Search results for "Scaling"
showing 10 items of 754 documents
Comparison of cartesian and lobe function Gaussian basis sets
1970
The lobe function and cartesian (spherical harmonic) gaussian are compared with reference to calculations for second-row atoms. Single and grouped gaussian basis sets which have been reported for cartesian functions are taken over directly to construct corresponding lobe function bases with identical sets of exponents and with lobe separations chosen by a scaling procedure. Total and orbital energies and SCF coefficients resulting from calculations on the second-row atoms using the two types of functions for both primitive and grouped gaussian basis sets are seen to be in excellent agreement, thereby emphasizing the essential equivalence of lobe functions and cartesian gaussians, at the ver…
Phonon-to-spin mapping in a system of a trapped ion via optimal control
2015
We propose a protocol for measurement of the phonon number distribution of a harmonic oscillator based on selective mapping to a discrete spin-1/2 degree of freedom. We consider a system of a harmonically trapped ion, where a transition between two long-lived states can be driven with resolved motional sidebands. The required unitary transforms are generated by amplitude-modulated polychromatic radiation fields, where the time-domain ramps are obtained from numerical optimization by application of the chopped random basis algorithm (CRAB). We provide a detailed analysis of the scaling behavior of the attainable fidelities and required times for the mapping transform with respect to the size…
Critical Dynamics in a Binary Fluid: Simulations and Finite-Size Scaling
2006
We report comprehensive simulations of the critical dynamics of a symmetric binary Lennard-Jones mixture near its consolute point. The self-diffusion coefficient exhibits no detectable anomaly. The data for the shear viscosity and the mutual-diffusion coefficient are fully consistent with the asymptotic power laws and amplitudes predicted by renormalization-group and mode-coupling theories {\it provided} finite-size effects and the background contribution to the relevant Onsager coefficient are suitably accounted for. This resolves a controversy raised by recent molecular simulations.
Applications of Finite-Size-Scaling Techniques to the Simulation of Critical Fluids
1995
A finite-size scaling theory is described that takes account of the lack of symmetry between the coexisting phases of fluids. This broken symmetry is manifest in the so-called ‘field mixing’ phenomenon which is a central feature of the non-universal critical behaviour of fluids. It is shown that the presence of field mixing leads to an alteration to the limiting form of the critical energy distribution and to a finite-size correction to the critical order parameter (particle density) distribution. As a result, finite-size shifts occur in the critical particle and energy densities. The theoretical predictions are tested with an extensive Monte-Carlo study of the critical density and energy f…
Universal Dynamic Fragmentation inDDimensions
2004
A generic model is introduced for brittle fragmentation in $D$ dimensions, and this model is shown to lead to a fragment-size distribution with two distinct components. In the small fragment-size limit a scale-invariant size distribution results from a crack branching-merging process. At larger sizes the distribution becomes exponential as a result of a Poisson process, which introduces a large-scale cutoff. Numerical simulations are used to demonstrate the validity of the distribution for $D=2$. Data from laboratory-scale experiments and large-scale quarry blastings of granitic gneiss confirm its validity for $D=3$. In the experiments the nonzero grain size of rock causes deviation from th…
Exponential and power-law mass distributions in brittle fragmentation
2004
Generic arguments, a minimal numerical model, and fragmentation experiments with gypsum disk are used to investigate the fragment-size distribution that results from dynamic brittle fragmentation. Fragmentation is initiated by random nucleation of cracks due to material inhomogeneities, and its dynamics are pictured as a process of propagating cracks that are unstable against side-branch formation. The initial cracks and side branches both merge mutually to form fragments. The side branches have a finite penetration depth as a result of inherent damping. Generic arguments imply that close to the minimum strain (or impact energy) required for fragmentation, the number of fragments of size $s…
Elastic constants from microscopic strain fluctuations
1999
Fluctuations of the instantaneous local Lagrangian strain $\epsilon_{ij}(\bf{r},t)$, measured with respect to a static ``reference'' lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse- grained by averaging them within subsystems (of size $L_b$) of a system (of total size $L$) in the canonical ensemble. Using a simple finite size scaling theory we predict the behaviour of the fluctuations $$ as a function of $L_b/L$ and extract elastic constants of the system {\em in the thermodynamic limit} at nonzero temperature. Our method is simple to implement, efficient and general e…
Self-consistent field theory based molecular dynamics with linear system-size scaling
2012
We present an improved field-theoretic approach to the grand-canonical potential suitable for linear scaling molecular dynamics simulations using forces from self-consistent electronic structure calculations. It is based on an exact decomposition of the grand canonical potential for independent fermions and does neither rely on the ability to localize the orbitals nor that the Hamilton operator is well-conditioned. Hence, this scheme enables highly accurate all-electron linear scaling calculations even for metallic systems. The inherent energy drift of Born-Oppenheimer molecular dynamics simulations, arising from an incomplete convergence of the self-consistent field cycle, is circumvented …
Numerical evidence of hyperscaling violation in wetting transitions of the random-bond Ising model in d = 2 dimensions
2017
We performed extensive simulations of the random-bond Ising model confined between walls where competitive surface fields act. By properly taking the thermodynamic limit we unambiguously determined wetting transition points of the system, as extrapolation of localization-delocalization transitions of the interface between domains of different orientation driven by the respective fields. The finite-size scaling theory for wetting with short-range fields establishes that the average magnetization of the sample, with critical exponent β, is the proper order parameter for the study of wetting. While the hyperscaling relationship given by γ+2β=ν +ν requires β=1/2 (γ=4, ν =3, and ν =2), the therm…
Dimensional effects in dynamic fragmentation of brittle materials.
2005
It has been shown previously that dynamic fragmentation of brittle $D$-dimensional objects in a $D$-dimensional space gives rise to a power-law contribution to the fragment-size distribution with a universal scaling exponent $2\ensuremath{-}1∕D$. We demonstrate that in fragmentation of two-dimensional brittle objects in three-dimensional space, an additional fragmentation mechanism appears, which causes scale-invariant secondary breaking of existing fragments. Due to this mechanism, the power law in the fragment-size distribution has now a scaling exponent of $\ensuremath{\sim}1.17$.