Scaling, Optimality, and Landscape Evolution

A nonlinear model is studied which describes the evolution of a landscape under the effects of erosion and regeneration by geologic uplift by mean of a simple differential equation. The equation, already in wide use among geomorphologists and in that context obtained phenomenologically, is here derived by reparametrization invariance arguments and exactly solved in dimension d=1. Results of numerical simulations in d=2 show that the model is able to reproduce the critical scaling characterizing landscapes associated with natural river basins. We show that configurations minimizing the rate of energy dissipation (optimal channel networks) are stationary solutions of the equation describing the landscape evolution. Numerical simulations show that a careful annealing of the equation in the presence of additive noise leads to configurations very close to the global minimum of the dissipated energy, characterized by mean field exponents. We further show that if one considers generalized river network configurations in which splitting of the flow (i.e., braiding) and loops are allowed, the minimization of the dissipated energy results in spanning loopless configurations, under the constraints imposed by the continuity equations. This is stated in the form of a general theorem applicable to generic networks, suggesting that other branching structures occurring in nature may possibly arise as optimal structures minimizing a cost function.     

Modeling urban street patterns

Urban street patterns form planar networks whose empirical properties cannot be accounted for by simple models such as regular grids or Voronoi tesselations. Striking statistical regularities across different cities have been recently empirically found, suggesting that a general and detail-independent mechanism may be in action. We propose a simple model based on a local optimization process combined with ideas previously proposed in studies of leaf pattern formation. The statistical properties of this model are in good agreement with the observed empirical patterns. Our results thus suggest that in the absence of a global design strategy, the evolution of many different transportation networks indeed follows a simple universal mechanism.     

Weak values of electron spin in a double quantum dot

We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device. The weak value is obtained by a two step procedure--weak measurement followed by a strong one (postselection), where the outcome of the first measurement is kept provided a second postselected outcome occurs. The setup consists of a double quantum dot and a weakly coupled quantum point contact to be used as a detector. Anomalously large values of the spin of a two electron system are predicted, as well as negative values of the total spin. We also show how to incorporate the adverse effect of decoherence into this procedure.     

Investigation of Terra Cotta artefacts with terahertz

Terahertz Time Domain Imaging has been used in the last few years for the investigation of cultural heritage. In this article, the authors demonstrate the possibility to apply it for the investigation of clay artifacts. Tomographic images were obtained of a model in reflection, and an Egyptian vessel in transmission.     

Quantum learning algorithms for quantum measurements

We study quantum learning algorithms for quantum measurements. The optimal learning algorithm is derived for arbitrary von Neumann measurements in the case of training with one or two examples. The analysis of the case of three examples reveals that, differently from the learning of unitary gates, the optimal algorithm for learning of quantum measurements cannot be parallelized, and requires quantum memories for the storage of information.     

First glances at the transversity parton distribution through dihadron fragmentation functions

We present first observations of the transversity parton distribution based on an analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets. The extraction of transversity relies on the knowledge of dihadron fragmentation functions, which we take from electron-positron annihilation measurements. This is the first attempt to determine the transversity distribution in the framework of collinear factorization.     

Phase-shifted Bragg microstructured optical fiber gratings utilizing infiltrated ferrofluids

Results are presented on the efficient spectral manipulation of uniform and chirped Bragg reflectors inscribed in microstructured optical fibers utilizing short lengths of ferrofluids infiltrated in their capillaries. The infiltrated ferrofluidic defects can generate either parasitic reflection notch features in uniform Bragg reflectors of up to 80% visibility and ~0.1 nm spectral shift or tunability of the bandwidth and strength reflection up to 100% when introduced into chirped gratings. Spectra are presented for different spatial positions and optical characteristics of the ferrofluidic section.     

Hardy's paradox and violation of a state-independent Bell inequality in time

Tests such as Bell's inequality and Hardy's paradox show that joint probabilities and correlations between distant particles in quantum mechanics are inconsistent with local realistic theories. Here we experimentally demonstrate these concepts in the time domain, using a photonic entangling gate to perform nondestructive measurements on a single photon at different times. We show that Hardy's paradox is much stronger in time and demonstrate the violation of a temporal Bell inequality independent of the quantum state, including for fully mixed states.     

The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.     

Geometrothermodynamics of higher dimensional black holes

We study the thermodynamics and geometrothermodynamics of different black hole configurations in more than four spacetime dimensions. We use the response functions to find the conditions under which second order phase transitions occur in higher-dimensional static Reissner–Nordström and stationary Kerr black holes. Our results indicate that the equilibrium manifold of all these black hole configurations is in general curved and that curvature singularities appear exactly at those places where second order phase transitions occur.