Extension of a Spectral Bounding Method to Complex Rotated Hamiltonians, with Application to p2−ix3p^2-ix^3

We show that a recently developed method for generating bounds for the discrete energy states of the non-hermitian $-ix^3$ potential (Handy 2001) is applicable to complex rotated versions of the Hamiltonian. This has important implications for extension of the method in the analysis of resonant states, Regge poles, and general bound states in the complex plane (Bender and Boettcher (1998)).Comment: Submitted to J. Phys.

Generating Converging Bounds to the (Complex) Discrete States of the P2+iX3+iαXP^2 + iX^3 + i\alpha X Hamiltonian

The Eigenvalue Moment Method (EMM), Handy (2001), Handy and Wang (2001)) is applied to the $H_\alpha \equiv P^2 + iX^3 + i\alpha X$ Hamiltonian, enabling the algebraic/numerical generation of converging bounds to the complex energies of the $L^2$ states, as argued (through asymptotic methods) by Delabaere and Trinh (J. Phys. A: Math. Gen. {\bf 33} 8771 (2000)).Comment: Submitted to J. Phys.

Silicon oxide films grown and deposited in a microwave discharge

Growth and deposition of silicon dioxide films in microwave discharg

Generating Bounds for the Ground State Energy of the Infinite Quantum Lens Potential

Moment based methods have produced efficient multiscale quantization algorithms for solving singular perturbation/strong coupling problems. One of these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev. Lett.{\bf 55}, 931 (1985); ibid, {\bf 60}, 253 (1988b)), generates converging lower and upper bounds to a specific discrete state energy, once the signature property of the associated wavefunction is known. This method is particularly effective for multidimensional, bosonic ground state problems, since the corresponding wavefunction must be of uniform signature, and can be taken to be positive. Despite this, the vast majority of problems studied have been on unbounded domains. The important problem of an electron in an infinite quantum lens potential defines a challenging extension of EMM to systems defined on a compact domain. We investigate this here, and introduce novel modifications to the conventional EMM formalism that facilitate its adaptability to the required boundary conditions.Comment: Submitted to J. Phys.

STRUCTURAL CHANGE IN THE U.S. MEAT AND POULTRY INDUSTRIES

Market structure, concentration, meat industry, poultry industry, Industrial Organization,

CONSOLIDATION IN U.S. MEATPACKING

Meatpacking consolidated rapidly in the last two decades: slaughter plants became much larger, and concentration increased as smaller firms left the industry. We use establishment-based data from the U.S. Census Bureau to describe consolidation and to identify the roles of scale economies and technological change in driving consolidation. Through the 1970's, larger plants paid higher wages, generating a pecuniary scale diseconomy that largely offset the cost advantages that technological scale economies offered large plants. The larger plants' wage premium disappeared in the 1980's, and technological change created larger and more extensive technological scale economies. As a result, large plants realized growing cost advantages over smaller plants, and production shifted to larger plants.Concentration, consolidation, meatpacking, scale economies, structural change, Industrial Organization, Livestock Production/Industries,

Generating Converging Eigenenergy Bounds for the Discrete States of the -ix^3 Non-Hermitian Potential

Recent investigations by Bender and Boettcher (Phys. Rev. Lett 80, 5243 (1998)) and Mezincescu (J. Phys. A. 33, 4911 (2000)) have argued that the discrete spectrum of the non-hermitian potential $V(x) = -ix^3$ should be real. We give further evidence for this through a novel formulation which transforms the general one dimensional Schrodinger equation (with complex potential) into a fourth order linear differential equation for $|\Psi(x)|^2$. This permits the application of the Eigenvalue Moment Method, developed by Handy, Bessis, and coworkers (Phys. Rev. Lett. 55, 931 (1985);60, 253 (1988a,b)), yielding rapidly converging lower and upper bounds to the low lying discrete state energies. We adapt this formalism to the pure imaginary cubic potential, generating tight bounds for the first five discrete state energy levels.Comment: Work to appear in J. Phys. A: Math & Ge

Eigenvalues of PT-symmetric oscillators with polynomial potentials

We study the eigenvalue problem $-u^{\prime\prime}(z)-[(iz)^m+P_{m-1}(iz)]u(z)=\lambda u(z)$ with the boundary conditions that $u(z)$ decays to zero as $z$ tends to infinity along the rays $\arg z=-\frac{\pi}{2}\pm \frac{2\pi}{m+2}$, where $P_{m-1}(z)=a_1 z^{m-1}+a_2 z^{m-2}+...+a_{m-1} z$ is a polynomial and integers $m\geq 3$. We provide an asymptotic expansion of the eigenvalues $\lambda_n$ as $n\to+\infty$, and prove that for each {\it real} polynomial $P_{m-1}$, the eigenvalues are all real and positive, with only finitely many exceptions.Comment: 23 pages, 1 figure. v2: equation (14) as well as a few subsequent equations has been changed. v3: typos correcte

