Scaling and universality in the aging kinetics of the two-dimensional clock model

We study numerically the aging dynamics of the two-dimensional p-state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior characteristic of non-disordered coarsening systems. For quenches to the ferromagnetic phase, the value of the dynamical exponents, suggests that the model belongs to the Ising-type universality class. Specifically, for the integrated response function $\chi (t,s)\simeq s^{-a_\chi}f(t/s)$, we find $a_\chi$ consistent with the value $a_\chi =0.28$ found in the two-dimensional Ising model.Comment: 16 pages, 14 figures (please contact the authors for figures

Vortex Particle-Mesh with Immersed Lifting Lines for Aerospace and Wind Engineering

AbstractWe present the treatment of lifting lines with a Vortex Particle-Mesh (VPM) methodology. The VPM method relies on the Lagrangian discretization of the Navier-Stokes equations in vorticity-velocity formulation. The use of this hybrid discretization offers several advantages. The particles are used solely for the advection, thereby waiving classical time stability constraints. They also exploit the compactness of vorticity support, leading to high computational gains for external flow simulations. The mesh, on the other hand, handles all the other computationally intensive tasks, such as the evaluation of the differential operators and the use of fast Fourier-based Poisson solvers, which allow the combination of unbounded directions and inlet/outlet boundaries. Both discretizations communicate through high order interpolation. The mesh and the interpolation also allow for additional advances; they are used to handle Lagrangian distortion by reinitializing the particle positions onto a regular grid. This crucial step, referred to as remeshing, guarantees the accuracy of the method. In addition, the resulting methodology provides computational efficiency and scalability to massively parallel architectures.Sources of vorticity are accounted for through a lifting line approach. This line handles the attached and shed vorticity contributions in a Lagrangian manner. Its immersed treatment efficiently captures the development of vorticity from thin sheets into a three-dimensional field. We apply this approach to the simulation of wake flows encountered in aeronautical and wind energy applications. An important aspect in these fields is the handling of turbulent inflows. We have developed a technique for the introduction of pre-computed or synthetic turbulent flow fields in vorticity form. Our treatment is based on particles as well and consistent with the Lagrangian character of the method. We apply here our method to the investigation of wind turbine wakes over very large distances, reaching cluster or wind farm sizes

Aging phenomena in critical semi-infinite systems

Nonequilibrium surface autocorrelation and autoresponse functions are studied numerically in semi-infinite critical systems in the dynamical scaling regime. Dynamical critical behaviour is examined for a nonconserved order parameter in semi-infinite two- and three-dimensional Ising models as well as in the Hilhorst-van Leeuwen model. The latter model permits a systematic study of surface aging phenomena, as the surface critical exponents change continuously as function of a model parameter. The scaling behaviour of surface two-time quantities is investigated and scaling functions are confronted with predictions coming from the theory of local scale invariance. Furthermore, surface fluctuation-dissipation ratios are computed and their asymptotic values are shown to depend on the values of surface critical exponents.Comment: 12 pages, figures included, version to appear in Phys. Rev.

Critical Behavior and Lack of Self Averaging in the Dynamics of the Random Potts Model in Two Dimensions

We study the dynamics of the q-state random bond Potts ferromagnet on the square lattice at its critical point by Monte Carlo simulations with single spin-flip dynamics. We concentrate on q=3 and q=24 and find, in both cases, conventional, rather than activated, dynamics. We also look at the distribution of relaxation times among different samples, finding different results for the two q values. For q=3 the relative variance of the relaxation time tau at the critical point is finite. However, for q=24 this appears to diverge in the thermodynamic limit and it is ln(tau) which has a finite relative variance. We speculate that this difference occurs because the transition of the corresponding pure system is second order for q=3 but first order for q=24.Comment: 9 pages, 13 figures, final published versio

Measuring the fluctuation-dissipation ratio in glassy systems with no perturbing field

A method is presented for measuring the integrated response in Ising spin system without applying any perturbing field. Large-scale simulations are performed in order to show how the method works. Very precise measurements of the fluctuation-dissipation ratio are presented for 3 different Ising models: the 2-dimensional ferromagnetic model, the mean-field diluted 3-spin model, and the 3-dimensional Edwards-Anderson model.Comment: 4 pages, 4 figure

Watersheds are Schramm-Loewner Evolution curves

We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner Evolution (SLE) curves, being described by one single parameter $\kappa$. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLE$_\kappa$, with $\kappa=1.734\pm0.005$, being the only known physical example of an SLE with $\kappa<2$. This lies outside the well-known duality conjecture, bringing up new questions regarding the existence and reversibility of dual models. Furthermore it constitutes a strong indication for conformal invariance in random landscapes and suggests that watersheds likely correspond to a logarithmic Conformal Field Theory (CFT) with central charge $c\approx-7/2$.Comment: 5 pages and 4 figure

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

Enhance knowledge communication and learning: a surprise paradox

Human-computer interface is a pivotal factor that can promote or deter the effectiveness of Web-based knowledge communication. There is abundant research that strain to improve interfaces by considering user needs through usability studies; however, few researches consider the incorporation of automatic brain mechanisms in order to improve knowledge communication performance. The objective of this research is not to establish a relationship between the negative stimulus presence and improved knowledge communication, but rather to show that the shape of this function follows the Yerkes–Dodson Law. Partial least squares (PLS) was utilized to analyze the data. Results found in this study support the evidence that surprising negative events enhance knowledge communication effectiveness, but more importantly that the surprise-performance relationship is not a linear function but follows the inverted U shape

Critical Behavior of the Random Potts Chain

We study the critical behavior of the random q-state Potts quantum chain by density matrix renormalization techniques. Critical exponents are calculated by scaling analysis of finite lattice data of short chains ($L \leq 16$) averaging over all possible realizations of disorder configurations chosen according to a binary distribution. Our numerical results show that the critical properties of the model are independent of q in agreement with a renormalization group analysis of Senthil and Majumdar (Phys. Rev. Lett.{\bf 76}, 3001 (1996)). We show how an accurate analysis of moments of the distribution of magnetizations allows a precise determination of critical exponents, circumventing some problems related to binary disorder. Multiscaling properties of the model and dynamical correlation functions are also investigated.Comment: LaTeX2e file with Revtex, 9 pages, 8 eps figures, 4 tables; typos correcte

Short-time dynamics and magnetic critical behavior of two-dimensional random-bond Potts model

The critical behavior in the short-time dynamics for the random-bond Potts ferromagnet in two-dimensions is investigated by short-time dynamic Monte Carlo simulations. The numerical calculations show that this dynamic approach can be applied efficiently to study the scaling characteristic, which is used to estimate the critical exponents theta, beta/nu and z for the quenched disorered systems from the power-law behavior of the kth moments of magnetizations.Comment: 10 pages, 4 figures Soft Condensed Matte