Analytic solutions of the Madelung equation

We present analytic self-similar solutions for the one, two and three dimensional Madelung hydrodynamical equation for a free particle. There is a direct connection between the zeros of the Madelung fluid density and the magnitude of the quantum potential.Comment: 10 pages, 3 figure

Lissajous curves with a finite sum of prime number frequencies

The Ulam spiral inspired us to calculate and present Lissajous curves where the orthogonally added functions are a finite sum of sinus and cosines functions with consecutive prime number frequencies.Comment: 5 pages and 4 figure

Angular distribution in two-photon double ionization of helium by intense attosecond soft X-ray pulses

We investigate two-photon double ionization of helium by intense ($10^{15} W/cm^2$) ultrashort ($\approx 300$ as) soft X-ray pulses (E = 91.6 eV). The time-dependent two-electron Schr\"odinger equation is solved using a coupled channel method. We show that for ultrashort pulses the angular distribution of ejected electrons depends on the pulse duration and provides novel insights into the role of electron correlations in the two-electron photoemission process. The angular distribution at energies near the ``independent electron'' peaks is close to dipolar while it acquires in the ``valley'' of correlated emission a significant quadrupolar component within a few hundred attoseconds.Comment: 17 pages, 6 fig

Scaling Hydrodynamical Evolution of a Gravitating Dark-fluid Universe

We present a dark fluid model which contains the general linear equation of state including the gravitation term. The obtained spherical symmetric Euler equation and the continuity equation was investigated with the Sedov-type time-dependent self-similar {\it ansatz} which is capable to describe physically relevant diffusive and dispersive solutions. %The role of the parameter in the equation of state is investigated. As results the space and time dependent fluid density and radial velocity fields are presented and analyzed. Additionally, the role of the initial velocity on the kinetic and total energy densities of the fluid is discussed.Comment: 8 pages and 5 figure

Diatomic molecule in a strong infrared laser field: level-shifts and bond-length change due to laser-dressed Morse potential

We present a general mathematical procedure to handle interactions described by a Morse potential in the presence of a strong harmonic excitation. We account for permanent and field-induced terms and their gradients in the dipole moment function, and we derive analytic formulae for the bond-length change and for the shifted energy eigenvalues of the vibrations, by using the Kramers-Henneberger frame. We apply these results to the important cases of $\mathrm{H}_{2}$ and $\mathrm{LiH}$, driven by a near- or mid-infrared laser in the $10^{13}$ $\mathrm{ W/cm^2}$ intensity range

Analytic self-similar solutions of the Kardar-Parisi-Zhang interface growing equation with various noise terms

The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation with the self-similar ansatz is analyzed. As a new feature additional analytic terms are added. From the mathematical point of view, these can be considered as various noise distribution functions. Six different cases were investigated among others Gaussian, Lorentzian, white or even pink noise. Analytic solutions are evaluated and analyzed for all cases. All results are expressible with various special functions like Kummer, Heun, Whittaker or error functions showing a very rich mathematical structure with some common general characteristics

Homogeneous bubble nucleation limit of mercury under the normal working conditions of the planned European Spallation Source

In spallation neutron sources, liquid mercury is the subject of big thermal and pressure shocks, upon adsorbing the proton beam. These changes can cause unstable bubbles in the liquid, which can damage the structural material. While there are methods to deal with the pressure shock, the local temperature shock cannot be avoided. In our paper we calculated the work of the critical cluster formation (i.e. for mercury micro-bubbles) together with the rate of their formation (nucleation rate). It is shown that the homogeneous nucleation rates are very low even after adsorbing several proton pulses, therefore the probability of temperature induced homogeneous bubble nucleation is negligible.Comment: 22 Pages, 11 figures, one of them is colour, we plan to publish it in Eur. Phys. J.

