arXiv subjects

Mikhail Belyaev

Publications and source records attributed to Mikhail Belyaev.

46 records · Page 3Linked to original sources

arXiv2016

Kernel classification of connectomes based on earth mover's distance between graph spectra

In this paper, we tackle a problem of predicting phenotypes from structural connectomes. We propose that normalized Laplacian spectra can capture structural properties of brain networks, and hence graph spectral distributions are useful for a task of connectome-based classification. We introduce a kernel that is based on earth mover's distance (EMD) between spectral distributions of brain networks. We access performance of an SVM classifier with the proposed kernel for a task of classification of autism spectrum disorder versus typical development based on a publicly available dataset. Classification quality (area under the ROC-curve) obtained with the EMD-based kernel on spectral distributions is 0.71, which is higher than that based on simpler graph embedding methods.

cs.CV↗

arXiv2016

Incompressible Modes Excited by Supersonic Shear in Boundary Layers: Acoustic CFS Instability

We present an instability for exciting incompressible modes (e.g. gravity or Rossby modes) at the surface of a star accreting through a boundary layer. The instability excites a stellar mode by sourcing an acoustic wave in the disk at the boundary layer, which carries a flux of energy and angular momentum with the opposite sign as the energy and angular momentum density of the stellar mode. We call this instability the acoustic CFS instability, because of the direct analogy to the Chandrasekhar-Friedman-Schutz instability for exciting modes on a rotating star by emission of energy in the form of gravitational waves. However, the acoustic CFS instability differs from its gravitational wave counterpart in that the fluid medium in which the acoustic wave propagates (i.e.\ the accretion disk) typically rotates faster than the star in which the incompressible mode is sourced. For this reason, the instability can operate even for a non-rotating star in the presence of an accretion disk. We discuss applications of our results to high-frequency quasi-periodic oscillations in accreting black hole and neutron star systems and dwarf nova oscillations in cataclysmic variables.

astro-ph.HE↗

arXiv2016

GTApprox: surrogate modeling for industrial design

We describe GTApprox - a new tool for medium-scale surrogate modeling in industrial design. Compared to existing software, GTApprox brings several innovations: a few novel approximation algorithms, several advanced methods of automated model selection, novel options in the form of hints. We demonstrate the efficiency of GTApprox on a large collection of test problems. In addition, we describe several applications of GTApprox to real engineering problems.

cs.MS↗

arXiv2016

PICsar: A 2.5D Axisymmetric, Relativistic, Electromagnetic, Particle in Cell Code with a Radiation Absorbing Boundary

We present PICsar -- a new Particle in Cell code geared towards efficiently simulating the magnetosphere of the aligned rotator. PICsar is a special relativistic, electromagnetic, charge conservative code that can be used to simulate arbitrary electromagnetics problems in axisymmetry. It features stretchable body-fitted coordinates that follow the surface of a sphere, simplifying the application of boundary conditions in the case of the aligned rotator; a radiation absorbing outer boundary, which allows a steady state to be set up dynamically and maintained indefinitely from transient initial conditions; and algorithms for injection of charged particles into the simulation domain. The code is parallelized using MPI and scales well to a large number of processors. We discuss the numerical methods used in PICsar and present tests of the code. In particular, we show that PICsar can accurately and efficiently simulate the magnetosphere of the aligned monopole rotator in the force free limit. We present simulations of the aligned dipole rotator in a forthcoming paper.

astro-ph.HE↗

arXiv2015

The Properties of G-modes in Layered Semi-Convection

We study low frequency waves that propagate in a region of layered semi-convection. Layered semi-convection is predicted to be present in stellar and planetary interiors and can significantly modify the rate of thermal and compositional mixing. We derive a series of analytical dispersion relations for plane-parallel layered semi-convection in the Boussinesq approximation using a matrix transfer formalism. We find that like a continuously stratified medium, a semi-convective staircase -- in which small convective regions are separated by sharp density jumps -- supports internal gravity waves (g-modes). When the wavelength is much longer than the distance between semi-convective steps, these behave nearly like g-modes in a continuously stratified medium. However, the g-mode period spacing in a semi-convective region is systematically {\em smaller} than in a continuously stratified medium, and it decreases with decreasing mode frequency. When the g-mode wavelength becomes comparable to the distance between semi-convective steps, the g-mode frequencies deviate significantly from those of a continuously stratified medium (the frequencies are higher). G-modes with vertical wavelengths smaller than the distance between semi-convective steps are evanescent and do not propagate in the staircase. Thus, there is a lower cutoff frequency for a given horizontal wavenumber. We generalize our results to gravito-inertial waves relevant for rapidly rotating stars and planets. Finally, we assess the prospects for detecting layered semi-convection using astero/planetary seismology.

astro-ph.SR↗

arXiv2014

Exact Inference for Gaussian Process Regression in case of Big Data with the Cartesian Product Structure

Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the most popular algorithms for approximation - Gaussian Process regression - can be hardly applied due to its computational complexity. In this paper a new approach for Gaussian Process regression in case of factorial design of experiments is proposed. It allows to efficiently compute exact inference and handle large multidimensional data sets. The proposed algorithm provides fast and accurate approximation and also handles anisotropic data.

stat.ME↗

arXiv2012

A New Way to Conserve Total Energy for Eulerian Hydrodynamic Simulations with Self-Gravity

We propose a new method to conserve the total energy to round-off error in grid-based codes for hydrodynamic simulations with self-gravity. A formula for the energy flux due to the work done by the the self-gravitational force is given, so the change in total energy can be written in conservative form. Numerical experiments with the code Athena show that the total energy is indeed conserved with our new algorithm and the new algorithm is second order accurate. We have performed a set of tests that show the numerical errors in the traditional, non-conservative algorithm can affect the dynamics of the system. The new algorithm only requires one extra solution of the Poisson equation, as compared to the traditional algorithm which includes self-gravity as a source term. If the Poisson solver takes a negligible fraction of the total simulation time, such as when FFTs are used, the new algorithm is almost as efficient as the original method. This new algorithm is useful in Eulerian hydrodynamic simulations with self-gravity, especially when results are sensitive to small energy errors, as for radiation pressure dominated flow.

astro-ph.IM↗

arXiv2011

Supersonic Shear Instabilities in Astrophysical Boundary Layers

Disk accretion onto weakly magnetized astrophysical objects often proceeds via a boundary layer that forms near the object's surface, in which the rotation speed of the accreted gas changes rapidly. Here we study the initial stages of formation for such a boundary layer around a white dwarf or a young star by examining the hydrodynamical shear instabilities that may initiate mixing and momentum transport between the two fluids of different densities moving supersonically with respect to each other. We find that an initially laminar boundary layer is unstable to two different kinds of instabilities. One is an instability of a supersonic vortex sheet (implying a discontinuous initial profile of the angular speed of the gas) in the presence of gravity, which we find to have a growth rate of order (but less than) the orbital frequency. The other is a sonic instability of a finite width, supersonic shear layer, which is similar to the Papaloizou-Pringle instability. It has a growth rate proportional to the shear inside the transition layer, which is of order the orbital frequency times the ratio of stellar radius to the boundary layer thickness. For a boundary layer that is thin compared to the radius of the star, the shear rate is much larger than the orbital frequency. Thus, we conclude that sonic instabilities play a dominant role in the initial stages of nonmagnetic boundary layer formation and give rise to very fast mixing between disk gas and stellar fluid in the supersonic regime.

astro-ph.SR↗

arXiv2011

Non-Power Law Behavior in Fragmentation Cascades

Collisions resulting in fragmentation are important in shaping the mass spectrum of minor bodies in the asteroid belt, the Kuiper belt, and debris disks. Models of fragmentation cascades typically find that in steady-state, the solution for the particle mass distribution is a power law in the mass. However, previous studies have typically assumed that the mass of the largest fragment produced in a collision with just enough energy to shatter the target and disperse half its mass to infinity is directly proportional to the target mass. We show that if this assumption is not satisfied, then the power law solution for the steady-state particle mass distribution is modified by a multiplicative factor, which is a slowly varying function of the mass. We derive analytic solutions for this correction factor and confirm our results numerically. We find that this correction factor proves important when extrapolating over many orders of magnitude in mass, such as when inferring the number of large objects in a system based on infrared observations. In the course of our work, we have also discovered an unrelated type of non-power law behavior: waves can persist in the mass distribution of objects even in the absence of upper or lower cutoffs to the mass distribution or breaks in the strength law.

astro-ph.EP↗

arXiv2010

The Dynamics of Dust Grains in the Outer Solar System

We study the dynamics of large dust grains >1 micron with orbits outside of the heliosphere (beyond 250 AU). Motion of the Solar System through the interstellar medium (ISM) at a velocity of 26 km/s subjects these particles to gas and Coulomb drag (grains are expected to be photoelectrically charged) as well as the Lorentz force and the electric force caused by the induction electric field. We show that to zeroth order the combined effect of these forces can be well described in the framework of the classical Stark problem: particle motion in a Keplerian potential subject to an additional constant force. Based on this analogy, we elucidate the circumstances in which the motion becomes unbound, and show that under local ISM conditions dust grains smaller than ~100 microns originating in the Oort Cloud (e.g. in collisions of comets) beyond 10000 AU are ejected from the Solar System under the action of the electric force. Orbital motion of larger, bound grains is described analytically using the orbit-averaged Hamiltonian approach and consists of orbital plane precession at a fixed semi-major axis, accompanied by the periodic variations of the inclination and eccentricity (the latter may approach unity in some cases). A more detailed analysis of the combined effect of gas and Coulomb drag shows it is possible to reduce particle semi-major axes, but that the degree of orbital decay is limited (a factor of several at best) by passages through atomic and molecular clouds, which easily eject small particles.

astro-ph.EP↗