Soliton Interactions in Perturbed Nonlinear Schroedinger Equations

We use multiscale perturbation theory in conjunction with the inverse scattering transform to study the interaction of a number of solitons of the cubic nonlinear Schroedinger equation under the influence of a small correction to the nonlinear potential. We assume that the solitons are all moving with the same velocity at the initial instant; this maximizes the effect each soliton has on the others as a consequence of the perturbation. Over the long time scales that we consider, the amplitudes of the solitons remain fixed, while their center of mass coordinates obey Newton's equations with a force law for which we present an integral formula. For the interaction of two solitons with a quintic perturbation term we present more details since symmetries -- one related to the form of the perturbation and one related to the small number of particles involved -- allow the problem to be reduced to a one-dimensional one with a single parameter, an effective mass. The main results include calculations of the binding energy and oscillation frequency of nearby solitons in the stable case when the perturbation is an attractive correction to the potential and of the asymptotic "ejection" velocity in the unstable case. Numerical experiments illustrate the accuracy of the perturbative calculations and indicate their range of validity.Comment: 28 pages, 7 figures, Submitted to Phys Rev E Revised: 21 pages, 6 figures, To appear in Phys Rev E (many displayed equations moved inline to shorten manuscript

A regolith lead isoscape of Australia

We present the first national-scale lead (Pb) isotope maps of Australia based on surface regolith for five isotope ratios, 206Pb/204Pb, 207Pb/204Pb, 208Pb/204Pb, 207Pb/206Pb, and 208Pb/206Pb, determined by single-collector sector field inductively coupled plasma mass spectrometry after an ammonium acetate leach followed by aqua regia digestion. The dataset is underpinned principally by the National Geochemical Survey of Australia (NGSA) archived floodplain sediment samples. We analysed 1219 samples (0–10 cm depth, &lt;2 mm grain size), collected near the outlet of 1119 large catchments covering 5.647×106 km2 (∼75 % of Australia). The samples consist of mixtures of the dominant soils and rocks weathering in their respective catchments (and possibly those upstream) and are therefore assumed to form a reasonable representation of the average isotopic signature of those catchments. This assumption was tested in one of the NGSA catchments, within which 12 similar samples were also taken; results show that the Pb isotope ratios of the NGSA catchment outlet sediment sample are close to the average of the 12 upstream sub-catchment samples. National minimum, median, and maximum values were 15.56, 18.84, and 30.64 for 206Pb/204Pb; 14.36, 15.69, and 18.01 for 207Pb/204Pb; 33.56, 38.99, and 48.87 for 208Pb/204Pb; 0.5880, 0.8318, and 0.9847 for 207Pb/206Pb; and 1.4149, 2.0665, and 2.3002 for 208Pb/206Pb, respectively. The new dataset was compared with published bedrock and ore Pb isotope data, and it was found to dependably represent crustal elements of various ages from Archaean to Phanerozoic. This suggests that floodplain sediment samples are a suitable proxy for basement and basin geology at this scale, despite various degrees of transport, mixing, and weathering experienced in the regolith environment, locally over protracted periods of time. An example of atmospheric Pb contamination around Port Pirie, South Australia, where a Pb smelter has operated since the 1890s, is shown to illustrate potential environmental applications of this new dataset. Other applications may include elucidating details of Australian crustal evolution and mineralisation-related investigations. The new regolith Pb isotope dataset for Australia is publicly available (Desem et al., 2023; https://doi.org/10.26186/5ea8f6fd3de64).</p

Experimental feasibility of measuring the gravitational redshift of light using dispersion in optical fibers

This paper describes a new class of experiments that use dispersion in optical fibers to convert the gravitational frequency shift of light into a measurable phase shift or time delay. Two conceptual models are explored. In the first model, long counter-propagating pulses are used in a vertical fiber optic Sagnac interferometer. The second model uses optical solitons in vertically separated fiber optic storage rings. We discuss the feasibility of using such an instrument to make a high precision measurement of the gravitational frequency shift of light.Comment: 11 pages, 12 figure

Stability of stationary states in the cubic nonlinear Schroedinger equation: applications to the Bose-Einstein condensate

The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a harmonic potential. Our comprehensive studies emphasize physical interpretations useful to experimentalists. Perturbation by stochastic white noise, phase engineering, and higher order nonlinearity are considered. We treat both attractive and repulsive nonlinearity and illustrate the soliton-train nature of the stationary states.Comment: 9 pages, 11 figure

Potential of novel Mycobacterium tuberculosis infection phase-dependent antigens in the diagnosis of TB disease in a high burden setting

<p>Abstract</p> <p>Background</p> <p>Confirming tuberculosis (TB) disease in suspects in resource limited settings is challenging and calls for the development of more suitable diagnostic tools. Different <it>Mycobacterium tuberculosis (M.tb) </it>infection phase-dependent antigens may be differentially recognized in infected and diseased individuals and therefore useful as diagnostic tools for differentiating between <it>M.tb </it>infection states. In this study, we assessed the diagnostic potential of 118 different <it>M.tb </it>infection phase-dependent antigens in TB patients and household contacts (HHCs) in a high-burden setting.</p> <p>Methods</p> <p>Antigens were evaluated using the 7-day whole blood culture technique in 23 pulmonary TB patients and in 19 to 21 HHCs (total n = 101), who were recruited from a high-TB incidence community in Cape Town, South Africa. Interferon-gamma (IFN-γ) levels in culture supernatants were determined by ELISA.</p> <p>Results</p> <p>Eight classical TB vaccine candidate antigens, 51 DosR regulon encoded antigens, 23 TB reactivation antigens, 5 TB resuscitation promoting factors (rpfs), 6 starvation and 24 other stress response-associated TB antigens were evaluated in the study. The most promising antigens for ascertaining active TB were the rpfs (Rv0867c, Rv2389c, Rv2450c, Rv1009 and Rv1884c), with Areas under the receiver operating characteristics curves (AUCs) between 0.72 and 0.80. A combination of <it>M.tb </it>specific ESAT-6/CFP-10 fusion protein, Rv2624c and Rv0867c accurately predicted 73% of the TB patients and 80% of the non-TB cases after cross validation.</p> <p>Conclusions</p> <p>IFN-γ responses to TB rpfs show promise as TB diagnostic candidates and should be evaluated further for discrimination between <it>M.tb </it>infection states.</p