Rough flows and homogenization in stochastic turbulence

We provide in this work a tool-kit for the study of homogenisation of random ordinary differential equations, under the form of a friendly-user black box based on the tehcnology of rough flows. We illustrate the use of this setting on the example of stochastic turbulence.Comment: v2, 27 pages; presentation fairly improved; extended scope for the materia

Magnetic phase transitions in the two-dimensional frustrated quantum antiferromagnet Cs2CuCl4

We report magnetization and specific heat measurements in the 2D frustrated spin-1/2 Heisenberg antiferromagnet Cs2CuCl4 at temperatures down to 0.05 K and high magnetic fields up to 11.5 T applied along a, b and c-axes. The low-field susceptibility chi (T) M/B shows a broad maximum around 2.8 K characteristic of short-range antiferromagnetic correlations and the overall temperature dependence is well described by high temperature series expansion calculations for the partially frustrated triangular lattice with J=4.46 K and J'/J=1/3. At much lower temperatures (< 0.4 K) and in in-plane field (along b and c-axes) several new intermediate-field ordered phases are observed in-between the low-field incommensurate spiral and the high-field saturated ferromagnetic state. The ground state energy extracted from the magnetization curve shows strong zero-point quantum fluctuations in the ground state at low and intermediate fields

Ground states of a frustrated spin-1/2 antifferomagnet: Cs_2CuCl_4 in a magnetic field

We present detailed calculations of the magnetic ground state properties of Cs$_2$CuCl$_4$ in an applied magnetic field, and compare our results with recent experiments. The material is described by a spin Hamiltonian, determined with precision in high field measurements, in which the main interaction is antiferromagnetic Heisenberg exchange between neighboring spins on an anisotropic triangular lattice. An additional, weak Dzyaloshinkii-Moriya interaction introduces easy-plane anisotropy, so that behavior is different for transverse and longitudinal field directions. We determine the phase diagram as a function of field strength for both field directions at zero temperature, using a classical approximation as a first step. Building on this, we calculate the effect of quantum fluctuations on the ordering wavevector and components of the ordered moments, using both linear spinwave theory and a mapping to a Bose gas which gives exact results when the magnetization is almost saturated. Many aspects of the experimental data are well accounted for by this approach.Comment: 13 Pages, 9 Figure

Ancestral reconstruction of mammalian FMO1 enables structural determination, revealing unique features that explain its catalytic properties

Mammals rely on the oxidative flavin-containing monooxygenases (FMOs) to detoxify numerous and potentially deleterious xenobiotics; this activity extends to many drugs, giving FMOs high pharmacological relevance. However, our knowledge regarding these membrane-bound enzymes has been greatly impeded by the lack of structural information. We anticipated that ancestral-sequence reconstruction could help us identify protein sequences that are more amenable to structural analysis. As such, we hereby reconstructed the mammalian ancestral protein sequences of both FMO1 and FMO4, denoted as ancestral flavin-containing monooxygenase (AncFMO)1 and AncFMO4, respectively. AncFMO1, sharing 89.5% sequence identity with human FMO1, was successfully expressed as a functional enzyme. It displayed typical FMO activities as demonstrated by oxygenating benzydamine, tamoxifen, and thioanisole, drug-related compounds known to be also accepted by human FMO1, and both NADH and NADPH cofactors could act as electron donors, a feature only described for the FMO1 paralogs. AncFMO1 crystallized as a dimer and was structurally resolved at 3.0 Å resolution. The structure harbors typical FMO aspects with the flavin adenine dinucleotide and NAD(P)H binding domains and a C-terminal transmembrane helix. Intriguingly, AncFMO1 also contains some unique features, including a significantly porous and exposed active site, and NADPH adopting a new conformation with the 2'-phosphate being pushed inside the NADP+ binding domain instead of being stretched out in the solvent. Overall, the ancestrally reconstructed mammalian AncFMO1 serves as the first structural model to corroborate and rationalize the catalytic properties of FMO1

Distinct magnetic regimes through site-selective atom substitution in the frustrated quantum antiferromagnet Cs2_2CuCl4−x_{4-x}Brx_x

We report on a systematic study of the magnetic properties on single crystals of the solid solution Cs$_2$CuCl$_{4-x}$Br$_x$ (0 $\leq$ x $\leq$ 4), which include the two known end-member compounds Cs$_2$CuCl$_4$ and Cs$_2$CuBr$_4$, classified as quasi-two-dimensional quantum antiferromagnets with different degrees of magnetic frustration. By comparative measurements of the magnetic susceptibility $\chi$($T$) on as many as eighteen different Br concentrations, we found that the inplane and out-of-plane magnetic correlations, probed by the position and height of a maximum in the magnetic susceptibility, respectively, do not show a smooth variation with x. Instead three distinct concentration regimes can be identified, which are separated by critical concentrations x$_{c1}$ = 1 and x$_{c2}$ = 2. This unusual magnetic behavior can be explained by considering the structural peculiarities of the materials, especially the distorted Cu-halide tetrahedra, which support a site-selective replacement of Cl- by Br- ions. Consequently, the critical concentrations x$_{c1}$ (x$_{c2}$) mark particularly interesting systems, where one (two) halidesublattice positions are fully occupied.Comment: 15 pages, 4 figure

Relativistic diffusion with friction on a pseudoriemannian manifold

We study a relativistic diffusion equation on the Riemannian phase space defined by Franchi and Le Jan. We discuss stochastic Ito (Langevin) differential equations (defining the diffusion) as a perturbation by noise of the geodesic equation. We show that the expectation value of the angular momentum and the energy grow exponentially fast. We discuss drifts leading to an equilibrium. It is shown that the diffusion process corresponding to the Juettner or quantum equilibrium distributions has a bounded expectation value of angular momentum and energy. The energy and the angular momentum tend exponentially fast to their equilibrium values. As examples we discuss a particle in a plane fronted gravitational wave and a particle in de Sitter universe. It is shown that the relativistic diffusion of momentum in de Sitter space is the same as the relativistic diffusion on the Minkowski mass-shell with the temperature proportional to the de Sitter radius.Comment: the version published in CQ