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

Bohman-Frieze-Wormald model on the lattice, yielding a discontinuous percolation transition

The BFW model introduced by Bohman, Frieze, and Wormald [Random Struct. Algorithms, 25, 432 (2004)] and recently investigated in the framework of discontinuous percolation by Chen and D'Souza [Phys. Rev. Lett., 106, 115701 (2011)], is studied on the square and simple-cubic lattices. In two and three dimensions, we find numerical evidence for a strongly discontinuous transition. In two dimensions, the clusters at the threshold are compact with a fractal surface of fractal dimension $d_f=1.49\pm0.02$. On the simple-cubic lattice, distinct jumps in the size of the largest cluster are observed. We proceed to analyze the tree-like version of the model, where only merging bonds are sampled, for dimension two to seven. The transition is again discontinuous in any considered dimension. Finally, the dependence of the cluster-size distribution at the threshold on the spatial dimension is also investigated

Watersheds in disordered media

This is the final published version. It first appeared at http://journal.frontiersin.org/article/10.3389/fphy.2015.00005/full#h11.What is the best way to divide a rugged landscape? Since ancient times, watersheds separating adjacent water systems that flow, for example, toward different seas, have been used to delimit boundaries. Interestingly, serious and even tense border disputes between countries have relied on the subtle geometrical properties of these tortuous lines. For instance, slight and even anthropogenic modifications of landscapes can produce large changes in a watershed, and the effects can be highly nonlocal. Although the watershed concept arises naturally in geomorphology, where it plays a fundamental role in water management, landslide, and flood prevention, it also has important applications in seemingly unrelated fields such as image processing and medicine. Despite the far-reaching consequences of the scaling properties on watershed-related hydrological and political issues, it was only recently that a more profound and revealing connection has been disclosed between the concept of watershed and statistical physics of disordered systems. This review initially surveys the origin and definition of a watershed line in a geomorphological framework to subsequently introduce its basic geometrical and physical properties. Results on statistical properties of watersheds obtained from artificial model landscapes generated with long-range correlations are presented and shown to be in good qualitative and quantitative agreement with real landscapes.We acknowledge financial support from the European Research Council (ERC) Advanced Grant 319968-FlowCCS, the Brazilian Agencies CNPq, CAPES, FUNCAP and FINEP, the FUNCAP/CNPq Pronex grant, the National Institute of Science and Technology for Complex Systems in Brazil, the Portuguese Foundation for Science and Technology (FCT) under contracts no. IF/00255/2013, PEst-OE/FIS/UI0618/2014, and EXCL/FIS-NAN/0083/2012, and the Swiss National Science Foundation under Grant No. P2EZP2-152188

Fracturing ranked surfaces

Discretized landscapes can be mapped onto ranked surfaces, where every element (site or bond) has a unique rank associated with its corresponding relative height. By sequentially allocating these elements according to their ranks and systematically preventing the occupation of bridges, namely elements that, if occupied, would provide global connectivity, we disclose that bridges hide a new tricritical point at an occupation fraction $p=p_{c}$, where $p_{c}$ is the percolation threshold of random percolation. For any value of $p$ in the interval $p_{c}< p \leq 1$, our results show that the set of bridges has a fractal dimension $d_{BB} \approx 1.22$ in two dimensions. In the limit $p \rightarrow 1$, a self-similar fracture is revealed as a singly connected line that divides the system in two domains. We then unveil how several seemingly unrelated physical models tumble into the same universality class and also present results for higher dimensions

Recent highlights from BaBar

We report on recent results from the BaBar experiment using the complete dataset collected at the Υ(4S). Three of the analyses presented here are time-dependent: the first observation of time-reversal violation, a new measurement of CP violation in B0 → D∗+D∗− decays, and the search for CP violation in B0-¯B0 mixing by partially reconstructing B0 → D∗lν decays. Three time-independent analyses search for new physics in the decays: B → K(∗)ν¯ν, B → π/ηl+l−, and B → D(∗)τν

