397 research outputs found
Excitation of atoms in an optical lattice driven by polychromatic amplitude modulation
We investigate the mutiphoton process between different Bloch states in an
amplitude modulated optical lattice. In the experiment, we perform the
modulation with more than one frequency components, which includes a high
degree of freedom and provides a flexible way to coherently control quantum
states. Based on the study of single frequency modulation, we investigate the
collaborative effect of different frequency components in two aspects. Through
double frequency modulations, the spectrums of excitation rates for different
lattice depths are measured. Moreover, interference between two separated
excitation paths is shown, emphasizing the influence of modulation phases when
two modulation frequencies are commensurate. Finally, we demonstrate the
application of the double frequency modulation to design a
large-momentum-transfer beam splitter. The beam splitter is easy in practice
and would not introduce phase shift between two arms.Comment: 11pages, 7 figure
An SPH formulation for general plate and shell structures with finite deformation and large rotation
In this paper, we propose a reduced-dimensional smoothed particle
hydrodynamics (SPH) formulation for quasi-static and dynamic analyses of plate
and shell structures undergoing finite deformation and large rotation. By
exploiting Uflyand-Mindlin plate theory, the present surface-particle
formulation is able to resolve the thin structures by using only one layer of
particles at the mid-surface. To resolve the geometric non-linearity and
capture finite deformation and large rotation, two reduced-dimensional
linear-reproducing correction matrices are introduced, and weighted
non-singularity conversions between the rotation angle and pseudo normal are
formulated. A new non-isotropic Kelvin-Voigt damping is proposed especially for
the both thin and moderately thick plate and shell structures to increase the
numerical stability. In addition, a shear-scaled momentum-conserving hourglass
control algorithm with an adaptive limiter is introduced to suppress the
mismatches between the particle position and pseudo normal and those estimated
with the deformation gradient. A comprehensive set of test problems, for which
the analytical or numerical results from literature or those of the
volume-particle SPH model are available for quantitative and qualitative
comparison, are examined to demonstrate the accuracy and stability of the
present method.Comment: 62 pages and 25 figure
Quantum Dimensions and Quantum Galois Theory
The quantum dimensions of modules for vertex operator algebras are defined
and their properties are discussed. The possible values of the quantum
dimensions are obtained for rational vertex operator algebras. A criterion for
simple currents of a rational vertex operator algebra is given. A full Galois
theory for rational vertex operator algebras is established using the quantum
dimensions.Comment: 32 page
An hourglass-free formulation for total Lagrangian smoothed particle hydrodynamics
The total Lagrangian smoothed particle hydrodynamics (TL-SPH) for elastic
solid dynamics suffers from hourglass modes which can grow and lead to the
failure of simulation for problems with large deformation. To address this
long-standing issue, we present an hourglass-free formulation based on
volumetric-devioatric stress decomposition. Inspired by the fact that the
artifact of nonphysical zigzag particle distribution induced by the hourglass
modes is mainly characterized by shear deformation and the standard SPH
discretization for the viscous term in the Navier-Stokes (NS) equation, the
present formulation computes the action of shear stress directly through the
Laplacian of displacement other than from the divergence of shear stress. A
comprehensive set of challenging benchmark cases are simulated to demonstrate
that, while improving accuracy and computational efficiency, the present
formulation is able to eliminate the hourglass modes and achieves very good
numerical stability with a single general effective parameter. In addition, the
deformation of a practically relevant stent structure is simulated to
demonstrate the potential of the present method in the field of biomechanics.Comment: 38 pages 21 figure
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