Unbalanced superconductivity induced by the constant electron-phonon coupling on a square lattice

In the present paper, we analyze the properties of the unbalanced superconducting state on a square lattice with the constant value of the electron-phonon coupling function. We conduct our analysis in the framework of the Eliashberg formalism, explicitly considering {\bf k}-dependence of the electron and phonon dispersion relations. It is found that the balanced superconducting state does not induce itself in the system due to the high value of the electron effective mass. However, in the unbalanced case the thermodynamic properties of the superconducting condensate can be distinctly different from the predictions of the Bardeen-Cooper-Schieffer theory; when the coupling constant value in the diagonal channel of the self-energy is diminished comparing to the non-diagonal channel. This is due to the reduced dimensionality of the tested system and the strong-coupling effects included in the Eliashberg formalism.Comment: 7 pages, 4 figure

The unbalanced phonon-induced superconducting state on a square lattice beyond the static boundary

The paper presents our verification of induction of the superconducting state on a square lattice by the linear electron-phonon interaction for values of the unbalance parameter ($\gamma=\lambda_{D}/\lambda_{ND}$) less than $\gamma_{C}=0.42$. Symbols $\lambda_{D}$ and $\lambda_{ND}$ denote the values of the coupling constant in the diagonal and the non-diagonal channel of the self-energy. Calculations were carried out using the Eliashberg equations, in which the order parameter ($\Delta_{\bf k}\left(i\omega_{n}\right)$) and the wave function renormalising factor ($Z_{\bf k}\left(i\omega_{n}\right)$) depend explicitly on the Matsubara frequency ($\omega_{n}$) and the wave vector (${\bf k}$). The value of $\gamma_{C}$ in the static boundary ($\Delta_{\bf k}\left(i\omega_{n}\right)\rightarrow \Delta_{\bf k}\left(i\omega_{n=1}\right)$), equal to ($0.93$), is significantly greater than the obtained limit value of $0.42$. Values of the thermodynamic functions of the superconducting state determined for our assumptions are significantly different from the values calculated in accordance with the BCS theory. The results were obtained for the electron-phonon interaction function explicitly dependent on the momentum transfer between electron states.Comment: 12 pages, 9 figure

The Araucaria Project: The distance to the Small Magellanic Cloud from near infrared photometry of Type~II Cepheids

We have obtained deep near infrared J- and K-band observations of 14 BL Herculis and 5 W Virginis SMC stars from the OGLE III survey with the ESO New Technology Telescope equipped with the SOFI infrared camera. From these observations, period-luminosity (P-L) relations in the J and Ks 2MASS bands were derived. The slopes of the K and J band relations of -2.15 +- 0.19 and -1.95 +- 0.24, respectively, agree very well with the corresponding slopes derived previously for population II Cepheids in globular clusters, Galactic bulge and in the Large Magellanic Cloud. The distance modulus to the SMC obtained from our data using P-L relation derived for globular cluster Cepheids equals 18.85 +- 0.07 (statistical) +- 0.07 (systematic without including potential metallicity effect), which within the uncertainties agrees well with the results obtained with other methods.Comment: Acta Astonomica in pres

Influence of strong-coupling and retardation effects on superconducting state in YB6{\rm YB_{6}} compound

In the framework of strong-coupling formalism, we have calculated the thermodynamic parameters of superconducting state in the ${\rm YB_{6}}$ compound. The values of critical temperature ($T_{C}$) are $9.5$~K and $7.9$~K for the Coulomb pseudopotential $\mu^{\star}=0.1$ and $0.2$, respectively. In the paper, we have determined the low temperature values of order parameter ($\Delta(0)$), specific heat jump at the critical temperature ($\Delta C(T_{C})$), and thermodynamic critical field ($H_C(0)$). The dimensionless thermodynamic ratios: $R_{\Delta}=2\Delta\left(0\right)/{k_BT_C}$, $R_C=\Delta C\left(T_C\right)/C^N\left(T_C\right)$, and $R_H=T_CC^N\left(T_C\right)/H_C^2\left(0\right)$ are equal to: $R_{\Delta}\left(\mu^{\star}\right)\in\lbrace 4.48,4.35\rbrace$, $R_{C}\left(\mu^{\star}\right)\in\lbrace 2.62,2.55\rbrace$, and $R_{H}\left(\mu^{\star}\right)\in\lbrace 0.146,0.157\rbrace$. Due to the significant strong-coupling and retardation effects ($k_{B}T_{C} / \omega_{\rm ln}\sim 0.1$) those values highly deviate from the predictions of BCS theory.Comment: 5 pages, 4 figure