Measurement of the CP Violation Parameter sin(2phi_1) in B^0_d Meson Decays

We present a measurement of the Standard Model CP violation parameter sin(2phi_1) based on a 10.5 fb^{-1} data sample collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric e+e- collider. One neutral B meson is reconstructed in the J/psi K_S, psi(2S) K_S, chi_{c1} K_S, eta_c K_S, J/psi K_L or J/psi pi^0 CP-eigenstate decay channel and the flavor of the accompanying B meson is identified from its charged particle decay products. From the asymmetry in the distribution of the time interval between the two B-meson decay points, we determine sin(2phi_1) = 0.58 +0.32-0.34 (stat) +0.09-0.10 (syst).Comment: LaTex, 13 pages, 3 figures, submitted to P.R.

Observation of the decay B^0->D+D*-

We report the first observation of the decay B^0->D+-D*-+ with the Belle detector at the KEKB e^+e^- collider operated at the Upsilon(4S) resonance. The sum of branching fractions B(B^0->D+D*-)+B(B^0->D-D*+) is measured to be (1.17+-0.26+0.22-0.25)x10^-3 using the full reconstruction method where both charmed mesons from B^0 decays are reconstructed. A consistent value ((1.48+-0.38+0.28-0.31)x10^-3) is obtained using a partial reconstruction technique that only uses the slow pion from the D*- ->bar D^0pi- decay and a fully reconstructed D+ to reconstruct the B^0.Comment: 10 pages, 3 figure

Observation of B0bar --> D(*)0 p pbar

The B meson decay modes B --> D p pbar and B --> D* p pbar have been studied using 29.4 fb^{-1} of data collected with the Belle detector at KEKB. The B0bar --> D0 p pbar and B0bar --> D*0 p pbar decays have been observed for the first time with branching fractions Br(B0bar --> D0 p pbar) =(1.18\pm 0.15\pm 0.16) 10^{-4} and Br(B0bar --> D*0 p pbar) =(1.20^{+0.33}_{-0.29}\pm 0.21) 10^{-4}. No signal has been found for the B+ --> D+ p pbar and B+ --> D*+ p pbar decay modes, and the corresponding upper limits at 90% C.L. are presented.Comment: 6 pages, 3 figures, submited to Phys. Rev. Let

Search for Direct CP Violation in B -> K pi Decays

We search for direct CP violation in flavor specific B -> K pi decays by measuring the rate asymmetry between charge conjugate modes. The search is performed on a data sample of 11.1 million B B bar events recorded on the Upsilon(4S) resonance by the Belle experiment at KEKB. We measure 90% confidence intervals in the partial rate asymmetry A_CP of -0.25 < A_CP(K-/+ pi+/-) < 0.37, -0.40 < A_CP(K-/+ pi^0) < 0.36, and -0.53 < A_CP(K^0 pi-/+) < 0.82. By combining the K-/+ pi+/- and K-/+ pi^0 final states, we conclude that -0.22 < A_CP[K-/+(pi+/- + pi^0)] < 0.25 at the 90% confidence level.Comment: Submitted to PRD Rapid Communication

Production of Prompt Charmonia in e+e−e^+e^- Annihilation at s≈10.6\sqrt{s}\approx 10.6 GeV

The production of prompt $J/\psi$, $\psi(2S)$, $\chi_{c1}$ and $\chi_{c2}$ is studied using a $32.4 fb^{-1}$ data sample collected with the Belle detector at the $\Upsilon(4S)$ and 60 MeV below the resonance. The yield of prompt $J/\psi$ mesons in the $\Upsilon(4S)$ sample is compatible with that of continuum production; we set an upper limit ${\cal B}(\Upsilon(4S) \to J/\psi X) < 1.9 \times 10^{-4}$ at the 95% confidence level, and find $\sigma(e^{+}e^{-} \to J/\psi X)=1.47\pm 0.10 \pm 0.13$ pb. The cross-sections for prompt $\psi(2S)$ and direct $J/\psi$ are measured. The $J/\psi$ momentum spectrum, production angle distribution and polarization are studied.Comment: submitted to Phys. Rev. Let