Resonant generation and refraction of dispersive shock waves in one-dimensional nonlinear Schrödinger flows

In the Thesis, two important theoretical problems arising in the theory of one-dimensional defocusing nonlinear Schrödinger (NLS) flows are investigated analytically and numerically: (i) the resonant generation of dispersive shock waves (DSWs) in one-dimensional NLS flow past a broad repulsive penetrable barrier; and (ii) the interaction of counter-propagating DSW and a simple rarefaction wave (RW), which is referred to as the DSW refraction problem. The first problem is motivated by the recent experimental observations of dark soliton radiation in a cigar-shaped BEC by sweeping through it a localised repulsive potential; the second problem represents a dispersive-hydrodynamic counterpart of the classical gas-dynamics problem of the shock wave refraction on a RW, and, apart from its theoretical significance could also find applications in superfluid dynamics. Both problems also naturally arise in nonlinear optics, where the NLS equation is a standard mathematical model and the `superfluid dynamics of light' can be used for an all-optical modelling of BEC flows. The main results of the Thesis are as follows: (i) In the problem of the transcritical flow of a BEC through a wide repulsive penetrable barrier an asymptotic analytical description of the arising wave pattern is developed using the combination of the localised ``hydraulic'' solution of the 1D Gross-Pitaevskii (GP) equation with repulsion (the defocusing NLS equation with an added external potential) and the appropriate exact solutions of the Whitham-NLS modulation equations describing the resolution of the upstream and downstream discontinuities through DSWs. We show that the downstream DSW effectively represents the train of dark solitons, which can be associated with the excitations observed experimentally by Engels and Atherton (2008). (ii) The refraction of a DSW due to its head-on collision with the centred RW is considered in the frameworks of two one-dimensional defocusing NLS models: the standard cubic NLS equation and the NLS equation with saturable nonlinearity, the latter being a standard model for the light propagation through photorefractive optical crystals. For the cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain key parameters of the DSW refraction. In both problems, we undertake a detailed analysis of the flow structure for different parametric regimes and calculate physical quantities characterising the output flows in terms of relevant input parameters. Our modulation theory analytical results are supported by direct numerical simulations of the corresponding full dispersive initial value problems (IVP)

Intestinal microbiota transplant -current state of knowledge

Abstract Faecal microbiota transplantation (FMT) has induced a lot scientific interest and hopes for the last couple of years. FMT has been approved as a treatment of recurrent Clostridium difficile colitis. Highly sophisticated molecular DNA identification methods have been used to assess the healthy human microbiome as well as its disturbances in several diseases. The metabolic and immunologic functions of the microbiome have become more clear and understandable. A lot of pathological changes, such as production of short-chain fatty acids or components of the inflammatory cascade, caused by changes in microbiome diversity, variability and richness have been observed among patients suffering from inflammatory bowel diseases, irritable bowel syndrome, type 2 diabetes or rheumatoid arthritis. The published clinical results are encouraging, but still there is huge demand for FMT controlled clinical trials

Refraction of dispersive shock waves

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave, often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of the defocusing nonlinear Schrödinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem

Quasi 1D Bose-Einstein condensate flow past a nonlinear barrier

The problem of a quasi 1D {\it repulsive} BEC flow past through a nonlinear barrier is investigated. Two types of nonlinear barriers are considered, wide and short range ones. Steady state solutions for the BEC moving through a wide repulsive barrier and critical velocities have been found using hydrodynamical approach to the 1D Gross-Pitaevskii equation. It is shown that in contrast to the linear barrier case, for a wide {\it nonlinear} barrier an interval of velocities $0 < v < v_-$ {\it always} exists, where the flow is superfluid regardless of the barrier potential strength. For the case of the $\delta$ function-like barrier, below a critical velocity two steady solutions exist, stable and unstable one. An unstable solution is shown to decay into a gray soliton moving upstream and a stable solution. The decay is accompanied by a dispersive shock wave propagating downstream in front of the barrier.Comment: 6 pages, 7 figures, extended abstract, revised arguments in Sects 2,3 results unchanged, added reference

HIV-1 Subtype D Infections among Caucasians from Northwestern Poland—Phylogenetic and Clinical Analysis

