3,851 research outputs found
Total variation denoising in anisotropy
We aim at constructing solutions to the minimizing problem for the variant of
Rudin-Osher-Fatemi denoising model with rectilinear anisotropy and to the
gradient flow of its underlying anisotropic total variation functional. We
consider a naturally defined class of functions piecewise constant on
rectangles (PCR). This class forms a strictly dense subset of the space of
functions of bounded variation with an anisotropic norm. The main result shows
that if the given noisy image is a PCR function, then solutions to both
considered problems also have this property. For PCR data the problem of
finding the solution is reduced to a finite algorithm. We discuss some
implications of this result, for instance we use it to prove that continuity is
preserved by both considered problems.Comment: 34 pages, 9 figure
On the existence of traveling waves in the 3D Boussinesq system
We extend earlier work on traveling waves in premixed flames in a
gravitationally stratified medium, subject to the Boussinesq approximation. For
three-dimensional channels not aligned with the gravity direction and under the
Dirichlet boundary conditions in the fluid velocity, it is shown that a
non-planar traveling wave, corresponding to a non-zero reaction, exists, under
an explicit condition relating the geometry of the crossection of the channel
to the magnitude of the Prandtl and Rayleigh numbers, or when the advection
term in the flow equations is neglected.Comment: 15 pages, to appear in Communications in Mathematical Physic
Electronic Raman Scattering in Twistronic Few-Layer Graphene
We study electronic contribution to the Raman scattering signals of two-,
three- and four-layer graphene with layers at one of the interfaces twisted by
a small angle with respect to each other. We find that the Raman spectra of
these systems feature two peaks produced by van Hove singularities in moir\'{e}
minibands of twistronic graphene, one related to direct hybridization of Dirac
states, and the other resulting from band folding caused by moir\'{e}
superlattice. The positions of both peaks strongly depend on the twist angle,
so that their detection can be used for non-invasive characterization of the
twist, even in hBN-encapsulated structures.Comment: 7 pages (including 4 figures) + 10 pages (3 figures) supplemen
Directional approach to spatial structure of solutions to the Navier-Stokes equations in the plane
We investigate a steady flow of incompressible fluid in the plane. The motion
is governed by the Navier-Stokes equations with prescribed velocity
at infinity. The main result shows the existence of unique solutions for
arbitrary force, provided sufficient largeness of . Furthermore a
spacial structure of the solution is obtained in comparison with the Oseen
flow. A key element of our new approach is based on a setting which treats the
directino of the flow as \emph{time} direction. The analysis is done in
framework of the Fourier transform taken in one (perpendicular) direction and a
special choice of function spaces which take into account the inhomogeneous
character of the symbol of the Oseen system. From that point of view our
technique can be used as an effective tool in examining spatial asymptotics of
solutions to other systems modeled by elliptic equations
Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
Network science is an interdisciplinary endeavor, with methods and
applications drawn from across the natural, social, and information sciences. A
prominent problem in network science is the algorithmic detection of
tightly-connected groups of nodes known as communities. We developed a
generalized framework of network quality functions that allowed us to study the
community structure of arbitrary multislice networks, which are combinations of
individual networks coupled through links that connect each node in one network
slice to itself in other slices. This framework allows one to study community
structure in a very general setting encompassing networks that evolve over
time, have multiple types of links (multiplexity), and have multiple scales.Comment: 31 pages, 3 figures, 1 table. Includes main text and supporting
material. This is the accepted version of the manuscript (the definitive
version appeared in Science), with typographical corrections included her
Energy solutions to one-dimensional singular parabolic problems with data are viscosity solutions
We study one-dimensional very singular parabolic equations with periodic
boundary conditions and initial data in , which is the energy space. We
show existence of solutions in this energy space and then we prove that they
are viscosity solutions in the sense of Giga-Giga.Comment: 15 page
A caricature of a singular curvature flow in the plane
We study a singular parabolic equation of the total variation type in one
dimension. The problem is a simplification of the singular curvature flow. We
show existence and uniqueness of weak solutions. We also prove existence of
weak solutions to the semi-discretization of the problem as well as convergence
of the approximating sequences. The semi-discretization shows that facets must
form. For a class of initial data we are able to study in details the facet
formation and interactions and their asymptotic behavior. We notice that our
qualitative results may be interpreted with the help of a special composition
of multivalued operators
Quantum dynamics and spectroscopy of photodetachment in Cl-...H2O and Cl-...D2O complexes
We have modeled Zero Electron Kinetic Energy (ZEKE) spectra of Cl-…H2O and Cl-…D2O complexes using 3D quantum dynamical simulations on the three low-lying electronic states of the nascent neutral systems. Time-dependent quantum simulations combined with anionic and neutral stationary-state calculations by imaginary time propagation allowed for a detailed interpretation of the spectral features in terms of the underlying dynamics. Because of large differences between the anionic and neutral potential surfaces, the systems are found after electron photodetachment primarily high above the dissociation threshold. Nevertheless, pronounced long-lived resonances are observed, particularly for the lowest neutral state, reflecting the fact that a significant portion of the excess energy is initially deposited into nondissociative modes, that is, to (hindered) water rotation. These resonances form bands corresponding to water rotational states with a fine structure due to intermolecular stretch progressions. Comparison is made to experimental zero electron kinetic energy (ZEKE) spectra of the I-…H2O complex, where analogous anharmonic vibrational progressions have been observed
Smart operational load monitoring using decision trees and artificial neural networks: a comparative study
Operational Load Monitoring is an industrial process that allows to predict the remaining in-service life of a mechanical structure under variable loads. Data from sensors embedded or mounted on the structure is acquired and allows to estimate the number and amplitude of load cycles that the structure has withstood so far in its working environment. This process is especially important in the aerospace industry where mechanical structures of an aircraft are monitored in order to maximize their operating lifetime. Smart Operational Load Monitoring means implementation of artificial intelligence techniques to the process in order to make predictions based on measurements from reduced number of sensors. In this paper a composite lightweight structure of typical geometry used in aircraft structures is taken as an example for Smart Operational Load Monitoring. The predictions are made from measurements from six strain gauges mounted to the structure, using carefully prepared artificial intelligence-based models. Efficiency of the models is compared, in terms of their prediction accuracies and computational complexities.National Agency for Academic Exchange of PolandSilesian University of Technology. Faculty of Mechanical Engineerin
Valley-polarized tunneling currents in bilayer graphene tunneling transistors
We study theoretically the electron current across a monolayer graphene/hexagonal boron nitride/bilayer graphene tunneling junction in an external magnetic field perpendicular to the layers. We show that change in effective tunneling barrier width for electrons on different graphene layers of bilayer graphene, coupled with the fact that its Landau level wave functions are not equally distributed amongst the layers with a distribution that is reversed between the two valleys, lead to valley polarization of the tunneling current. We estimate that valley polarization ∼70% can be achieved in high quality devices at B=1 T. Moreover, we demonstrate that strong valley polarization can be obtained both in the limit of strong-momentum-conserving tunneling and in lower quality devices where this constraint is lifted
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