1,484 research outputs found
Equidistribution of polynomial sequences in function fields, with applications
We prove a function field analog of Weyl's classical theorem on
equidistribution of polynomial sequences. Our result covers the case when the
degree of the polynomial is greater than or equal to the characteristic of the
field, which is a natural barrier when applying the Weyl differencing process
to function fields. We also discuss applications to van der Corput and
intersective sets in function fields.Comment: 24 page
Retrieval of interatomic separations of molecules from laser-induced high-order harmonic spectra
We illustrate an iterative method for retrieving the internuclear separations
of N, O and CO molecules using the high-order harmonics generated
from these molecules by intense infrared laser pulses. We show that accurate
results can be retrieved with a small set of harmonics and with one or few
alignment angles of the molecules. For linear molecules the internuclear
separations can also be retrieved from harmonics generated using isotropically
distributed molecules. By extracting the transition dipole moment from the
high-order harmonic spectra, we further demonstrated that it is preferable to
retrieve the interatomic separation iteratively by fitting the extracted dipole
moment. Our results show that time-resolved chemical imaging of molecules using
infrared laser pulses with femtosecond temporal resolutions is possible.Comment: 14 pages, 9 figure
Retrieval of target structure information from laser-induced photoelectrons by few-cycle bicircular laser fields
Citation: Hoang, V. H., Le, V. H., Lin, C. D., & Le, A. T. (2017). Retrieval of target structure information from laser-induced photoelectrons by few-cycle bicircular laser fields. Physical Review A, 95(3), 6. doi:10.1103/PhysRevA.95.031402By analyzing theoretical results from a numerical solution of the time-dependent Schrodinger equation for atoms in few-cycle bicircular laser pulses, we show that high-energy photoelectron momentum spectra can be used to extract accurate elastic scattering differential cross sections of the target ion with free electrons. We find that the retrieval range for a scattering angle with bicircular pulses is wider than with linearly polarized pulses, although the retrieval method has to be modified to account for different returning directions of the electron in the continuum. This result can be used to extend the range of applicability of ultrafast imaging techniques such as laser-induced electron diffraction and for the accurate characterization of laser pulses
Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems
Many modern nonlinear control methods aim to endow systems with guaranteed
properties, such as stability or safety, and have been successfully applied to
the domain of robotics. However, model uncertainty remains a persistent
challenge, weakening theoretical guarantees and causing implementation failures
on physical systems. This paper develops a machine learning framework centered
around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and
unmodeled dynamics in general robotic systems. Our proposed method proceeds by
iteratively updating estimates of Lyapunov function derivatives and improving
controllers, ultimately yielding a stabilizing quadratic program model-based
controller. We validate our approach on a planar Segway simulation,
demonstrating substantial performance improvements by iteratively refining on a
base model-free controller
Theoretical analysis of dynamic chemical imaging with lasers using high-order harmonic generation
We report theoretical investigations of the tomographic procedure suggested
by Itatani {\it et al.} [Nature, {\bf 432} 867 (2004)] for reconstructing
highest occupied molecular orbitals (HOMO) using high-order harmonic generation
(HHG). Using the limited range of harmonics from the plateau region, we found
that under the most favorable assumptions, it is still very difficult to obtain
accurate HOMO wavefunction, but the symmetry of the HOMO and the internuclear
separation between the atoms can be accurately extracted, especially when
lasers of longer wavelengths are used to generate the HHG. We also considered
the possible removal or relaxation of the approximations used in the
tomographic method in actual applications. We suggest that for chemical
imaging, in the future it is better to use an iterative method to locate the
positions of atoms in the molecule such that the resulting HHG best fits the
macroscopic HHG data, rather than by the tomographic method.Comment: 13 pages, 14 figure
Retrieval of material properties of monolayer transition-metal dichalcogenides from magnetoexciton energy spectra
Reduced exciton mass, polarizability, and dielectric constant of the
surrounding medium are essential properties for semiconduction materials, and
they can be extracted recently from the magnetoexciton energies. However, the
acceptable accuracy of the previously suggested method requires very high
magnetic intensity. Therefore, in the present paper, we propose an alternative
method of extracting these material properties from recently available
experimental magnetoexciton s-state energies in monolayer transition-metal
dichalcogenides (TMDCs). The method is based on the high sensitivity of exciton
energies to the material parameters in the Rytova-Keldysh model. It allows us
to vary the considered material parameters to get the best fit of the
theoretical calculation to the experimental exciton energies for the ,
, and states. This procedure gives values of the exciton reduced mass
and 2D polarizability. Then, the experimental magnetoexciton spectra compared
to the theoretical calculation gives also the average dielectric constant.
Concrete applications are presented only for monolayers WSe and WS from
the recently available experimental data. However, the presented approach is
universal and can be applied to other monolayer TMDCs. The mentioned fitting
procedure requires a fast and effective method of solving the Schr\"{o}dinger
of an exciton in monolayer TMDCs with a magnetic field. Therefore, we also
develop such a method in this study for highly accurate magnetoexciton
energies.Comment: 8 pages, 4 figures, 4 table
- …