Airy wave packets accelerating in space-time

Although diffractive spreading is an unavoidable feature of all wave phenomena, certain waveforms can attain propagation-invariance. A lesser-explored strategy for achieving optical selfsimilar propagation exploits the modification of the spatio-temporal field structure when observed in reference frames moving at relativistic speeds. For such an observer, it is predicted that the associated Lorentz boost can bring to a halt the axial dynamics of a wave packet of arbitrary profile. This phenomenon is particularly striking in the case of a self-accelerating beam -- such as an Airy beam -- whose peak normally undergoes a transverse displacement upon free-propagation. Here we synthesize an acceleration-free Airy wave packet that travels in a straight line by deforming its spatio-temporal spectrum to reproduce the impact of a Lorentz boost. The roles of the axial spatial coordinate and time are swapped, leading to `time-diffraction' manifested in self-acceleration observed in the propagating Airy wave-packet frame.Comment: 5 pages, 4 figure

Improved Spectrum Mobility using Virtual Reservation in Collaborative Cognitive Radio Networks

Cognitive radio technology would enable a set of secondary users (SU) to opportunistically use the spectrum licensed to a primary user (PU). On the appearance of this PU on a specific frequency band, any SU occupying this band should free it for PUs. Typically, SUs may collaborate to reduce the impact of cognitive users on the primary network and to improve the performance of the SUs. In this paper, we propose and analyze the performance of virtual reservation in collaborative cognitive networks. Virtual reservation is a novel link maintenance strategy that aims to maximize the throughput of the cognitive network through full spectrum utilization. Our performance evaluation shows significant improvements not only in the SUs blocking and forced termination probabilities but also in the throughput of cognitive users.Comment: 7 pages, 10 figures, IEEE ISCC 201

Integrated Systems Modeling to Improve Watershed Habitat Management and Decision Making

Regulated rivers provide opportunities to improve habitat quality by managing the times, locations, and magnitudes of reservoir releases and diversions across the watershed. To identify these opportunities, managers select priority species and determine when, where, and how to allocate water between competing human and environmental users in the basin. Systems models have been used to recommend allocation of water between species. However, many models consider species’ water needs as constraints on instream flow that is managed to maximize human beneficial uses. Many models also incorporate uncertainty in the system and report an overwhelmingly large number of management alternatives. This dissertation presents three new novel models to recommend the allocation of water and money to improve habitat quality. The new models also facilitate communicating model results to managers and to the public. First, a new measurable and observable habitat metric quantifies habitat area and quality for priority aquatic, floodplain, and wetland habitat species. The metric is embedded in a systems model as an ecological objective to maximize. The systems model helps managers to identify times and locations at which to apply scarce water to most improve habitat area and quality for multiple competing species. Second, a cluster analysis approach is introduced to reduce large dimensional uncertainty problems in habitat models and focus management efforts on the important parameters to measure and monitor more carefully. The approach includes manager preferences in the search for clusters. It identifies a few, easy-to-interpret management options from a large multivariate space of possible alternatives. Third, an open-access web tool helps water resources modelers display model outputs on an interactive web map. The tool allows modelers to construct node-link networks on a web map and facilitates sharing and visualizing spatial and temporal model outputs. The dissertation applies all three studies to the Lower Bear River, Utah, to guide ongoing habitat conservation efforts, recommend water allocation strategies, and provide important insights on ways to improve overall habitat quality and area

Linear problems and hierarchies of Painlevé equations

In this paper, we show that the expansion of linear problems of the Painlev´e equation in powers of the spectral variable can be used to derive hierarchies of ordinary differential equations. We applied this approach to linear problems of the first, second, third and fourth Painlev´e equations. We derived a new hierarchy of the third Painlev´e equation and rederived known hierarchies of the other equations. Moreover some special solutions of the hierarchies of the second, third and fourth Painlev´e equations are also given.In this paper, we show that the expansion of linear problems of the Painlev´e equation in powers of the spectral variable can be used to derive hierarchies of ordinary differential equations. We applied this approach to linear problems of the first, second, third and fourth Painlev´e equations. We derived a new hierarchy of the third Painlev´e equation and rederived known hierarchies of the other equations. Moreover some special solutions of the hierarchies of the second, third and fourth Painlev´e equations are also given

Multi-Tap Mobile Phone Text Entry : Key-Press Operators For Keystroke Level Model

The Keystroke Level Model (KLM) has been utilized to predict the user behaviors and activities with desktop system. Recently, the mobile device application designers could use updated KLM model to predict the consumed time while users use mobile devices, but when designers use this method to evaluate the text entry they still face some difficulties with the calculation of long equations, due to multi-tap technology. This study proposes new KLM operators to facilitate the time calculation process for text entry using traditional mobile keypad. Updated KLM operators are used to predict the user behavior in interacting with mobile devices in general and text entry in specific. The expected results contribute in estimating the consumed time accurately