Bringing Coherence to Multistate Charter Leadership: A Collective Case Study

Multistate networks are arguably the purest expression of the charter sector’s original promise as an engine of innovation within the public school system. On its face, this contention may appear somewhat counterintuitive; the proliferation of schools affiliated with charter management organizations (CMOs) that have siphoned market share away from standalone, community-based operators is often faulted for bringing homogeneity to a corner of the education landscape that once valorized pluralism. Replicating networks that expand their proven models into more than one state, however, are subject to divergent policy landscapes, operational conditions, and community expectations. Accordingly, in order to comport with the dictates of discrete sets of external demands, the leaders of multistate networks necessarily preside over a rolling set of limited experiments through which they are able to assess the relative efficacy of varying approaches to educating students. With the public policy and private philanthropic incentive structures continuing to tilt in favor of replication, and with multistate operators generally struggling to match the success of their more geographically compact peers, it is imperative that leaders of these unique organizations understand how to meet the needs of their communities while simultaneously cultivating the sense of collective mission that promotes effective operation. This collective case study explores how the leaders of five multistate networks attempt to create coherence within their organizations notwithstanding these materially different environmental conditions. Data from interviews, observations, and artifacts were triangulated, and the resulting analysis revealed commonalities, distinctions, and trends that illuminate how these leaders navigate the barriers that imperil the creation of coherence within the multistate construct. This study assesses the leadership moves that the chief executives of multistate networks make when attempting to create coherence and proposes a novel categorization scheme that classifies these strategies as either ideological, structural, or interpersonal in nature. This study also provides a composite picture of the successful multistate charter leader by synthesizing the key attributes possessed by the study participants, explaining how they exercise humility and finesse while using the serial experimentation compelled by the multistate framework to seek out opportunities to drive continuous improvement throughout their networks. Examined through a conceptual framework that ties together the literature on coherence in educational organizations and charter school replication, these findings demonstrate how multistate leaders engage stakeholders based in their satellite regions in a dynamic process of calibrating the appropriate fit between network model and local conditions. Implications from this study are relevant to the policymakers and funders who have continued to provide regulatory and financial support to operators undertaking interstate expansion efforts, to the current and prospective leaders of multistate CMOs who are being entrusted to create high-quality learning environments for students in far-flung communities, and to the superintendents of traditional public school districts who can draw lessons from the manner in which this study’s participants are consistently experimenting, evaluating, and adapting

Azimuthally polarized spatial dark solitons: exact solutions of Maxwell's equations in a Kerr medium

Spatial Kerr solitons, typically associated with the standard paraxial nonlinear Schroedinger equation, are shown to exist to all nonparaxial orders, as exact solutions of Maxwell's equations in the presence of vectorial Kerr effect. More precisely, we prove the existence of azimuthally polarized, spatial, dark soliton solutions of Maxwell's equations, while exact linearly polarized (2+1)-D solitons do not exist. Our ab initio approach predicts the existence of dark solitons up to an upper value of the maximum field amplitude, corresponding to a minimum soliton width of about one fourth of the wavelength.Comment: 4 pages, 4 figure

Driven Morse Oscillator: Model for Multi-photon Dissociation of Nitrogen Oxide

Within a one-dimensional semi-classical model with a Morse potential the possibility of infrared multi-photon dissociation of vibrationally excited nitrogen oxide was studied. The dissociation thresholds of typical driving forces and couplings were found to be similar, which indicates that the results were robust to variations of the potential and of the definition of dissociation rate. PACS: 42.50.Hz, 33.80.WzComment: old paper, 8 pages 6 eps file

Approximate Analytic Solution for the Spatiotemporal Evolution of Wave Packets undergoing Arbitrary Dispersion

We apply expansion methods to obtain an approximate expression in terms of elementary functions for the space and time dependence of wave packets in a dispersive medium. The specific application to pulses in a cold plasma is considered in detail, and the explicit analytic formula that results is provided. When certain general initial conditions are satisfied, these expressions describe the packet evolution quite well. We conclude by employing the method to exhibit aspects of dispersive pulse propagation in a cold plasma, and suggest how predicted and experimental effects may be compared to improve the theoretical description of a medium's dispersive properties.Comment: 17 pages, 4 figures, RevTe

Optimal use of time dependent probability density data to extract potential energy surfaces

A novel algorithm was recently presented to utilize emerging time dependent probability density data to extract molecular potential energy surfaces. This paper builds on the previous work and seeks to enhance the capabilities of the extraction algorithm: An improved method of removing the generally ill-posed nature of the inverse problem is introduced via an extended Tikhonov regularization and methods for choosing the optimal regularization parameters are discussed. Several ways to incorporate multiple data sets are investigated, including the means to optimally combine data from many experiments exploring different portions of the potential. Results are presented on the stability of the inversion procedure, including the optimal combination scheme, under the influence of data noise. The method is applied to the simulated inversion of a double well system.Comment: 34 pages, 5 figures, LaTeX with REVTeX and Graphicx-Package; submitted to PhysRevA; several descriptions and explanations extended in Sec. I

Quantum phase retrieval of a Rydberg wave packet using a half-cycle pulse

A terahertz half-cycle pulse was used to retrieve information stored as quantum phase in an $N$-state Rydberg atom data register. The register was prepared as a wave packet with one state phase-reversed from the others (the "marked bit"). A half-cycle pulse then drove a significant portion of the electron probability into the flipped state via multimode interference.Comment: accepted by PR

Multi Mode Interferometer for Guided Matter Waves

We describe the fundamental features of an interferometer for guided matter waves based on Y-beam splitters and show that, in a quasi two-dimensional regime, such a device exhibits high contrast fringes even in a multi mode regime and fed from a thermal source.Comment: Final version (accepted to PRL

Del Pezzo surfaces of degree 1 and jacobians

We construct absolutely simple jacobians of non-hyperelliptic genus 4 curves, using Del Pezzo surfaces of degree 1. This paper is a natural continuation of author's paper math.AG/0405156.Comment: 24 page

Collective excitations of trapped Bose condensates in the energy and time domains

A time-dependent method for calculating the collective excitation frequencies and densities of a trapped, inhomogeneous Bose-Einstein condensate with circulation is presented. The results are compared with time-independent solutions of the Bogoliubov-deGennes equations. The method is based on time-dependent linear-response theory combined with spectral analysis of moments of the excitation modes of interest. The technique is straightforward to apply, is extremely efficient in our implementation with parallel FFT methods, and produces highly accurate results. The method is suitable for general trap geometries, condensate flows and condensates permeated with vortex structures.Comment: 6 pages, 3 figures small typos fixe