1,372 research outputs found
Minimal speed of fronts of reaction-convection-diffusion equations
We study the minimal speed of propagating fronts of convection reaction
diffusion equations of the form for
positive reaction terms with . The function is continuous
and vanishes at . A variational principle for the minimal speed of the
waves is constructed from which upper and lower bounds are obtained. This
permits the a priori assesment of the effect of the convective term on the
minimal speed of the traveling fronts. If the convective term is not strong
enough, it produces no effect on the minimal speed of the fronts. We show that
if , then the minimal speed is given by
the linear value , and the convective term has no effect on the
minimal speed. The results are illustrated by applying them to the exactly
solvable case . Results are also given for
the density dependent diffusion case .Comment: revised, new results adde
Density functional study of the adsorption of K on the Ag(111) surface
Full-potential gradient corrected density functional calculations of the
adsorption of potassium on the Ag(111) surface have been performed. The
considered structures are Ag(111) (root 3 x root 3) R30degree-K and Ag(111) (2
x 2)-K. For the lower coverage, fcc, hcp and bridge site; and for the higher
coverage all considered sites are practically degenerate.
Substrate rumpling is most important for the top adsorption site. The bond
length is found to be nearly identical for the two coverages, in agreement with
recent experiments. Results from Mulliken populations, bond lengths, core level
shifts and work functions consistently indicate a small charge transfer from
the potassium atom to the substrate, which is slightly larger for the lower
coverage.Comment: to appear in Phys Rev
On the relation of Thomas rotation and angular velocity of reference frames
In the extensive literature dealing with the relativistic phenomenon of
Thomas rotation several methods have been developed for calculating the Thomas
rotation angle of a gyroscope along a circular world line. One of the most
appealing concepts, introduced in \cite{rindler}, is to consider a rotating
reference frame co-moving with the gyroscope, and relate the precession of the
gyroscope to the angular velocity of the reference frame. A recent paper
\cite{herrera}, however, applies this principle to three different co-moving
rotating reference frames and arrives at three different Thomas rotation
angles. The reason for this apparent paradox is that the principle of
\cite{rindler} is used for a situation to which it does not apply. In this
paper we rigorously examine the theoretical background and limitations of
applicability of the principle of \cite{rindler}. Along the way we also
establish some general properties of {\it rotating reference frames}, which may
be of independent interest.Comment: 14 pages, 2 figure
The liquid-vapor interface of an ionic fluid
We investigate the liquid-vapor interface of the restricted primitive model
(RPM) for an ionic fluid using a density-functional approximation based on
correlation functions of the homogeneous fluid as obtained from the
mean-spherical approximation (MSA). In the limit of a homogeneous fluid our
approach yields the well-known MSA (energy) equation of state. The ionic
interfacial density profiles, which for the RPM are identical for both species,
have a shape similar to those of simple atomic fluids in that the decay towards
the bulk values is more rapid on the vapor side than on the liquid side. This
is the opposite asymmetry of the decay to that found in earlier calculations
for the RPM based on a square-gradient theory. The width of the interface is,
for a wide range of temperatures, approximately four times the second moment
correlation length of the liquid phase. We discuss the magnitude and
temperature dependence of the surface tension, and argue that for temperatures
near the triple point the ratio of the dimensionless surface tension and
critical temperature is much smaller for the RPM than for simple atomic fluids.Comment: 6 postscript figures, submitted to Phys. Rev.
Locally continuously perfect groups of homeomorphisms
The notion of a locally continuously perfect group is introduced and studied.
