345 research outputs found
Optimal Control of the Thermistor Problem in Three Spatial Dimensions
This paper is concerned with the state-constrained optimal control of the
three-dimensional thermistor problem, a fully quasilinear coupled system of a
parabolic and elliptic PDE with mixed boundary conditions. This system models
the heating of a conducting material by means of direct current. Local
existence, uniqueness and continuity for the state system are derived by
employing maximal parabolic regularity in the fundamental theorem of Pr\"uss.
Global solutions are addressed, which includes analysis of the linearized state
system via maximal parabolic regularity, and existence of optimal controls is
shown if the temperature gradient is under control. The adjoint system
involving measures is investigated using a duality argument. These results
allow to derive first-order necessary conditions for the optimal control
problem in form of a qualified optimality system. The theoretical findings are
illustrated by numerical results
Direct observation of twist mode in electroconvection in I52
I report on the direct observation of a uniform twist mode of the director
field in electroconvection in I52. Recent theoretical work suggests that such a
uniform twist mode of the director field is responsible for a number of
secondary bifurcations in both electroconvection and thermal convection in
nematics. I show here evidence that the proposed mechanisms are consistent with
being the source of the previously reported SO2 state of electroconvection in
I52. The same mechanisms also contribute to a tertiary Hopf bifurcation that I
observe in electroconvection in I52. There are quantitative differences between
the experiment and calculations that only include the twist mode. These
differences suggest that a complete description must include effects described
by the weak-electrolyte model of electroconvection
Pseudoscalars Mesons in Hot, Dense Matter
Phase transitions in hot and dense matter and the in--medium behavior of
pseudoscalar mesons () are investigated, in the framework of the three flavor Nambu--Jona-Lasinio
model, including the 't Hooft interaction, which breaks the symmetry.
Three different scenarios are considered: zero density and finite temperature,
zero temperature and finite density in quark matter with different degrees of
strangeness, and finite temperature and density. At T=0, the role of strange
valence quarks in the medium is discussed, in connection with the phase
transition and the mesonic behavior. It is found that the appearance of strange
quarks, above certain densities, leads to meaningful changes in different
observables, especially in matter with \betaT-\rho$ plane is analyzed in connection with possible signatures
of restoration of symmetries.Comment: 33 pages, 12 figures, PRC versio
Study of the optimal conditions for NV- center formation in type 1b diamond, using photoluminescence and positron annihilation spectroscopies
We studied the parameters to optimize the production of negatively-charged
nitrogen-vacancy color centers (NV-) in type~1b single crystal diamond using
proton irradiation followed by thermal annealing under vacuum. Several samples
were treated under different irradiation and annealing conditions and
characterized by slow positron beam Doppler-broadening and photoluminescence
(PL) spectroscopies. At high proton fluences another complex vacancy defect
appears limiting the formation of NV-. Concentrations as high as 2.3 x 10^18
cm^-3 of NV- have been estimated from PL measurements. Furthermore, we inferred
the trapping coefficient of positrons by NV-. This study brings insight into
the production of a high concentration of NV- in diamond, which is of utmost
importance in ultra-sensitive magnetometry and quantum hybrid systems
applications
Chiral symmetry breaking in hot matter
This series of three lectures covers (a) a basic introduction to symmetry
breaking in general and chiral symmetry breaking in QCD, (b) an overview of the
present status of lattice data and the knowlegde that we have at finite
temperature from chiral perturbation theory. (c) Results obtained from the
Nambu--Jona-Lasinio model describing static mesonic properties are discussed as
well as the bulk thermodynamic quantities. Divergences that are observed in the
elastic quark-antiquark scattering cross-section, reminiscent of the phenomenon
of critical opalescence in light scattering, is also discussed. (d) Finally, we
deal with the realm of systems out of equilibrium, and examine the effects of a
medium dependent condensate in a system of interacting quarks.Comment: 62 LaTex pages, incorporating 23 figures. Lectures given at the
eleventh Chris-Engelbrecht Summer School in Theoretical Physics, 4-13
February, 1998, to be published by Springer Verla
Via Hexagons to Squares in Ferrofluids: Experiments on Hysteretic Surface Transformations under Variation of the Normal Magnetic Field
We report on different surface patterns on magnetic liquids following the
Rosensweig instability. We compare the bifurcation from the flat surface to a
hexagonal array of spikes with the transition to squares at higher fields. From
a radioscopic mapping of the surface topography we extract amplitudes and
wavelengths. For the hexagon--square transition, which is complex because of
coexisting domains, we tailor a set of order parameters like peak--to--peak
distance, circularity, angular correlation function and pattern specific
amplitudes from Fourier space. These measures enable us to quantify the smooth
hysteretic transition. Voronoi diagrams indicate a pinning of the domains. Thus
the smoothness of the transition is roughness on a small scale.Comment: 17 pages, 14 figure
Thermally Induced Fluctuations Below the Onset of Rayleigh-B\'enard Convection
We report quantitative experimental results for the intensity of
noise-induced fluctuations below the critical temperature difference for Rayleigh-B\'enard convection. The structure factor of the fluctuating
convection rolls is consistent with the expected rotational invariance of the
system. In agreement with predictions based on stochastic hydrodynamic
equations, the fluctuation intensity is found to be proportional to
where . The
noise power necessary to explain the measurements agrees with the prediction
for thermal noise. (WAC95-1)Comment: 13 pages of text and 4 Figures in a tar-compressed and uuencoded file
(using uufiles package). Detailed instructions of unpacking are include
Fluctuation and Dissipation in Liquid Crystal Electroconvection
In this experiment a steady state current is maintained through a liquid
crystal thin film. When the applied voltage is increased through a threshold, a
phase transition is observed into a convective state characterized by the
chaotic motion of rolls. Above the threshold, an increase in power consumption
is observed that is manifested by an increase in the mean conductivity. A sharp
increase in the ratio of the power fluctuations to the mean power dissipated is
observed above the transition. This ratio is compared to the predictions of the
fluctuation theorem of Gallavotti and Cohen using an effective temperature
associated with the rolls' chaotic motion.Comment: 4 pages, 3 figures, revtex forma
Modulation of Localized States in Electroconvection
We report on the effects of temporal modulation of the driving force on a
particular class of localized states, known as worms, that have been observed
in electroconvection in nematic liquid crystals. The worms consist of the
superposition of traveling waves and have been observed to have unique, small
widths, but to vary in length. The transition from the pure conduction state to
worms occurs via a backward bifurcation. A possible explanation of the
formation of the worms has been given in terms of coupled amplitude equations.
Because the worms consist of the superposition of traveling waves, temporal
modulation of the control parameter is a useful probe of the dynamics of the
system. We observe that temporal modulation increases the average length of the
worms and stabilizes worms below the transition point in the absence of
modulation.Comment: 4 pages, 4 figure
Dynamic scaling and quasi-ordered states in the two dimensional Swift-Hohenberg equation
The process of pattern formation in the two dimensional Swift-Hohenberg
equation is examined through numerical and analytic methods. Dynamic scaling
relationships are developed for the collective ordering of convective rolls in
the limit of infinite aspect ratio. The stationary solutions are shown to be
strongly influenced by the strength of noise. Stationary states for small and
large noise strengths appear to be quasi-ordered and disordered respectively.
The dynamics of ordering from an initially inhomogeneous state is very slow in
the former case and fast in the latter. Both numerical and analytic
calculations indicate that the slow dynamics can be characterized by a simple
scaling relationship, with a characteristic dynamic exponent of in the
intermediate time regime
- …