Linear-time algorithms for scattering number and Hamilton-connectivity of interval graphs.

We prove that for all inline image an interval graph is inline image-Hamilton-connected if and only if its scattering number is at most k. This complements a previously known fact that an interval graph has a nonnegative scattering number if and only if it contains a Hamilton cycle, as well as a characterization of interval graphs with positive scattering numbers in terms of the minimum size of a path cover. We also give an inline image time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the previously best-known inline image time bound for solving this problem. As a consequence of our two results, the maximum k for which an interval graph is k-Hamilton-connected can be computed in inline image time

Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs

We show that for all k ≤ − 1 an interval graph is − (k + 1)-Hamilton-connected if and only if its scattering number is at most k. We also give an O(n + m) time algorithm for computing the scattering number of an interval graph with n vertices and m edges, which improves the O(n 3) time bound of Kratsch, Kloks and Müller. As a consequence of our two results the maximum k for which an interval graph is k-Hamilton-connected can be computed in O(n + m) time

Consistency test of general relativity from large scale structure of the Universe

We construct a consistency test of General Relativity (GR) on cosmological scales. This test enables us to distinguish between the two alternatives to explain the late-time accelerated expansion of the universe, that is, dark energy models based on GR and modified gravity models without dark energy. We derive the consistency relation in GR which is written only in terms of observables - the Hubble parameter, the density perturbations, the peculiar velocities and the lensing potential. The breakdown of this consistency relation implies that the Newton constant which governs large-scale structure is different from that in the background cosmology, which is a typical feature in modified gravity models. We propose a method to perform this test by reconstructing the weak lensing spectrum from measured density perturbations and peculiar velocities. This reconstruction relies on Poisson's equation in GR to convert the density perturbations to the lensing potential. Hence any inconsistency between the reconstructed lensing spectrum and the measured lensing spectrum indicates the failure of GR on cosmological scales. The difficulties in performing this test using actual observations are discussed.Comment: 7 pages, 1 figur

Dynamically generated resonances from the vector octet-baryon decuplet interaction

We study the interaction of the octet of vector mesons with the decuplet of baryons using Lagrangians of the hidden gauge theory for vector interactions. The unitary amplitudes in coupled channels develop poles that can be associated with some known baryonic resonances, while there are predictions for new ones at the energy frontier of the experimental research. The work offers guidelines on how to search for these resonances

Thermopower and thermal conductivity of superconducting perovskite MgCNi3MgCNi_3

The thermopower and thermal conductivity of superconducting perovskite $MgCNi_3$ ($T_c \approx$ 8 K) have been studied. The thermopower is negative from room temperature to 10 K. Combining with the negative Hall coefficient reported previously, the negative thermopower definetly indicates that the carrier in $MgCNi_3$ is electron-type. The nonlinear temperature dependence of thermopower below 150 K is explained by the electron-phonon interaction renormalization effects. The thermal conductivity is of the order for intermetallics, larger than that of borocarbides and smaller than $MgB_2$. In the normal state, the electronic contribution to the total thermal conductivity is slightly larger than the lattice contribution. The transverse magnetoresistance of $MgCNi_3$ is also measured. It is found that the classical Kohler's rule is valid above 50 K. An electronic crossover occures at $T^* \sim 50 K$, resulting in the abnormal behavior of resistivity, thermopower, and magnetoresistance below 50 K.Comment: Revised on 12 September 2001, Phys. Rev. B in pres

The influence of a seed crystal on the texture of a bulk YBaCuO specimen

Die ordnende Wirkung eines Saat-Kristalles auf die Textur einer massiven YBaCuO-Probe Um die Abhängigkeit der lokalen Textur von Teilen einer zylindrischen YBaCuO-Probe vom Abstand zum Saatkristall zu untersuchen, wurde eine sehr gut texturierte YBaCuO-Probe in 9 rechteckige und in 12 Randstücke zerschnitten. Von den einzelnen Teilen der YBaCuO-Probe wurden die Texturen mit Hilfe der Neutronen-Beugung am Reaktor in Geesthacht gemessen und zwar mit einem "equal-area"-Raster. Die Maschenweite betrug 1° bis zu einer Achsabweichung der Zylinderachse der originären YBaCuO-Probe von 10° und von 10° Achsabweichung bis zu 20° Achsabweichung betrug die Maschenweite 2°. Aus der Summe der gezählten Neutronen auf Kleinkreisen der Polkugel wurden die einzelnen Werte der Verteilung der Achsabweichungen der c-Achsen der kristallinen Domänen von der Zylinderachse berechnet. Die mittlere Achsabweichung der c-Achsen der kristallinen Domänen von der Zylinderachse der unzerschnittenen YBaCuO-Probe wächst vom inneren Stück mit dem Saatkristall zu den Randstücken der zylindrischen Probe hin an

Large Scale Pressure Fluctuations and Sunyaev-Zel'dovich Effect

The Sunyaev-Zel'dovich (SZ) effect associated with pressure fluctuations of the large scale structure gas distribution will be probed with current and upcoming wide-field small angular scale cosmic microwave background experiments. We study the generation of pressure fluctuations by baryons which are present in virialized dark matter halos and by baryons present in small overdensities. For collapsed halos, assuming the gas distribution is in hydrostatic equilibrium with matter density distribution, we predict the pressure power spectrum and bispectrum associated with the large scale structure gas distribution by extending the dark matter halo approach which describes the density field in terms of correlations between and within halos. The projected pressure power spectrum allows a determination of the resulting SZ power spectrum due to virialized structures. The unshocked photoionized baryons present in smaller overdensities trace the Jeans-scale smoothed dark matter distribution. They provide a lower limit to the SZ effect due to large scale structure in the absence of massive collapsed halos. We extend our calculations to discuss higher order statistics, such as bispectrum and skewness in SZ data. The SZ-weak lensing cross-correlation is suggested as a probe of correlations between dark matter and baryon density fields, while the probability distribution functions of peak statistics of SZ halos in wide field CMB data can be used as a probe of cosmology and non-Gaussian evolution of large scale structure pressure fluctuations.Comment: 16 pages, 9 figures; Revised with expanded discussions. Phys. Rev. D. (in press

Diquark Bose-Einstein Condensation and Nuclear Matter

We study a possible transition between symmetric nuclear matter and the diquark Bose-Einstein condensate (BEC) matter at zero temperature. We find that chiral restoration transition is first order and coincides with deconfinement. We investigate various possible coexistence patterns which may emerge from the first order deconfinement phase transition by assuming different values for the critical deconfinement chemical potential. If deconfinement takes place at higher chemical potential, there exists a mixed phase of nuclear and chirally restored diquark BEC matter. This coexistence region extends over a large density region for a bigger diquark BEC or a weaker diquark-diquark interaction. For model parameters with heavy diquark in vaccum, phase transition to diquark matter becomes of second-order. We also show that in the case of precocious deconfinement, droplets of nucleons and droplets of chirally restored Bose-Einstein condensed diquarks coexist surrounded by non-trivial vacuum. We show that a early deconfinement and a weak repulsive diquark-diquark interaction soften the equation of state. We propose a scenario in which nuclear matter saturates due to the formation of the diquark BEC and deconfinement phenomena. In this picture, instead of repulsive vector-meson exchange the compressibility of the equation of state is related to a repulsive diquark-diquark interaction. In general, we emphasize the importance of a diquark BEC phase at rather low density before quark BCS-pairing transition.Comment: 29 pages, 9 figures (eps), references added, Conclusion extended, version to appear in Nucl.Phys.