Related papers: Mean-field Modeling of Social Interactions Using C…
Many-body long-range interacting systems can remain approximately in a quasi-stationary state far-from-thermodynamic equilibrium. These states are typically characterized by a pair of counter-propagating density clusters, or by a single…
A density functional theory of two-dimensional freezing is presented for a soft interaction potential that scales as inverse cube of particle distance. This repulsive potential between parallel, induced dipoles is realized for paramagnetic…
Interacting particles on graphs are routinely used to study magnetic behaviour in physics, disease spread in epidemiology, and opinion dynamics in social sciences. The literature on mean-field approximations of such systems for large graphs…
Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game…
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…
In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…
We analyze a variant of the Desai-Zwanzig model [J. Stat. Phys. {\bf 19}1-24 (1978)]. In particular, we study stationary states of the mean field limit for a system of weakly interacting diffusions moving in a multi-well potential energy…
A dynamic mean-field theory for spin ensembles (spinDMFT) at infinite temperatures on arbitrary lattices is established. The approach is introduced for an isotropic Heisenberg model with $S = \tfrac12$ and external field. For large…
Dynamical mean-field theory is a powerful physics tool used to analyze the typical behavior of neural networks, where neurons can be recurrently connected, or multiple layers of neurons can be stacked. However, it is not easy for beginners…
Living cells respond to mechanical changes in the matrix surrounding them by applying contractile forces that are in turn transmitted to distant cells. We calculate the mechanical work that each cell performs in order to deform the matrix,…
We introduce a model of uncoupled pendula, which mimics the dynamical behavior of the Hamiltonian Mean Field (HMF) model. This model has become a paradigm for long-range interactions, like Coulomb or dipolar forces. As in the HMF model,…
We consider a system of particles interacting via a purely repulsive, soft-core potential recently introduced to model effective pair interactions between dendrimers, which is expected to lead to the formation of crystals with multiple…
Model Hamiltonians with long-range interaction yield energies that are corrected taking into account the universal behavior of the electron-electron interaction at short range. Although the intention of the paper is to explore the…
We study binary state contagion dynamics on a social network where nodes act in response to the average state of their neighborhood. We model the competing tendencies of imitation and non-conformity by incorporating an off-threshold into…
Neural computations emerge from myriads of neuronal interactions occurring in intricate spiking networks. Due to the inherent complexity of neural models, relating the spiking activity of a network to its structure requires simplifying…
For the modelling of pedestrian dynamics we treat persons as self-driven objects moving in a continuous space. On the basis of a modified social force model we qualitatively analyze the influence of various approaches for the interaction…
Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. We demonstrate how the long-ranged interactions responsible for this behavior arise naturally upon integrating out mechanical…
We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a…
Temporal networks of face-to-face interactions between individuals are useful proxies of the dynamics of social systems on fast time scales. Several empirical statistical properties of these networks have been shown to be robust across a…
Given an arbitrary finite dimensional Hamiltonian H_0, we consider the model H=H_0+\Delta H, where \Delta H is a generic fully connected interaction. By using the strong law of large numbers we easily prove that, for all such models, a…