Nonlinear optical probe of tunable surface electrons on a topological insulator

We use ultrafast laser pulses to experimentally demonstrate that the second-order optical response of bulk single crystals of the topological insulator Bi$_2$Se$_3$ is sensitive to its surface electrons. By performing surface doping dependence measurements as a function of photon polarization and sample orientation we show that second harmonic generation can simultaneously probe both the surface crystalline structure and the surface charge of Bi$_2$Se$_3$. Furthermore, we find that second harmonic generation using circularly polarized photons reveals the time-reversal symmetry properties of the system and is surprisingly robust against surface charging, which makes it a promising tool for spectroscopic studies of topological surfaces and buried interfaces

Algorithmic Analysis of Qualitative and Quantitative Termination Problems for Affine Probabilistic Programs

In this paper, we consider termination of probabilistic programs with real-valued variables. The questions concerned are: 1. qualitative ones that ask (i) whether the program terminates with probability 1 (almost-sure termination) and (ii) whether the expected termination time is finite (finite termination); 2. quantitative ones that ask (i) to approximate the expected termination time (expectation problem) and (ii) to compute a bound B such that the probability to terminate after B steps decreases exponentially (concentration problem). To solve these questions, we utilize the notion of ranking supermartingales which is a powerful approach for proving termination of probabilistic programs. In detail, we focus on algorithmic synthesis of linear ranking-supermartingales over affine probabilistic programs (APP's) with both angelic and demonic non-determinism. An important subclass of APP's is LRAPP which is defined as the class of all APP's over which a linear ranking-supermartingale exists. Our main contributions are as follows. Firstly, we show that the membership problem of LRAPP (i) can be decided in polynomial time for APP's with at most demonic non-determinism, and (ii) is NP-hard and in PSPACE for APP's with angelic non-determinism; moreover, the NP-hardness result holds already for APP's without probability and demonic non-determinism. Secondly, we show that the concentration problem over LRAPP can be solved in the same complexity as for the membership problem of LRAPP. Finally, we show that the expectation problem over LRAPP can be solved in 2EXPTIME and is PSPACE-hard even for APP's without probability and non-determinism (i.e., deterministic programs). Our experimental results demonstrate the effectiveness of our approach to answer the qualitative and quantitative questions over APP's with at most demonic non-determinism.Comment: 24 pages, full version to the conference paper on POPL 201

Wrinkling of a bilayer membrane

The buckling of elastic bodies is a common phenomenon in the mechanics of solids. Wrinkling of membranes can often be interpreted as buckling under constraints that prohibit large amplitude deformation. We present a combination of analytic calculations, experiments, and simulations to understand wrinkling patterns generated in a bilayer membrane. The model membrane is composed of a flexible spherical shell that is under tension and that is circumscribed by a stiff, essentially incompressible strip with bending modulus B. When the tension is reduced sufficiently to a value \sigma, the strip forms wrinkles with a uniform wavelength found theoretically and experimentally to be \lambda = 2\pi(B/\sigma)^{1/3}. Defects in this pattern appear for rapid changes in tension. Comparison between experiment and simulation further shows that, with larger reduction of tension, a second generation of wrinkles with longer wavelength appears only when B is sufficiently small.Comment: 9 pages, 5 color figure

Stochastic Invariants for Probabilistic Termination

Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates with probability~1 (almost-sure termination). A powerful approach for this qualitative problem is the notion of ranking supermartingales with respect to a given set of invariants. The quantitative problem (probabilistic termination) asks for bounds on the termination probability. A fundamental and conceptual drawback of the existing approaches to address probabilistic termination is that even though the supermartingales consider the probabilistic behavior of the programs, the invariants are obtained completely ignoring the probabilistic aspect. In this work we address the probabilistic termination problem for linear-arithmetic probabilistic programs with nondeterminism. We define the notion of {\em stochastic invariants}, which are constraints along with a probability bound that the constraints hold. We introduce a concept of {\em repulsing supermartingales}. First, we show that repulsing supermartingales can be used to obtain bounds on the probability of the stochastic invariants. Second, we show the effectiveness of repulsing supermartingales in the following three ways: (1)~With a combination of ranking and repulsing supermartingales we can compute lower bounds on the probability of termination; (2)~repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3)~with a combination of ranking and repulsing supermartingales we can establish persistence properties of probabilistic programs. We also present results on related computational problems and an experimental evaluation of our approach on academic examples.Comment: Full version of a paper published at POPL 2017. 20 page

Gravity and Light: Combining Gravitational Wave and Electromagnetic Observations in the 2020s

