3,225 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
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
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
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
Analysis of Neighbourhoods in Multi-layered Dynamic Social Networks
Social networks existing among employees, customers or users of various IT
systems have become one of the research areas of growing importance. A social
network consists of nodes - social entities and edges linking pairs of nodes.
In regular, one-layered social networks, two nodes - i.e. people are connected
with a single edge whereas in the multi-layered social networks, there may be
many links of different types for a pair of nodes. Nowadays data about people
and their interactions, which exists in all social media, provides information
about many different types of relationships within one network. Analysing this
data one can obtain knowledge not only about the structure and characteristics
of the network but also gain understanding about semantic of human relations.
Are they direct or not? Do people tend to sustain single or multiple relations
with a given person? What types of communication is the most important for
them? Answers to these and more questions enable us to draw conclusions about
semantic of human interactions. Unfortunately, most of the methods used for
social network analysis (SNA) may be applied only to one-layered social
networks. Thus, some new structural measures for multi-layered social networks
are proposed in the paper, in particular: cross-layer clustering coefficient,
cross-layer degree centrality and various versions of multi-layered degree
centralities. Authors also investigated the dynamics of multi-layered
neighbourhood for five different layers within the social network. The
evaluation of the presented concepts on the real-world dataset is presented.
The measures proposed in the paper may directly be used to various methods for
collective classification, in which nodes are assigned to labels according to
their structural input features.Comment: 16 pages, International Journal of Computational Intelligence System
Coexistence of opposite opinions in a network with communities
The Majority Rule is applied to a topology that consists of two coupled
random networks, thereby mimicking the modular structure observed in social
networks. We calculate analytically the asymptotic behaviour of the model and
derive a phase diagram that depends on the frequency of random opinion flips
and on the inter-connectivity between the two communities. It is shown that
three regimes may take place: a disordered regime, where no collective
phenomena takes place; a symmetric regime, where the nodes in both communities
reach the same average opinion; an asymmetric regime, where the nodes in each
community reach an opposite average opinion. The transition from the asymmetric
regime to the symmetric regime is shown to be discontinuous.Comment: 14 pages, 4 figure
Magneto-optical Selection Rules in Bilayer Bernal Graphene
The low-frequency magneto-optical properties of bilayer Bernal graphene are
studied by the tight-binding model with four most important interlayer
interactions taken into account. Since the main features of the wave functions
are well depicted, the Landau levels can be divided into two groups based on
the characteristics of the wave functions. These Landau levels lead to four
categories of absorption peaks in the optical absorption spectra. Such
absorption peaks own complex optical selection rules and these rules can be
reasonably explained by the characteristics of the wave functions. In addition,
twin-peak structures, regular frequency-dependent absorption rates and complex
field-dependent frequencies are also obtained in this work. The main features
of the absorption peaks are very different from those in monolayer graphene and
have their origin in the interlayer interactions
Singular Cucker-Smale Dynamics
The existing state of the art for singular models of flocking is overviewed,
starting from microscopic model of Cucker and Smale with singular communication
weight, through its mesoscopic mean-filed limit, up to the corresponding
macroscopic regime. For the microscopic Cucker-Smale (CS) model, the
collision-avoidance phenomenon is discussed, also in the presence of bonding
forces and the decentralized control. For the kinetic mean-field model, the
existence of global-in-time measure-valued solutions, with a special emphasis
on a weak atomic uniqueness of solutions is sketched. Ultimately, for the
macroscopic singular model, the summary of the existence results for the
Euler-type alignment system is provided, including existence of strong
solutions on one-dimensional torus, and the extension of this result to higher
dimensions upon restriction on the smallness of initial data. Additionally, the
pressureless Navier-Stokes-type system corresponding to particular choice of
alignment kernel is presented, and compared - analytically and numerically - to
the porous medium equation
Graphene-based modulation-doped superlattice structures
The electronic transport properties of graphene-based superlattice structures
are investigated. A graphene-based modulation-doped superlattice structure
geometry is proposed and consist of periodically arranged alternate layers:
InAs/graphene/GaAs/graphene/GaSb. Undoped graphene/GaAs/graphene structure
displays relatively high conductance and enhanced mobilities at elevated
temperatures unlike modulation-doped superlattice structure more steady and
less sensitive to temperature and robust electrical tunable control on the
screening length scale. Thermionic current density exhibits enhanced behaviour
due to presence of metallic (graphene) mono-layers in superlattice structure.
The proposed superlattice structure might become of great use for new types of
wide-band energy gap quantum devices.Comment: 5 figure
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