83 research outputs found
Yang-Baxter equation for the asymmetric eight-vertex model
In this note we study `a la Baxter [1] the possible integrable manifolds of
the asymmetric eight-vertex model. As expected they occur when the Boltzmann
weights are either symmetric or satisfy the free-fermion condition but our
analysis clarify the reason both manifolds need to share a universal invariant.
We also show that the free-fermion condition implies three distinct classes of
integrable models.Comment: Latex, 12 pages, 1 figur
Analysis of the current state of the Zapadno-Malobalykskoye oil field development (KHMAO-Yugra)
Mücrim
François Coppée'nin Servet-i Fünun'da yayımlanan Mücrim adlı romanının ilk ve son tefrikalar
Charge and Current Sum Rules in Quantum Media Coupled to Radiation
This paper concerns the equilibrium bulk charge and current density
correlation functions in quantum media, conductors and dielectrics, fully
coupled to the radiation (the retarded regime). A sequence of static and
time-dependent sum rules, which fix the values of certain moments of the charge
and current density correlation functions, is obtained by using Rytov's
fluctuational electrodynamics. A technique is developed to extract the
classical and purely quantum-mechanical parts of these sum rules. The sum rules
are critically tested in the classical limit and on the jellium model. A
comparison is made with microscopic approaches to systems of particles
interacting through Coulomb forces only (the non-retarded regime). In contrast
with microscopic results, the current-current correlation function is found to
be integrable in space, in both classical and quantum regimes.Comment: 19 pages, 1 figur
Diffusion in disordered systems under iterative measurement
We consider a sequence of idealized measurements of time-separation onto a discrete one-dimensional disordered system. A connection with Markov
chains is found. For a rapid sequence of measurements, a diffusive regime
occurs and the diffusion coefficient is analytically calculated. In a
general point of view, this result suggests the possibility to break the
Anderson localization due to decoherence effects. Quantum Zeno effect emerges
because the diffusion coefficient vanishes at the limit .Comment: 8 pages, 0 figures, LATEX. accepted in Phys.Rev.
Alternating Kinetics of Annihilating Random Walks Near a Free Interface
The kinetics of annihilating random walks in one dimension, with the
half-line x>0 initially filled, is investigated. The survival probability of
the nth particle from the interface exhibits power-law decay,
S_n(t)~t^{-alpha_n}, with alpha_n approximately equal to 0.225 for n=1 and all
odd values of n; for all n even, a faster decay with alpha_n approximately
equal to 0.865 is observed. From consideration of the eventual survival
probability in a finite cluster of particles, the rigorous bound alpha_1<1/4 is
derived, while a heuristic argument gives alpha_1 approximately equal to 3
sqrt{3}/8 = 0.2067.... Numerically, this latter value appears to be a stringent
lower bound for alpha_1. The average position of the first particle moves to
the right approximately as 1.7 t^{1/2}, with a relatively sharp and asymmetric
probability distribution.Comment: 6 pages, RevTeX, 5 eps figures include
The Clausius-Mossotti formula and its nonlocal generalization for a dielectric suspension of spherical inclusions
Employing a recently developed cluster expansion for the effective dielectric constant of a suspension of spherical inclusions, we show which parts of the cluster integrals give rise to the Clausius-Mossotti formula. The same selection of terms is then used to obtain an approximate expression for the wave-vector-dependent effective dielectric tensor. For a system of hard spheres with only dipole polarizability this expression is evaluated in closed form. This last result is then used to derive the form of the electrostatic potential due to a point charge in the effective medium. For physically reasonable values of the polarizability, the potential has asymptotically the form corresponding to a medium with the Clausius-Mossotti dielectric constant, while at short range it oscillates about this form. For values of the polarizability beyond the physical range critical points are found at which the oscillations become long range.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45147/1/10955_2005_Article_BF01009796.pd
Colored Vertex Models, Colored IRF Models and Invariants of Trivalent Colored Graphs
We present formulas for the Clebsch-Gordan coefficients and the Racah
coefficients for the root of unity representations (-dimensional
representations with ) of . We discuss colored vertex
models and colored IRF (Interaction Round a Face) models from the color
representations of . We construct invariants of trivalent colored
oriented framed graphs from color representations of .Comment: 39 pages, January 199
Hydrodynamic Synchronisation of Model Microswimmers
We define a model microswimmer with a variable cycle time, thus allowing the
possibility of phase locking driven by hydrodynamic interactions between
swimmers. We find that, for extensile or contractile swimmers, phase locking
does occur, with the relative phase of the two swimmers being, in general,
close to 0 or pi, depending on their relative position and orientation. We show
that, as expected on grounds of symmetry, self T-dual swimmers, which are
time-reversal covariant, do not phase-lock. We also discuss the phase behaviour
of a line of tethered swimmers, or pumps. These show oscillations in their
relative phases reminiscent of the metachronal waves of cilia.Comment: 17 pages, 8 figure
Hydrodynamic interactions in colloidal ferrofluids: A lattice Boltzmann study
We use lattice Boltzmann simulations, in conjunction with Ewald summation
methods, to investigate the role of hydrodynamic interactions in colloidal
suspensions of dipolar particles, such as ferrofluids. Our work addresses
volume fractions of up to 0.20 and dimensionless dipolar interaction
parameters of up to 8. We compare quantitatively with Brownian
dynamics simulations, in which many-body hydrodynamic interactions are absent.
Monte Carlo data are also used to check the accuracy of static properties
measured with the lattice Boltzmann technique. At equilibrium, hydrodynamic
interactions slow down both the long-time and the short-time decays of the
intermediate scattering function , for wavevectors close to the peak of
the static structure factor , by a factor of roughly two. The long-time
slowing is diminished at high interaction strengths whereas the short-time
slowing (quantified via the hydrodynamic factor ) is less affected by the
dipolar interactions, despite their strong effect on the pair distribution
function arising from cluster formation. Cluster formation is also studied in
transient data following a quench from ; hydrodynamic interactions
slow the formation rate, again by a factor of roughly two
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