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"Explosive Percolation" Transition is Actually Continuous
"Explosive Percolation" Transition Continuous
2010/12/15
The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value.
Synchronization Transition in the Kuramoto Model with Colored Noise
Synchronization Transition Colored No Kuramoto Model
2010/4/6
We present a linear stability analysis of the incoherent state in a system of globally coupled, identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scal...
A Note on Symplecticity of Step-Transition Mappings for Multi-Step Methods
Linear multi-step method Infinitesimally symplectic Symplecticity General linear method
2012/8/1
We prove that for a linear multi-step methodm
k=0kZk =m
k=0kf (Zk), even though the mappings Z0 → Z1, . . . , Zm−2 →
Zm−1 are chosen to be symplectic, Zm−1 → Zm will be non-s...
Expansions of Step-transition Operators of Multi-step Methods and Order Barriers for Dahlquist Pairs
Linear Multi-Step Method Step-Transition Operator B-series Dahlquist (Conjugate) Relation Symplecticity
2012/7/31
Using least parameters, we expand the step-transition operator of any linear multistep method (LMSM) up to O(?s+5) with order s = 1 and rewrite the expansion of the step-transition operator for s = 2 ...