Search results for "Graph theory"
showing 10 items of 784 documents
Engineering the Success of Quantum Walk Search Using Weighted Graphs
2016
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked vertex is limited. We give an example with two linked cliques, proving that the captive probability can be liberated by increasing the weights of the links. This allows the search to succeed with probability 1 without increasing the energy scaling of the algorithm. Further increasing the weights, however, slows the runtime, so the optimal search requires weights that are neither too weak nor too strong.
Faster Quantum Walk Search on a Weighted Graph
2015
A randomly walking quantum particle evolving by Schr\"odinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time $\Theta(N^{3/4})$. In this paper, we give a weighted version of this graph that preserves vertex-transitivity, and we show that the time to search on it can be reduced to nearly $\Theta(\sqrt{N})$. To prove this, we introduce two novel extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges, and a method to determine how precisely the jumping rate of the quantum walk must be chosen.
Optimization of field-free molecular alignment by phase-shaped laser pulses
2007
We theoretically demonstrate the optimization of field-free molecular alignment by phase-shaped femtosecond laser pulses. The effect is assessed in ${\mathrm{O}}_{2}$ at $T=60\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ under realistic conditions of intensity and pulse shaping. The spectral laser phase is sampled through 128 control parameters and a self-learning evolutionary algorithm combined with a nonperturbative regime calculation is used in order to design the specific phase that maximizes the degree of alignment. The postpulse molecular alignment appears significantly enhanced compared to a Fourier-transform-limited pulse of same energy. The analysis of the target state reveals that the so…
The Peregrine breather of order nine and its deformations with sixteen parameters solutions to the NLS equation
2015
Abstract We construct new deformations of the Peregrine breather ( P 9 ) of order 9 with 16 real parameters. With this method, we obtain explicitly new families of quasi-rational solutions to the NLS equation in terms of a product of an exponential depending on t by a ratio of two polynomials of degree 90 in x and t; when all the parameters are equal to 0, we recover the classical P 9 breather. We construct new patterns of different types of rogue waves as triangular configurations of 45 peaks as well as rings and concentric rings.
A study on the distribution of the envelope and the capacity of underwater acoustic channels
2014
This paper deals with the statistical analysis of the instantaneous capacity of shallow underwater acoustic communication (UWAC) channels under the assumption that the scatterers are randomly distributed on the surface and bottom of the ocean. We start by deriving exact closed-form expressions for the probability density function (PDF) of the total propagation path length from which the PDF of the path gains is obtained. Then, we study the distributions of the channel envelope and the capacity under line-of-sight (LOS) conditions. By performing the chi-square goodness-of-fit test, it is shown that the channel envelope is Rice distributed. Moreover, we investigate the effect of the ocean dep…
Elucidating the electron transport in semiconductors via Monte Carlo simulations: An inquiry-driven learning path for engineering undergraduates
2015
Within the context of higher education for science or engineering undergraduates, we present an inquiry-driven learning path aimed at developing a more meaningful conceptual understanding of the electron dynamics in semiconductors in the presence of applied electric fields. The electron transport in a nondegenerate n-type indium phosphide bulk semiconductor is modelled using a multivalley Monte Carlo approach. The main characteristics of the electron dynamics are explored under different values of the driving electric field, lattice temperature and impurity density. Simulation results are presented by following a question-driven path of exploration, starting from the validation of the model…
On the Path and Area J<sub>x1</sub>-Integral Components and their Relationship to the Out-of-Plane Constraint in Elastic Cracked Plates
2009
In this paper, the path and area components of the Jx1-integral, JP and JA, in three dimensional elastic cracked plates under mode-I loading are investigated aiming at relating them to the out-of-plane constraint conditions resulting from different specimen thicknesses. It is concluded that the JP and JA components of the Jx1-integral vary in the region where the out-of-plane constraint extends. Sufficiently far from the crack front, these integrals tend to stabilize, indicating that the thickness constraint vanishes and that a 2D-like stress and strain fields have been reached. A pure plane strain condition is only attained when the specimen thickness is very large when compared to the in-…
PHOTOMETRY OF STARS FOR ASTRONEGATIVES WITH A SINGLE EXPOSURE
2019
The paper discusses the construction of characteristic curves for various astronegatives with a single exposure. Particular attention is paid to the question of extrapolation of the characteristic curve for the region of the weakest stars in the absence of standards. A new method for constructing an individual characteristic curve for digitized films and plates in the UBVR system has been proposed and implemented. The processing of frames of digitized plates and films with sky areas is car- ried out using LINUX/MIDAS/ROMAFOT software tools. ROMAFOT application allows us to extract astro- metric rectangular coordinates X,Y and photometric char- acteristics such as instrumental photometric ma…
First Observation of Atomic Levels for the Element Fermium (Z=100)
2003
The atomic level structure of the element fermium was investigated for the first time using a sample of $2.7\ifmmode\times\else\texttimes\fi{}{10}^{10}$ atoms of the isotope $^{255}\mathrm{F}\mathrm{m}$ with a half-life of 20.1 h. The atoms were evaporated from a filament and stored in the argon buffer gas of an optical cell. Atomic levels were sought by the method of resonance ionization spectroscopy using an excimer-dye-laser combination. Two atomic levels were found at wave numbers $(25\text{ }099.8\ifmmode\pm\else\textpm\fi{}0.2)$ and $(25\text{ }111.8\ifmmode\pm\else\textpm\fi{}0.2)\text{ }\text{ }{\mathrm{c}\mathrm{m}}^{\ensuremath{-}1}$. Partial transition rates to the $5{f}^{12}7{s}…
Chandra X-ray observations of the stellar group near the Herbig Be star MWC 297
2006
We present a Chandra ACIS-I X-ray observation of the region near the Herbig early-Be star MWC 297, where we detect a tight group of point X-ray sources. These are probably physically associated to MWC 297, because of their obvious clustering with respect to the more scattered field-source population. These data are compared to earlier ASCA data with much poorer spatial resolution, from which the detection of strong quiescent and flaring emission from MWC 297 itself was claimed. We argue that this star, contributing only 5% to the total X-ray emission of the group, was probably not the dominant contributor to the observed ASCA emission, while the X-ray brightest star in the group is a much b…