Theory of the spatial structure of non-linear lasing modes

A self-consistent integral equation is formulated and solved iteratively which determines the steady-state lasing modes of open multi-mode lasers. These modes are naturally decomposed in terms of frequency dependent biorthogonal modes of a linear wave equation and not in terms of resonances of the cold cavity. A one-dimensional cavity laser is analyzed and the lasing mode is found to have non-trivial spatial structure even in the single-mode limit. In the multi-mode regime spatial hole-burning and mode competition is treated exactly. The formalism generalizes to complex, chaotic and random laser media.Comment: 4 pages, 3 figure

Self-consistent multi-mode lasing theory for complex or random lasing media

A semiclassical theory of single and multi-mode lasing is derived for open complex or random media using a self-consistent linear response formulation. Unlike standard approaches which use closed cavity solutions to describe the lasing modes, we introduce an appropriate discrete basis of functions which describe also the intensity and angular emission pattern outside the cavity. This constant flux (CF) basis is dictated by the Green function which arises when formulating the steady state Maxwell-Bloch equations as a self-consistent linear response problem. This basis is similar to the quasi-bound state basis which is familiar in resonator theory and it obeys biorthogonality relations with a set of dual functions. Within a single-pole approximation for the Green function the lasing modes are proportional to these CF states and their intensities and lasing frequencies are determined by a set of non-linear equations. When a near threshold approximation is made to these equations a generalized version of the Haken-Sauermann equations for multi-mode lasing is obtained, appropriate for open cavities. Illustrative results from these equations are given for single and few mode lasing states, for the case of dielectric cavity lasers. The standard near threshold approximation is found to be unreliable. Applications to wave-chaotic cavities and random lasers are discussed.Comment: 18 pages, 9 figure

Thermodynamics and Fractional Fokker-Planck Equations

The relaxation to equilibrium in many systems which show strange kinetics is described by fractional Fokker-Planck equations (FFPEs). These can be considered as phenomenological equations of linear nonequilibrium theory. We show that the FFPEs describe the system whose noise in equilibrium funfills the Nyquist theorem. Moreover, we show that for subdiffusive dynamics the solutions of the corresponding FFPEs are probability densities for all cases where the solutions of normal Fokker-Planck equation (with the same Fokker-Planck operator and with the same initial and boundary conditions) exist. The solutions of the FFPEs for superdiffusive dynamics are not always probability densities. This fact means only that the corresponding kinetic coefficients are incompatible with each other and with the initial conditions

On the Inequivalence of Weak-Localization and Coherent Backscattering

We define a current-conserving approximation for the local conductivity tensor of a disordered system which includes the effects of weak localization. Using this approximation we show that the weak localization effect in conductance is not obtained simply from the diagram corresponding to the coherent back-scattering peak observed in optical experiments. Other diagrams contribute to the effect at the same order and decrease its value. These diagrams appear to have no semiclassical analogues, a fact which may have implications for the semiclassical theory of chaotic systems. The effects of discrete symmetries on weak localization in disordered conductors is evaluated and and compared to results from chaotic scatterers.Comment: 24 pages revtex + 12 figures on request; hub.94.

