79 research outputs found
Revised research about chaotic dynamics in Manko et al. spacetime
A recent work by Dubeibe et al. [Phys. Rev. D 75, 023008 (2007)] stated that
chaos phenomenon of test particles in gravitational field of rotating neutron
stars which are described by Manko, Sanabria-Gomez, and Manko (Manko et al.)
metric can only occur when the stars have oblate deformation. But the chaotic
motions they found are limited in a very narrow zone which is very close to the
center of the massive bodies. This paper argues that this is impossible because
the region is actually inside of the stars, so the motions cannot exist at this
place. In this paper, we scan all parameters space and find chaos and unstable
fixed points outside of stars with big mass-quadrupole moments. The
calculations show that chaos can only occur when the stars have prolate
deformation. Because real deformation of stars should be oblate, all orbits of
test particles around the rotating neutron stars described by Manko et al.
solutions are regular. The case of nonzero dipolar magnetic moment has also
been taken into account in this study.Comment: 6 pages, 5 figure
Non-Abelian Quantum Hall States and their Quasiparticles: from the Pattern of Zeros to Vertex Algebra
In the pattern-of-zeros approach to quantum Hall states, a set of data
{n;m;S_a|a=1,...,n; n,m,S_a in N} (called the pattern of zeros) is introduced
to characterize a quantum Hall wave function. In this paper we find sufficient
conditions on the pattern of zeros so that the data correspond to a valid wave
function. Some times, a set of data {n;m;S_a} corresponds to a unique quantum
Hall state, while other times, a set of data corresponds to several different
quantum Hall states. So in the latter cases, the patterns of zeros alone does
not completely characterize the quantum Hall states. In this paper, We find
that the following expanded set of data {n;m;S_a;c|a=1,...,n; n,m,S_a in N; c
in R} provides a more complete characterization of quantum Hall states. Each
expanded set of data completely characterize a unique quantum Hall state, at
least for the examples discussed in this paper. The result is obtained by
combining the pattern of zeros and Z_n simple-current vertex algebra which
describes a large class of Abelian and non-Abelian quantum Hall states
\Phi_{Z_n}^sc. The more complete characterization in terms of {n;m;S_a;c}
allows us to obtain more topological properties of those states, which include
the central charge c of edge states, the scaling dimensions and the statistics
of quasiparticle excitations.Comment: 42 pages. RevTeX
A Host–parasite Model Explains Variation in Liana Infestation Among Co‐occurring Tree Species
Lianas are structural parasites of trees that reduce the growth, survival and reproduction of their hosts. Given that co‐occurring tree species differ strongly in the proportion of individuals that are infested by lianas (liana prevalence), lianas could differentially impact tree species and thereby influence tree community composition. Surprisingly, little is known about what governs variation in liana prevalence. Here, we apply an approach inspired by disease ecology to investigate the dynamics of liana prevalence over 11 years on Barro Colorado Island, Panama. We followed the fate of 1,938 individual trees from 21 tree species, recording deaths and change in liana infestation status. With these data, we fit species‐specific Markov chain models to estimate four rates: colonization by lianas (analogous to disease transmission), shedding or loss of lianas (analogous to host recovery), baseline mortality of uninfested trees (baseline mortality) and additional mortality of infested trees (parasite lethality). Models explained 58% of variation in liana prevalence among tree species, and revealed that host shedding of lianas and parasite lethality were the most important contributors to interspecific variation in liana prevalence at our site. These rates were also strongly related to shade tolerance, with light‐demanding species having greater rates of shedding and lethality, and lower rates of liana prevalence. An indirect path analysis with a structural equation model revealed that both greater rates of liana shedding and liana‐induced lethality contribute to the observed lower rates of liana prevalence for light‐demanding tree species. Synthesis. Our approach revealed that the prevalence of liana infestation among tree species is driven via indirect pathways operating on the rates of shedding and lethality, which relate to the ability (or inability) of trees to shed and/or tolerate lianas. Shade‐tolerant trees have greater proportions of trees infested by lianas because they are both less able to shed lianas and more able to tolerate infestation
