A multiscale finite element framework for additive manufacturing process modeling

This thesis describes a finite element framework for solving partial differential equations with highly varying spatial coefficients. The goal is to model the heat transfer in a heterogeneous powder medium of the selective laser melting process. An operator based framework is developed and the implementation details are discussed. The main idea of the work is based on the two level domain decomposition and construction of special operators to transfer the system between the coarse and fine levels. The system of equations is solved on a coarse level and the solution is transferred to the fine level. The operators are computed using Localized Orthogonal Decomposition (LOD) method. The method is applied to several numerical experiments and an optimal convergence rates in the H1 and L2 norms are observed. The computational efficiency of LOD is studied and its limitations are discussed

Bringing PDEs to JAX with forward and reverse modes automatic differentiation

Partial differential equations (PDEs) are used to describe a variety of physical phenomena. Often these equations do not have analytical solutions and numerical approximations are used instead. One of the common methods to solve PDEs is the finite element method. Computing derivative information of the solution with respect to the input parameters is important in many tasks in scientific computing. We extend JAX automatic differentiation library with an interface to Firedrake finite element library. High-level symbolic representation of PDEs allows bypassing differentiating through low-level possibly many iterations of the underlying nonlinear solvers. Differentiating through Firedrake solvers is done using tangent-linear and adjoint equations. This enables the efficient composition of finite element solvers with arbitrary differentiable programs. The code is available at github.com/IvanYashchuk/jax-firedrake.Comment: Published as a workshop paper at ICLR 2020 DeepDiffEq worksho

Variable Free Spectral Range Spherical Mirror Fabry-Perot Interferometer

A spherical Fabry-Perot interferometer with adjustable mirror spacing is used to produce interference fringes with frequency separation (c/2L)/N, N=2-15. The conditions for observation of these fringes are derived from the consideration of the eigenmodes of the cavity with high transverse indices.Comment: 11 pages, 7 figures, accepted to Siberian Journal of Physic

The Predicative Construction

Aim of investigation. The aim of the study is to investigate, to learn and improve the state of the studied problem of the Predicative construction. Object of investigation. The object of study is the Predicative construction itself. Methods of investigaton. For implementation of the tasks during the investigation of the given subject such methods are used: the analysis and systematization of the material and sources, the content analysis of the literary texts, generalization and comparison of the given theoretical material

Funktioning of the Noun Form (with an Article or without it) in the English Language

The aim of the research is to prove that the article is just a grammatical morpheme which has no meaning of its own, that the whole noun form determines its contextual meaning. The object of the research is the noun form, its functioning in speech with an article or without it. The method which was used is descriptive method. We explore the problem and find out that a noun form with an article or without it has some meanings

Detection of radio frequency magnetic fields using nonlinear magneto-optical rotation

We describe a room-temperature alkali-metal atomic magnetometer for detection of small, high frequency magnetic fields. The magnetometer operates by detecting optical rotation due to the precession of an aligned ground state in the presence of a small oscillating magnetic field. The resonance frequency of the magnetometer can be adjusted to any desired value by tuning the bias magnetic field. We demonstrate a sensitivity of $100\thinspace{\rm pG/\sqrt{Hz}\thinspace(RMS)}$ in a 3.5 cm diameter, paraffin coated cell. Based on detection at the photon shot-noise limit, we project a sensitivity of $20\thinspace{\rm pG/\sqrt{Hz}\thinspace(RMS)}$.Comment: 6 pages, 6 figure

Hyperpolarized xenon nuclear spins detected by optical atomic magnetometry

We report the use of an atomic magnetometer based on nonlinear magneto-optical rotation with frequency modulated light (FM NMOR) to detect nuclear magnetization of xenon gas. The magnetization of a spin-exchange-polarized xenon sample ($1.7$cm$^3$ at a pressure of $5$bar, natural isotopic abundance, polarization 1%), prepared remotely to the detection apparatus, is measured with an atomic sensor (which is insensitive to the leading field of 0.45 G applied to the sample; an independent bias field at the sensor is $140 \mu$G). An average magnetic field of $\sim 10$nG induced by the xenon sample on the 10-cm diameter atomic sensor is detected with signal-to-noise ratio $\sim 10$, limited by residual noise in the magnetic environment. The possibility of using modern atomic magnetometers as detectors of nuclear magnetic resonance and in magnetic resonance imaging is discussed. Atomic magnetometers appear to be ideally suited for emerging low-field and remote-detection magnetic resonance applications.Comment: 4 pages, 4 figure