21,624 research outputs found
Field-induced structure transformation in electrorheological solids
We have computed the local electric field in a body-centered tetragonal (BCT)
lattice of point dipoles via the Ewald-Kornfeld formulation, in an attempt to
examine the effects of a structure transformation on the local field strength.
For the ground state of an electrorheological solid of hard spheres, we
identified a novel structure transformation from the BCT to the face-centered
cubic (FCC) lattices by changing the uniaxial lattice constant c under the hard
sphere constraint. In contrast to the previous results, the local field
exhibits a non-monotonic transition from BCT to FCC. As c increases from the
BCT ground state, the local field initially decreases rapidly towards the
isotropic value at the body-centered cubic lattice, decreases further, reaching
a minimum value and increases, passing through the isotropic value again at an
intermediate lattice, reaches a maximum value and finally decreases to the FCC
value. An experimental realization of the structure transformation is
suggested. Moreover, the change in the local field can lead to a generalized
Clausius-Mossotti equation for the BCT lattices.Comment: Submitted to Phys. Rev.
Equivariant wave maps exterior to a ball
We consider the exterior Cauchy-Dirichlet problem for equivariant wave maps
from 3+1 dimensional Minkowski spacetime into the three-sphere. Using mixed
analytical and numerical methods we show that, for a given topological degree
of the map, all solutions starting from smooth finite energy initial data
converge to the unique static solution (harmonic map). The asymptotics of this
relaxation process is described in detail. We hope that our model will provide
an attractive mathematical setting for gaining insight into
dissipation-by-dispersion phenomena, in particular the soliton resolution
conjecture.Comment: 16 pages, 9 figure
Fermion Resonances on a Thick Brane with a Piecewise Warp Factor
In this paper, we mainly investigate the problems of resonances of massive KK
fermions on a single scalar constructed thick brane with a piecewise warp
factor matching smoothly. The distance between two boundaries and the other
parameters are determined by one free parameter through three junction
conditions. For the generalized Yukawa coupling
with odd , the mass eigenvalue , width , lifetime
, and maximal probability of fermion resonances are obtained.
Our numerical calculations show that the brane without internal structure also
favors the appearance of resonant states for both left- and right-handed
fermions. The scalar-fermion coupling and the thickness of the brane influence
the resonant behaviors of the massive KK fermions.Comment: V3: 15 pages, 7 figures, published versio
Spin-one ferromagnets with single-ion anisotropy in a perpendicular external field
In this paper, the conventional Holstein-Primakoff method is generalized with
the help of the characteristic angle transformation [Lei Zhou and Ruibao Tao,
J. Phys. A {\bf 27} 5599 (1994)] for the spin-one magnetic systems with
single-ion anisotropies. We find that the weakness of the conventional method
for such systems can be overcome by the new approach. Two models will be
discussed to illuminate the main idea, which are the ``easy-plane" and the
``easy-axis" spin-one ferromagnet, respectively. Comparisons show that the
current approach can give reasonable ground state properties for the magnetic
system with ``easy-plane" anisotropy though the conventional method never can,
and can give a better representation than the conventional one for the magnetic
system with ``easy-axis" anisotropy though the latter is usually believed to be
a good approximation in such case. Study of the easy-plane model shows that
there is a phase transition induced by the external field, and the
low-temperature specific heat may have a peak as the field reaches the critical
value.Comment: Using LaTex. To be published in the September 1 issue of Physical
Review B (1996). Email address: [email protected]
Pressure Raman effects and internal stress in network glasses
Raman scattering from binary GexSe1-x glasses under hydrostatic pressure
shows onset of a steady increase in the frequency of modes of corner-sharing
GeSe4 tetrahedral units when the external pressure P exceeds a threshold value
Pc. The threshold pressure Pc(x) decreases with x in the 0.15 < x < 0.20 range,
nearly vanishes in the 0.20 < x < 0.25 range, and then increases in the 0.25 <
x < 1/3 range. These Pc(x) trends closely track those in the non-reversing
enthalpy, DHnr(x), near glass transitions (Tgs), and in particular, both
DHnr(x) and Pc(x) vanish in the reversibility window (0.20 < x < 0.25). It is
suggested that Pc provides a measure of stress at the Raman active units; and
its vanishing in the reversibility window suggests that these units are part of
an isostatically rigid backbone. Isostaticity also accounts for the non-aging
behavior of glasses observed in the reversibility window
Field-induced Tomonaga-Luttinger liquid phase of a two-leg spin-1/2 ladder with strong leg interactions
We study the magnetic-field-induced quantum phase transition from a gapped
quantum phase that has no magnetic long-range order into a gapless phase in the
spin-1/2 ladder compound bis(2,3-dimethylpyridinium) tetrabromocuprate (DIMPY).
At temperatures below about 1 K, the specific heat in the gapless phase attains
an asymptotic linear temperature dependence, characteristic of a
Tomonaga-Luttinger liquid. Inelastic neutron scattering and the specific heat
measurements in both phases are in good agreement with theoretical
calculations, demonstrating that DIMPY is the first model material for an S=1/2
two-leg spin ladder in the strong-leg regime.Comment: 4.1 pages, 4 figures (Fig. 4 updated), to appear in Physical Review
Letter
Self-Diffusion of a Polymer Chain in a Melt
Self-diffusion of a polymer chain in a melt is studied by Monte Carlo
simulations of the bond fluctuation model, where only the excluded volume
interaction is taken into account. Polymer chains, each of which consists of
segments, are located on an simple cubic lattice
under periodic boundary conditions, where each segment occupies unit cells. The results for
and 512 at the volume fraction are reported, where
for and L=192 for . The -dependence of the
self-diffusion constant is examined. Here, is estimated from the mean
square displacements of the center of mass of a single polymer chain at the
times larger than the longest relaxation time. From the data for , 384
and 512, the apparent exponent , which describes the apparent power
law dependence of on as , is estimated as
. The ratio seems to be a
constant for and 512, where and
denote the longest relaxation time and the mean square end-to-end distance,
respectively.Comment: 4 pages, 3 figures, submitted to J. Phys. Soc. Jp
On the determination of the deceleration parameter from Supernovae data
Supernovae searches have shown that a simple matter-dominated and
decelerating universe should be ruled out. However a determination of the
present deceleration parameter through a simple kinematical description
is not exempt of possible drawbacks. We show that, with a time dependent
equation of state for the dark energy, a bias is present for : models
which are very far from the so-called Concordance Model can be accommodated by
the data and a simple kinematical analysis can lead to wrong conclusions. We
present a quantitative treatment of this bias and we present our conclusions
when a possible dynamical dark energy is taken into account.Comment: 4 pages, 3 figures, submitte
Small ball probability, Inverse theorems, and applications
Let be a real random variable with mean zero and variance one and
be a multi-set in . The random sum
where are iid copies of
is of fundamental importance in probability and its applications.
We discuss the small ball problem, the aim of which is to estimate the
maximum probability that belongs to a ball with given small radius,
following the discovery made by Littlewood-Offord and Erdos almost 70 years
ago. We will mainly focus on recent developments that characterize the
structure of those sets where the small ball probability is relatively
large. Applications of these results include full solutions or significant
progresses of many open problems in different areas.Comment: 47 page
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