Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice [PDF]
, 2013 We present an a priori error analysis of a practical energy based atomistic/continuum coupling method (A. V. Shapeev, Multiscale Model. Simul., 9(3):905-932, 2011) in two dimensions, for finite-range pair-potential interactions, in the presence of ...
Ortner, C. +2 more
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Binary-state dynamics on complex networks: Stochastic pair approximation and beyond
Physical Review Research, 2020 Theoretical approaches to binary-state models on complex networks are generally restricted to infinite size systems, where a set of nonlinear deterministic equations is assumed to characterize its dynamical and stationary properties.
A. F. Peralta, R. Toral
doaj +1 more source
Tensor networks contraction and the belief propagation algorithm
Physical Review Research, 2021 Belief propagation is a well-studied message-passing algorithm that runs over graphical models and can be used for approximate inference and approximation of local marginals.
R. Alkabetz, I. Arad
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Binary-State Dynamics on Complex Networks: Pair Approximation and Beyond
Physical Review X, 2013 A wide class of binary-state dynamics on networks—including, for example, the voter model, the Bass diffusion model, and threshold models—can be described in terms of transition rates (spin-flip probabilities) that depend on the number of nearest ...
James P. Gleeson
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Approximate Solution of the Pairing Hamiltonian in the Berggren Basis [PDF]
Acta Physica Polonica B, 2016 We derive the approximate solution for the pairing Hamiltonian in the Berggren ensemble of single particle states including bound, resonance and non-resonant scattering states. We show that this solution is reliable in the limit of a weak pairing interaction.
Mercenne, A. +2 more
openaire +3 more sources
A posteriori error control for a quasi-continuum approximation of a periodic chain [PDF]
, 2013 We consider a one-dimensional periodic atomistic model, for which we formulate and analyse an adaptive variant of a quasicontinuum method. We establish a posteriori error estimators for the energy norm and for the energy, based on a posteriori residual ...
Wang, Hoa, Ortner, Christoph
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Predicting community level dynamics from local rules using pair-approximation.
, 2022 Here we derive the community level properties from the local interaction rules by applying pair-approximation to a graph based model. (PDF)
Martin Ackermann (36108) +4 more
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An improvement of a nonuniform bound for unbounded exchangeable pairs
Journal of Inequalities and Applications, 2023 In this paper, we obtain a nonuniform Berry–Esseen bound for a normal approximation via the Stein method and the exchangeable-pair coupling technique where the boundedness condition of the difference between the exchangeable pair is not required.
Patcharee Sumritnorrapong +1 more
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Heterogeneous pair-approximation for the contact process on complex networks
New Journal of Physics, 2014 Recent works have shown that the contact process running on the top of highly heterogeneous random networks is described by the heterogeneous mean-field theory.
Angélica S Mata +2 more
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Electromagnetic processes at the LHC : nuclear parton distributions from deep inelastic pair production and exclusive photoproduction of single W bosons [PDF]
, 2007 Ultra-peripheral collisions at ion colliders, such as the Large Hadron Collider (LHC) at CERN, offer the possibility to study electromagnetic processes at hitherto unexplored energies.
Dreyer, Ute
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