7,796 research outputs found
The centripetal force law and the equation of motion for a particle on a curved hypersurface
It is pointed out that the current form of extrinsic equation of motion for a
particle constrained to remain on a hypersurface is in fact a half-finished
version for it is established without regard to the fact that the particle can
never depart from the geodesics on the surface. Once the fact be taken into
consideration, the equation takes that same form as that for centripetal force
law, provided that the symbols are re-interpreted so that the law is applicable
for higher dimensions. The controversial issue of constructing operator forms
of these equations is addressed, and our studies show the quantization of
constrained system based on the extrinsic equation of motion is favorable.Comment: 5 pages, major revisio
Heisenberg equation for a nonrelativistic particle on a hypersurface: from the centripetal force to a curvature induced force
In classical mechanics, a nonrelativistic particle constrained on an
curved hypersurface embedded in flat space experiences the centripetal
force only. In quantum mechanics, the situation is totally different for the
presence of the geometric potential. We demonstrate that the motion of the
quantum particle is "driven" by not only the the centripetal force, but also a
curvature induced force proportional to the Laplacian of the mean curvature,
which is fundamental in the interface physics, causing curvature driven
interface evolution.Comment: 4 page
Fast ground-state cooling of mechanical resonator with time-dependent optical cavities
We propose a feasible scheme to cool down a mechanical resonator (MR) in a
three-mirror cavity optomechanical system with controllable external optical
drives. Under the Born-Oppenheimer (BO) approximation, the whole dynamics of
the mechanical resonator and cavities is reduced to that of a time-dependent
harmonic oscillator, whose effective frequency can be controlled through the
optical driving fields. The fast cooling of the MR can be realized by
controlling the amplitude of the optical drives. Significantly, we further show
that the ground-state cooling may be achieved via the three-mirror cavity
optomechanical system without the resolved sideband condition.Comment: Some references including our previous works on cooling of mechanical
resonators are added, and some typos are corrected in this new version.
Comments are welcom
Learned Belief-Propagation Decoding with Simple Scaling and SNR Adaptation
We consider the weighted belief-propagation (WBP) decoder recently proposed
by Nachmani et al. where different weights are introduced for each Tanner graph
edge and optimized using machine learning techniques. Our focus is on
simple-scaling models that use the same weights across certain edges to reduce
the storage and computational burden. The main contribution is to show that
simple scaling with few parameters often achieves the same gain as the full
parameterization. Moreover, several training improvements for WBP are proposed.
For example, it is shown that minimizing average binary cross-entropy is
suboptimal in general in terms of bit error rate (BER) and a new "soft-BER"
loss is proposed which can lead to better performance. We also investigate
parameter adapter networks (PANs) that learn the relation between the
signal-to-noise ratio and the WBP parameters. As an example, for the (32,16)
Reed-Muller code with a highly redundant parity-check matrix, training a PAN
with soft-BER loss gives near-maximum-likelihood performance assuming simple
scaling with only three parameters.Comment: 5 pages, 5 figures, submitted to ISIT 201
Looking into DNA breathing dynamics via quantum physics
We study generic aspects of bubble dynamics in DNA under time dependent
perturbations, for example temperature change, by mapping the associated
Fokker-Planck equation to a quantum time-dependent Schroedinger equation with
imaginary time. In the static case we show that the eigenequation is exactly
the same as that of the -deformed nuclear liquid drop model, without the
issue of non-integer angular momentum. A universal breathing dynamics is
demonstrated by using an approximate method in quantum mechanics. The
calculated bubble autocorrelation function qualitatively agrees with
experimental data. Under time dependent modulations, utilizing the adiabatic
approximation, bubble properties reveal memory effects.Comment: 5 pages, 1 figur
Perfect Function Transfer in two- and three- dimensions without initialization
We find analytic models that can perfectly transfer, without state
initializati$ or remote collaboration, arbitrary functions in two- and
three-dimensional interacting bosonic and fermionic networks. We elaborate on a
possible implementation of state transfer through bosonic or fermionic atoms
trapped in optical lattices. A significant finding is that the state of a spin
qubit can be perfectly transferred through a fermionic system. Families of
Hamiltonians, both linear and nonlinear, are described which are related to the
linear Boson model and that enable the perfect transfer of arbitrary functions.
This includes entangled states such as decoherence-free subsystems enabling
noise protection of the transferred state.Comment: 4 pages, no figur
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Leaf-inspired microcontact printing vascular patterns.
The vascularization of tissue grafts is critical for maintaining viability of the cells within a transplanted graft. A number of strategies are currently being investigated including very promising microfluidics systems. Here, we explored the potential for generating a vasculature-patterned endothelial cells that could be integrated into distinct layers between sheets of primary cells. Bioinspired from the leaf veins, we generated a reverse mold with a fractal vascular-branching pattern that models the unique spatial arrangement over multiple length scales that precisely mimic branching vasculature. By coating the reverse mold with 50 μg ml-1 of fibronectin and stamping enabled selective adhesion of the human umbilical vein endothelial cells (HUVECs) to the patterned adhesive matrix, we show that a vascular-branching pattern can be transferred by microcontact printing. Moreover, this pattern can be maintained and transferred to a 3D hydrogel matrix and remains stable for up to 4 d. After 4 d, HUVECs can be observed migrating and sprouting into Matrigel. These printed vascular branching patterns, especially after transfer to 3D hydrogels, provide a viable alternative strategy to the prevascularization of complex tissues
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