Re-orientation Transition in Molecular Thin Films: Potts Model with Dipolar Interaction
We study the low-temperature behavior and the phase transition of a thin film
by Monte Carlo simulation. The thin film has a simple cubic lattice structure
where each site is occupied by a Potts parameter which indicates the molecular
orientation of the site. We take only three molecular orientations in this
paper which correspond to the 3-state Potts model. The Hamiltonian of the
system includes: (i) the exchange interaction between nearest-neighbor
sites and (ii) the long-range dipolar interaction of amplitude
truncated at a cutoff distance (iii) a single-ion perpendicular
anisotropy of amplitude . We allow between surface spins, and
otherwise. We show that the ground state depends on the the ratio
and . For a single layer, for a given , there is a critical value
below (above) which the ground-state (GS) configuration of molecular axes
is perpendicular (parallel) to the film surface. When the temperature is
increased, a re-orientation transition occurs near : the low- in-plane
ordering undergoes a transition to the perpendicular ordering at a finite ,
below the transition to the paramagnetic phase. The same phenomenon is observed
in the case of a film with a thickness. We show that the surface phase
transition can occur below or above the bulk transition depending on the ratio
. Surface and bulk order parameters as well as other physical quantities
are shown and discussed.Comment: 7 pages, 11 figures, submitted for publicatio
Convergence rate of dimension reduction in Bose-Einstein condensates
In this paper, we study dimension reduction of the three-dimensional (3D)
Gross-Pitaevskii equation
(GPE) modelling Bose-Einstein condensation under different limiting
interaction and trapping frequencies parameter regimes.
Convergence rates for the dimension reduction of 3D ground state and dynamics
of the GPE in the case of disk-shaped condensation and cigar-shaped
condensation are reported based on our asymptotic and numerical results. In
addition, the parameter regimes in which the 3D GPE cannot be reduced to lower
dimensions are identified.Comment: 27pages; 9 figure
Ground state solution of Bose-Einstein condensate by directly minimizing the energy functional
In this paper, we propose a new numerical method to compute the ground state
solution of trapped interacting Bose-Einstein condensation (BEC) at zero or
very low temperature by directly minimizing the energy functional via finite
element approximation. As preparatory steps we begin with the 3d
Gross-Pitaevskii equation (GPE), scale it to get a three-parameter model and
show how to reduce it to 2d and 1d GPEs. The ground state solution is
formulated by minimizing the energy functional under a constraint, which is
discretized by the finite element method. The finite element approximation for
1d, 2d with radial symmetry and 3d with spherical symmetry and cylindrical
symmetry are presented in detail and approximate ground state solutions, which
are used as initial guess in our practical numerical computation of the
minimization problem, of the GPE in two extreme regimes: very weak interactions
and strong repulsive interactions are provided. Numerical results in 1d, 2d
with radial symmetry and 3d with spherical symmetry and cylindrical symmetry
for atoms ranging up to millions in the condensation are reported to
demonstrate the novel numerical method. Furthermore, comparisons between the
ground state solutions and their Thomas-Fermi approximations are also reported.
