Absolute instability in plasma jet

Stability features of a plasma jet are investigated by means of Linear StabilityTheory. The convective/absolute nature of the instabilities is determined by local spatio-temporal analyses of the impulse response of the flow for different stream-wise positionsand different operative conditions. Frequencies, shapes and growth rate of the leadingstability mode are compared to available experimental high speed camera recordings of thejet unsteadiness. The frequency range and mode shapes retrieved theoretically are in goodagreement with the experimental results. However, the growth-rates of these modes indicatea fast transition to the turbulent regime which is not observed in the facility, which couldbe explained by non-parallel base flow or non-linear modal growth of the mode effects

Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game

We study the variant of the stable marriage problem in which the preferences of the agents are allowed to include indifferences. We present a mechanism for producing Pareto-stable matchings in stable marriage markets with indifferences that is group strategyproof for one side of the market. Our key technique involves modeling the stable marriage market as a generalized assignment game. We also show that our mechanism can be implemented efficiently. These results can be extended to the college admissions problem with indifferences

The Advice Complexity of a Class of Hard Online Problems

The advice complexity of an online problem is a measure of how much knowledge of the future an online algorithm needs in order to achieve a certain competitive ratio. Using advice complexity, we define the first online complexity class, AOC. The class includes independent set, vertex cover, dominating set, and several others as complete problems. AOC-complete problems are hard, since a single wrong answer by the online algorithm can have devastating consequences. For each of these problems, we show that $\log\left(1+(c-1)^{c-1}/c^{c}\right)n=\Theta (n/c)$ bits of advice are necessary and sufficient (up to an additive term of $O(\log n)$) to achieve a competitive ratio of $c$. The results are obtained by introducing a new string guessing problem related to those of Emek et al. (TCS 2011) and B\"ockenhauer et al. (TCS 2014). It turns out that this gives a powerful but easy-to-use method for providing both upper and lower bounds on the advice complexity of an entire class of online problems, the AOC-complete problems. Previous results of Halld\'orsson et al. (TCS 2002) on online independent set, in a related model, imply that the advice complexity of the problem is $\Theta (n/c)$. Our results improve on this by providing an exact formula for the higher-order term. For online disjoint path allocation, B\"ockenhauer et al. (ISAAC 2009) gave a lower bound of $\Omega (n/c)$ and an upper bound of $O((n\log c)/c)$ on the advice complexity. We improve on the upper bound by a factor of $\log c$. For the remaining problems, no bounds on their advice complexity were previously known.Comment: Full paper to appear in Theory of Computing Systems. A preliminary version appeared in STACS 201

Biorthogonal quantum mechanics

The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called 'biorthogonal quantum mechanics', is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems. © 2014 IOP Publishing Ltd

Temperature activated absorption during laser-induced damage: the evolution of laser-supported solid-state absorption fronts

Previously we have shown that the size of laser induced damage sites in both KDP and SiO{sub 2} is largely governed by the duration of the laser pulse which creates them. Here we present a model based on experiment and simulation that accounts for this behavior. Specifically, we show that solid-state laser-supported absorption fronts are generated during a damage event and that these fronts propagate at constant velocities for laser intensities up to 4 GW/cm{sup 2}. It is the constant absorption front velocity that leads to the dependence of laser damage site size on pulse duration. We show that these absorption fronts are driven principally by the temperature-activated deep sub band-gap optical absorptivity, free electron transport, and thermal diffusion in defect-free silica for temperatures up to 15,000K and pressures < 15GPa. In addition to the practical application of selecting an optimal laser for pre-initiation of large aperture optics, this work serves as a platform for understanding general laser-matter interactions in dielectrics under a variety of conditions

Time-Resolved Imaging of Material Response Following Laser-Induced Breakdown in the Bulk and Surface of Fused Silica

Optical components within high energy laser systems are susceptible to laser-induced material modification when the breakdown threshold is exceeded or damage is initiated by pre-existing impurities or defects. These modifications are the result of exposure to extreme conditions involving the generation of high temperatures and pressures and occur on a volumetric scale of the order of a few cubic microns. The response of the material following localized energy deposition, including the timeline of events and the individual processes involved during this timeline, is still largely unknown. In this work, we investigate the events taking place during the entire timeline in both bulk and surface damage in fused silica using a set of time-resolved microscopy systems. These microscope systems offer up to 1 micron spatial resolution when imaging static or dynamic effects, allowing for imaging of the entire process with adequate temporal and spatial resolution. These systems incorporate various pump-probe geometries designed to optimize the sensitivity for detecting individual aspects of the process such as the propagation of shock waves, near-surface material motion, the speed of ejecta, and material transformations. The experimental results indicate that the material response can be separated into distinct phases, some terminating within a few tens of nanoseconds but some extending up to about 100 microseconds. Overall the results demonstrate that the final characteristics of the modified region depend on the material response to the energy deposition and not on the laser parameters

A new expedited approach to evaluate the importance of different crystal growth parameters on laser damage performance in KDP and DKDP

In this work, we investigate the laser-induced damage resistance at 355 nm in DKDP crystals grown with varying growth parameters, including temperature, speed of growth and impurity concentration. In order to perform this work, a DKDP crystal was grown over 34 days by the rapid-growth technique with varied growth conditions. By using the same crystal, we are able to isolate growth-related parameters affecting LID from raw material or other variations that are encountered when testing in different crystals. The objective is to find correlations of damage performance to growth conditions and reveal the key parameters for achieving DKDP material in which the number of damage initiating defects is reduced. This approach can lead to reliable and expedite information regarding the importance of different crystal growth parameters on the laser damage characteristics of these crystals

Quantum catastrophes: a case study

The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty domain D of physical values of parameters. This means that for these parameters, H may be called crypto-Hermitian, i.e., made Hermitian via an {\it ad hoc} choice of the inner product in the physical Hilbert space of quantum bound states (i.e., via an {\it ad hoc} construction of the so called metric). The name of quantum catastrophe is then assigned to the N-tuple-exceptional-point crossing, i.e., to the scenario in which we leave domain D along such a path that at the boundary of D, an N-plet of bound state energies degenerates and, subsequently, complexifies. At any fixed $N \geq 2$, this process is simulated via an N by N benchmark effective matrix Hamiltonian H. Finally, it is being assigned such a closed-form metric which is made unique via an N-extrapolation-friendliness requirement.Comment: 23 p