Prognostic impact of reduced connexin43 expression and gap junction coupling of neoplastic stromal cells in giant cell tumor of bone

Missense mutations of the GJA1 gene encoding the gap junction channel protein connexin43 (Cx43) cause bone malformations resulting in oculodentodigital dysplasia (ODDD), while GJA1 null and ODDD mutant mice develop osteopenia. In this study we investigated Cx43 expression and channel functions in giant cell tumor of bone (GCTB), a locally aggressive osteolytic lesion with uncertain progression. Cx43 protein levels assessed by immunohistochemistry were correlated with GCTB cell types, clinico-radiological stages and progression free survival in tissue microarrays of 89 primary and 34 recurrent GCTB cases. Cx43 expression, phosphorylation, subcellular distribution and gap junction coupling was also investigated and compared between cultured neoplastic GCTB stromal cells and bone marow stromal cells or HDFa fibroblasts as a control. In GCTB tissues, most Cx43 was produced by CD163 negative neoplastic stromal cells and less by CD163 positive reactive monocytes/macrophages or by giant cells. Significantly less Cx43 was detected in alpha-smooth muscle actin positive than alpha-smooth muscle actin negative stromal cells and in osteoclast-rich tumor nests than in the adjacent reactive stroma. Progressively reduced Cx43 production in GCTB was significantly linked to advanced clinico-radiological stages and worse progression free survival. In neoplastic GCTB stromal cell cultures most Cx43 protein was localized in the paranuclear-Golgi region, while it was concentrated in the cell membranes both in bone marrow stromal cells and HDFa fibroblasts. In Western blots, alkaline phosphatase sensitive bands, linked to serine residues (Ser369, Ser372 or Ser373) detected in control cells, were missing in GCTB stromal cells. Defective cell membrane localization of Cx43 channels was in line with the significantly reduced transfer of the 622 Da fluorescing calcein dye between GCTB stromal cells. Our results show that significant downregulation of Cx43 expression and gap junction coupling in neoplastic stromal cells are associated with the clinical progression and worse prognosis in GCTB

Omecamtiv mecarbil in chronic heart failure with reduced ejection fraction, GALACTIC‐HF: baseline characteristics and comparison with contemporary clinical trials

Aims: The safety and efficacy of the novel selective cardiac myosin activator, omecamtiv mecarbil, in patients with heart failure with reduced ejection fraction (HFrEF) is tested in the Global Approach to Lowering Adverse Cardiac outcomes Through Improving Contractility in Heart Failure (GALACTIC‐HF) trial. Here we describe the baseline characteristics of participants in GALACTIC‐HF and how these compare with other contemporary trials. Methods and Results: Adults with established HFrEF, New York Heart Association functional class (NYHA) ≥ II, EF ≤35%, elevated natriuretic peptides and either current hospitalization for HF or history of hospitalization/ emergency department visit for HF within a year were randomized to either placebo or omecamtiv mecarbil (pharmacokinetic‐guided dosing: 25, 37.5 or 50 mg bid). 8256 patients [male (79%), non‐white (22%), mean age 65 years] were enrolled with a mean EF 27%, ischemic etiology in 54%, NYHA II 53% and III/IV 47%, and median NT‐proBNP 1971 pg/mL. HF therapies at baseline were among the most effectively employed in contemporary HF trials. GALACTIC‐HF randomized patients representative of recent HF registries and trials with substantial numbers of patients also having characteristics understudied in previous trials including more from North America (n = 1386), enrolled as inpatients (n = 2084), systolic blood pressure < 100 mmHg (n = 1127), estimated glomerular filtration rate < 30 mL/min/1.73 m2 (n = 528), and treated with sacubitril‐valsartan at baseline (n = 1594). Conclusions: GALACTIC‐HF enrolled a well‐treated, high‐risk population from both inpatient and outpatient settings, which will provide a definitive evaluation of the efficacy and safety of this novel therapy, as well as informing its potential future implementation

Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form

In the present study a particular case of Gross-Pitaevskii or nonlinear Schrödinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation. The obtained system of differential equations is highly nonlinear. Regarding the solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case