Related papers: Concepts of polymer statistical topology
Recent discoveries have demonstrated that matter can be distinguished on the basis of topological considerations, giving rise to the concept of topological phase. Introduced originally in condensed matter physics, the physics of topological…
The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From…
Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their…
Although not as wide, and popular, as that of quantum mechanics, the investigation of fundamental aspects of statistical mechanics constitutes an important research field in the building of modern physics. Besides the interest for itself,…
This works explores and illustrates recent results developed by the author in field of dynamical network analysis. The considered approach is blind, i.e., no a priori assumptions on the interconnected systems are available. Moreover, the…
Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the…
We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…
Polymer networks invariably possess topological inhomogeneities in the form of loops and dangling ends. The macroscopic properties of such materials are directly dependent on the local cyclic topology around nodes and chains. Here, a new…
In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…
This contribution, to be published in Imagine Math 8 to celebrate Michele Emmer's 75th birthday, can be seen as the second part of my previous considerations on the relationships between topology and physics (Mouchet, 2018). Nevertheless,…
The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
Topological data analysis asks when balls in a metric space $(X,d)$ intersect. Geometric data analysis asks how much balls have to be enlarged to intersect. We connect this principle to the traditional core geometric concept of curvature.…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
Symmetry Protected Topological (SPT) phases describe trivially-acting symmetries. We argue that a symmetry-based description of SPT phases ought to include the topological twist fields associated to the symmetry. Doing so allows us to…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
Statistical physics provides a useful perspective for the analysis of many complex systems; it allows us to relate microscopic fluctuations to macroscopic observations. Developmental biology, but also cell biology more generally, are…
Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…