1,891 research outputs found
Percolation properties of growing networks under an Achlioptas process
We study the percolation transition in growing networks under an Achlioptas
process (AP). At each time step, a node is added in the network and, with the
probability , a link is formed between two nodes chosen by an AP. We
find that there occurs the percolation transition with varying and the
critical point is determined from the power-law behavior
of order parameter and the crossing of the fourth-order cumulant at the
critical point, also confirmed by the movement of the peak positions of the
second largest cluster size to the . Using the finite-size scaling
analysis, we get and , which
implies and . The Fisher exponent
for the cluster size distribution is obtained and shown to
satisfy the hyperscaling relation.Comment: 4 pages, 5 figures, 1 table, journal submitte
Transferable empirical pseudopotenials from machine learning
Machine learning is used to generate empirical pseudopotentials that
characterize the local screened interactions in the Kohn-Sham Hamiltonian. Our
approach incorporates momentum-range-separated rotation-covariant descriptors
to capture crystal symmetries as well as crucial directional information of
bonds, thus realizing accurate descriptions of anisotropic solids. Trained
empirical potentials are shown to be versatile and transferable such that the
calculated energy bands and wave functions without cumbersome self-consistency
reproduce conventional ab initio results even for semiconductors with defects,
thus fostering faster and faithful data-driven materials researches.Comment: 10 pages, 9 figures, 3 table
Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling
We study the collective behaviors in a ring of coupled nonidentical nonlinear
oscillators with unidirectional coupling, of which natural frequencies are
distributed in a random way. We find the amplitude death phenomena in the case
of unidirectional couplings and discuss the differences between the cases of
bidirectional and unidirectional couplings. There are three main differences;
there exists neither partial amplitude death nor local clustering behavior but
oblique line structure which represents directional signal flow on the
spatio-temporal patterns in the unidirectional coupling case. The
unidirectional coupling has the advantage of easily obtaining global amplitude
death in a ring of coupled oscillators with randomly distributed natural
frequency. Finally, we explain the results using the eigenvalue analysis of
Jacobian matrix at the origin and also discuss the transition of dynamical
behavior coming from connection structure as coupling strength increases.Comment: 14 pages, 11 figure
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