Theory of Orbital Ordering, Fluctuation and Resonant X-ray Scattering in Manganites

A theory of resonant x-ray scattering in perovskite manganites is developed by applying the group theory to the correlation functions of the pseudospin operators for the orbital degree of freedom. It is shown that static and dynamical informations of the orbital state are directly obtained from the elastic, diffuse and inelastic scatterings due to the tensor character of the scattering factor. We propose that the interaction and its anisotropy between orbitals are directly identified by the intensity contour of the diffuse scattering in the momentum space.Comment: 4 pages, 1 figur

Snowmelt Runoff Model in Japan

The preliminary Japanese snowmelt runoff model was modified so that all the input variables arc of the antecedent days and the inflow of the previous day is taken into account. A few LANDSAT images obtained in the past were effectively used to verify and modify the depletion curve induced from the snow water equivalent distribution at maximum stage and the accumulated degree days at one representative point selected in the basin. Together with the depletion curve, the relationship between the basin ide daily snowmelt amount and the air temperature at the point above are exhibited homograph form for the convenience of the model user. The runoff forecasting procedure is summarized

Numerical Study of Photo-Induced Dynamics in Double-Exchange Model

Photo-induced spin and charge dynamics in double-exchange model are numerically studied. The Lanczos method and the density-matrix renormalization-group method are applied to one-dimensional finite-size clusters. By photon irradiation in a charge ordered (CO) insulator associated with antiferromagnetic (AFM) correlation, both the CO and AFM correlations collapse rapidly, and appearances of new peaks inside of an insulating gap are observed in the optical spectra and the one-particle excitation spectra. Time evolutions of the spin correlation and the in-gap state are correlated with each other, and are governed by the transfer integral of conduction electrons. Results are interpreted by the charge kink/anti-kink picture and their effective motions which depend on the localized spin correlation. Pump-photon density dependence of spin and charge dynamics are also studied. Roles of spin degree of freedom are remarkable in a case of weak photon density. Implications of the numerical results for the pump-probe experiments in perovskite manganites are discussed.Comment: 16 pages, 16 figure

Magnetic Ordering, Orbital Ordering and Resonant X-ray Scattering in Perovskite Titanates

The effective Hamiltonian for perovskite titanates is derived by taking into account the three-fold degeneracy of $t_{2g}$ orbitals and the strong electron-electron interactions. The magnetic and orbital ordered phases are studied in the mean-field approximation applied to the effective Hamiltonian. A large degeneracy of the orbital states in the ferromagnetic phase is found in contrast to the case of the doubly degenerate $e_g$ orbitals. Lifting of this orbital degeneracy due to lattice distortions and spin-orbit coupling is examined. A general form for the scattering cross section of the resonant x-ray scattering is derived and is applied to the recent experimental results in YTiO$_3$. The spin wave dispersion relation in the orbital ordered YTiO$_3$ is also studied.Comment: 10 pages, 6 figure

Robustness of force and stress inference in an epithelial tissue

During morphogenesis, the shape of a tissue emerges from collective cellular behaviors, which are in part regulated by mechanical and biochemical interactions between cells. Quantification of force and stress is therefore necessary to analyze the mechanisms controlling tissue morphogenesis. Recently, a mechanical measurement method based on force inference from cell shapes and connectivity has been developed. It is non-invasive, and can provide space-time maps of force and stress within an epithelial tissue, up to prefactors. We previously performed a comparative study of three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces. In the present study, to further validate and compare the three force inference methods, we tested their robustness by measuring temporal fluctuation of estimated forces. Quantitative data of cell-level dynamics in a developing tissue suggests that variation of forces and stress will remain small within a short period of time ($\sim$minutes). Here, we showed that cell-junction tensions and global stress inferred by the Bayesian force inference method varied less with time than those inferred by the method that estimates only tension. In contrast, the amplitude of temporal fluctuations of estimated cell pressures differs less between different methods. Altogether, the present study strengthens the validity and robustness of the Bayesian force-inference method.Comment: 4 pages, 4 figure

Topology Change of Coalescing Black Holes on Eguchi-Hanson Space

We construct multi-black hole solutions in the five-dimensional Einstein-Maxwell theory with a positive cosmological constant on the Eguchi-Hanson space, which is an asymptotically locally Euclidean space. The solutions describe the physical process such that two black holes with the topology of S^3 coalesce into a single black hole with the topology of the lens space L(2;1)=S^3/Z_2. We discuss how the area of the single black hole after the coalescence depends on the topology of the horizon.Comment: 10 pages, Some comments are added. to be published as a letter in Classical and Quantum Gravit

On a generalization of the global attractivity for a periodically forced Pielou's equation

In this paper, we study the global attractivity for a class of periodic difference equation with delay which has a generalized form of Pielou's difference equation. The global dynamics of the equation is characterized by using a relation between the upper limit and lower limit of the solution. There are two possible global dynamics: zero solution is globally attractive or there exists a periodic solution which is globally attractive. Recent results by Camouzis and Ladas [Periodically forced Pielou's equation, J. Math. Anal. Appl. 333 (1) (2007) 117-127] are generalized. Two examples are given to illustrate our results

Resonant Inelastic X-ray Scattering from Charge and Orbital Excitations in Manganites

We present a theory of the resonant inelastic x-ray scattering (RIXS) to study electronic excitations in orbital ordered manganites. The charge and orbital excitations of the Mn 3d electron are caused by the Coulomb interactions in the intermediate scattering state. The scattering cross section is formulated by the Liouville operator method where the local and itinerant natures of the excitations are taken into account on an equal footing. As a result, the cross section is expressed by the charge and orbital correlation functions associated with local corrections. The RIXS spectra are calculated numerically as functions of momentum and polarization of x ray. Through the calculations, we propose that RIXS provides a great opportunity to study the unique electronic excitations in correlated electron systems with orbital degeneracy.Comment: 8 pages, 5 figure