As of today, we have directly detected exactly one source in both gravitational waves (GWs) and electromagnetic (EM) radiation, the binary neutron star merger GW170817, its associated gamma-ray burst GRB170817A, and the subsequent kilonova SSS17a/AT 2017gfo. Within ten years, we will detect hundreds of events, including new classes of events such as neutron-star-black-hole mergers, core-collapse supernovae, and almost certainly something completely unexpected. As we build this sample, we will explore exotic astrophysical topics ranging from nucleosynthesis, stellar evolution, general relativity, high-energy astrophysics, nuclear matter, to cosmology. The discovery potential is extraordinary, and investments in this area will yield major scientific breakthroughs. Here we outline some of the most exciting scientific questions that can be answered by combining GW and EM observations

Parametric and sensitivity analysis for a proposed filtered tailings storage facility in challenging topography

Parametric and sensitivity analyses were performed for a proposed filtered tail- ings storage facility in challenging topography from the Southern Peru region. The purpose was to identify elements which are likely to dictate performance and stability, and to understand the risk profile for the facility. The analyses were performed varying: foundation material physical and hydraulic properties, tailings physical and hydraulic properties, foundation configuration, seismicity, and staged construction. The physical properties of the foundation material were varied by changing the Mohr-Coulomb strength parameters c’ and φ’, whereas the hydraulic properties were varied by moving the groundwater table upwards or saturating a larger amount of the foundation material. A similar approach was adopted in order to vary the physical and hydraulic properties of the tailings. The foundation configuration was varied by hypothetically moving the starter buttress closer to the edge of steep slopes further downhill from the facility. Staged construction stability analyses were simulated by analyzing filtered tailings fill configurations, which followed the overall design slope but varied in height. All analyses presented herein were conducted for the most critical failure mode for each scenario. The results from these parametric analyses showed that the design of the facility was highly sensitive to tailings potential saturation. In the simulation scenarios, saturation of the tailings caused instability in both static and seismic conditions. This sensitivity to moisture conditions highlighted the importance of properly defining the unsaturated filtered tailings parameters and simulating water infiltration processes through the vadose zone.Fil: Preciado, H. F. AMEC S.A; Perú.Fil: Ale, J. AMEC S.A; Perú.Fil: Byler, B. AMEC Englewood; USA.Fil: Perez, F. AMEC S.A; Perú.Fil: Mejía, V. AMEC S.A; Perú.Fil: McIver, D. Minera IRL SA; Perú.Otras Ingeniería Civi

Theoretical and experimental study of second harmonic generation from the surface of the topological insulator Bi_2Se_3

We develop a theoretical model that describes the second harmonic generation of light from the surface of the topological insulator Bi_2Se_3 and experimentally demonstrate that the technique is sensitive to the surface electrons. By performing a crystal symmetry analysis of Bi_2Se_3 (111) we determine the nonlinear electric susceptibility tensor elements that give rise to second harmonic generation. Using these results, we present a phenomenological model that shows that the relative magnitudes of these tensor elements can be determined by measuring the polarization and intensity of the radiated second harmonic light as a function of the in-plane crystal orientation and incident laser polarization. We describe optical techniques capable of isolating second harmonic light and, using these techniques, we measure the first-order linear optical and second-order nonlinear optical responses as a function of crystal orientation and laser polarization on bulk single crystals of Bi_2Se_3 (111). The experimental results are consistent with our theoretical description. By comparing the data to our theoretical model we determine that a portion of the measured second harmonic light originates from the accumulation region of Bi_2Se_3 (111), which we confirm by performing surface doping-dependent studies. Our results show that second harmonic generation is a promising tool for spectroscopic studies of topological surfaces and buried interfaces

Perfect Information Stochastic Priority Games

International audienceWe introduce stochastic priority games - a new class of perfect information stochastic games. These games can take two different, but equivalent, forms. In stopping priority games a play can be stopped by the environment after a finite number of stages, however, infinite plays are also possible. In discounted priority games only infinite plays are possible and the payoff is a linear combination of the classical discount payoff and of a limit payoff evaluating the performance at infinity. Shapley games and parity games are special extreme cases of priority games

Selective probing of photo-induced charge and spin dynamics in the bulk and surface of a topological insulator

Topological insulators possess completely different spin-orbit coupled bulk and surface electronic spectra that are each predicted to exhibit exotic responses to light. Here we report time-resolved fundamental and second harmonic optical pump-probe measurements on the topological insulator Bi2Se3 to independently measure its photo-induced charge and spin dynamics with bulk and surface selectivity. Our results show that a transient net spin density can be optically induced in both the bulk and surface, which may drive spin transport in topological insulators. By utilizing a novel rotational anisotropy analysis we are able to separately resolve the spin de-polarization, intraband cooling and interband recombination processes following photo-excitation, which reveal that spin and charge degrees of freedom relax on very different time scales owing to strong spin-orbit coupling.Comment: Accepted to Phys. Rev. Let