Inverse medium problem for a singular contrast

We consider an inverse medium problem in two- and three-dimensional cases. Namely, we investigate the problem of reconstruction of unknown compactly supported refractive index (contrast) from L-2 with a fixed positive wave number. The proof is based on the new estimates for the Green-Faddeev function in L-infinity space. The main goal of this work is to prove a uniqueness result in the two- and three-dimensional cases and to discuss some possible constructive methods for solving the problem. Finally, we present some numerical examples to demonstrate the results in two dimensions. Published under license by AIP Publishing.Peer reviewe

Topological Coherent Modes for Nonlinear Schr\"odinger Equation

Nonlinear Schr\"odinger equation, complemented by a confining potential, possesses a discrete set of stationary solutions. These are called coherent modes, since the nonlinear Schr\"odinger equation describes coherent states. Such modes are also named topological because the solutions corresponding to different spectral levels have principally different spatial dependences. The theory of resonant excitation of these topological coherent modes is presented. The method of multiscale averaging is employed in deriving the evolution equations for resonant guiding centers. A rigorous qualitative analysis for these nonlinear differential equations is given. Temporal behaviour of fractional populations is illustrated by numerical solutions.Comment: 14 pages, Latex, no figure

Increased power generation in supercapacitive microbial fuel cell stack using Fe-N-C cathode catalyst

The anode and cathode electrodes of a microbial fuel cell (MFC) stack, composed of 28 single MFCs, were used as the negative and positive electrodes, respectively of an internal self-charged supercapacitor. Particularly, carbon veil was used as the negative electrode and activated carbon with a Fe-based catalyst as the positive electrode. The red-ox reactions on the anode and cathode, self-charged these electrodes creating an internal electrochemical double layer capacitor. Galvanostatic discharges were performed at different current and time pulses. Supercapacitive-MFC (SC-MFC) was also tested at four different solution conductivities. SC-MFC had an equivalent series resistance (ESR) decreasing from 6.00 Ω to 3.42 Ω in four solutions with conductivity between 2.5 mScm−1 and 40 mScm−1. The ohmic resistance of the positive electrode corresponded to 75–80% of the overall ESR. The highest performance was achieved with a solution conductivity of 40 mS cm−1 and this was due to the positive electrode potential enhancement for the utilization of Fe-based catalysts. Maximum power was 36.9mW (36.9Wm−3) that decreased with increasing pulse time. SC-MFC was subjected to 4520 cycles (8 days) with a pulse time of 5 s (ipulse 55 mA) and a self-recharging time of 150 s showing robust reproducibility

Wave packet evolution approach to ionization of hydrogen molecular ion by fast electrons

The multiply differential cross section of the ionization of hydrogen molecular ion by fast electron impact is calculated by a direct approach, which involves the reduction of the initial 6D Schr\"{o}dinger equation to a 3D evolution problem followed by the modeling of the wave packet dynamics. This approach avoids the use of stationary Coulomb two-centre functions of the continuous spectrum of the ejected electron which demands cumbersome calculations. The results obtained, after verification of the procedure in the case atomic hydrogen, reveal interesting mechanisms in the case of small scattering angles.Comment: 7 pages, 8 Postscript figure

Symmetry Influence on the Rotation of Molecules in Crystals

© 2017 American Chemical Society. It was shown that rotational mobility of molecules in crystals is affected by the symmetry of their surroundings. A hypothesis was proposed for the discovered correlation. Three cases are possible for the location of the molecules with respect to the crystallographic symmetry elements: I - the location in a general position; II - the location in special positions without symmetry disordering; III - the location in special positions with symmetry disordering. According to the experimental data, the rotation barrier heights at the location of the molecules in cases I and III are lower than in case II. This fact is explained by the amplitude and p hase shifts of the rotational energy profiles of two parts of the molecule in case I and by increasing the number of minima on the rotation barrier profile at disordering the molecules by symmetry in case III. The way is proposed for lowering the rotational barrier of molecules in crystals

INFLUENCE OF THERAPY UPON LPS-INDUCED CYTOKINE SECRETION BY THE BLOOD-DERIVED INNATE IMMUNITY CELLS OF THE BRONCHIAL ASTHMA PATIENTS

Bronchial asthma (BA) is the most widespread chronic inflammatory disease. Since BA is associated with a systemic inflammation state, a comprehensive study of its effect in this disease, and influence of pathogenetic therapy should be performed, by studying the whole blood cytokine status of the patients suffering with BA. The cells from respiratory tract in acute-phase BA patients may produce pro-, as well as anti-inflammatory mediators. The anti-inflammatory mediators are able to suppress activity of immune cells in peripheral blood. Thus, the aim of present study was to evaluate eventual inflammation-associated and functional activity of immune cells from the patients’ peripheral blood in BA and following appropriate therapy. Bacterial lipopolysaccharide (LPS) a classical pro-inflammatory agent. We have studied an LPSinduced cytokine-induced ex vivo secretion model by peripheral blood immune cells, as a relevant test for their functional activity. The LPS-induced responses of whole blood cells from patients with proven BA diagnosis have been studied at pre-treatment time points, and following two weeks of basic anti-inflammatory therapy. According to clinical indications, the antagonists of CysLTR1, or combinations of glucocorticosteroids and β-adrenoreceptor agonists were administered by inhalation to BA patients. LPS-induced production of TNFα, IL-6, IL-8 (at 6 h) and IFNγ, IL-17A or IL-1β (at 24 h) by whole blood cells from BA patients or healthy volunteers has been assessed by ELISA technique. The cytokine production from non-stimulated whole blood cells from BA patients and healthy volunteers were used as the baseline control. IL-4 concentrations in plasma of BA patients and healthy volunteers were also measured. We have shown a decrease of IL-6 production in control blood samples from BA patients after two weeks of therapy. This may indicate the attenuation of the observed inflammatory process. The therapy applied did not influence the background levels and LPS-induced secretion of IL-1β, IL-1ra, IFNγ, and IL-8 in whole blood samples from BA patients. IL-4 plasma levels in BA patients were not changed after two weeks of therapy. It has been shown that whole blood from BA patients produced less TNFα and IL-8, both in control samples, and during their response to LPS, than the values obtained in healthy volunteers. These findings are in agreement with a notion that BA causes partial depression of innate immune cells activity. The increased LPS-induced TNFα secretion by the whole blood cells from BA patients has been observed following two weeks of basic anti-inflammatory therapy. We suggest that the increased LPS-induced TNFα secretion could be explained by partial restoration of peripheral blood immune cell activity associated with anti-inflammatory BA therapy. To elucidate the mechanism of increased LPS-induced TNFα secretion, we have estimated whole blood concentration of soluble CD14 (sCD14) in BA patients. No significant differences between sCD14 concentrations have been found. Obtained result presume existence of sCD14-independent mechanism of TNFα regulation by whole blood cells in response on LPS which may occur during anti-inflammatory therapy of BA. We suppose that basic anti-inflammatory therapy of BA does not simply reduce IL-6 concentration in peripheral blood, but may also partially restore the activity of innate immune cells in BA patients