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Vertex intrinsic fitness: how to produce arbitrary scale-free networks.
TLDR
It is found that, irrespective of the particular choices, the generation of scale-free networks is straightforward and the general conditions under which scale- free behavior appears are derived.
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Slow Motion and Metastability for a Nonlocal Evolution Equation
In this paper we consider a nonlocal evolution equation in one dimension, which describes the dynamics of a ferromagnetic system in the mean field approximation. In the presence of a small magnetic…
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Large-Deviation Principle for One-Dimensional Vector Spin Models with Kac Potentials
We consider the one-dimensional planar rotator and classical Heisenberg models with a ferromagnetic Kac potential Jγ(r)=γJ(yr), J with compact support. Below the Lebowitz-Penrose critical temperature…
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A New and Stable Estimation Method of Country Economic Fitness and Product Complexity
TLDR
The new indicator of country net-efficiency quantifying how a country efficiently invests in capabilities able to generate innovative complex high quality products is defined, and analytically the local convergence of the algorithm involved is demonstrated.
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Long Time Evolution of Concentrated Euler Flows with Planar Symmetry
TLDR
A toy model is analyzed that shows a similar behavior to an incompressible Euler fluid with planar symmetry when the vorticity is initially concentrated in small disks, showing that in some cases this happens for quite long times.
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Time Evolution of Concentrated Vortex Rings
We study the time evolution of an incompressible fluid with axisymmetry without swirl when the vorticity is sharply concentrated. In particular, we consider N disjoint vortex rings of size…
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Stochastic Phase Field Equations: Existence and Uniqueness
Abstract. We consider a conservative system of stochastic PDE's, namely a one dimensional phase field model perturbed by an additive space-time white noise. We prove a global existence and uniqueness…
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Dobrushin States in the φ 41 Model
We consider the van der Waals free energy functional in a bounded interval with inhomogeneous Dirichlet boundary conditions imposing the two stable phases at the endpoints. We compute the asymptotic…
On the validity of an einstein relation in models of interface dynamics
We consider models of interface dynamics derived from Ising systems with Kac interactions and we prove the validity of the “Einstein relation”θ=μσ, whereθ is the proportionality coefficient in the…
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Sharp Interface Limits for Non-Local Anisotropic Interactions
Abstract We prove a convexity property of the surface tension corresponding to a non-local, anisotropic free-energy functional of van der Waals type which implies that the Wulff shape is strictly…
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