Stable scalable control of soliton propagation in broadband nonlinear optical waveguides

We develop a method for achieving scalable transmission stabilization and switching of $N$ colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of soliton amplitudes in $N$-sequence transmission is described by a generalized $N$-dimensional predator-prey model. Stability and bifurcation analysis for the predator-prey model are used to obtain simple conditions on the physical parameters for robust transmission stabilization as well as on-off and off-on switching of $M$ out of $N$ soliton sequences. Numerical simulations for single-waveguide transmission with a system of $N$ coupled nonlinear Schr\"odinger equations with $2 \le N \le 4$ show excellent agreement with the predator-prey model's predictions and stable propagation over significantly larger distances compared with other broadband nonlinear single-waveguide systems. Moreover, stable on-off and off-on switching of multiple soliton sequences and stable multiple transmission switching events are demonstrated by the simulations. We discuss the reasons for the robustness and scalability of transmission stabilization and switching in waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss, and explain their advantages compared with other broadband nonlinear waveguides.Comment: 37 pages, 7 figures, Eur. Phys. J. D (accepted

Strong effects of fast collisions between pulsed optical beams in a linear medium with weak cubic loss

We investigate fast collisions between pulsed optical beams in a linear medium with weak cubic loss that arises due to nondegenerate two-photon absorption. We introduce a perturbation method with two small parameters and use it to obtain general formulas for the collision-induced changes in the pulsed-beam's shape and amplitude. Moreover, we use the method to design and characterize collision setups that lead to strong localized and nonlocalized intensity reduction effects. The values of the collision-induced changes in the pulsed-beam's shape in both setups are larger by one to two orders of magnitude compared with the values obtained in previous studies of fast two-pulse collisions. Furthermore, we show that for nonlocalized setups, the graph of the collision-induced amplitude shift vs the difference between the first-order dispersion coefficients for the two pulsed-beams has two local minima. This finding represents the first observation of a deviation of the graph from the common funnel shape that was obtained in all previous studies of fast two-pulse collisions in the presence of weak nonlinear loss. The predictions of our perturbation theory are in good agreement with results of numerical simulations with the perturbed linear propagation model, despite the strong collision-induced effects. Our results can be useful for multisequence optical communication links and for reshaping of pulsed optical beams.Comment: 44 pages, 12 figures. The paper contains a brief description of a generalization of the perturbation approach that was introduced in arXiv:2102.07438 for fast collisions between time independent optical beams. The paper is devoted to an investigation of strong effects in fast collisions between pulsed optical beams, whereas in arXiv:2102.07438, only weak collision-induced effects for time-independent beams were considered

Fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2

We investigate the dynamics of fast two-pulse collisions in linear diffusion-advection systems with weak quadratic loss in spatial dimension 2. We introduce a two-dimensional perturbation method, which generalizes the perturbation method used for studying two-pulse collisions in spatial dimension 1. We then use the generalized perturbation method to show that a fast collision in spatial dimension 2 leads to a change in the pulse shape in the direction transverse to the advection velocity vector. Moreover, we show that in the important case of a separable initial condition, the longitudinal part in the expression for the amplitude shift has a simple universal form, while the transverse part does not. Additionally, we show that anisotropy in the initial condition leads to a complex dependence of the amplitude shift on the orientation angle between the pulses. Our perturbation theory predictions are in very good agreement with results of extensive numerical simulations with the weakly perturbed diffusion-advection model. Thus, our study significantly enhances and generalizes the results of previous works on fast collisions in diffusion-advection systems, which were limited to spatial dimension 1.Comment: The paper presents a perturbation method for fast two-pulse collisions in diffusion-advection systems with weak nonlinear loss in dimension higher than 1. It generalizes the method that was used in arXiv:1702.05583 and arXiv:1808.04323 for the 1-dimensional problem. It complements the method that was presented in arXiv:2102.07438 for the high-dimensional problem in weakly nonlinear optical medi

Area-preserving dynamics of a long slender finger by curvature: a test case for the globally conserved phase ordering

A long and slender finger can serve as a simple ``test bed'' for different phase ordering models. In this work, the globally-conserved, interface-controlled dynamics of a long finger is investigated, analytically and numerically, in two dimensions. An important limit is considered when the finger dynamics are reducible to the area-preserving motion by curvature. A free boundary problem for the finger shape is formulated. An asymptotic perturbation theory is developed that uses the finger aspect ratio as a small parameter. The leading-order approximation is a modification of ``the Mullins finger" (a well-known analytic solution) which width is allowed to slowly vary with time. This time dependence is described, in the leading order, by an exponential law with the characteristic time proportional to the (constant) finger area. The subleading terms of the asymptotic theory are also calculated. Finally, the finger dynamics is investigated numerically, employing the Ginzburg-Landau equation with a global conservation law. The theory is in a very good agreement with the numerical solution.Comment: 8 pages, 4 figures, Latex; corrected typo

Normal scaling in globally conserved interface-controlled coarsening of fractal clusters

Globally conserved interface-controlled coarsening of fractal clusters exhibits dynamic scale invariance and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The sharp-interface limit of this equation is volume preserving motion by mean curvature. The scaled form of the correlation function has a power-law tail accommodating the fractal initial condition. The coarsening length exhibits normal scaling with time. Finally, shrinking of the fractal clusters with time is observed. The difference between global and local conservation is discussed.Comment: 4 pages, 3 eps figure

Occurrence and sources of radium in groundwater associated with oil fields in the southern San Joaquin Valley, California

