105,552 research outputs found
On homotopies with triple points of classical knots
We consider a knot homotopy as a cylinder in 4-space. An ordinary triple
point of the cylinder is called {\em coherent} if all three branches
intersect at pairwise with the same index. A {\em triple unknotting} of a
classical knot is a homotopy which connects with the trivial knot and
which has as singularities only coherent triple points. We give a new formula
for the first Vassiliev invariant by using triple unknottings. As a
corollary we obtain a very simple proof of the fact that passing a coherent
triple point always changes the knot type. As another corollary we show that
there are triple unknottings which are not homotopic as triple unknottings even
if we allow more complicated singularities to appear in the homotopy of the
homotopy.Comment: 10 pages, 13 figures, bugs in figures correcte
Capacitively-coupled rf discharge with a large amount of microparticles: spatiotemporal emission pattern and microparticle arrangement
The effect of micron-sized particles on a low-pressure capacitively-coupled
rf discharge is studied both experimentally and using numerical simulations. In
the laboratory experiments, microparticle clouds occupying a considerable
fraction of the discharge volume are supported against gravity with the help of
the thermophoretic force. The spatiotemporally resolved optical emission
measurements are performed with different arrangements of microparticles. The
numerical simulations are carried out on the basis of a one-dimensional hybrid
(fluid-kinetic) discharge model describing the interaction between plasma and
microparticles in a self-consistent way. The study is focused on the role of
microparticle arrangement in interpreting the spatiotemporal emission
measurements. We show that it is not possible to reproduce simultaneously the
observed microparticle arrangement and emission pattern in the framework of the
considered one-dimensional model. This disagreement is discussed and attributed
to two-dimensional effects, e.g., radial diffusion of the plasma components
Quasi-Chemical and Structural Analysis of Polarizable Anion Hydration
Quasi-chemical theory is utilized to analyze the roles of solute polarization
and size in determining the structure and thermodynamics of bulk anion
hydration for the Hofmeister series Cl, Br, and I. Excellent
agreement with experiment is obtained for whole salt hydration free energies
using the polarizable AMOEBA force field. The quasi-chemical approach exactly
partitions the solvation free energy into inner-shell, outer-shell packing, and
outer-shell long-ranged contributions by means of a hard-sphere condition.
Small conditioning radii, even well inside the first maximum of the
ion-water(oxygen) radial distribution function, result in Gaussian behavior for
the long-ranged contribution that dominates the ion hydration free energy. The
spatial partitioning allows for a mean-field treatment of the long-ranged
contribution, leading to a natural division into first-order electrostatic,
induction, and van der Waals terms. The induction piece exhibits the strongest
ion polarizability dependence, while the larger-magnitude first-order
electrostatic piece yields an opposing but weaker polarizability dependence. In
addition, a structural analysis is performed to examine the solvation
anisotropy around the anions. As opposed to the hydration free energies, the
solvation anisotropy depends more on ion polarizability than on ion size:
increased polarizability leads to increased anisotropy. The water dipole
moments near the ion are similar in magnitude to bulk water, while the ion
dipole moments are found to be significantly larger than those observed in
quantum mechanical studies. Possible impacts of the observed over-polarization
of the ions on simulated anion surface segregation are discussed.Comment: slight revision, in press at J. Chem. Phy
Decoherence of an -qubit quantum memory
We analyze decoherence of a quantum register in the absence of non-local
operations i.e. of non-interacting qubits coupled to an environment. The
problem is solved in terms of a sum rule which implies linear scaling in the
number of qubits. Each term involves a single qubit and its entanglement with
the remaining ones. Two conditions are essential: first decoherence must be
small and second the coupling of different qubits must be uncorrelated in the
interaction picture. We apply the result to a random matrix model, and
illustrate its reach considering a GHZ state coupled to a spin bath.Comment: 4 pages, 2 figure
Electricity deregulation and the valuation of visibility loss in wilderness areas: A research note.
