Feed-forward and its role in conditional linear optical quantum dynamics

Nonlinear optical quantum gates can be created probabilistically using only single photon sources, linear optical elements and photon-number resolving detectors. These gates are heralded but operate with probabilities much less than one. There is currently a large gap between the performance of the known circuits and the established upper bounds on their success probabilities. One possibility for increasing the probability of success of such gates is feed-forward, where one attempts to correct certain failure events that occurred in the gate's operation. In this brief report we examine the role of feed-forward in improving the success probability. In particular, for the non-linear sign shift gate, we find that in a three-mode implementation with a single round of feed-forward the optimal average probability of success is approximately given by p= 0.272. This value is only slightly larger than the general optimal success probability without feed-forward, P= 0.25.Comment: 4 pages, 3 eps figures, typeset using RevTex4, problems with figures resolve

Lyapunov exponents for small aspect ratio Rayleigh-Bénard convection

Leading order Lyapunov exponents and their corresponding eigenvectors have been computed numerically for small aspect ratio, three-dimensional Rayleigh-Benard convection cells with no-slip boundary conditions. The parameters are the same as those used by Ahlers and Behringer [Phys. Rev. Lett. 40, 712 (1978)] and Gollub and Benson [J. Fluid Mech. 100, 449 (1980)] in their work on a periodic time dependence in Rayleigh-Benard convection cells. Our work confirms that the dynamics in these cells truly are chaotic as defined by a positive Lyapunov exponent. The time evolution of the leading order Lyapunov eigenvector in the chaotic regime will also be discussed. In addition we study the contributions to the leading order Lyapunov exponent for both time periodic and aperiodic states and find that while repeated dynamical events such as dislocation creation/annihilation and roll compression do contribute to the short time Lyapunov exponent dynamics, they do not contribute to the long time Lyapunov exponent. We find instead that nonrepeated events provide the most significant contribution to the long time leading order Lyapunov exponent

Scaling laws for rotating Rayleigh-Bénard convection

Numerical simulations of large aspect ratio, three-dimensional rotating Rayleigh-Bénard convection for no-slip boundary conditions have been performed in both cylinders and periodic boxes. We have focused near the threshold for the supercritical bifurcation from the conducting state to a convecting state exhibiting domain chaos. A detailed analysis of these simulations has been carried out and is compared with experimental results, as well as predictions from multiple scale perturbation theory. We find that the time scaling law agrees with the theoretical prediction, which is in contradiction to experimental results. We also have looked at the scaling of defect lengths and defect glide velocities. We find a separation of scales in defect diameters perpendicular and parallel to the rolls as expected, but the scaling laws for the two different lengths are in contradiction to theory. The defect velocity scaling law agrees with our theoretical prediction from multiple scale perturbation theory

Black Hole Boundary Conditions and Coordinate Conditions

This paper treats boundary conditions on black hole horizons for the full 3+1D Einstein equations. Following a number of authors, the apparent horizon is employed as the inner boundary on a space slice. It is emphasized that a further condition is necessary for the system to be well posed; the ``prescribed curvature conditions" are therefore proposed to complete the coordinate conditions at the black hole. These conditions lead to a system of two 2D elliptic differential equations on the inner boundary surface, which coexist nicely to the 3D equation for maximal slicing (or related slicing conditions). The overall 2D/3D system is argued to be well posed and globally well behaved. The importance of ``boundary conditions without boundary values" is emphasized. This paper is the first of a series. This revised version makes minor additions and corrections to the previous version.Comment: 13 pages LaTeX, revtex. No figure

Experiences from the Fukushima Disaster

The nuclear accident of the Fukushima Daiichi reactors on March 11, 2011, could have been prevented if the owner and the responsible Japanese ministries had considered the worst-case scenario when planning the reactors near the coast, including at least double redundancy of the emergency system. After the exceptionally strong earthquake, the reactors correctly switched off. The problem started due to the tsunami that destroyed the emergency generators, which should have driven the cooling pumps after the reactor-power had switched off. The Zr-alloy mantles of the fuel rods reacted at the high temperature with water to form ZrO2 and hydrogen. The following explosions, destruction of the reactor buildings and meltdown caused large radioactive clouds and the evacuation of 150,000 people. This chapter shows how by immediate efforts most of this cloud could have been sucked off. The radioactive soil from large contaminated areas was later collected in plastic sacks. Continuous cooling led to huge amounts of contaminated water that was collected in large tanks. In future, the reactor has to be dismantled resulting in contaminated debris. In this chapter, the possible solutions of radioactive cloud, soil, water and rubble problems and the final deposit of used fuel rods are discussed. The experiences could become useful in case of a future nuclear accident

Simulating merging binary black holes with nearly extremal spins

Astrophysically realistic black holes may have spins that are nearly extremal (i.e., close to 1 in dimensionless units). Numerical simulations of binary black holes are important tools both for calibrating analytical templates for gravitational-wave detection and for exploring the nonlinear dynamics of curved spacetime. However, all previous simulations of binary-black-hole inspiral, merger, and ringdown have been limited by an apparently insurmountable barrier: the merging holes' spins could not exceed 0.93, which is still a long way from the maximum possible value in terms of the physical effects of the spin. In this paper, we surpass this limit for the first time, opening the way to explore numerically the behavior of merging, nearly extremal black holes. Specifically, using an improved initial-data method suitable for binary black holes with nearly extremal spins, we simulate the inspiral (through 12.5 orbits), merger and ringdown of two equal-mass black holes with equal spins of magnitude 0.95 antialigned with the orbital angular momentum.Comment: 4 pages, 2 figures, updated with version accepted for publication in Phys. Rev. D, removed a plot that was incorrectly included at the end of the article in version v

Characterization of the domain chaos convection state by the largest Lyapunov exponent

Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent lambda1 for a variety of aspect ratios and driving strengths. We study in particular the domain chaos state, which bifurcates supercritically from the conducting fluid state and involves extended propagating fronts as well as point defects. We compare our results with those from Egolf et al., [Nature 404, 733 (2000)], who suggested that the value of lambda1 for the spiral defect chaos state of a convecting fluid was determined primarily by bursts of instability arising from short-lived, spatially localized dislocation nucleation events. We also show that the quantity lambda1 is not intensive for aspect ratios Gamma over the range 20<Gamma<40 and that the scaling exponent of lambda1 near onset is consistent with the value predicted by the amplitude equation formalism