Reduction and reconstruction of stochastic differential equations via symmetries

An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is proposed. As a side result the well-known solution formula for linear one-dimensional stochastic differential equations is obtained within this symmetry approach. The complete procedure is applied to several examples with both theoretical and applied relevance

Dynamics of Vortex Pair in Radial Flow

The problem of vortex pair motion in two-dimensional plane radial flow is solved. Under certain conditions for flow parameters, the vortex pair can reverse its motion within a bounded region. The vortex-pair translational velocity decreases or increases after passing through the source/sink region, depending on whether the flow is diverging or converging, respectively. The rotational motion of two corotating vortexes in a quiescent environment transforms into motion along a logarithmic spiral in the presence of radial flow. The problem may have applications in astrophysics and geophysics.Comment: 13 pages, 9 figure

A Dipole Vortex Model of Obscuring Tori in Active Galaxy Nuclei

The torus concept as an essential structural component of active galactic nuclei (AGN) is generally accepted. Here, the situation is discussed when the torus "twisting" by the radiation or wind transforms it into a dipole toroidal vortex which in turn can be a source of matter replenishing the accretion disk. Thus emerging instability which can be responsible for quasar radiation flares accompanied by matter outbursts is also discussed. The "Matreshka" scheme for an obscuring vortex torus structure capable of explaining the AGN variability and evolution is proposed. The model parameters estimated numerically for the luminosity close to the Eddington limit agree well with the observations.Comment: 17 pages, 11 figures, version of this paper is published in Astronomy Report

Stokes flow in a rectangular cavity by rotlet forcing

The Stokes flow inside a two-dimensional rectangular cavity |x|a, |y|b is analyzed for a highly viscous, incompressible fluid flow, driven by a single rotlet placed at position (0,c). Specifically, a rigorous solution of the governing two-dimensional biharmonic equation for the stream function is constructed analytically by means of the superposition principle. With this solution, multicellular flow patterns can be described for narrow cavities, in which the number of flow cells is directly related to the value of the aspect ratio A=b/a. The solution also shows that for a certain rotlet position (0,c0), which depends on a and b, the flow has a stagnation point (0,-c0) symmetrically placed inside the rectangle. As the flow would not be affected by placing a second (inactive) rotlet in this stagnation point, this allows us to construct a blinking rotlet model for the rectangular cavity, with the inactive rotlet in the stagnation point of the flow induced by the active rotlet. For rectangular cavities, it holds that more than one of these special rotlet positions can be found for cavities that are elongated to sufficiently large aspect ratios. The blinking rotlet model is applied to illustrate several aspects of stirring in a Stokes flow in a rectangular domain

Cloud feedback in atmospheric general circulation models: An update

Six years ago, we compared the climate sensitivity of 19 atmospheric general circulation models and found a roughly threefold variation among the models; most of this variation was attributed to differences in the models' depictions of cloud feedback. In an update of this comparison, current models showed considerably smaller differences in net cloud feedback, with most producing modest values. There are, however, substantial differences in the feedback components, indicating that the models still have physical disagreements

Effect of hydrogen on ground state structures of small silicon clusters

We present results for ground state structures of small Si$_{n}$H (2 \leq \emph{n} \leq 10) clusters using the Car-Parrinello molecular dynamics. In particular, we focus on how the addition of a hydrogen atom affects the ground state geometry, total energy and the first excited electronic level gap of an Si$_{n}$ cluster. We discuss the nature of bonding of hydrogen in these clusters. We find that hydrogen bonds with two silicon atoms only in Si$_{2}$H, Si$_{3}$H and Si$_{5}$H clusters, while in other clusters (i.e. Si$_{4}$H, Si$_{6}$H, Si$_{7}$H, Si$_{8}$H, Si$_{9}$H and Si$_{10}$H) hydrogen is bonded to only one silicon atom. Also in the case of a compact and closed silicon cluster hydrogen bonds to the cluster from outside. We find that the first excited electronic level gap of Si$_{n}$ and Si$_{n}$H fluctuates as a function of size and this may provide a first principles basis for the short-range potential fluctuations in hydrogenated amorphous silicon. Our results show that the addition of a single hydrogen can cause large changes in the electronic structure of a silicon cluster, though the geometry is not much affected. Our calculation of the lowest energy fragmentation products of Si$_{n}$H clusters shows that hydrogen is easily removed from Si$_{n}$H clusters.Comment: one latex file named script.tex including table and figure caption. Six postscript figure files. figure_1a.ps and figure_1b.ps are files representing Fig. 1 in the main tex

Nonclassical equivalence transformations associated with a parameter identification problem

A special class of symmetry reductions called nonclassical equivalence transformations is discussed in connection to a class of parameter identification problems represented by partial differential equations. These symmetry reductions relate the forward and inverse problems, reduce the dimension of the equation, yield special types of solutions, and may be incorporated into the boundary conditions as well. As an example, we discuss the nonlinear stationary heat conduction equation and show that this approach permits the study of the model on new types of domains. Our MAPLE routine GENDEFNC which uses the package DESOLV (authors Carminati and Vu) has been updated for this propose and its output is the nonlinear partial differential equation system of the determining equations of the nonclassical equivalence transformations.Comment: 18 page

Vortex merger near a topographic slope in a homogeneous rotating fluid

This work is a contribution to the PHYSINDIEN research program. It was supported by CNRS-RFBR contract PRC 1069/16-55-150001.The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This along shelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclone sand near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.PostprintPeer reviewe