Distributed leadership, trust and online communities

This paper analyses the role of distributed leadership and trust in online communities. The team-based informal ethos of online collaboration requires a different kind of leadership from that in formal positional hierarchies. Such leadership may be more flexible and sophisticated, capable of encompassing ambiguity and rapid change. Online leaders need to be partially invisible, delegating power and distributing tasks. Yet, simultaneously, online communities are facilitated by the high visibility and subtle control of expert leaders. This paradox: that leaders need to be both highly visible and invisible as appropriate, was derived from prior research and tested in the analysis of online community discussions using a pattern-matching process. It is argued that both leader visibility and invisibility are important for the facilitation of trusting collaboration via distributed leadership. Advanced leadership responses to complex situations in online communities foster positive group interaction and decision-making, facilitated through active distribution of specific tasks

Imaging structure and geometry of slabs in the greater Alpine area – a P-wave travel-time tomography using AlpArray Seismic Network data

We perform a teleseismic P-wave travel-time tomography to examine the geometry and structure of subducted lithosphere in the upper mantle beneath the Alpine orogen. The tomography is based on waveforms recorded at over 600 temporary and permanent broadband stations of the dense AlpArray Seismic Network deployed by 24 different European institutions in the greater Alpine region, reaching from the Massif Central to the Pannonian Basin and from the Po Plain to the river Main. Teleseismic travel times and travel-time residuals of direct teleseismic P waves from 331 teleseismic events of magnitude 5.5 and higher recorded between 2015 and 2019 by the AlpArray Seismic Network are extracted from the recorded waveforms using a combination of automatic picking, beamforming and cross-correlation. The resulting database contains over 162 000 highly accurate absolute P-wave travel times and travel-time residuals. For tomographic inversion, we define a model domain encompassing the entire Alpine region down to a depth of 600 km. Predictions of travel times are computed in a hybrid way applying a fast TauP method outside the model domain and continuing the wave fronts into the model domain using a fast marching method. We iteratively invert demeaned travel-time residuals for P-wave velocities in the model domain using a regular discretization with an average lateral spacing of about 25 km and a vertical spacing of 15 km. The inversion is regularized towards an initial model constructed from a 3D a priori model of the crust and uppermost mantle and a 1D standard earth model beneath. The resulting model provides a detailed image of slab configuration beneath the Alpine and Apenninic orogens. Major features are a partly overturned Adriatic slab beneath the Apennines reaching down to 400 km depth still attached in its northern part to the crust but exhibiting detachment towards the southeast. A fast anomaly beneath the western Alps indicates a short western Alpine slab whose easternmost end is located at about 100 km depth beneath the Penninic front. Further to the east and following the arcuate shape of the western Periadriatic Fault System, a deep-reaching coherent fast anomaly with complex internal structure generally dipping to the SE down to about 400 km suggests a slab of European origin limited to the east by the Giudicarie fault in the upper 200 km but extending beyond this fault at greater depths. In its eastern part it is detached from overlying lithosphere. Further to the east, well-separated in the upper 200 km from the slab beneath the central Alps but merging with it below, another deep-reaching, nearly vertically dipping high-velocity anomaly suggests the existence of a slab beneath the eastern Alps of presumably the same origin which is completely detached from the orogenic root. Our image of this slab does not require a polarity switch because of its nearly vertical dip and full detachment from the overlying lithosphere. Fast anomalies beneath the Dinarides are weak and concentrated to the northernmost part and shallow depths. Low-velocity regions surrounding the fast anomalies beneath the Alps to the west and northwest follow the same dipping trend as the overlying fast ones, indicating a kinematically coherent thick subducting lithosphere in this region. Alternatively, these regions may signify the presence of seismic anisotropy with a horizontal fast axis parallel to the Alpine belt due to asthenospheric flow around the Alpine slabs. In contrast, low-velocity anomalies to the east suggest asthenospheric upwelling presumably driven by retreat of the Carpathian slab and extrusion of eastern Alpine lithosphere towards the east while low velocities to the south are presumably evidence of asthenospheric upwelling and mantle hydration due to their position above the European slab