Background: HIV-1 subtype D infections, which are associated with a faster rate of progression and lymphocyte CD4 decline, cognitive deficit and higher mortality, have rarely been found in native Europeans. In Northwestern Poland, however, infections with this subtype had been identified. This study aimed to analyze the sequence and clinical data for patients with subtype D using molecular phylogeography and identify transmission clusters and ancestry, as well as drug resistance, baseline HIV tropism and antiretroviral treatment efficacy. Methods: Phylogenetic analyses of local HIV-1 subtype D sequences were performed, with time to the most recent common ancestor inferred using Bayesian modeling. Sequence and drug resistance data were linked with the clinical and epidemiological information. Results: Subtype D was found in 24 non-immigrant Caucasian, heterosexually infected patients (75 % of females, median age at diagnosis of 49.5 years; IQR: 29–56 years). Partial pol sequences clustered monophyletically with the clades of Ugandan origin and no evidence of transmission from other European countries was found. Time to the most common recent ancestor was 1989.24 (95 % HPD: 1968.83–1994.46). Baseline drug resistance to nucleoside reverse transcriptase inhibitors was observed in 54.5 % of cases (mutations: M41L, K103N, T215S/D) with evidence of clustering, no baseline integrase or protease resistance and infrequent non-R5 tropism (13.6%). Virologic failure was observed in 60 % of cases an

Transcritical flow of a Bose-Einstein condensate through a penetrable barrier

The problem of the transcritical flow of a Bose-Einstein condensate through a wide repulsive penetrable barrier is studied analytically using the combination of the localized "hydraulic" solution of the 1D Gross-Pitaevskii equation and the solutions of the Whitham modulation equations describing the resolution of the upstream and downstream discontinuities through dispersive shocks. It is shown that within the physically reasonable range of parameters the downstream dispersive shock is attached to the barrier and effectively represents the train of very slow dark solitons, which can be observed in experiments. The rate of the soliton emission, the amplitudes of the solitons in the train and the drag force are determined in terms of the BEC oncoming flow velocity and the strength of the potential barrier. A good agreement with direct numerical solutions is demonstrated. Connection with recent experiments is discussed.Comment: Revised version. 22 pages, 24 figures. Accepted for publication in Phys. Rev.

Adolescent Crash Rates and School Start Times in Two Central Virginia Counties, 2009-2011: A Follow-Up Study to a Southeastern Virginia Study, 2007-2008

Background and Objective: Early high school start times (EHSST) may lead to sleep loss in adolescents ( teens ), thus resulting in higher crash rates. (Vorona et al., 2011). In this study, we examined two other adjacent Virginia counties for the two years subsequent to the above-mentioned study. We again hypothesized that teens from jurisdictions with EHSST (versus later) experience higher crash rates. Methods: Virginia Department of Motor Vehicles supplied de-identified aggregate data on weekday crashes and time-of- day for 16-18 year old (teen) and adult drivers for school years 2009-2010 and 2010-2011 in Henrico and Chesterfield Counties (HC and CC, respectively). Teen crash rates for counties with early (CC) versus later (HC) school start-times were compared using two-sample Z-tests and these compared to adult crash rates using pair-wise tests. Results: Chesterfield teens manifested a statistically higher crash rate of 48.8/1,000 licensed drivers versus Henrico\u27s 37.9/1,000 (p = 0.04) for 2009-2010. For 2010-2011, CC 16-17 year old teens demonstrated a statistically significant higher crash rate (53.2/1,000 versus 42.0/1,000), while for 16-18 teens a similar trend was found, albeit nonsignificant (p = 0.09). Crash peaks occurred 1 hour earlier in the morning and 2 hours earlier in the afternoon in Chesterfield, consistent with commute times. Post hoc analyses found significantly more run-off road crashes to the right (potentially sleep-related) in Chesterfield teens. Adult crash rates and traffic congestion did not differ between counties. Conclusions: Higher teen crash rates occurred in jurisdictions with EHSST, as in our prior study. This study contributes to and extends existing data on preventable teen crashes and high school start times

Risk of All-Cause Mortality in HIV Infected Patients Is Associated with Clinical, Immunologic Predictors and the CCR5 Δ32 Deletion

OBJECTIVE: Investigation of the interplay between the CCR5 Δ32/wt genotype and demographic, epidemiological, clinical and immunological factors associated with mortality in the cART era. DESIGN: Longitudinal data from 507 HIV-infected patients following the Δ32 allele detection were analyzed. METHODS: Cumulative 15 years mortality was calculated using Kaplan-Meyer methodology. Hazard ratios were estimated using univariate Cox models. Basing on Akakie information criteria and statistical significance multivariate Cox model was constructed and effect plots presenting adjusted hazard ratio time-dependency were drawn. Analysis of the association of all-cause mortality and CCR5 Δ32/wt genotype prior to the antiretroviral treatment (cART) initiation (n = 507) and on the therapy (n = 422) was also performed. RESULTS: A mortality rate of 2.66 (CI 2.57-3.19) per 100 person-years was observed. Univariate analysis factors modifying the risk of death included the CCR5 genotype, gender, history of cART, AIDS diagnosis and also CD4 lymphocyte nadir, zenith, the latest CD4 count and stable levels >500 cells/µl. For multivariate analysis the following predictors were selected: CCR5 genotype (HR for wt/wt 2.53, CI 1.16-5.53, p = 0.02), gender (HR for males 1.91, 95%CI 1.1-3.36, p = 0.023), introduction of combined antiretroviral treatment (HR 4.85, CI 3.0-7.89, if untreated or treated <1 month, p<0.0001) CD4 count of 500 cells/µl for six months or more (HR 4.16, CI 1.95-8.88 if not achieved, p = 0.028), the latest CD4 count (HR 5.44, CI 3.39-8.74 for <100 cells/µl, p<0.0001) and history of AIDS (HR 1.69, CI 1.03-2.79, p = 0.039). Among untreated individuals the Δ32/wt genotype was associated with notably better survival (p = 0.026), while among cART treated individuals the Δ32 mutation did not correlate significantly with higher survival rates (p = 0.23). CONCLUSIONS: The Δ32 CCR5 allele is associated with a reduction of the risk of all-cause mortality in HIV (+) patients alongside clinical and immunologic predictors such as AIDS, history of cART, lymphocyte CD4 cell count and gender

