429 research outputs found
Boundary-Induced Pattern Formation from Temporal Oscillation: Spatial Map Analysis
Boundary-induced pattern formation from a spatially uniform state is
investigated using one-dimensional reaction-diffusion equations. The temporal
oscillation is successively transformed into a spatially periodic pattern,
triggered by diffusion from the fixed boundary. We introduced a spatial map,
whose temporal sequence, under selection criteria from multiple stationary
solutions, can completely reproduce the emergent pattern, by replacing the time
with space. The relationship of the pattern wavelength with the period of
oscillation is also obtained. The generality of the pattern selection process
and algorithm is discussed with possible relevance to biological morphogenesis.Comment: 17page
Stochastic extension of the Lanczos method for nuclear shell-model calculations with variational Monte Carlo method
We propose a new variational Monte Carlo (VMC) approach based on the Krylov
subspace for large-scale shell-model calculations. A random walker in the VMC
is formulated with the -scheme representation, and samples a small number of
configurations from a whole Hilbert space stochastically. This VMC framework is
demonstrated in the shell-model calculations of Cr and Zn, and we
discuss its relation to a small number of Lanczos iterations. By utilizing the
wave function obtained by the conventional particle-hole-excitation truncation
as an initial state, this VMC approach provides us with a sequence of
systematically improved results.Comment: 5 pages, 4 figures, submitted to Physics Letters
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