3,713 research outputs found
Entropy of polydisperse chains: solution on the Bethe lattice
We consider the entropy of polydisperse chains placed on a lattice. In
particular, we study a model for equilibrium polymerization, where the
polydispersivity is determined by two activities, for internal and endpoint
monomers of a chain. We solve the problem exactly on a Bethe lattice with
arbitrary coordination number, obtaining an expression for the entropy as a
function of the density of monomers and mean molecular weight of the chains. We
compare this entropy with the one for the monodisperse case, and find that the
excess of entropy due to polydispersivity is identical to the one obtained for
the one-dimensional case. Finally, we obtain an exponential distribution of
molecular weights.Comment: 5 pages, 2 figures. Reference place
Asymptotic behavior of the entropy of chains placed on stripes
By using the transfer matrix approach, we investigate the asymptotic behavior
of the entropy of flexible chains with monomers each placed on stripes. In
the limit of high density of monomers, we study the behavior of the entropy as
a function of the density of monomers and the width of the stripe, inspired by
recent analytical studies of this problem for the particular case of dimers
(M=2). We obtain the entropy in the asymptotic regime of high densities for
chains with monomers, as well as for the special case of polymers,
where , and find that the results show a regular behavior similar
to the one found analytically for dimers. We also verify that in the
low-density limit the mean-field expression for the entropy is followed by the
results from our transfer matrix calculations
Exact entropy of dimer coverings for a class of lattices in three or more dimensions
We construct a class of lattices in three and higher dimensions for which the
number of dimer coverings can be determined exactly using elementary arguments.
These lattices are a generalization of the two-dimensional kagome lattice, and
the method also works for graphs without translational symmetry. The partition
function for dimer coverings on these lattices can be determined also for a
class of assignments of different activities to different edges.Comment: 4 pages, 2 figures; added results on partition function when
different edges have different weights; modified abstract; added reference
Dimers on two-dimensional lattices
We consider close-packed dimers, or perfect matchings, on two-dimensional
regular lattices. We review known results and derive new expressions for the
free energy, entropy, and the molecular freedom of dimers for a number of
lattices including the simple-quartic (4^4), honeycomb (6^3), triangular (3^6),
kagome (3.6.3.6), 3-12 (3.12^2) and its dual [3.12^2], and 4-8 (4.8^2) and its
dual Union Jack [4.8^2] Archimedean tilings. The occurrence and nature of phase
transitions are also analyzed and discussed.Comment: Typos corrections in Eqs. (28), (32) and (43
Phase Behavior of Models with Competing Interactions
Models with competing nearest-neighbor and very long-range interactions are solved exactly for several one-dimensional cases, including the usual Ising chain (lCCI) , the X Y model (XYCI) , the transverse Ising model (TICCI), and the spherical model (SCCI). For certain ratios of the competing interaction strengths, ICCI and XYCI display triple points and two critical points in a field. In addition TICCI has an apparently enclosed phase in an H-T phase diagram; however, this phase is really paramagnetic as can be seen when an extended phase diagram is used. The extended phase diagrams for ICCI, XYCI, and TICCI display tricritical points and the tricritical exponents have different values from the usual classical values. In contrast to the rich phase behavior of the preceding models, SCCI shows very simple phase behavior, which is directly related to the ground state. Finally, the introduction of a staggered field to ICCI and a simple transformation allows reinterpretation as a metamagnetic model. Using ICCI as a guide the observability of the tricritical exponents is discussed
Quasi-Particle Degrees of Freedom versus the Perfect Fluid as Descriptors of the Quark-Gluon Plasma
The hot nuclear matter created at the Relativistic Heavy Ion Collider (RHIC)
has been characterized by near-perfect fluid behavior. We demonstrate that this
stands in contradiction to the identification of QCD quasi-particles with the
thermodynamic degrees of freedom in the early (fluid) stage of heavy ion
collisions. The empirical observation of constituent quark ``'' scaling of
elliptic flow is juxtaposed with the lack of such scaling behavior in
hydrodynamic fluid calculations followed by Cooper-Frye freeze-out to hadrons.
A ``quasi-particle transport'' time stage after viscous effects break down the
hydrodynamic fluid stage, but prior to hadronization, is proposed to reconcile
these apparent contradictions. However, without a detailed understanding of the
transitions between these stages, the ``'' scaling is not a necessary
consequence of this prescription. Also, if the duration of this stage is too
short, it may not support well defined quasi-particles. By comparing and
contrasting the coalescence of quarks into hadrons with the similar process of
producing light nuclei from nucleons, it is shown that the observation of
``'' scaling in the final state does not necessarily imply that the
constituent degrees of freedom were the relevant ones in the initial state.Comment: 9 pages, 7 figures, Updated text and figure
The Kasteleyn model and a cellular automaton approach to traffic flow
We propose a bridge between the theory of exactly solvable models and the
investigation of traffic flow. By choosing the activities in an apropriate way
the dimer configurations of the Kasteleyn model on a hexagonal lattice can be
interpreted as space-time trajectories of cars. This then allows for a
calculation of the flow-density relationship (fundamental diagram). We further
introduce a closely-related cellular automaton model. This model can be viewed
as a variant of the Nagel-Schreckenberg model in which the cars do not have a
velocity memory. It is also exactly solvable and the fundamental diagram is
calculated.Comment: Latex, 13 pages including 3 ps-figure
Predictors of Two Kilometer Rowing Ergometer Time Trial Performance
Please download pdf version here
Conicoid Mirrors
The first order equation relating object and image location for a mirror of
arbitrary conic-sectional shape is derived. It is also shown that the parabolic
reflecting surface is the only one free of aberration and only in the limiting
case of distant sources.Comment: 9 page
Magnetization dynamics in dysprosium orthoferrites via inverse Faraday effect
The ultrafast non-thermal control of magnetization has recently become
feasible in canted antiferromagnets through photomagnetic instantaneous pulses
[A.V. Kimel {\it et al.}, Nature {\bf 435}, 655 (2005)]. In this experiment
circularly polarized femtosecond laser pulses set up a strong magnetic field
along the wave vector of the radiation through the inverse Faraday effect,
thereby exciting non-thermally the spin dynamics of dysprosium orthoferrites. A
theoretical study is performed by using a model for orthoferrites based on a
general form of free energy whose parameters are extracted from experimental
measurements. The magnetization dynamics is described by solving coupled
sublattice Landau-Lifshitz-Gilbert equations whose damping term is associated
with the scattering rate due to magnon-magnon interaction. Due to the inverse
Faraday effect and the non-thermal excitation, the effect of the laser is
simulated by magnetic field Gaussian pulses with temporal width of the order of
hundred femtoseconds. When the field is along the z-axis, a single resonance
mode of the magnetization is excited. The amplitude of the magnetization and
out-of-phase behavior of the oscillations for fields in z and -z directions are
in good agreement with the cited experiment. The analysis of the effect of the
temperature shows that magnon-magnon scattering mechanism affects the decay of
the oscillations on the picosecond scale. Finally, when the field pulse is
along the x-axis, another mode is excited, as observed in experiments. In this
case the comparison between theoretical and experimental results shows some
discrepancies whose origin is related to the role played by anisotropies in
orthoferrites.Comment: 10 pages, 6 figure
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