The effect of B and C addition on structure and properties of sintered Mn-Cr-Mo steels

The effect of boron and/or carbon additions on the microstructure and properties of sintered manganese steels was investigated. Thesesteels were produced based on following powders: pre-alloyed Astaloy CrL and ferromanganese. Sintering was carried out at 1150oC and1250oC in hydrogen atmosphere. The density, hardness and microstructure were investigated. The main objective of this work was to find correlation between sintering temperature and chemical composition of steel and theirs properties. It was shown that both alloying elements and sintering temperature influence the microstructure and properties of sintered manganese steels. When boron or graphite was added, density and also hardness of the Fe-Mn-Cr-Mo steels were increased. Significant change in hardness were related to changes in the microstructure. Boron has a beneficial effect on the densification process, due to faster and more efficient sintering kinetics. In general, it can be observed that by sintering at higher temperature the microstructure and properties were improved

Study of hydroxyapatite behaviour during sintering of 316L steel

316L stainless steel – hydroxyapatite composite biomaterials with different hydroxyapatite weight fraction in the composite wereinvestigated. Hydroxyapatite (HAp – Ca10(PO4)6(OH)2) is well known biomaterial. HAp reveals excellent chemical and biological affinitywith bony tissues. On the other hand hydroxyapatite shows low mechanical properties. The combination of very good biocompatibility of hydroxyapatite and high mechanical properties of stainless steel seems to be a good solution. In presented research natural originhydroxyapatite and 316L austenitic stainless steel were used. In this work, metal-ceramics composites were fabricated by the powdermetallurgy technology (involving pressing and sintering process). Sintering was carried out at 1250oC in hydrogen atmosphere. Thedensity, porosity and hardness were investigated. Metallographic microscope and SEM were carried out in order to investigate themicrostructure. The horizontal NETZSCH DIL 402E dilatometer was used to evaluate the dimensional changes and phenomena occurringduring sintering. The research displayed that physical properties of sintered 316L-HAp composites decrease with increase ofhydroxyapatite content. Microstructure of investigated composites consists of austenitic and probably inclusions of hydroxyapatite andheterogeneous eutectic occurring on the grain boundaries. It was shown that amount of hydroxyapatite in the powder mixtures influencethe dimensional changes occurring during sintering

Interaction of the hydrogen molecule with the environment: stability of the system

We study the stability of the hydrogen molecule interacting with the environment according to the balanced gain and loss energy scheme. We determined the properties of the molecule taking into account all electronic interactions, where the parameters of the Hamiltonian have been computed by using the variational method. The interaction of the hydrogen molecule with the environment was modeled parametrically ($\gamma$) with the help of the non-hermitian operator. We have shown that the hydrogen molecule is dynamically unstable. The dissociation time ($T_{D}$) decreases, if the $\gamma$ parameter increases (for $\gamma\rightarrow 0$, we get $T_{D}\rightarrow +\infty$). At the dynamic instability of the hydrogen molecule overlaps its static instability as the coupling constant $\gamma$ increases. We observed the decrease in the dissociation energy and the existence of the metastable state of the molecule ($\gamma_{MS}=0.659374$~Ry). The hydrogen molecule is statically unstable for $\gamma >\gamma_{D}=1.024638$~Ry. One can also observed the $\mathcal{PT}$ symmetry breaking effect for the electronic Hamiltonian ($\gamma_{\mathcal {PT}}=0.520873$~Ry). However, it does not affect the properties of the hydrogen molecule, such as: the electronic Hamiltonian parameters, the phonon and rotational energy, and the values of the electron-phonon coupling constants.Comment: 16 pages, 8 figure

The Optical Gravitational Lensing Experiment. Additional Planetary and Low-Luminosity Object Transits from the OGLE 2001 and 2002 Observational Campaigns

