Random-cluster multi-histogram sampling for the q-state Potts model

Using the random-cluster representation of the $q$-state Potts models we consider the pooling of data from cluster-update Monte Carlo simulations for different thermal couplings $K$ and number of states per spin $q$. Proper combination of histograms allows for the evaluation of thermal averages in a broad range of $K$ and $q$ values, including non-integer values of $q$. Due to restrictions in the sampling process proper normalization of the combined histogram data is non-trivial. We discuss the different possibilities and analyze their respective ranges of applicability.Comment: 12 pages, 9 figures, RevTeX

A test of the CPL parameterization for rapid dark energy equation of state transitions

We test the robustness and flexibility of the Chevallier-Polarski-Linder (CPL) parameterization of the Dark Energy equation of state $w(z)=w_0+w_a \frac{z}{1+z}$ in recovering a four-parameter step-like fiducial model. We constrain the parameter space region of the underlying fiducial model where the CPL parameterization offers a reliable reconstruction. It turns out that non negligible biases leak into the results for recent ($z<2.5$) rapid transitions, but that CPL yields a good reconstruction in all other cases. The presented analysis is performed with supernova Ia data as forecasted for a space mission like SNAP/JDEM, combined with future expectations for the CMB shift parameter $R$ and the BAO parameter $A$.Comment: 8 pages, 6 ps figure

Finite-size scaling for the Ising model on the Moebius strip and the Klein bottle

We study the finite-size scaling properties of the Ising model on the Moebius strip and the Klein bottle. The results are compared with those of the Ising model under different boundary conditions, that is, the free, cylindrical, and toroidal boundary conditions. The difference in the magnetization distribution function $p(m)$ for various boundary conditions is discussed in terms of the number of the percolating clusters and the cluster size. We also find interesting aspect-ratio dependence of the value of the Binder parameter at $T=T_c$ for various boundary conditions. We discuss the relation to the finite-size correction calculations for the dimer statistics.Comment: 4 pages including 5 eps figures, RevTex, to appear in Phys. Rev. Let

CMB Anisotropies Reveal Quantized Gravity

A novel primordial spectrum with a dynamical scale of quantum gravity origin is proposed to explain the sharp fall off of the angular power spectra at low multipoles in the COBE and WMAP observations. The spectrum is derived from quantum fluctuations of the scalar curvature in a renormalizable model of induced gravity. This model describes the very early universe by the conformal field fluctuating about an inflationary background with the expansion time constant of order of the Planck mass.Comment: 12 pages, 2 figure

A Lensing Reconstruction of Primordial Cosmic Microwave Background Polarization

We discuss a possibility to directly reconstruct the CMB polarization field at the last scattering surface by accounting for modifications imposed by the gravitational lensing effect. The suggested method requires a tracer field of the large scale structure lensing potentials that deflected propagating CMB photons from the last scattering surface. This required information can come from a variety of observations on the large scale structure matter distribution, including convergence reconstructed from lensing shear studies involving galaxy shapes. In the case of so-called curl, or B,-modes of CMB polarization, the reconstruction allows one to identify the distinct signature of inflationary gravitational waves.Comment: 6 pages, 2 figures; PRD submitte

An Analysis Of Fatigue Crack Growth Of A Notched Aircraft Component Under Compression-Dominated Spectrum Loading

In engineering structures, fatigue cracks often emanate from geometrical discontinuities such as holes and notches. Experimentally it has been observed that there exists a notch-affected zone, in which the crack growth exhibits a transitional behaviour. Depending on the loading level and the geometry of the notch, the crack growth rate may initially decrease with crack length to reach a minimum. It will then either grow at an accelerated rate, or stop growing. This report details ongoing work in modelling crack growth in the presence of notch plasticity. The local stress-strain distribution ahead of a notch root is determined based on an empirical distribution of the equivalent stress, and the evolution of the notch root stress and strain is calculated using Neuber's rule and an Armstrong-Chaboche type nonlinear kinematic hardening model. The stress intensity factor is then calculated using a Green's function approach. A crack growth analysis program has been developed, implementing the above procedures

Exact Ampitude Ratio and Finite-Size Corrections for the M x N Square Lattice Ising Model The :

Let f, U and C represent, respectively, the free energy, the internal energy and the specific heat of the critical Ising model on the square M x N lattice with periodic boundary conditions. We find that N f and U are well-defined odd function of 1/N. We also find that ratios of subdominant (N^(-2 i - 1)) finite-size corrections amplitudes for the internal energy and the specific heat are constant. The free energy and the internal energy at the critical point are calculated asymtotically up to N^(-5) order, and the specific heat up to N^(-3) order.Comment: 18 pages, 4 figures, to be published in Phys. Rev. E 65, 1 February 200

Indirect exchange of magnetic impurities in zigzag graphene ribbon

We use quantum Monte Carlo method to study the indirect coupling between two magnetic impurities on the zigzag edge of graphene ribbon, with respect to the chemical potential $\mu$. We find that the spin-spin correlation between two adatoms located on the nearest sites in the zigzag edge are drastically suppressed around the zero-energy. As we switch the system away from half-filling, the antiferromagnetic correlation is first enhanced and then decreased. If the two adatoms are adsorbed on the sites belonging to the same sublattice, we find similar behavior of spin-spin correlation except for a crossover from ferromagnetic to antiferromagentic correlation in the vicinity of zero-energy. We also calculated the weight of different components of d-electron wave function and local magnet moment for various values of parameters, and all the results are consistent with those of spin-spin correlation between two magnetic impurities.Comment: 3 pages, 4 figures, conference proceedin

Using nonlinear optical networks for optimization: primer of the ant colony algorithm

Using nonlinear Erbium doped optical fiber network we have implemented an optimization algorithm for the famous problem of finding the shortest path on the map for the ant colony to travel to the foraging area