781 research outputs found
Consistent operator semigroups and their interpolation
Under a mild regularity condition we prove that the generator of the
interpolation of two C0-semigroups is the interpolation of the two generators
H\"older estimates for parabolic operators on domains with rough boundary
We investigate linear parabolic, second-order boundary value problems with
mixed boundary conditions on rough domains. Assuming only boundedness and
ellipticity on the coefficient function and very mild conditions on the
geometry of the domain, including a very weak compatibility condition between
the Dirichlet boundary part and its complement, we prove H\"older continuity of
the solution in space and time.Comment: 1 figur
Fingering Instability in a Water-Sand Mixture
The temporal evolution of a water-sand interface driven by gravity is
experimentally investigated. By means of a Fourier analysis of the evolving
interface the growth rates are determined for the different modes appearing in
the developing front. To model the observed behavior we apply the idea of the
Rayleigh-Taylor instability for two stratified fluids. Carrying out a linear
stability analysis we calculate the growth rates from the corresponding
dispersion relations for finite and infinite cell sizes. Based on the
theoretical results the viscosity of the suspension is estimated to be
approximately 100 times higher than that of pure water, in agreement with other
experimental findings.Comment: 11 pages, 12 figures, RevTeX; final versio
Parabolic equations with dynamical boundary conditions and source terms on interfaces
We consider parabolic equations with mixed boundary conditions and domain
inhomogeneities supported on a lower dimensional hypersurface, enforcing a jump
in the conormal derivative. Only minimal regularity assumptions on the domain
and the coefficients are imposed. It is shown that the corresponding linear
operator enjoys maximal parabolic regularity in a suitable -setting. The
linear results suffice to treat also the corresponding nondegenerate
quasilinear problems.Comment: 30 pages. Revised version. To appear in Annali di Matematica Pura ed
Applicat
The evidence of quasi-free positronium state in GiPS-AMOC spectra of glycerol
We present the results of processing of Age-Momentum Correlation (AMOC)
spectra that were measured for glycerol by the Gamma-induced positron
spectroscopy (GiPS) facility. Our research has shown that the shape of
experimental s(t) curve cannot be explained without introduction of the
intermediate state of positronium (Ps), called quasi-free Ps. This state yields
the wide Doppler line near zero lifetimes. We discuss the possible properties
of this intermediate Ps state from the viewpoint of developed model. The amount
of annihilation events produced by quasi-free Ps is estimated to be less than
5% of total annihilations. In the proposed model, quasi-free Ps serves as a
precursor for trapped Ps of para- and ortho-states
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
A Non-Equilibrium Defect-Unbinding Transition: Defect Trajectories and Loop Statistics
In a Ginzburg-Landau model for parametrically driven waves a transition
between a state of ordered and one of disordered spatio-temporal defect chaos
is found. To characterize the two different chaotic states and to get insight
into the break-down of the order, the trajectories of the defects are tracked
in detail. Since the defects are always created and annihilated in pairs the
trajectories form loops in space time. The probability distribution functions
for the size of the loops and the number of defects involved in them undergo a
transition from exponential decay in the ordered regime to a power-law decay in
the disordered regime. These power laws are also found in a simple lattice
model of randomly created defect pairs that diffuse and annihilate upon
collision.Comment: 4 pages 5 figure
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
Hölder estimates for second-order operators with mixed boundary conditions
In this paper we investigate linear elliptic, second-order boundary value problems with mixed boundary conditions. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain -- including a very weak compatibility condition between the Dirichlet boundary part and its complement -- we prove first Hölder continuity of the solution. Secondly, Gaussian Hölder estimates for the corresponding heat kernel are derived. The essential instruments are De Giorgi and Morrey-Campanato estimates
The Regulation of Glutaminolysis and Citric Acid Cycle Activity During Mammalian Cell Cultivation
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