4,024 research outputs found
The Gaussian free field and Hadamard's variational formula
We relate the Gaussian free field on a planar domain to the variational
formula of Hadamard which explains the change of the Green function under a
perturbation of the domain. This is accomplished by means of a natural integral
operator related to Hadamard's formula.Comment: 9 page
Weak compactness and essential norms of integration operators
Let be an analytic function on the unit disc and consider the integration
operator of the form . We show that on the
spaces and the operator is weakly compact if and only if it
is compact. In the case of this answers a question of Siskakis and Zhao.
More generally, we estimate the essential and weak essential norms of on
and
Molecular ordering of precursor films during spreading of tiny liquid droplets
In this work we address a novel feature of spreading dynamics of tiny liquid
droplets on solid surfaces, namely the case where the ends of the molecules
feel different interactions to the surface. We consider a simple model of
dimers and short chain--like molecules which cannot form chemical bonds with
the surface. We study the spreading dynamics by Molecular Dynamics techniques.
In particular, we examine the microscopic structure of the time--dependent
precursor film and find that in some cases it can exhibit a high degree of
local order. This order persists even for flexible chains. Our results suggest
the possibility of extracting information about molecular interactions from the
structure of the precursor film.Comment: 4 pages, revtex, no figures, complete file available from
ftp://rock.helsinki.fi/pub/preprints/tft/ or at
http://www.physics.helsinki.fi/tft/tft_preprints.html (to appear in Phys.
Rev. E Rapid Comm.
Dynamics of Spreading of Small Droplets of Chainlike Molecules on Surfaces
Dynamics of spreading of small droplets on surfaces has been studied by the
molecular dynamics method. Simulations have been performed for mixtures of
solvent and dimer, and solvent and tetramer droplets. For solvent particles and
dimers, layering occurs leading to stepped droplet shapes. For tetramers such
shapes occur for relatively deep and strong surface potentials only. For wider
and more shallow potentials, more rapid spreading and rounded droplet shapes
occur. These results are in accordance with experimental data on small non -
volatile polymer droplets. PACS numbers: 68.10Gw, 05.70.Ln, 61.20.Ja, 68.45GdComment: to appear in Europhys. Letters (1994), Latex, 12 page
Grazing-angle scattering of electromagnetic waves in gratings with varying mean parameters: grating eigenmodes
A highly unusual pattern of strong multiple resonances for bulk
electromagnetic waves is predicted and analysed numerically in thick periodic
holographic gratings in a slab with the mean permittivity that is larger than
that of the surrounding media. This pattern is shown to exist in the geometry
of grazing-angle scattering (GAS), that is when the scattered wave (+1
diffracted order) in the slab propagates almost parallel to the slab (grating)
boundaries. The predicted resonances are demonstrated to be unrelated to
resonant generation of the conventional guided modes of the slab. Their
physical explanation is associated with resonant generation of a completely new
type of eigenmodes in a thick slab with a periodic grating. These new slab
eigenmodes are generically related to the grating; they do not exist if the
grating amplitude is zero. The field structure of these eigenmodes and their
dependence on structural and wave parameters is analysed. The results are
extended to the case of GAS of guided modes in a slab with a periodic groove
array of small corrugation amplitude and small variations in the mean thickness
of the slab at the array boundaries.Comment: 16 pages, 6 figure
Wigner molecules in polygonal quantum dots: A density functional study
We investigate the properties of many-electron systems in two-dimensional
polygonal (triangle, square, pentagon, hexagon) potential wells by using the
density functional theory. The development of the ground state electronic
structure as a function of the dot size is of particular interest. First we
show that in the case of two electrons, the Wigner molecule formation agrees
with the previous exact diagonalization studies. Then we present in detail how
the spin symmetry breaks in polygonal geometries as the spin density functional
theory is applied. In several cases with more than two electrons, we find a
transition to the crystallized state, yielding coincidence with the number of
density maxima and the electron number. We show that this transition density,
which agrees reasonably well with previous estimations, is rather insensitive
to both the shape of the dot and the electron number.Comment: 8 pages, 11 figure
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