Extension of the numerical method to compute the excited states of GPE is also
presented.Comment: 33 pages, 22 figure
Functional Traits of Tropical Trees and Lianas Explain Spatial Structure across Multiple Scales
Dispersal and density dependence are major determinants of spatial structure, population dynamics and coexistence for tropical forest plants. However, because these two processes can jointly influence spatial structure at similar scales, analysing spatial patterns to separate and quantify them is often difficult. Species functional traits can be useful indicators of dispersal and density dependence. However, few methods exist for linking functional traits to quantitative estimates of these processes that can be compared across multiple species. We analysed static spatial patterns of woody plant populations in the 50 ha Forest Dynamics Plot on Barro Colorado Island, Panama with methods that distinguished scale‐specific differences in species aggregation. We then tested how these differences related to seven functional traits: growth form, dispersal syndrome, tree canopy layer, adult stature, seed mass, wood density and shade tolerance. Next, we fit analytically tractable spatial moment models to the observed spatial structure of species characterized by similar trait values, which allowed us to estimate relationships of functional traits with the spatial scale of dispersal, and the spatial scale and intensity of negative density dependence. Our results confirm that lianas are more aggregated than trees, and exhibit increased aggregation within canopy gaps. For trees, increased seed mass, wood density and shade tolerance were associated with less intense negative density dependence, while higher canopy layers and increased stature were associated with decreased aggregation and better dispersal. Spatial structure for trees was also strongly determined by dispersal syndrome. Averaged across all spatial scales, zoochory was more effective than wind dispersal, which was more effective than explosive dispersal. However, at intermediate scales, zoochory was associated with more aggregation than wind dispersal, potentially because of differences in short‐distance dispersal and the intensity of negative density dependence. Synthesis. We develop new tools for identifying significant associations between functional traits and spatial structure, and for linking these associations to quantitative estimates of dispersal scale and the strength and scale of density dependence. Our results help clarify how these processes influence woody plant species on Barro Colorado, and demonstrate how these tools can be applied to other sites and systems
Electroviscous effects of simple electrolytes under shear
On the basis of a hydrodynamical model analogous to that in critical fluids,
we investigate the influences of shear flow upon the electrostatic contribution
to the viscosity of binary electrolyte solutions in the Debye-H\"{u}ckel
approximation. Within the linear-response theory, we reproduce the classical
limiting law that the excess viscosity is proportional to the square root of
the concentration of the electrolyte. We also extend this result for finite
shear. An analytic expression of the anisotropic structure factor of the charge
density under shear is obtained, and its deformation at large shear rates is
discussed. A non-Newtonian effect caused by deformations of the ionic
atmosphere is also elucidated for . This finding
concludes that the maximum shear stress that the ionic atmosphere can support
is proportional to , where , and
are, respectively, the shear rate, the Debye screening
length and the Debye relaxation time with being the relative diffusivity at
the infinite dilution limit of the electrolyte.Comment: 13pages, 2figure
Features of Motion Around Global Monopole in Asymptotically dS/AdS Spacetime
In this paper, we study the motion of test particle and light around the
Global Monopole in asymptotically dS/AdS spacetime. The motion of a test
particle and light in the exterior region of the global monopole in dS/AdS
spacetime has been investigated. Although the test particle's motion is quite
different from the case in asymptotically flat spacetime, the behaviors of
light(null geodesic) remain unchanged except a energy(frequency) shift. Through
a phase-plane analysis, we prove analytically that the existence of a periodic
solution to the equation of motion for a test particle will not be altered by
the presence of cosmological constant and the deficit angle, whose presence
only affects the position and type of the critical point on the phase plane. We
also show that the apparent capture section of the global monopole in dS/AdS
spacetime is quite different from that in flat spacetime.Comment: 15 pages, 4 PS figures, accepted for publication in Class. Quantum
Gra
Effect of Dipolar Interaction in Molecular Crystals
We investigate in this paper the ground state and the nature of the
transition from an orientational ordered phase at low temperature to the
disordered state at high temperature in a molecular crystal. Our model is a
Potts model which takes into account the exchange interaction between
nearest-neighbor molecules and a dipolar interaction between molecular axes in
three dimensions. The dipolar interaction is characterized by two parameters:
its amplitude and the cutoff distance . If the molecular axis at a
lattice site has three orientations, say the , or axes, then when
D=0, the system is equivalent to the 3-state Potts model: the transition to the
disordered phase is known to be of first order. When , the
ground-state configuration is shown to be composed of two independent
interpenetrating layered subsystems which form a sandwich whose periodicity
depends on and . We show by extensive Monte Carlo simulation with a
histogram method that the phase transition remains of first order at relatively
large values of .Comment: 6 pages, 7 figure
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