Multiple relaxations in temporal planning

CRIKEY is a planner that separates out the scheduling from the classical parts of temporal planning. This can be seen as a relaxation of the temporal information during the classical planning phase. Relaxations in planning are used to guide the search. However, the quality of the relaxation greatly affects the performance of the planner, and in some cases can lead the search into a dead end. This can happen whilst separating out the planning and scheduling problems, leading to the production of an unschedulable plan. CRIKEY can detect these cases and change the relaxation accordingly

High-Dimensional Diffusive Growth

We consider a model of aggregation, both diffusion-limited and ballistic, based on the Cayley tree. Growth is from the leaves of the tree towards the root, leading to non-trivial screening and branch competition effects. The model exhibits a phase transition between ballistic and diffusion-controlled growth, with non-trivial corrections to cluster size at the critical point. Even in the ballistic regime, cluster scaling is controlled by extremal statistics due to the branching structure of the Cayley tree; it is the extremal nature of the fluctuations that enables us to solve the model.Comment: 5 pages, 3 figures; reference adde

Multifractal Dimensions for Branched Growth

A recently proposed theory for diffusion-limited aggregation (DLA), which models this system as a random branched growth process, is reviewed. Like DLA, this process is stochastic, and ensemble averaging is needed in order to define multifractal dimensions. In an earlier work [T. C. Halsey and M. Leibig, Phys. Rev. A46, 7793 (1992)], annealed average dimensions were computed for this model. In this paper, we compute the quenched average dimensions, which are expected to apply to typical members of the ensemble. We develop a perturbative expansion for the average of the logarithm of the multifractal partition function; the leading and sub-leading divergent terms in this expansion are then resummed to all orders. The result is that in the limit where the number of particles n -> \infty, the quenched and annealed dimensions are {\it identical}; however, the attainment of this limit requires enormous values of n. At smaller, more realistic values of n, the apparent quenched dimensions differ from the annealed dimensions. We interpret these results to mean that while multifractality as an ensemble property of random branched growth (and hence of DLA) is quite robust, it subtly fails for typical members of the ensemble.Comment: 82 pages, 24 included figures in 16 files, 1 included tabl

Exact Multifractal Spectra for Arbitrary Laplacian Random Walks

Iterated conformal mappings are used to obtain exact multifractal spectra of the harmonic measure for arbitrary Laplacian random walks in two dimensions. Separate spectra are found to describe scaling of the growth measure in time, of the measure near the growth tip, and of the measure away from the growth tip. The spectra away from the tip coincide with those of conformally invariant equilibrium systems with arbitrary central charge $c\leq 1$, with $c$ related to the particular walk chosen, while the scaling in time and near the tip cannot be obtained from the equilibrium properties.Comment: 4 pages, 3 figures; references added, minor correction

Branched Growth with η≈4\eta \approx 4 Walkers

Diffusion-limited aggregation has a natural generalization to the "$\eta$-models", in which $\eta$ random walkers must arrive at a point on the cluster surface in order for growth to occur. It has recently been proposed that in spatial dimensionality $d=2$, there is an upper critical $\eta_c=4$ above which the fractal dimensionality of the clusters is D=1. I compute the first order correction to $D$ for $\eta <4$, obtaining $D=1+{1/2}(4-\eta)$. The methods used can also determine multifractal dimensions to first order in $4-\eta$.Comment: 6 pages, 1 figur

Mechanics\u27 Liens

In 1977 and 1978 the Florida Legislature made extensive amendments to the Mechanics\u27 Lien Law. The statute, however, remains intricate and elusive for builder, lawyer and lienor alike. The authors review the amendments and case law of the past two years and offer suggestions on how to avoid the many pitfalls of the statute. In addition, the article contains a section devoted to the equitable lien

Transfer across Random versus Deterministic Fractal Interfaces

A numerical study of the transfer across random fractal surfaces shows that their responses are very close to the response of deterministic model geometries with the same fractal dimension. The simulations of several interfaces with prefractal geometries show that, within very good approximation, the flux depends only on a few characteristic features of the interface geometry: the lower and higher cut-offs and the fractal dimension. Although the active zones are different for different geometries, the electrode reponses are very nearly the same. In that sense, the fractal dimension is the essential "universal" exponent which determines the net transfer.Comment: 4 pages, 6 figure

Diffusion-Reorganized Aggregates: Attractors in Diffusion Processes?

A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures. Independently of initial geometry, the structures found after long time present fractal geometry with a fractal dimension around 1.75. The final morphology, which constantly evolves in time, can be considered as the dynamic attractor of this evaporation-diffusion-redeposition operator. The ensemble of these fractal shapes can be considered to be the {\em dynamical equilibrium} geometry of a diffusion controlled self-transformation process.Comment: 4 pages, 5 figure

Multiphase PC/PL Relations: Comparison between Theory and observations

Cepheids are fundamental objects astrophysically in that they hold the key to a CMB independent estimate of Hubble's constant. A number of researchers have pointed out the possibilities of breaking degeneracies between Omega_Matter and H0 if there is a CMB independent distance scale accurate to a few percent (Hu 2005). Current uncertainties in the distance scale are about 10% but future observations, with, for example, the JWST, will be capable of estimating H0 to within a few percent. A crucial step in this process is the Cepheid PL relation. Recent evidence has emerged that the PL relation, at least in optical bands, is nonlinear and that neglect of such a nonlinearity can lead to errors in estimating H0 of up to 2 percent. Hence it is important to critically examine this possible nonlinearity both observationally and theoretically. Existing PC/PL relations rely exclusively on evaluating these relations at mean light. However, since such relations are the average of relations at different phases. Here we report on recent attempts to compare theory and observation in the multiphase PC/PL planes. We construct state of the art Cepheid pulsations models appropriate for the LMC/Galaxy and compare the resulting PC/PL relations as a function of phase with observations. For the LMC, the (V-I) period-color relation at minimum light can have quite a narrow dispersion (0.2-0.3 mags) and thus could be useful in placing constraints on models. At longer periods, the models predict significantly redder (by about 0.2-0.3 mags) V-I colors. We discuss possible reasons for this and also compare PL relations at various phases of pulsation and find clear evidence in both theory and observations for a nonlinear PL relation.Comment: 5 pages, 8 figures, proceeding for "Stellar Pulsation: Challenges for Theory and Observation", Santa Fe 200

Diffusion Limited Aggregation with Power-Law Pinning

Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth $R_N^{-\gamma}$ (where $R_N$ is the radius of the $N-$ particle cluster). For $\gamma > 1$ the growth pattern is in the same universality class as diffusion limited aggregation (DLA) growth, while for $\gamma < 1$ the resulting patterns have a lower fractal dimension $D(\gamma)$ than a DLA cluster due to the enhancement of growth at the hot tips of the developing pattern. Our results indicate that a pinning transition occurs at $\gamma = 1/2$, significantly smaller than might be expected from the lower bound $\alpha_{min} \simeq 0.67$ of multifractal spectrum of DLA. This limiting case shows that the most singular tips in the pruned cluster now correspond to those expected for a purely one-dimensional line. Using multifractal analysis, analytic expressions are established for $D(\gamma)$ both close to the breakdown of DLA universality class, i.e., $\gamma \lesssim 1$, and close to the pinning transition, i.e., $\gamma \gtrsim 1/2$.Comment: 5 pages, e figures, submitted to Phys. Rev.