The photometric data collected by OGLE-III during the 2001 and 2002 observational campaigns aiming at detection of planetary or low-luminosity object transits were corrected for small scale systematic effects using the data pipeline by Kruszewski and Semeniuk and searched again for low amplitude transits. Sixteen new objects with small transiting companions, additional to previously found samples, were discovered. Most of them are small amplitude cases which remained undetected in the original data. Several new objects seem to be very promising candidates for systems containing substellar objects: extrasolar planets or brown dwarfs. Those include OGLE-TR-122, OGLE-TR-125, OGLE-TR-130, OGLE-TR-131 and a few others. Those objects are particularly worth spectroscopic follow-up observations for radial velocity measurements and mass determination. With well known photometric orbit only a few RV measurements should allow to confirm their actual status. All photometric data of presented objects are available to the astronomical community from the OGLE Internet archive.Comment: 8 pages. Appendix in 'jpg' format. Minor changes. Full resolution pages of Appendix and photometric data presented in the paper are available from the OGLE Internet archive: See http://ogle.astrouw.edu.pl or its US mirror, at http://bulge.princeton.edu/~ogl

The Optical Gravitational Lensing Experiment. Period-Luminosity Relations of Variable Red Giant Stars

Period-luminosity (PL) relations of variable red giants in the Large (LMC) and Small Magellanic Clouds (SMC) are presented. The PL diagrams are plotted in three planes: logP-K_S, logP-W_{JK}, and logP-W_I. Fourteen PL sequences are distinguishable, and some of them consist of three closely spaced ridges. Each of the sequences is fitted with a linear or quadratic function. The similarities and differences between the PL relations in both galaxies are discussed for four types of red giant variability: OGLE Small Amplitude Red Giants (OSARGs), Miras and Semiregular Variables (SRVs), Long Secondary Periods (LSPs) and ellipsoidal variables. We propose a new method of separating OSARGs from non-variable stars and SRVs. The method employs the position in the reddening-free PL diagrams and the characteristic period ratios of these multiperiodic variables. The PL relations for the LMC OSARG are compared with the calculated relations for RGB models along isochrones of relevant ages and metallicities. We also compare measured periods and amplitudes of the OSARGs with predictions based on the relations valid for less luminous solar-like pulsators. Miras and SRVs seem to follow PL relation of the same slopes in the LMC and SMC, while for LSP and ellipsoidal variables slopes in both galaxies are different. The PL sequences defined by LSP variables and binary systems overlap in the whole range of analyzed wavebands. We put forward new arguments for the binary star scenario as an explanation of the LSP variability and elaborate on it further. The measured pulsation to orbital period ratio implies nearly constant ratio of the star radius to orbital distance, R/A=0.4, as we find. Combined effect of tidal friction and mass loss enhanced by the low-mass companion may explain why such a value is preferred.Comment: 25 pages, 8 figure

The Optical Gravitational Lensing Experiment. Small Amplitude Variable Red Giants in the Magellanic Clouds

We present analysis of the large sample of variable red giants from the Large and Small Magellanic Clouds detected during the second phase of the Optical Gravitational Lensing Experiment (OGLE-II) and supplemented with OGLE-III photometry. Comparing pulsation properties of detected objects we find that they constitute two groups with clearly distinct features. In this paper we analyze in detail small amplitude variable red giants (about 15400 and 3000 objects in the LMC and SMC, respectively). The vast majority of these objects are multi-periodic. At least 30% of them exhibit two modes closely spaced in the power spectrum, what likely indicates non-radial oscillations. About 50% exhibit additional so called Long Secondary Period. To distinguish between AGB and RGB red giants we compare PL diagrams of multi-periodic red giants located above and below the tip of the Red Giant Branch (TRGB). The giants above the TRGB form four parallel ridges in the PL diagram. Among much more numerous sample of giants below the TRGB we find objects located on the low luminosity extensions of these ridges, but most of the stars are located on the ridges slightly shifted in logP. We interpret the former as the second ascent AGB red giants and the latter as the first ascent RGB objects. Thus, we empirically show that the pulsating red giants fainter than the TRGB are a mixture of RGB and AGB giants. Finally, we compare the Petersen diagrams of the LMC, SMC and Galactic bulge variable red giants and find that they are basically identical indicating that the variable red giants in all these different stellar environments share similar pulsation properties.Comment: 23 pages, 13 figures included in GIF forma