Flux limitation in ultrafiltration: Osmotic pressure model and gel layer model

The characteristic permeate flux behaviour in ultrafiltration, i.e., the existence of a limiting flux which is independent of applied pressure and membrane resistance and a linear plot of the limiting flux versus the logarithm of the feed concentration, is explained by the osmotic pressure model. In the mathematical description presented here, a quantity ΔΠn/(Rmk) is introduced which is the ratio of the resistance caused by the osmotic pressure and the resistance of the membrane itself. For high values of this quantity (19) the flux is practically limited by the osmotic pressure. p]Factors leading to high values of the quantityΔΠnn/(Rmk) are discussed and it is concluded that in the ultrafiltration of medium molecular weight solutes (10,000 to 100,000 daltons) osmotic pressure limitation is more likely than gel layer limitatio

Electrons doped in cubic perovskite SrMnO3: isotropic metal versus chainlike ordering of Jahn-Teller polarons

Single crystals of electron-doped SrMnO3 with a cubic perovskite structure have been systematically investigated as the most canonical (orbital-degenerate) double-exchange system, whose ground states have been still theoretically controversial. With only 1-2% electron doping by Ce substitution for Sr, a G-type antiferromagnetic metal with a tiny spin canting in a cubic lattice shows up as the ground state, where the Jahn-Teller polarons with heavy mass are likely to form. Further electron doping above 4%, however, replaces this isotropic metal with an insulator with tetragonal lattice distortion, accompanied by a quasi-one-dimensional 3z^2-r^2 orbital ordering with the C-type antiferromagnetism. The self-organization of such dilute polarons may reflect the critical role of the cooperative Jahn-Teller effect that is most effective in the originally cubic system.Comment: 5 pages, 4 figure

Diffusion-induced instability and chaos in random oscillator networks

We demonstrate that diffusively coupled limit-cycle oscillators on random networks can exhibit various complex dynamical patterns. Reducing the system to a network analog of the complex Ginzburg-Landau equation, we argue that uniform oscillations can be linearly unstable with respect to spontaneous phase modulations due to diffusional coupling - the effect corresponding to the Benjamin-Feir instability in continuous media. Numerical investigations under this instability in random scale-free networks reveal a wealth of complex dynamical regimes, including partial amplitude death, clustering, and chaos. A dynamic mean-field theory explaining different kinds of nonlinear dynamics is constructed.Comment: 6 pages, 3 figure

Effect of cation size variance on spin and orbital order in Eu1−x_{1-x}(La0.254_{0.254}Y0.746_{0.746})x_{x}VO3_3

We have investigated the $R$-ion ($R$ = rare earth or Y) size variance effect on spin/orbital order in Eu$_{1-x}$(La$_{0.254}$Y$_{0.746}$)$_{x}$VO$_3$. The size variance disturbs one-dimensional orbital correlation in $C$-type spin/$G$-type orbital ordered states and suppresses this spin/orbital order. In contrast, it stabilizes the other spin/orbital order. The results of neutron and resonant X-ray scattering denote that in the other ordered phase, the spin/orbital patterns are $G$-type/$C$-type, respectively.Comment: 4 pages, 4 figures, accepted to Rapid Communication in Physical Review

Critical Collapse of Einstein Cluster

We observe critical phenomena in spherically symmetric gravitational collapse of Einstein Cluster. We show analytically that the collapse evolution ends either in formation of a black hole or in dispersal depending on the values of initial parameters which characterize initial density and angular momentum of the collapsing cloud. Near the threshold of black hole formation, we obtain scaling relation for the mass of the black hole and find the critical exponent value to be 3/2. We numerically confirm that there exist wide ranges of initial parameter values around the critical configuration for which the model remains shell-crossing free.Comment: Accepted for publication in Prog. Theor. Phy