Serum leptin and adiponectin concentrations in patients infected with human immunodeficiency virus type 1 (HIV-1) on antiretroviral therapy

Efektem ubocznym skojarzonej terapii antyretrowirusowej (STA) jest zespół lipodystrofii z dyslipidemią oraz insulinoopornością. Cel pracy: określenie wpływu STA na stężenia leptyny i adiponektyny w powiązaniu ze zmianami poziomu lipidów krwi chorych zakażonych HIV leczonych antyretrowirusowo. U 56 chorych HIV(+) określono BMI i oznaczono we krwi stężenia leptyny, adiponektyny oraz triglicerydów, cholesterolu całkowitego, HDL- i LDL-cholesterolu przed oraz w trakcie STA, trwającej średnio 38,4 &plusmn; 13,2 miesięcy. Stwierdzono istotny (p = 0,0268) wzrost BMI (odpowiednio 22,6 &plusmn; 3,3 przed i 23,5 &plusmn; 3,4 kg/m2 po leczeniu) oraz analizowanych parametrów gospodarki lipidowej. Średnia stężeń adiponektyny u chorych leczonych była istotnie niższa (7,256 &plusmn; 3,551 &micro;g/ml) od średniej wartości sprzed rozpoczęcia terapii (8,395 &plusmn; 3,568 &micro;g/ml; p = 0,0011). Średnie stężeń leptyny nie różniły się istotnie (przed leczeniem 3,721 &plusmn; 0,347 log10; na leczeniu 3,1737 &plusmn; 0,353 log10). Zarówno przed, jak i w trakcie STA stwierdzono istotną, dodatnią korelację pomiędzy BMI a stężeniami leptyny (r = 0,5333; p < 0,0001), natomiast ujemną korelację pomiędzy stężeniami adiponektyny i leptyny (r = -0,2677; p = 0,042). Przed leczeniem nie wykazano istotnej korelacji pomiędzy stężeniami leptyny i adiponektyny w surowicy krwi a stężeniami lipidów. Stwierdzany w trakcie STA spadek stężenia adiponektyny korelował ujemnie z poziomami cholesterolu całkowitego (r = -0,2912; p = 0,0310) i LDL-cholesterolu (r = -0,310; p = 0,0225). STA trwająca ponad 2 lata spowodowała zmniejszenie stężenia adiponektyny, przy braku wpływu na stężenie leptyny u badanych chorych. Wzrost poziomu cholesterolu całkowitego i LDL-cholesterolu korelujący ze spadkiem stężenia adiponektyny potwierdza indukowanie przez STA zaburzeń metabolicznych zwiększających ryzyko rozwoju miażdżycy i jej następstw.The lipodystrophy syndrome with dyslipidaemia and insuline resistance is side-effect of combined antiretroviral therapy (CART). Aim of the study: to describe the influence of CART on leptin and adiponectin concentration in connection with lipids levels in HIV-infected patients on antiretroviral therapy.BMI, serum leptin, adiponectin, triglycerides, total cholesterol, HDL- and LDL-cholesterol concentrations were measured in 56 HIV(+) patients before and on CART; average of treatment duration 38.4 &plusmn; 13.2 months. Significant increase of BMI (p=0.0268) of (22.6 &plusmn; 3.3 before and 23.5 &plusmn; 3.4 kg/m2 on therapy, respectively) and all analyzed lipids were found. Mean adiponectin concentration in treated patients was significantly (7.256 &plusmn; 3.551 &micro;g/ml) lower than mean value before treatment (8.395 &plusmn; 3.568 &micro;g/ml; p=0.0011). Mean values of leptin concentrations did not differ significantly (before therapy 3.721 &plusmn; 0.347 log10; on therapy 3.1737 &plusmn; 0.353 log10). Significant positive correlation between BMI and leptin concentrations was found before, as well as during CART (r=0.5333;