers onto a complex Ginzburg-Landau field theory using techniques of functional integration. It is shown in the limit of low number density of monomers in a melt of…
Two fluid simulations using local Landau-fluid closures derived from linear theory provide an efficient computational framework for plasma modelling, since they bridge the gap between computationally intensive kinetic simulations and fluid…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
This paper studies synchronization in coupled nonlinear dynamic networks with unknown parameters. Adaptation can be added to one or several elements in the network, while preserving the global synchronization conditions derived in…
The aim of this work is to address issues where formal specifications cannot be realized on a given dynamical system subjected to a changing environment. Such failures occur whenever the dynamics of the system restrict the robot in such a…
On the basis of phenomenological Ginzburg-Landau approach we investigate the problem of order parameter nucleation in hybrid superconductor/ferromagnetic systems with a domain structure in applied external magnetic field. Both the isolated…
Emergent phenomena share the fascinating property of not being obvious consequences of the design of the system in which they appear. This characteristic is no less relevant when attempting to simulate such phenomena, given that the outcome…
We propose a computationally lean, two-stage approach that reliably predicts self-assembly behavior of complex charged molecules on a metallic surfaces under electrochemical conditions. Stage one uses ab initio simulations to provide…
Mathematical models of cognition are often memoryless and ignore potential fluctuations of their parameters. However, human cognition is inherently dynamic. Thus, we propose to augment mechanistic cognitive models with a temporal dimension…