756 research outputs found
Blow-up dynamics of self-attracting diffusive particles driven by competing convexities
In this paper, we analyze the dynamics of an particles system evolving
according the gradient flow of an energy functional. The particle system is a
consistent approximation of the Lagrangian formulation of a one parameter
family of non-local drift-diffusion equations in one spatial dimension. We
shall prove the global in time existence of the trajectories of the particles
(under a sufficient condition on the initial distribution) and give two blow-up
criteria. All these results are consequences of the competition between the
discrete entropy and the discrete interaction energy. They are also consistent
with the continuous setting, that in turn is a one dimension reformulation of
the parabolic-elliptic Keller-Segel in high dimensions
Investigation of phase-separated electronic states in 1.5”m GaInNAs/GaAs heterostructures by optical spectroscopy
We report on the comparative electronic state characteristics of particular GaInNAs/GaAs quantum well structures that emit near 1.3 and 1.5 ”m wavelength at room temperature. While the electronic structure of the 1.3 ”m sample is consistent with a standard quantum well, the 1.5 ”m sample demonstrate quite different characteristics. By using photoluminescence sPLd excitation spectroscopy at various detection wavelengths, we demonstrate that the macroscopic electronic states in the 1.5 ”m structures originate from phase-separated quantum dots instead of quantum wells. PL measurements with spectrally selective excitation provide further evidence for the existence of composition-separated phases. The evidence is consistent with phase segregation during the growth leading to two phases, one with high In and N content which accounts for the efficient low energy 1.5 ”m emission, and the other one having lower In and N content which contributes metastable states and only emits under excitation in a particular wavelength range
Stably non-synchronizable maps of the plane
Pecora and Carroll presented a notion of synchronization where an
(n-1)-dimensional nonautonomous system is constructed from a given
-dimensional dynamical system by imposing the evolution of one coordinate.
They noticed that the resulting dynamics may be contracting even if the
original dynamics are not. It is easy to construct flows or maps such that no
coordinate has synchronizing properties, but this cannot be done in an open set
of linear maps or flows in , . In this paper we give examples of
real analytic homeomorphisms of such that the non-synchronizability is
stable in the sense that in a full neighborhood of the given map, no
homeomorphism is synchronizable
Particle approximation of the one dimensional Keller-Segel equation, stability and rigidity of the blow-up
We investigate a particle system which is a discrete and deterministic
approximation of the one-dimensional Keller-Segel equation with a logarithmic
potential. The particle system is derived from the gradient flow of the
homogeneous free energy written in Lagrangian coordinates. We focus on the
description of the blow-up of the particle system, namely: the number of
particles involved in the first aggregate, and the limiting profile of the
rescaled system. We exhibit basins of stability for which the number of
particles is critical, and we prove a weak rigidity result concerning the
rescaled dynamics. This work is complemented with a detailed analysis of the
case where only three particles interact
Structural investigation of crystallized Ge-Ga-Se chalcogenide glasses
H. Klym thanks to the Ministry of Education and Science of Ukraine for support and Dr. P. Demchenko for the assistance in XRD experiments.Crystallization transformation in the 80GeSe2-20Ga2Se3 chalcogenide glasses caused by annealing at 380 °C during different duration (25, 50, 80 and 100 hours) are studied using X-ray diffraction and atomic force microscopy methods. It is established that GeGa4Se phase of low- and high-temperature modification, Ga2Se3 phase (α- and Îł-modification) and GeSe2 phases are crystallized during this process. It is shown that annealing duration over 50 h does not lead to further internal structural crystallization, while annealing for 80 h result in processes of surface crystallization.Ministry of Education and Science of Ukraine; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Unionâs Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART
GaN directional couplers for integrated quantum photonics
Large cross-section GaN waveguides are proposed as a suitable architecture to
achieve integrated quantum photonic circuits. Directional couplers with this
geometry have been designed with aid of the beam propagation method and
fabricated using inductively coupled plasma etching. Scanning electron
microscopy inspection shows high quality facets for end coupling and a well
defined gap between rib pairs in the coupling region. Optical characterization
at 800 nm shows single-mode operation and coupling-length-dependent splitting
ratios. Two photon interference of degenerate photon pairs has been observed in
the directional coupler by measurement of the Hong-Ou-Mandel dip with 96%
visibility.Comment: 4 pages, 5 figure
The one-dimensional Keller-Segel model with fractional diffusion of cells
We investigate the one-dimensional Keller-Segel model where the diffusion is
replaced by a non-local operator, namely the fractional diffusion with exponent
. We prove some features related to the classical
two-dimensional Keller-Segel system: blow-up may or may not occur depending on
the initial data. More precisely a singularity appears in finite time when
and the initial configuration of cells is sufficiently concentrated.
On the opposite, global existence holds true for if the initial
density is small enough in the sense of the norm.Comment: 12 page
Joule overheating poisons the fractional ac Josephson effect in topological Josephson junctions
Topological Josephson junctions designed on the surface of a 3D-topological
insulator (TI) harbor Majorana bound states (MBS's) among a continuum of
conventional Andreev bound states. The distinct feature of these MBS's lies in
the -periodicity of their energy-phase relation that yields a fractional
ac Josephson effect and a suppression of odd Shapiro steps under
irradiation. Yet, recent experiments showed that a few, or only the first, odd
Shapiro steps are missing, casting doubts on the interpretation. Here, we show
that Josephson junctions tailored on the large bandgap 3D TI BiSe
exhibit a fractional ac Josephson effect acting on the first Shapiro step only.
With a modified resistively shunted junction model, we demonstrate that the
resilience of higher order odd Shapiro steps can be accounted for by thermal
poisoning driven by Joule overheating. Furthermore, we uncover a residual
supercurrent at the nodes between Shapiro lobes, which provides a direct and
novel signature of the current carried by the MBS. Our findings showcase the
crucial role of thermal effects in topological Josephson junctions and lend
support to the Majorana origin of the partial suppression of odd Shapiro steps.Comment: Revised article and Supplemental materia
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