Related papers: Glass transition and random walks on complex energ…
Networks are powerful tools for modeling interactions in complex systems. While traditional networks use scalar edge weights, many real-world systems involve multidimensional interactions. For example, in social networks, individuals often…
By means of molecular dynamics, we study the structure and the dynamics of a microscopic model for colloidal gels at low volume fractions. The presence of directional interactions leads to the formation of a persistent interconnected…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
Amorphous materials exhibit structural heterogeneities that relax only on long timescales. Using machine learning techniques, we construct a Markov state model (MSM) for model glass formers that coarse-grains the dynamics into a…
We propose a random walks based model to generate complex networks. Many authors studied and developed different methods and tools to analyze complex networks by random walk processes. Just to cite a few, random walks have been adopted to…
We propose and study a model with glassy behavior. The state space of the model is given by all triangulations of a sphere with $n$ nodes, half of which are red and half are blue. Red nodes want to have 5 neighbors while blue ones want 7.…
We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With…
The relationship between short and long time relaxation dynamics is obtained for a simple solvable two-level energy landscape model of a glass. This is done through means of the Kramers transition theory, which arises in very natural manner…
The effects of floppy modes in the thermodynamical properties of a system are studied. From thermodynamical arguments, we deduce that floppy modes are not at zero frequency and thus a modified Debye model is used to take into account this…
We study the dynamics of a glassy model with infinite range interactions externally driven by an oscillatory force. We find a well-defined transition in the (Temperature-Amplitude-Frequency) phase diagram between (i) a `glassy' state…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
Potential energy landscapes can be represented as a network of minima linked by transition states. The community structure of such networks has been obtained for a series of small Lennard-Jones clusters. This community structure is compared…
A molecular theory of the glass transition of network forming liquids is developed using a combination of self-consistent phonon and liquid state approaches. Both the dynamical transition and the entropy crisis characteristic of random…
Consider the following routing problem in the context of a large scale network $G$, with particular interest paid to power law networks, although our results do not assume a particular degree distribution. A small number of nodes want to…
We analyze the probability distribution for entropy production rates of trajectories evolving on a class of out-of-equilibrium kinetic networks. These networks can serve as simple models for driven dynamical systems, which are of particular…
In the past years, a remarkable mapping has been found between the dynamics of a population of M individuals undergoing random mutations and selection, and that of a single system in contact with a thermal bath with temperature 1/M. This…
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
Energetic correlations due to polymeric constraints and the locality of interactions, in conjunction with the apriori specification of the existence of a particularly low energy state, provides a method of introducing the aspect of minimal…
Glass transitions are widely observed in various types of soft matter systems. However, the physical mechanism of these transitions remains {elusive}, despite years of ambitious research. In particular, an important unanswered question is…
The evolution of many dynamical systems that describe relationships or interactions between objects can be effectively modeled by temporal networks, which are typically represented as a sequence of static network snapshots. In this paper,…