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 $M$ 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 $M=2,..,9$ monomers, as well as for the special case of polymers, where $M\to\infty$, 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 ``$n_q$'' 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 ``$n_q$'' 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 ``$n_{q}$'' 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

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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