Author Posting. © American Chemical Society, 2019. This is an open access article published under an ACS AuthorChoice License. The definitive version was published in Environmental Science and Technology 53(16), (2019): 9398-9406, doi:10.1021/acs.est.9b02395.Geochemical data from 40 water wells were used to examine the occurrence and sources of radium (Ra) in groundwater associated with three oil fields in California (Fruitvale, Lost Hills, South Belridge). 226Ra+228Ra activities (range = 0.010–0.51 Bq/L) exceeded the 0.185 Bq/L drinking-water standard in 18% of the wells (not drinking-water wells). Radium activities were correlated with TDS concentrations (p < 0.001, ρ = 0.90, range = 145–15,900 mg/L), Mn + Fe concentrations (p < 0.001, ρ = 0.82, range = <0.005–18.5 mg/L), and pH (p < 0.001, ρ = −0.67, range = 6.2–9.2), indicating Ra in groundwater was influenced by salinity, redox, and pH. Ra-rich groundwater was mixed with up to 45% oil-field water at some locations, primarily infiltrating through unlined disposal ponds, based on Cl, Li, noble-gas, and other data. Yet 228Ra/226Ra ratios in pond-impacted groundwater (median = 3.1) differed from those in oil-field water (median = 0.51). PHREEQC mixing calculations and spatial geochemical variations suggest that the Ra in the oil-field water was removed by coprecipitation with secondary barite and adsorption on Mn–Fe precipitates in the near-pond environment. The saline, organic-rich oil-field water subsequently mobilized Ra from downgradient aquifer sediments via Ra-desorption and Mn/Fe-reduction processes. This study demonstrates that infiltration of oil-field water may leach Ra into groundwater by changing salinity and redox conditions in the subsurface rather than by mixing with a high-Ra source.This article was improved by the reviews of John Izbicki and anonymous reviewers for the journal. This work was funded by the California State Water Resources Control Board’s Regional Groundwater Monitoring in Areas of Oil and Gas Production Program and the USGS Cooperative Water Program. A.V., A.J.K., and Z.W were supported by USDA-NIFA grant (#2017-68007-26308). Any use of trade, firm, or product names is for description purposes only and does not imply endorsement by the U.S. Government

Different paths to the modern state in Europe: the interaction between domestic political economy and interstate competition

Theoretical work on state formation and capacity has focused mostly on early modern Europe and on the experience of western European states during this period. While a number of European states monopolized domestic tax collection and achieved gains in state capacity during the early modern era, for others revenues stagnated or even declined, and these variations motivated alternative hypotheses for determinants of fiscal and state capacity. In this study we test the basic hypotheses in the existing literature making use of the large date set we have compiled for all of the leading states across the continent. We find strong empirical support for two prevailing threads in the literature, arguing respectively that interstate wars and changes in economic structure towards an urbanized economy had positive fiscal impact. Regarding the main point of contention in the theoretical literature, whether it was representative or authoritarian political regimes that facilitated the gains in fiscal capacity, we do not find conclusive evidence that one performed better than the other. Instead, the empirical evidence we have gathered lends supports to the hypothesis that when under pressure of war, the fiscal performance of representative regimes was better in the more urbanized-commercial economies and the fiscal performance of authoritarian regimes was better in rural-agrarian economie

Are proton pump inhibitors the first choice for acute treatment of gastric ulcers? A meta analysis of randomized clinical trials

BACKGROUND: Gastric ulcers are a frequent problem in the United States. Proton pump inhibitors have been shown to increase healing rates and improve clinical symptoms. The objective of this study is to compare gastric ulcer healing rates for patients treated with a proton pump inhibitor (PPI) (omeprazole, rabeprazole, pantoprazole, or lansoprazole), an histamine 2- receptor antagonist (ranitidine) or placebo. METHODS: A literature search was conducted to identify randomized, controlled clinical trials that included a PPI in at least one treatment arm and assessed the gastric ulcer healing rates endoscopically. The healing rates were estimated for each treatment at specific time points, and Rate Ratios (RR) and 95% confidence intervals (CI) were estimated for each trial. RESULTS: Sixteen trials met the inclusion criteria: four compared a PPI versus placebo, nine compared a PPI versus ranitidine (no trials of rabeprazole versus ranitidine met the inclusion criteria), and three compared a newer PPI (lansoprazole, pantoprazole or rabeprazole) versus omeprazole. In relation to ranitidine, the pooled RR of PPIs (lansoprazole, omeprazole and pantoprazole) was 1.33 (95% CI 1.24 to 1.42) at four weeks. In each trial, greater improvement in the studied clinical symptoms was found with the newer PPIs (rabeprazole, pantoprazole and lansoprazole) when compared to omeprazole. CONCLUSION: In this study treatment with PPIs resulted in higher healing rates than ranitidine or placebo. This evidence suggests that the first choice for gastric ulcer treatment for the greater relief of symptoms is one of the newer PPIs

GATE : a simulation toolkit for PET and SPECT

Monte Carlo simulation is an essential tool in emission tomography that can assist in the design of new medical imaging devices, the optimization of acquisition protocols, and the development or assessment of image reconstruction algorithms and correction techniques. GATE, the Geant4 Application for Tomographic Emission, encapsulates the Geant4 libraries to achieve a modular, versatile, scripted simulation toolkit adapted to the field of nuclear medicine. In particular, GATE allows the description of time-dependent phenomena such as source or detector movement, and source decay kinetics. This feature makes it possible to simulate time curves under realistic acquisition conditions and to test dynamic reconstruction algorithms. A public release of GATE licensed under the GNU Lesser General Public License can be downloaded at the address http://www-lphe.epfl.ch/GATE/