8,003 research outputs found
Homotopy on spatial graphs and generalized Sato-Levine invariants
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs
which are generalizations of Milnor's link-homotopy. Fleming and the author
introduced some edge (resp. vertex)-homotopy invariants of spatial graphs by
applying the Sato-Levine invariant for the constituent 2-component
algebraically split links. In this paper, we construct some new edge (resp.
vertex)-homotopy invariants of spatial graphs without any restriction of
linking numbers of the constituent 2-component links by applying the
generalized Sato-Levine invariant.Comment: 16 pages, 13 figure
Fact Sheet no.1: Nonpoint Source Pollution and Water Quality of Northwest Arkansas
Preservation of a clean, safe, and biologically diverse environment can capture public attention as few other issues can. Indeed, recent international cooperative efforts indicate that there is an increasing global desire to pass on to future generations an environment at least equal in quality to the one we inherited
Rigorous approach to the comparison between experiment and theory in Casimir force measurements
In most experiments on the Casimir force the comparison between measurement
data and theory was done using the concept of the root-mean-square deviation, a
procedure that has been criticized in literature. Here we propose a special
statistical analysis which should be performed separately for the experimental
data and for the results of the theoretical computations. In so doing, the
random, systematic, and total experimental errors are found as functions of
separation, taking into account the distribution laws for each error at 95%
confidence. Independently, all theoretical errors are combined to obtain the
total theoretical error at the same confidence. Finally, the confidence
interval for the differences between theoretical and experimental values is
obtained as a function of separation. This rigorous approach is applied to two
recent experiments on the Casimir effect.Comment: 10 pages, iopart.cls is used, to appear in J. Phys. A (special issue:
Proceedings of QFEXT05, Barcelona, Sept. 5-9, 2005
The bends on a quantum waveguide and cross-products of Bessel functions
A detailed analysis of the wave-mode structure in a bend and its
incorporation into a stable algorithm for calculation of the scattering matrix
of the bend is presented. The calculations are based on the modal approach. The
stability and precision of the algorithm is numerically and analytically
analysed. The algorithm enables precise numerical calculations of scattering
across the bend. The reflection is a purely quantum phenomenon and is discussed
in more detail over a larger energy interval. The behaviour of the reflection
is explained partially by a one-dimensional scattering model and heuristic
calculations of the scattering matrix for narrow bends. In the same spirit we
explain the numerical results for the Wigner-Smith delay time in the bend.Comment: 34 pages, 21 figure
Disorder-Driven Pretransitional Tweed in Martensitic Transformations
Defying the conventional wisdom regarding first--order transitions, {\it
solid--solid displacive transformations} are often accompanied by pronounced
pretransitional phenomena. Generally, these phenomena are indicative of some
mesoscopic lattice deformation that ``anticipates'' the upcoming phase
transition. Among these precursive effects is the observation of the so-called
``tweed'' pattern in transmission electron microscopy in a wide variety of
materials. We have investigated the tweed deformation in a two dimensional
model system, and found that it arises because the compositional disorder
intrinsic to any alloy conspires with the natural geometric constraints of the
lattice to produce a frustrated, glassy phase. The predicted phase diagram and
glassy behavior have been verified by numerical simulations, and diffraction
patterns of simulated systems are found to compare well with experimental data.
Analytically comparing to alternative models of strain-disorder coupling, we
show that the present model best accounts for experimental observations.Comment: 43 pages in TeX, plus figures. Most figures supplied separately in
uuencoded format. Three other figures available via anonymous ftp
Kepler Observations of Transiting Hot Compact Objects
Kepler photometry has revealed two unusual transiting companions orbiting an
early A-star and a late B-star. In both cases the occultation of the companion
is deeper than the transit. The occultation and transit with follow-up optical
spectroscopy reveal a 9400 K early A-star, KOI-74 (KIC 6889235), with a
companion in a 5.2 day orbit with a radius of 0.08 Rsun and a 10000 K late
B-star KOI-81 (KIC 8823868) that has a companion in a 24 day orbit with a
radius of 0.2 Rsun. We infer a temperature of 12250 K for KOI-74b and 13500 K
for KOI-81b.
We present 43 days of high duty cycle, 30 minute cadence photometry, with
models demonstrating the intriguing properties of these object, and speculate
on their nature.Comment: 12 pages, 3 figures, submitted to ApJL (updated to correct KOI74
lightcurve
Universal Static and Dynamic Properties of the Structural Transition in Pb(Zn1/3Nb2/3)O3
The relaxors Pb(ZnNb)O (PZN) and
Pb(MgNb)O (PMN) have very similar properties based on the
dielectric response around the critical temperature (defined by the
structural transition under the application of an electric field). It has been
widely believed that these materials are quite different below with the
unit cell of PMN remaining cubic while in PZN the low temperature unit cell is
rhombohedral in shape. However, this has been clarified by recent high-energy
x-ray studies which have shown that PZN is rhombohedral only in the skin while
the shape of the unit cell in the bulk is nearly cubic. In this study we have
performed both neutron elastic and inelastic scattering to show that the
temperature dependence of both the diffuse and phonon scattering in PZN and PMN
is very similar. Both compounds show a nearly identical recovery of the soft
optic mode and a broadening of the acoustic mode below . The diffuse
scattering in PZN is suggestive of an onset at the high temperature Burns
temperature similar to that in PMN. In contrast to PMN, we observe a broadening
of the Bragg peaks in both the longitudinal and transverse directions below
. We reconcile this additional broadening, not observed in PMN, in terms
of structural inhomogeneity in PZN. Based on the strong similarities between
PMN and PZN, we suggest that both materials belong to the same universality
class and discuss the relaxor transition in terms of the three-dimensional
Heisenberg model with cubic anisotropy in a random field.Comment: 11 pages, 10 figures. Updated version after helpful referee comment
Giant Anharmonic Phonon Scattering in PbTe
Understanding the microscopic processes affecting the bulk thermal
conductivity is crucial to develop more efficient thermoelectric materials.
PbTe is currently one of the leading thermoelectric materials, largely thanks
to its low thermal conductivity. However, the origin of this low thermal
conductivity in a simple rocksalt structure has so far been elusive. Using a
combination of inelastic neutron scattering measurements and first-principles
computations of the phonons, we identify a strong anharmonic coupling between
the ferroelectric transverse optic (TO) mode and the longitudinal acoustic (LA)
modes in PbTe. This interaction extends over a large portion of reciprocal
space, and directly affects the heat-carrying LA phonons. The LA-TO anharmonic
coupling is likely to play a central role in explaining the low thermal
conductivity of PbTe. The present results provide a microscopic picture of why
many good thermoelectric materials are found near a lattice instability of the
ferroelectric type
- …