Related papers: An analytical method to quantify the statistics of…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
Predicting which crystalline modifications can be present in a chemical system requires the global exploration of its energy landscape. Due to the large computational effort involved, in the past this search for sufficiently stable minima…
We present a technique for calculating free-energy profiles for the nucleation of multicomponent structures that contain as many species as building blocks. We find that a key factor is the topology of the graph describing the connectivity…
Energy piles are gaining increased popularity due to a growing demand for clean energy. To further advance the understanding of soil-structure interaction in energy piles, recently-derived analytical solutions have been implemented to…
Site-occupancy disorder, defined as the non-periodic occupation of lattice sites in a crystal structure, is a ubiquitous phenomenon in solid-state physics and chemistry. Examples are mineral solid solutions, synthetic non-stoichiometric…
Accurate calculations of solvation free energies remain a central challenge in molecular simulations, often requiring extensive sampling and numerous alchemical intermediates to ensure sufficient overlap between phase-space distributions of…
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…
The stochastic properties of the total internal energy of a dilute granular gas in the steady uniform shear flow state are investigated. A recent theory formulated for fluctuations about the homogeneous cooling state is extended by analogy…
In order to better understand the occurrence of phase transitions, we adopt an approach based on the study of energy landscapes: The relation between stationary points of the potential energy landscape of a classical many-particle system…
We investigate the relation between the dynamical features of a supercooled liquid and those of its potential energy landscape, focusing on a model liquid with density anomalies. We consider, at fixed temperature, pairs of state points with…
Real ecosystems are characterized by sparse and asymmetric interactions, posing a major challenge to theoretical analysis. We introduce a new method to study the generalized Lotka-Volterra model with stochastic dynamics on sparse graphs. By…
Specific aspects of time series analysis are discussed. They are related to the analysis of atmospheric data that are pertinent to clouds. A brief introduction on some of the most interesting topics of current research on climate/weather…
We model a close-knit community of friends and enemies as a fully connected network with positive and negative signs on its edges. Theories from social psychology suggest that certain sign patterns are more stable than others. This notion…
The theory of the effect of external fluctuation force on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using classical…
Quantitative evaluations of the free energy of materials must take into account thermal and zero-point energy fluctuations. While these effects can easily be estimated within a harmonic approximation, corrections arising from the anharmonic…
Understanding the physics of non-equilibrium systems remains as one of the major open questions in statistical physics. This problem can be partially handled by investigating macroscopic fluctuations of key magnitudes that characterise the…
Energy landscape analysis is a data-driven method to analyze multidimensional time series, including functional magnetic resonance imaging (fMRI) data. It has been shown to be a useful characterization of fMRI data in health and disease. It…
We develop a mathematical model for the energy landscape of polyhedral supramolecular cages recently synthesized by self-assembly [Sun et al., Science 2010]. Our model includes two essential features of the experiment: (i) geometry of the…
The climate belongs to the class of non-equilibrium forced and dissipative systems, for which most results of quasi-equilibrium statistical mechanics, including the fluctuation-dissipation theorem, do not apply. We show for the first time…