Green Function Simulation of Hamiltonian Lattice Models with Stochastic Reconfiguration

We apply a recently proposed Green Function Monte Carlo to the study of Hamiltonian lattice gauge theories. This class of algorithms computes quantum vacuum expectation values by averaging over a set of suitable weighted random walkers. By means of a procedure called Stochastic Reconfiguration the long standing problem of keeping fixed the walker population without a priori knowledge on the ground state is completely solved. In the $U(1)_2$ model, which we choose as our theoretical laboratory, we evaluate the mean plaquette and the vacuum energy per plaquette. We find good agreement with previous works using model dependent guiding functions for the random walkers.Comment: 14 pages, 5 PostScript Figures, RevTeX, two references adde

The McCoy-Wu Model in the Mean-field Approximation

We consider a system with randomly layered ferromagnetic bonds (McCoy-Wu model) and study its critical properties in the frame of mean-field theory. In the low-temperature phase there is an average spontaneous magnetization in the system, which vanishes as a power law at the critical point with the critical exponents $\beta \approx 3.6$ and $\beta_1 \approx 4.1$ in the bulk and at the surface of the system, respectively. The singularity of the specific heat is characterized by an exponent $\alpha \approx -3.1$. The samples reduced critical temperature $t_c=T_c^{av}-T_c$ has a power law distribution $P(t_c) \sim t_c^{\omega}$ and we show that the difference between the values of the critical exponents in the pure and in the random system is just $\omega \approx 3.1$. Above the critical temperature the thermodynamic quantities behave analytically, thus the system does not exhibit Griffiths singularities.Comment: LaTeX file with iop macros, 13 pages, 7 eps figures, to appear in J. Phys.

The Random-bond Potts model in the large-q limit

We study the critical behavior of the q-state Potts model with random ferromagnetic couplings. Working with the cluster representation the partition sum of the model in the large-q limit is dominated by a single graph, the fractal properties of which are related to the critical singularities of the random Potts model. The optimization problem of finding the dominant graph, is studied on the square lattice by simulated annealing and by a combinatorial algorithm. Critical exponents of the magnetization and the correlation length are estimated and conformal predictions are compared with numerical results.Comment: 7 pages, 6 figure

Non-uniform central airways ventilation model based on vascular segmentation

Improvements in the understanding of the physiology of the central airways require an appropriate representation of the non-uniform ventilation at its terminal branches. This paper proposes a new technique for estimating the non-uniform ventilation at the terminal branches by modelling the volume change of their distal peripheral airways, based on vascular segmentation. The vascular tree is used for sectioning the dynamic CT-based 3D volume of the lung at 11 time points over the breathing cycle of a research animal. Based on the mechanical coupling between the vascular tree and the remaining lung tissues, the volume change of each individual lung segment over the breathing cycle was used to estimate the non-uniform ventilation of its associated terminal branch. The 3D lung sectioning technique was validated on an airway cast model of the same animal pruned to represent the truncated dynamic CT based airway geometry. The results showed that the 3D lung sectioning technique was able to estimate the volume of the missing peripheral airways within a tolerance of 2%. In addition, the time-varying non-uniform ventilation distribution predicted by the proposed sectioning technique was validated against CT measurements of lobar ventilation and showed good agreement. This significant modelling advance can be used to estimate subject-specific non-uniform boundary conditions to obtain subject-specific numerical models of the central airway flow

Surface critical behavior of random systems at the ordinary transition

We calculate the surface critical exponents of the ordinary transition occuring in semi-infinite, quenched dilute Ising-like systems. This is done by applying the field theoretic approach directly in d=3 dimensions up to the two-loop approximation, as well as in $d=4-\epsilon$ dimensions. At $d=4-\epsilon$ we extend, up to the next-to-leading order, the previous first-order results of the $\sqrt{\epsilon}$ expansion by Ohno and Okabe [Phys.Rev.B 46, 5917 (1992)]. In both cases the numerical estimates for surface exponents are computed using Pade approximants extrapolating the perturbation theory expansions. The obtained results indicate that the critical behavior of semi-infinite systems with quenched bulk disorder is characterized by the new set of surface critical exponents.Comment: 11 pages, 11 figure

3D Parallel Thinning Algorithms Based on Isthmuses

Abstract. Thinning is a widely used technique to obtain skeleton-like shape features (i.e., centerlines and medial surfaces) from digital binary objects. Conventional thinning algorithms preserve endpoints to provide important geometric information relative to the object to be represented. An alternative strategy is also proposed that preserves isthmuses (i.e., generalization of curve/surface interior points). In this paper we present ten 3D parallel isthmus-based thinning algorithm variants that are derived from some sufficient conditions for topology preserving reductions