Visibility in most wilderness areas in the northeastern United States has declined substantially since the 1970s. As noted by Hill et al. (2000), despite the 1977 Clean Air Act and subsequent amendments, human induced smog conditions are becoming increasingly worse. Average visibility in class I airsheds, such as the Great Gulf Wilderness in New Hampshire’s White Mountains, is now about one-third of natural conditions. A particular concern is that deregulation of electricity production could result in further degradation because consumers may switch to lower cost fossil fuel generation (Harper 2000). To the extent that this system reduces electricity costs, it may also affect firm location decisions (Halstead and Deller 1997). Yet, little is known about the extent to which consumers are likely to make tradeoffs between electric bills and reduced visibility in nearby wilderness areas. This applied research uses a contingent valuation approach in an empirical case study of consumers’ tradeoffs between cheaper electric bills and reduced visibility in New Hampshire’s White Mountains. We also examine some of the problems associated with uncertainty with this type of analysis; that is, how confident respondents are in their answers to the valuation questions. Finally, policy implications of decreased visibility due to electricity deregulation are discussed
A Superluminal Subway: The Krasnikov Tube
The ``warp drive'' metric recently presented by Alcubierre has the problem
that an observer at the center of the warp bubble is causally separated from
the outer edge of the bubble wall. Hence such an observer can neither create a
warp bubble on demand nor control one once it has been created. In addition,
such a bubble requires negative energy densities. One might hope that
elimination of the first problem might ameliorate the second as well. We
analyze and generalize a metric, originally proposed by Krasnikov for two
spacetime dimensions, which does not suffer from the first difficulty. As a
consequence, the Krasnikov metric has the interesting property that although
the time for a one-way trip to a distant star cannot be shortened, the time for
a round trip, as measured by clocks on Earth, can be made arbitrarily short. In
our four dimensional extension of this metric, a ``tube'' is constructed along
the path of an outbound spaceship, which connects the Earth and the star.
Inside the tube spacetime is flat, but the light cones are opened out so as to
allow superluminal travel in one direction. We show that, although a single
Krasnikov tube does not involve closed timelike curves, a time machine can be
constructed with a system of two non-overlapping tubes. Furthermore, it is
demonstrated that Krasnikov tubes, like warp bubbles and traversable wormholes,
also involve unphysically thin layers of negative energy density, as well as
large total negative energies, and therefore probably cannot be realized in
practice.Comment: 20 pages, LATEX, 5 eps figures, uses \eps
Gravity compensation in complex plasmas by application of a temperature gradient
Micron sized particles are suspended or even lifted up in a gas by
thermophoresis. This allows the study of many processes occurring in strongly
coupled complex plasmas at the kinetic level in a relatively stress-free
environment. First results are presented. The technique is also of interest for
technological applications.Comment: 4 pages, 4 figures, final version to be published in Phys. Rev. Let
Black Hole - Neutron Star Mergers as Central Engines of Gamma-Ray Bursts
Hydrodynamic simulations of the merger of stellar mass black hole - neutron
star binaries (BH/NS) are compared with mergers of binary neutron stars
(NS/NS). The simulations are Newtonian, but take into account the emission and
backreaction of gravitational waves. The use of a physical nuclear equation of
state allows us to include the effects of neutrino emission. For low neutron
star to black hole mass ratios the neutron star transfers mass to the black
hole during a few cycles of orbital decay and subsequent widening before
finally being disrupted, whereas for ratios near unity the neutron star is
already distroyed during its first approach. A gas mass between about 0.3 and
about 0.7 solar masses is left in an accretion torus around the black hole and
radiates neutrinos at a luminosity of several 10^{53} erg/s during an estimated
accretion time scale of about 0.1 s. The emitted neutrinos and antineutrinos
annihilate into electron-positron pairs with efficiencies of 1-3% percent and
rates of up to 2*10^{52} erg/s, thus depositing an energy of up to 10^{51} erg
above the poles of the black hole in a region which contains less than 10^{-5}
solar masses of baryonic matter. This could allow for relativistic expansion
with Lorentz factors around 100 and is sufficient to explain apparent burst
luminosities of up to several 10^{53} erg/s for burst durations of
approximately 0.1-1 s, if the gamma emission is collimated in two moderately
focussed jets in a fraction of about 1/100-1/10 of the sky.Comment: 8 pages, LaTex, 4 postscript figures, 2 tables. ApJ Letters,
accepted; revised and shortened version, Fig. 2 change
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