Lean NOx Trap Catalysis for Lean Natural Gas Engine Applications

Distributed energy is an approach for meeting energy needs that has several advantages. Distributed energy improves energy security during natural disasters or terrorist actions, improves transmission grid reliability by reducing grid load, and enhances power quality through voltage support and reactive power. In addition, distributed energy can be efficient since transmission losses are minimized. One prime mover for distributed energy is the natural gas reciprocating engine generator set. Natural gas reciprocating engines are flexible and scalable solutions for many distributed energy needs. The engines can be run continuously or occasionally as peak demand requires, and their operation and maintenance is straightforward. Furthermore, system efficiencies can be maximized when natural gas reciprocating engines are combined with thermal energy recovery for cooling, heating, and power applications. Expansion of natural gas reciprocating engines for distributed energy is dependent on several factors, but two prominent factors are efficiency and emissions. Efficiencies must be high enough to enable low operating costs, and emissions must be low enough to permit significant operation hours, especially in non-attainment areas where emissions are stringently regulated. To address these issues the U.S. Department of Energy and the California Energy Commission launched research and development programs called Advanced Reciprocating Engine Systems (ARES) and Advanced Reciprocating Internal Combustion Engines (ARICE), respectively. Fuel efficiency and low emissions are two primary goals of these programs. The work presented here was funded by the ARES program and, thus, addresses the ARES 2010 goals of 50% thermal efficiency (fuel efficiency) and <0.1 g/bhp-hr emissions of oxides of nitrogen (NOx). A summary of the goals for the ARES program is given in Table 1-1. ARICE 2007 goals are 45% thermal efficiency and <0.015 g/bhp-hr NOx. Several approaches for improving the efficiency and emissions of natural gas reciprocating engines are being pursued. Approaches include: stoichiometric engine operation with exhaust gas recirculation and three-way catalysis, advanced combustion modes such as homogeneous charge compression ignition, and extension of the lean combustion limit with advanced ignition concepts and/or hydrogen mixing. The research presented here addresses the technical approach of combining efficient lean spark-ignited natural gas combustion with low emissions obtained from a lean NOx trap catalyst aftertreatment system. This approach can be applied to current lean engine technology or advanced lean engines that may result from related efforts in lean limit extension. Furthermore, the lean NOx trap technology has synergy with hydrogen-assisted lean limit extension since hydrogen is produced from natural gas during the lean NOx trap catalyst system process. The approach is also applicable to other lean engines such as diesel engines, natural gas turbines, and lean gasoline engines; other research activities have focused on those applications. Some commercialization of the technology has occurred for automotive applications (both diesel and lean gasoline engine vehicles) and natural gas turbines for stationary power. The research here specifically addresses barriers to commercialization of the technology for large lean natural gas reciprocating engines for stationary power. The report presented here is a comprehensive collection of research conducted by Oak Ridge National Laboratory (ORNL) on lean NOx trap catalysis for lean natural gas reciprocating engines. The research was performed in the Department of Energy's ARES program from 2003 to 2007 and covers several aspects of the technology. All studies were conducted at ORNL on a Cummins C8.3G+ natural gas engine chosen based on industry input to simulate large lean natural gas engines. Specific technical areas addressed by the research include: NOx reduction efficiency, partial oxidation and reforming chemistry, and the effects of sulfur poisons on the partial oxidation, reformer, and lean NOx trap catalysts. The initial work on NOx reduction efficiency demonstrated that NOx emissions <0.1 g/bhp-hr (the ARES goal) can be achieved with the lean NOx trap catalyst technology. Subsequent work focused on cost and size optimization and durability issues which addressed two specific ARES areas of interest to industry ('Cost of Power' and 'Availability, Reliability, and Maintainability', respectively). Thus, the research addressed the approach of the lean NOx trap catalyst technology toward the ARES goals as shown in Table 1-1

Quantum chaos in a deformable billiard: Applications to quantum dots

We perform a detailed numerical study of energy-level and wavefunction statistics of a deformable quantum billiard focusing on properties relevant to semiconductor quantum dots. We consider the family of Robnik billiards generated by simple conformal maps of the unit disk; the shape of this family of billiards may be varied continuously at fixed area by tuning the parameters of the map. The classical dynamics of these billiards is well-understood and this allows us to study the quantum properties of subfamilies which span the transition from integrability to chaos as well as families at approximately constant degree of chaoticity (Kolmogorov entropy). In the regime of hard chaos we find that the statistical properties of interest are well-described by random-matrix theory and completely insensitive to the particular shape of the dot. However in the nearly-integrable regime non-universal behavior is found. Specifically, the level-width distribution is well-described by the predicted $\chi^2$ distribution both in the presence and absence of magnetic flux when the system is fully chaotic; however it departs substantially from this behavior in the mixed regime. The chaotic behavior corroborates the previously predicted behavior of the peak-height distribution for deformed quantum dots. We also investigate the energy-level correlation functions which are found to agree well with the behavior calculated for quasi-zero-dimensional disordered systems.Comment: 25 pages (revtex 3.0). 16 figures are available by mail or fax upon request at [email protected]

Mesoscopic conductance and its fluctuations at non-zero Hall angle

We consider the bilocal conductivity tensor, the two-probe conductance and its fluctuations for a disordered phase-coherent two-dimensional system of non-interacting electrons in the presence of a magnetic field, including correctly the edge effects. Analytical results are obtained by perturbation theory in the limit $\sigma_{xx} \gg 1$. For mesoscopic systems the conduction process is dominated by diffusion but we show that, due to the lack of time-reversal symmetry, the boundary condition for diffusion is altered at the reflecting edges. Instead of the usual condition, that the derivative along the direction normal to the wall of the diffusing variable vanishes, the derivative at the Hall angle to the normal vanishes. We demonstrate the origin of this boundary condition from different starting points, using (i) a simplified Chalker-Coddington network model, (ii) the standard diagrammatic perturbation expansion, and (iii) the nonlinear sigma-model with the topological term, thus establishing connections between the different approaches. Further boundary effects are found in quantum interference phenomena. We evaluate the mean bilocal conductivity tensor $\sigma_{\mu\nu}(r,r')$, and the mean and variance of the conductance, to leading order in $1/\sigma_{xx}$ and to order $(\sigma_{xy}/\sigma_{xx})^2$, and find that the variance of the conductance increases with the Hall ratio. Thus the conductance fluctuations are no longer simply described by the unitary universality class of the $\sigma_{xy}=0$ case, but instead there is a one-parameter family of probability distributions. In the quasi-one-dimensional limit, the usual universal result for the conductance fluctuations of the unitary ensemble is recovered, in contrast to results of previous authors. Also, a long discussion of current conservation.Comment: Latex, uses RevTex, 58 pages, 5 figures available on request at [email protected]. Submitted to Phys. Rev.

