56 research outputs found
Atom lithography without laser cooling
Using direct-write atom lithography, Fe nanolines are deposited with a pitch
of 186 nm, a full width at half maximum (FWHM) of 50 nm, and a height of up to
6 nm. These values are achieved by relying on geometrical collimation of the
atomic beam, thus without using laser collimation techniques. This opens the
way for applying direct-write atom lithography to a wide variety of elements.Comment: 7 pages, 11 figure
Incompressible flow in porous media with fractional diffusion
In this paper we study the heat transfer with a general fractional diffusion
term of an incompressible fluid in a porous medium governed by Darcy's law. We
show formation of singularities with infinite energy and for finite energy we
obtain existence and uniqueness results of strong solutions for the
sub-critical and critical cases. We prove global existence of weak solutions
for different cases. Moreover, we obtain the decay of the solution in ,
for any , and the asymptotic behavior is shown. Finally, we prove the
existence of an attractor in a weak sense and, for the sub-critical dissipative
case with , we obtain the existence of the global attractor
for the solutions in the space for any
A Sucrose Solution Application to the Study of Model Biological Membranes
The small-angle X-ray and neutron scattering, time resolved X-ray small-angle
and wide-angle diffraction coupled with differential scanning calorimetry have
been applied to the investigation of unilamellar and multilamellar
dimyristoylphosphatidylcholine (DMPC) vesicles in sucrose buffers with sucrose
concentrations from 0 to 60%. Sucrose buffer decreased vesicle size and
polydispersity and increased an X-ray contrast between phospholipid membrane
and bulk solvent sufficiently. No influence of sucrose on the membrane
thickness or mutual packing of hydrocarbon chains has been detected. The region
of sucrose concentrations 30%-40% created the best experimental conditions for
X-ray small-angle experiments with phospholipid vesicles.Comment: PDF: 10 pages, 6 figures. MS Word sours
Optimal Sobolev regularity for linear second-order divergence elliptic operators occurring in real-world problems
On bounded three-dimensional domains, we consider divergence-type operators including mixed homogeneous Dirichlet and Neumann boundary conditions and discontinuous coefficient functions. We develop a geometric framework in which it is possible to prove that the operator provides an isomorphism of suitable function spaces. In particular, in these spaces, the gradient of solutions turns out to be integrable with exponent larger than the space dimension three. Relevant examples from real-world applications are provided in great detail
Finite-dimensional global and exponential attractors for the reaction-diffusion problem with an obstacle potential
A reaction-diffusion problem with an obstacle potential is considered in a
bounded domain of . Under the assumption that the obstacle \K is a
closed convex and bounded subset of with smooth boundary or it
is a closed -dimensional simplex, we prove that the long-time behavior of
the solution semigroup associated with this problem can be described in terms
of an exponential attractor. In particular, the latter means that the fractal
dimension of the associated global attractor is also finite
Global and exponential attractors for a Ginzburg-Landau model of superfluidity
The long-time behavior of the solutions for a non-isothermal model in
superfluidity is investigated. The model describes the transition between the
normal and the superfluid phase in liquid 4He by means of a non-linear
differential system, where the concentration of the superfluid phase satisfies
a non-isothermal Ginzburg-Landau equation. This system, which turns out to be
consistent with thermodynamical principles and whose well-posedness has been
recently proved, has been shown to admit a Lyapunov functional. This allows to
prove existence of the global attractor which consists of the unstable manifold
of the stationary solutions. Finally, by exploiting recent techniques of
semigroups theory, we prove the existence of an exponential attractor of finite
fractal dimension which contains the global attractor.Comment: 39 page
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