Weak Lensing as a Calibrator of the Cluster Mass-Temperature Relation

The abundance of clusters at the present epoch and weak gravitational lensing shear both constrain roughly the same combination of the power spectrum normalization sigma_8 and matter energy density Omega_M. The cluster constraint further depends on the normalization of the mass-temperature relation. Therefore, combining the weak lensing and cluster abundance data can be used to accurately calibrate the mass-temperature relation. We discuss this approach and illustrate it using data from recent surveys.Comment: Matches the version in ApJL. Equation 4 corrected. Improvements in the analysis move the cluster contours in Fig1 slightly upwards. No changes in the conclusion

The effect of Mach number on unstable disturbances in shock/boundary-layer interactions

The effect of Mach number on the growth of unstable disturbances in a boundary layer undergoing a strong interaction with an impinging oblique shock wave is studied by direct numerical simulation and linear stability theory (LST). To reduce the number of independent parameters, test cases are arranged so that both the interaction location Reynolds number (based on the distance from the plate leading edge to the shock impingement location for a corresponding inviscid flow) and the separation bubble length Reynolds number are held fixed. Small-amplitude disturbances are introduced via both white-noise and harmonic forcing and, after verification that the disturbances are convective in nature, linear growth rates are extracted from the simulations for comparison with parallel flow LST and solutions of the parabolized stability equations (PSE). At Mach 2.0, the oblique modes are dominant and consistent results are obtained from simulation and theory. At Mach 4.5 and Mach 6.85, the linear Navier-Stokes results show large reductions in disturbance energy at the point where the shock impinges on the top of the separated shear layer. The most unstable second mode has only weak growth over the bubble region, which instead shows significant growth of streamwise structures. The two higher Mach number cases are not well predicted by parallel flow LST, which gives frequencies and spanwise wave numbers that are significantly different from the simulations. The PSE approach leads to good qualitative predictions of the dominant frequency and wavenumber at Mach 2.0 and 4.5, but suffers from reduced accuracy in the region immediately after the shock impingement. Three-dimensional Navier-Stokes simulations are used to demonstrate that at finite amplitudes the flow structures undergo a nonlinear breakdown to turbulence. This breakdown is enhanced when the oblique-mode disturbances are supplemented with unstable Mack modes

Different Methods of Forming Cold Fronts in Non-Merging Clusters

Sharp edges in X-ray surface brightness with continuous gas pressure called cold fronts have been often found in relaxed galaxy clusters such as Abell 496. Models that explain cold fronts as surviving cores of head-on subcluster mergers do not work well for these clusters and competing models involving gas sloshing have been recently proposed. Here, we test some concrete predictions of these models in a combined analysis of density, temperature, metal abundances and abundance ratios in a deep Chandra exposure of Abell 496. We confirm that the chemical discontinuities found in this cluster are not consistent with a core merger remnant scenario. However, we find chemical gradients across a spiral "arm" discovered at 73 kpc north of the cluster center and coincident with the sharp edge of the main cold front in the cluster. Despite the overall SN Ia iron mass fraction dominance found within the cooling radius of this cluster, the metal enrichment along the arm, determined from silicon and iron abundances, is consistent with a lower SN Ia iron mass fraction (51% +- 14%) than that measured in the surrounding regions (85% +- 14%). The "arm" is also significantly colder than the surroundings by 0.5-1.6 keV. The arm extends from a boxy colder region surrounding the center of the cluster, where two other cold fronts are found. This cold arm is a prediction of current high resolution numerical simulations as a result of an off-center encounter with a less massive pure dark matter halo and we suggest that the cold fronts in A496 provide the first clear corroboration of such model, where the closest encounter happened ~ 0.5 Gyr ago. We also argue for a possible candidate dark matter halo responsible for the cold fronts in the outskirts of A496.Comment: 11 ApJ pages, 1 Table, 16 Figures, accepted for publication in the Astrophysical Journal. For full version with all hi-res figures click on http://www.astro.lsa.umich.edu/~rdupke/a496sub.pd

Numerical Latent Heat Observation of the q=5 Potts Model

Site energy of the five-state ferromagnetic Potts model is numerically calculated at the first-order transition temperature using corner transfer matrix renormalization group (CTMRG) method. The calculated energy of the disordered phase $U^{+}$ is clearly different from that of the ordered phase $U^{-}$. The obtained latent heat $L = U^{-} - U^{+}$ is 0.027, which quantitatively agrees with the exact solution.Comment: 2 pages, Latex(JPSJ style files are included), 2 ps figures, submitted to J. Phys. Soc. Jpn.(short note

