Synteny Paths for Assembly Graphs Comparison

Despite the recent developments of long-read sequencing technologies, it is still difficult to produce complete assemblies of eukaryotic genomes in an automated fashion. Genome assembly software typically output assembled fragments (contigs) along with assembly graphs, that encode all possible layouts of these contigs. Graph representation of the assembled genome can be useful for gene discovery, haplotyping, structural variations analysis and other applications. To facilitate the development of new graph-based approaches, it is important to develop algorithms for comparison and evaluation of assembly graphs produced by different software. In this work, we introduce synteny paths: maximal paths of homologous sequence between the compared assembly graphs. We describe Asgan - an algorithm for efficient synteny paths decomposition, and use it to evaluate assembly graphs of various bacterial assemblies produced by different approaches. We then apply Asgan to discover structural variations between the assemblies of 15 Drosophila genomes, and show that synteny paths are robust to contig fragmentation. The Asgan tool is freely available at: https://github.com/epolevikov/Asgan

Numerical modeling of a static magnetic fluid seal subject to diffusion of ferromagnetic particles

Because magnetic fluid is a stable colloidal suspension of small ferromagnetic particles in a carrier liquid, its macroscopic interaction with an external nonuniform magnetic field is determined by the force acting on each separate particle

Numerical modelling of magnetic shielding by a cylindrical ferrofluid layer

A coupled method of finite differences and boundary elements is applied to solve a nonlinear transmission problem of magnetostatics. The problem describes an interaction of a uniform magnetic field with a cylindrical ferrofluid layer. Ferrofluid magnetisations, based on expansions over the Langevin law, are considered to model ferrofluids with a different concentration of ferroparticles. The shielding effectiveness factor of the cylindrical thick-walled ferrofluid layer is calculated depending on intensities of the uniform magnetic field and on thickness of the ferrofluid layer

ADI approach to the particle diffusion problem in magnetic fluids

The present study is devoted to the development of an ADI approach to simulate two-dimensional time-dependent diffusion process of ferromagnetic particles in magnetic fluids. Specific features of the problem are the Neumann boundary conditions. We construct an ADI scheme of formally second order accuracy approximation in time and space. It is proved that the scheme is absolutely stable and it has the accuracy in the energy norm of the second order in time and the order 3/2 in space. The numerical results of a test problem indicate that the convergence rate in space is of the second order as wel

Instability of magnetic fluid in a narrow gap between plates

The behavior of a layer of magnetic fluid in a plane capillary subjected to a uniform magnetic field is studied numerically. Two different types of instabilities arise as the intensity of the magnetic field increases. For small contact angles the layer breaks along the capillary axis and spreads over the capillary wall whereas for large contact angles the layer elongates in the central part up to its separation from the walls. Critical parameters and shapes are studied by solving the coupled nonlinear system of differential equations numericall

Numerical Study of Diffusion of Interacting Particles in a Magnetic Fluid Layer

The paper is devoted to construction of mathematical model and computational algorithm for determining equilibrium shapes of a free surface of a magnetic fluid subject to diffusion of ferromagnetic particles in the fluid. The mathematical model consists of the Maxwell equations to determine the structure of magnetic field, the mass transfer equation for the particles, and the Young-Laplace equations for the fluid-air interface as well. Models of the uniform distribution of the particles, the nonuniform distribution without considering the particle interaction, and the nonuniform distribution subject to the particle interaction are considered. Numerical comparison of the models is carried out on the ferrohydrostatic problem of stability of a magnetic-fluid layer under a uniform magnetic fiel

Influence of diffusion of magnetic particles on stability of a static magnetic fluid seal under the action of external pressure drop

We derive a mathematical model for studying the stability of magnetic fluid seal under the action of external pressure drop in the static case. We propose a numerical algorithm for computing the free surface shape under the influence of diffusion of magnetic particles. We include also the case in which the particle concentration achieves its maximum corresponding to the dense packing of the particles. Numerical experiments for various sets of parameters give interesting insights in the dependence of the burst pressure on different parameter

Numerical study of the Rosensweig instability in a magnetic fluid subject to diffusion of magnetic particles

The present study is devoted to the classical problem on stability of a magnetic fluid layer under the influence of gravity and a uniform magnetic field. A periodical peak-shaped stable structure is formed on the fluid surface when the applied magnetic field exceeds a critical value. The mathematical model describes a single peak in the pattern assuming axial symmetry of the peak shape. The field configuration in the whole space, the magnetic particle concentration inside the fluid and the free surface structure are unknown quantities in this model. The unknown free surface is treated explicitly, using a parametric representation with respect to the arc length. The nonlinear problem is discretized by means of a finite element method for the Maxwell's equations and a finite-difference method for the free surface equations. Numerical modeling allows to get overcritical equilibrium free surface shapes in a wide range of applied field intensities. Our numerical results show a significant influence of the particle diffusion on the overcritical shape

Equilibrium shapes of a ferrofluid drop

A numerical solution strategy for calculating equilibrium free surfaces of a ferrofluid drop under the action of uniform magnetic fields is proposed. Based on this strategy, drop shapes of nonlinear magnetizable fluids are obtained numerically in a wide range of field intensities and compared with existing theoretical result

Numerical modeling of the equilibrium shapes of a ferrofluid drop in an external magnetic field

A numerical solution strategy for calculating equilibrium free surfaces of a magnetic fluid under the action of a magnetic field is proposed and applied to determine shapes of a linear magnetizable ferrofluid drop in a uniform magnetic field. Hysteresis phenomena for the drop deformation and the drop shapes with ends, close to conical, were observed numericall