This notion generalizes locally smoothly perfect groups introduced by Haller
and Teichmann. Next, we prove that the path connected identity component of the
group of all homeomorphisms of a manifold is locally continuously perfect. The
case of equivariant homeomorphism group and other examples are also considered.Comment: 14 page
Flow Computations on Imprecise Terrains
We study the computation of the flow of water on imprecise terrains. We
consider two approaches to modeling flow on a terrain: one where water flows
across the surface of a polyhedral terrain in the direction of steepest
descent, and one where water only flows along the edges of a predefined graph,
for example a grid or a triangulation. In both cases each vertex has an
imprecise elevation, given by an interval of possible values, while its
(x,y)-coordinates are fixed. For the first model, we show that the problem of
deciding whether one vertex may be contained in the watershed of another is
NP-hard. In contrast, for the second model we give a simple O(n log n) time
algorithm to compute the minimal and the maximal watershed of a vertex, where n
is the number of edges of the graph. On a grid model, we can compute the same
in O(n) time
Two-Dimensional Quantum XY Model with Ring Exchange and External Field
We present the zero-temperature phase diagram of a square lattice quantum
spin 1/2 XY model with four-site ring exchange in a uniform external magnetic
field. Using quantum Monte Carlo techniques, we identify various quantum phase
transitions between the XY-order, striped or valence bond solid, staggered Neel
antiferromagnet and fully polarized ground states of the model. We find no
evidence for a quantum spin liquid phase.Comment: 4 pages, 4 figure
Dust Devil Tracks
Dust devils that leave dark- or light-toned tracks are common on Mars and they can also be found on the Earth’s surface. Dust devil tracks (hereinafter DDTs) are ephemeral surface features with mostly sub-annual lifetimes. Regarding their size, DDT widths can range between ∼1 m and ∼1 km, depending on the diameter of dust devil that created the track, and DDT lengths range from a few tens of meters to several kilometers, limited by the duration and horizontal ground speed of dust devils. DDTs can be classified into three main types based on their morphology and albedo in contrast to their surroundings; all are found on both planets: (a) dark continuous DDTs, (b) dark cycloidal DDTs, and (c) bright DDTs. Dark continuous DDTs are the most common type on Mars. They are characterized by their relatively homogenous and continuous low albedo surface tracks. Based on terrestrial and martian in situ studies, these DDTs most likely form when surficial dust layers are removed to expose larger-grained substrate material (coarse sands of ≥500 μm in diameter). The exposure of larger-grained materials changes the photometric properties of the surface; hence leading to lower albedo tracks because grain size is photometrically inversely proportional to the surface reflectance. However, although not observed so far, compositional differences (i.e., color differences) might also lead to albedo contrasts when dust is removed to expose substrate materials with mineralogical differences. For dark continuous DDTs, albedo drop measurements are around 2.5 % in the wavelength range of 550–850 nm on Mars and around 0.5 % in the wavelength range from 300–1100 nm on Earth. The removal of an equivalent layer thickness around 1 μm is sufficient for the formation of visible dark continuous DDTs on Mars and Earth. The next type of DDTs, dark cycloidal DDTs, are characterized by their low albedo pattern of overlapping scallops. Terrestrial in situ studies imply that they are formed when sand-sized material that is eroded from the outer vortex area of a dust devil is redeposited in annular patterns in the central vortex region. This type of DDT can also be found in on Mars in orbital image data, and although in situ studies are lacking, terrestrial analog studies, laboratory work, and numerical modeling suggest they have the same formation mechanism as those on Earth. Finally, bright DDTs are characterized by their continuous track pattern and high albedo compared to their undisturbed surroundings. They are found on both planets, but to date they have only been analyzed in situ on Earth. Here, the destruction of aggregates of dust, silt and sand by dust devils leads to smooth surfaces in contrast to the undisturbed rough surfaces surrounding the track. The resulting change in photometric properties occurs because the smoother surfaces have a higher reflectance compared to the surrounding rough surface, leading to bright DDTs. On Mars, the destruction of surficial dust-aggregates may also lead to bright DDTs. However, higher reflective surfaces may be produced by other formation mechanisms, such as dust compaction by passing dust devils, as this may also cause changes in photometric properties. On Mars, DDTs in general are found at all elevations and on a global scale, except on the permanent polar caps. DDT maximum areal densities occur during spring and summer in both hemispheres produced by an increase in dust devil activity caused by maximum insolation. Regionally, dust devil densities vary spatially likely controlled by changes in dust cover thicknesses and substrate materials. This variability makes it difficult to infer dust devil activity from DDT frequencies. Furthermore, only a fraction of dust devils leave tracks. However, DDTs can be used as proxies for dust devil lifetimes and wind directions and speeds, and they can also be used to predict lander or rover solar panel clearing events. Overall, the high DDT frequency in many areas on Mars leads to drastic albedo changes that affect large-scale weather patterns
Effects of Pore Walls and Randomness on Phase Transitions in Porous Media
We study spin models within the mean field approximation to elucidate the
topology of the phase diagrams of systems modeling the liquid-vapor transition
and the separation of He--He mixtures in periodic porous media. These
topologies are found to be identical to those of the corresponding random field
and random anisotropy spin systems with a bimodal distribution of the
randomness. Our results suggest that the presence of walls (periodic or
otherwise) are a key factor determining the nature of the phase diagram in
porous media.Comment: REVTeX, 11 eps figures, to appear in Phys. Rev.
Breaking of general rotational symmetries by multi-dimensional classical ratchets
We demonstrate that a particle driven by a set of spatially uncorrelated,
independent colored noise forces in a bounded, multidimensional potential
exhibits rotations that are independent of the initial conditions. We calculate
the particle currents in terms of the noise statistics and the potential
asymmetries by deriving an n-dimensional Fokker-Planck equation in the small
correlation time limit. We analyze a variety of flow patterns for various
potential structures, generating various combinations of laminar and rotational
flows.Comment: Accepted, Physical Review
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