Confinement and Chiral Symmetry Breaking via Domain-Like Structures in the QCD Vacuum

A qualitative mechanism for the emergence of domain structured background gluon fields due to singularities in gauge field configurations is considered, and a model displaying a type of mean field approximation to the QCD partition function based on this mechanism is formulated. Estimation of the vacuum parameters (gluon condensate, topological susceptibility, string constant and quark condensate) indicates that domain-like structures lead to an area law for the Wilson loop, nonzero topological susceptibility and spontaneous breakdown of chiral symmetry. Gluon and ghost propagators in the presence of domains are calculated explicitly and their analytical properties are discussed. The Fourier transforms of the propagators are entire functions and thus describe confined dynamical fields.Comment: RevTeX, 48 pages (32 pages + Appendices A-E), new references added [1,2,4,5] and minor formulae corrected for typographical error

Perspectives of San Juan healthcare practitioners on the detection deficit in oral premalignant and early cancers in Puerto Rico: a qualitative research study

<p>Abstract</p> <p>Background</p> <p>In Puerto Rico, relative to the United States, a disparity exists in detecting oral precancers and early cancers. To identify factors leading to the deficit in early detection, we obtained the perspectives of San Juan healthcare practitioners whose practice could be involved in the detection of such oral lesions.</p> <p>Methods</p> <p>Key informant (KI) interviews were conducted with ten clinicians practicing in or around San Juan, Puerto Rico. We then triangulated our KI interview findings with other data sources, including recent literature on oral cancer detection from various geographic areas, current curricula at the University of Puerto Rico Schools of Medicine and Dental Medicine, as well as local health insurance regulations.</p> <p>Results</p> <p>Key informant-identified factors that likely contribute to the detection deficit include: many practitioners are deficient in knowledge regarding oral cancer and precancer; oral cancer screening examinations are limited regarding which patients receive them and the elements included. In Puerto Rico, specialists generally perform oral biopsies, and patient referral can be delayed by various factors, including government-subsidized health insurance, often referred to as Reforma. Reforma-based issues include often inadequate clinician knowledge regarding Reforma requirements/provisions, diagnostic delays related to Reforma bureaucracy, and among primary physicians, a perceived financial disincentive in referring Reforma patients.</p> <p>Conclusions</p> <p>Addressing these issues may be useful in reducing the deficit in detecting oral precancers and early oral cancer in Puerto Rico.</p

Smoking and drinking in relation to oral potentially malignant disorders in Puerto Rico: a case-control study

<p>Abstract</p> <p>Background</p> <p>Oral cancer incidence is high on the Island of Puerto Rico (PR), particularly among males. As part of a larger study conducted in PR, we evaluated smoking and drinking as risk factors for oral potentially malignant disorders (OPMDs).</p> <p>Methods</p> <p>Persons diagnosed with either an OPMD (n = 86) [oral epithelial dysplasia (OED), oral hyperkeratosis/epithelial hyperplasia without OED] or a benign oral tissue condition (n = 155) were identified through PR pathology laboratories. Subjects were interviewed using a standardized, structured questionnaire that obtained information, including detailed histories of smoking and drinking. Odds ratios (ORs) for smoking and drinking in relation to having an OPMD, relative to persons with a benign oral tissue condition, were obtained using logistic regression and adjusted for age, gender, education, fruit/vegetable intake and smoking or drinking.</p> <p>Results</p> <p>For persons with an OPMD and relative to individuals with a benign oral tissue condition, the adjusted OR for current smoking was 4.32 (95% CI: 1.99-9.38), while for former smokers, the OR_adjwas 1.47 (95% CI: 0.67-3.21), each OR_adjrelative to never smokers. With regard to drinking, no adjusted ORs approached statistical significance, and few point estimates exceeded 1.0, whether consumption was defined in terms of ever, current, level (drinks/week), or beverage type.</p> <p>Conclusions</p> <p>In this study, conducted in Puerto Rico, current smoking was a substantial risk factor for OPMDs while former smokers had a considerably reduced risk compared to current smokers. There was little evidence suggesting that alcohol consumption was positively associated with OPMD risk.</p