DNA loop statistics and torsional modulus

The modelling of DNA mechanics under external constraints is discussed. Two analytical models are widely known, but disagree for instance on the value of the torsional modulus. The origin of this embarassing situation is located in the concept of writhe. This letter presents a unified model for DNA establishing a relation between the different approaches. I show that the writhe created by the loops of DNA is at the origin of the discrepancy. To take this into account, I propose a new treatment of loop statistics based on numerical simulations using the most general formula for the writhe, and on analytic calculations with only one fit parameter. One can then compute the value of the torsional modulus of DNA without the need of any cut-off.Comment: 8 pages, 1 figure. Accepted by Europhysics Letter

Application of the Density Matrix Renormalization Group in momentum space

We investigate the application of the Density Matrix Renormalization Group (DMRG) to the Hubbard model in momentum-space. We treat the one-dimensional models with dispersion relations corresponding to nearest-neighbor hopping and $1/r$ hopping and the two-dimensional model with isotropic nearest-neighbor hopping. By comparing with the exact solutions for both one-dimensional models and with exact diagonalization in two dimensions, we first investigate the convergence of the ground-state energy. We find variational convergence of the energy with the number of states kept for all models and parameter sets. In contrast to the real-space algorithm, the accuracy becomes rapidly worse with increasing interaction and is not significantly better at half filling. We compare the results for different dispersion relations at fixed interaction strength over bandwidth and find that extending the range of the hopping in one dimension has little effect, but that changing the dimensionality from one to two leads to lower accuracy at weak to moderate interaction strength. In the one-dimensional models at half-filling, we also investigate the behavior of the single-particle gap, the dispersion of spinon excitations, and the momentum distribution function. For the single-particle gap, we find that proper extrapolation in the number of states kept is important. For the spinon dispersion, we find that good agreement with the exact forms can be achieved at weak coupling if the large momentum-dependent finite-size effects are taken into account for nearest-neighbor hopping. For the momentum distribution, we compare with various weak-coupling and strong-coupling approximations and discuss the importance of finite-size effects as well as the accuracy of the DMRG.Comment: 15 pages, 11 eps figures, revtex

Above- and belowground herbivory jointly impact defense and seed dispersal traits in Taraxacum officinale

Plants are able to cope with herbivores by inducing defensive traits or growth responses that allow them to reduce or avoid the impact of herbivores. Since above- and belowground herbivores differ substantially in life-history traits, for example feeding types, and their spatial distribution, it is likely that they induce different responses in plants. Moreover, strong interactive effects on defense and plant growth are expected when above- and belowground herbivores are jointly present. The strengths and directions of these responses have been scarcely addressed in the literature. Using Taraxacum officinale, the root-feeding nematode Meloidogyne hapla and the locust Schistocerca gregaria as a model species, we examined to what degree above- and belowground herbivory affect (1) plant growth responses, (2) the induction of plant defensive traits, that is, leaf trichomes, and (3) changes in dispersal-related seed traits and seed germination. We compared the performance of plants originating from different populations to address whether plant responses are conserved across putative different genotypes. Overall, aboveground herbivory resulted in increased plant biomass. Root herbivory had no effect on plant growth. Plants exposed to the two herbivores showed fewer leaf trichomes than plants challenged only by one herbivore and consequently experienced greater aboveground herbivory. In addition, herbivory had effects that reached beyond the individual plant by modifying seed morphology, producing seeds with longer pappus, and germination success

Density Matrix Renormalization Group Study of the Spin 1/2 Heisenberg Ladder with Antiferromagnetic Legs and Ferromagnetic Rungs

The ground state and low lying excitation of the spin 1/2 Heisenberg ladder with antiferromagnetic leg ($J$) and ferromagnetic rung ($-\lambda J, \lambda >0$) interaction is studied by means of the density matrix renormalization group method. It is found that the state remains in the Haldane phase even for small $\lambda \sim 0.02$ suggesting the continuous transition to the gapless phase at $\lambda = 0$. The critical behavior for small $\lambda$ is studied by the finite size scaling analysis. The result is consistent with the recent field theoretical prediction.Comment: 11 pages, revtex, figures upon reques

Edge states in Open Antiferromagnetic Heisenberg Chains

In this letter we report our results in investigating edge effects of open antiferromagnetic Heisenberg spin chains with spin magnitudes $S=1/2, 1,3/2,2$ using the density-matrix renormalization group (DMRG) method initiated by White. For integer spin chains, we find that edge states with spin magnitude $S_{edge}=S/2$ exist, in agreement with Valence-Bond-Solid model picture. For half-integer spin chains, we find that no edge states exist for $S=1/2$ spin chain, but edge state exists in $S=3/2$ spin chain with $S_{edge}=1/2$, in agreement with previous conjecture by Ng. Strong finite size effects associated with spin dimmerization in half-integer spin chains will also be discussed.Comment: 4 pages, RevTeX 3.0, 5 figures in a separate uuencoded postscript file. Replaced once to enlarge the acknowlegement