266 research outputs found
Comparison of topologies on *-algebras of locally measurable operators
We consider the locally measure topology on the *-algebra
of all locally measurable operators affiliated with a von
Neumann algebra . We prove that coincides with
the -topology on if
and only if the algebra is -finite and a finite algebra.
We study relationships between the topology and various
topologies generated by faithful normal semifinite traces on .Comment: 21 page
Global exponential convergence to variational traveling waves in cylinders
We prove, under generic assumptions, that the special variational traveling
wave that minimizes the exponentially weighted Ginzburg-Landau functional
associated with scalar reaction-diffusion equations in infinite cylinders is
the long-time attractor for the solutions of the initial value problems with
front-like initial data. The convergence to this traveling wave is
exponentially fast. The obtained result is mainly a consequence of the gradient
flow structure of the considered equation in the exponentially weighted spaces
and does not depend on the precise details of the problem. It strengthens our
earlier generic propagation and selection result for "pushed" fronts.Comment: 23 page
Nonlinear electro-hydrodynamics of liquid crystals
We present nonlinear dynamic equations for nematic and smectic liquid
crystals in the presence of an alternating electric field and explain their
derivation in detail. The local electric field acting in any liquid-crystalline
system is expressed as a sum of external electric field and the fields
originating from feedback of liquid crystal order parameter, and a field,
created by charged impurities. The system tends to decrease the total electric
field, because it lowers the energy density. This basically nonlinear problem
is not a pure academic interest. In the realm of liquid crystals and their
applications, utilized nowadays modern experimental techniques have progressed
to the point where even small deviations from the linear behavior can be
observed and measured with a high accuracy. Hydrodynamics is the macroscopic
description of condensed matter systems in the low frequency, long wavelength
limit. Nonlinear hydrodynamic equations are well established to describe simple
fluids. Similar approaches (with degrees of freedom related to the broken
orientational or translational symmetry included) have been used also for
liquid crystals. However to study behavior of strongly perturbed well above the
thresholds of various electro-hydrodynamic instabilities of liquid crystals the
nonlinear equations should include soft electromagnetic degrees of freedom as
well. The self-consistent derivation of the complete set of the nonlinear
electro-hydrodynamic equations for liquid crystals became an actual task. The
aim of our work is to present these equations, which is a mandatory step to
handle any nonlinear phenomenon in liquid crystals.Comment: 12 pages, no figure
The effects of liquid-phase oxidation of multiwall carbon nanotubes on their surface characteristics
The development of new sorbents based on nanostructured carbon materials recently became a perspective field of research. Main topic of current study is to investigate the effect of different regimes of multiwall carbon nanotubes (MWCNT) surface modification process on their structural characteristics. MWCNT samples were treated with nitric acid at high temperature. Structural properties were studied using low temperature nitrogen adsorption and acid-base back titration methods. The study showed that diluted nitric acid does not affect MWCNT structure. Concentrated nitric acid treatment leads to formation of 2.8 carboxylic groups per 1 nm{2} of the sample surface
Synthesis and characterisation of nanocrystalline ZrN PVD coatings on AISI 430 stainless steel
The nanocrystalline films of zirconium nitride have been synthesized using ion-plasma vacuum-arc deposition technique in combination with high-frequency discharge (RF) on AISI 430 stainless steel at 150oC. Structure examinations X-ray fluorescent analysis (XRF), X-ray diffraction analysis (XRD), scanning electron microscopy (SEM) with microanalysis (EDS), and transmission electron microscopy (TEM), nanoidentation method – were performed to study phase and chemical composition, surface morphology, microstructure and nanohardness of coatings. The developed technology provided low-temperature coatings synthesis, minimized discharge breakdown decreasing formation of macroparticles (MPs) and allowed to deposit ZrN coatings with hardness variation 26.6…31.5 GPa. It was revealed that ZrN single-phase coatings of cubic modification with finecrystalline grains of 20 nm in size were formed
Amorphous VO films with high temperature coefficient of the resistivity grown by reactive e-beam evaporation of V metal
Amorphous VO films without a hysteretic phase transition are stable with
respect to thermal cycling and highly demanded as sensitive elements of the
resistive thermometers and microbolometers. In this paper we present simple and
low-temperature growth of amorphous vanadium oxide films by reactive electron
beam evaporation of vanadium metal in mBar oxygen atmosphere.
The temperature coefficient of the resistivity (TCR) of the films is weakly
sensitive to substrate material and temperature and could be tuned by oxygen
pressure in the growth chamber up to -2.2\% /K. The resistivity value is stable
for months. It depends on the substrate material and substrate temperature
during the evaporation. Simplicity and controllability of the method should
lead to various laboratory and industrial applications
Self-similar dynamics of morphogen gradients
We discovered a class of self-similar solutions in nonlinear models
describing the formation of morphogen gradients, the concentration fields of
molecules acting as spatial regulators of cell differention in developing
tissues. These models account for diffusion and self-induced degration of
locally produced chemical signals. When production starts, the signal
concentration is equal to zero throughout the system. We found that in the
limit of infinitely large signal production strength the solution of this
problem is given by the product of the steady state concentration profile and a
function of the diffusion similarity variable. We derived a nonlinear boundary
value problem satisfied by this function and used a variational approach to
prove that this problem has a unique solution in a natural setting. Using the
asymptotic behavior of the solutions established by the analysis, we
constructed these solutions numerically by the shooting method. Finally, we
demonstrated that the obtained solutions may be easily approximated by simple
analytical expressions, thus providing an accurate global characterization of
the dynamics in an important class of non-linear models of morphogen gradient
formation. Our results illustrate the power of analytical approaches to
studying nonlinear models of biophysical processes.Comment: 17 pages, 5 figure
The N-ary in the Coal Mine: Avoiding Mixture Model Failure with Proper Validation
Modeling the properties of chemical mixtures is a difficult but important
part of any modeling process intended to be applicable to the often messy and
impure phenomena of everyday life, including food and environmental safety,
healthcare, etc. Part of this difficulty stems from the increased complexity of
designing suitable model validation schemes for mixture data, a fact which has
been elucidated in previous work only in the case of binary mixture models. We
extend these previously defined validation strategies for QSAR modeling of
binary mixtures to the more complex case of general, -ary mixtures and argue
that these strategies are applicable to many modeling tasks beyond simple
chemical mixtures. Additionally, we propose a method of establishing a baseline
model performance for each mixture dataset to be in used in model selection
comparisons. This baseline is intended to account for the statistical
dependence generically present between the properties of mixtures that share
constituents. We contend that without such a baseline, estimates of model
performance can be dramatically overestimated, and we demonstrate this with
multiple case studies using real and simulated data.Comment: 22 pages, 1 figur
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