arXiv subjects

Dmitry Pavlov

Publications and source records attributed to Dmitry Pavlov.

At least 19 recordsLinked to original sources

arXiv2025

Definition and Realization of the International Lunar Reference Frame

All future lunar missions require a definition of the lunar reference system and a realization in the form of the lunar reference frame to ensure consistent products for positioning, navigation, cartography, and timing. This paper defines the origin, orientation, and scale of the Lunar Reference System (LRS), as well as provides numerical solutions for the first realization of the International Lunar Reference Frame (ILRF). ILRF is defined as the Principal Axis (PA) system, attached to the surface and co-rotating with the Moon, with its origin in the lunar center of mass (lunocenter). The ILRF realization is based on variance component estimation of the three lunar ephemeris solutions: INPOP21a, DE430, and EPM2021 for the series of the position of the lunar center of mass and rotation Euler angles -- precession, nutation, and proper rotation. The solution is valid starting with the period covered by Lunar Laser Ranging (LLR) data in 1970 and ending with extrapolated ILRF realizations in 2052 for future lunar missions. Results. The combined ILRF is characterized by the mean error of 17.6 cm for 2010-2030, where 15.3 cm comes from the origin and 8.6 cm from the orientation realization. The error in the realization of the origin is mainly caused by a poor geometry of the retroreflector network, resulting in a high correlation between the scale and the X component of the lunocenter in PA. The LLR post-fit residuals in ILRF are at the level of 2-3 cm in terms of the standard deviations of one-way ranges for best-performing LLR stations. The mean errors of the transformation between ILRF and other reference frame realizations in PA are at the level of 3 cm, whereas the mean transformation error to the DE421 Mean Earth frame equals 5 cm.

astro-ph.EP↗

arXiv2023

Velocity of viscous fingers in miscible displacement: Intermediate concentration

We investigate one-phase flow in porous medium corresponding to a miscible displacement process in which the viscosity of the injected fluid is smaller than the viscosity in the reservoir fluid, which frequently leads to the formation of a mixing zone characterized by thin fingers. The mixing zone grows in time due to the difference in speed between its leading and trailing edges. The transverse flow equilibrium (TFE) model provides estimates of these speeds. We propose an enhancement for the TFE estimates, and provide its theoretical justification. It is based on the assumption that an intermediate concentration exists near the tip of the finger, which allows to reduce the integration interval in the speed estimate. Numerical simulations were conducted that corroborate the new estimates within the computational fluid dynamics model. The refined estimates offer greater accuracy than those provided by the original TFE model.

physics.flu-dyn↗

arXiv2023

Reducing roundoff errors in numerical integration of planetary ephemeris

Modern lunar-planetary ephemerides are numerically integrated on the observational timespan of more than 100 years (with the last 20 years having very precise astrometrical data). On such long timespans, not only finite difference approximation errors, but also the accumulating arithmetic roundoff errors become important because they exceed random errors of high-precision range observables of Moon, Mars, and Mercury. One way to tackle this problem is using extended-precision arithmetics available on x86 processors. Noting the drawbacks of this approach, we propose an alternative: using double-double arithmetics where appropriate. This will allow to use only double precision floating-point primitives which have ubiquitous support.

astro-ph.EP↗

arXiv2021

Improving the Solar Wind Density Model Used in Processing of Spacecraft Ranging Observations

Solar plasma as a cause of radio signal delay has been playing an important role in solar and planetary science. Early experiments studying the distribution of electrons near the Sun from spacecraft ranging measurements were designed so that the radio signal was passing close to the Sun. At present, processing of spacecraft tracking observations serves a different goal: precise (at meter level) determination of orbits of planets, most importantly Mars. Solar plasma adds a time-varying delay to those observations, which is, in this case, unwanted and must be subtracted prior to putting the data into planetary solution. Present planetary ephemeris calculate the delay assuming symmetric stationary power-law model of solar plasma. The present work, based on a custom variant of the EPM lunar-planetary ephemeris, raises the question of accuracy and correctness of that assumption and examines alternative models based on in situ data provided by OMNI and on the ENLIL numerical model of solar wind.

physics.space-ph↗

arXiv2019

Role of lunar laser ranging in realization of terrestrial, lunar, and ephemeris reference frames

Three possible applications of lunar laser ranging to space geodesy are studied. First, the determination of daily Earth orientation parameters (UT0 and variation of latitude), which is rarely used nowadays in presence of all-year VLBI, SLR, and GNSS data. The second application is the determination of two (out of three) lunar orientation parameters, i.e. daily corrections to the rotational ephemeris of the Moon. It may be of importance for the future lunar satellite-based navigational systems. The third application is the tie of ephemeris frame (BCRF) to the ICRF. It has been studied before, though in this work it is extensively compared to another realization of the same tie, obtained by spacecraft VLBI observations; also, two different EOP series and two different models of tidal variations of geopotential are applied, with different outcomes on the tie. The EPM lunar-planetary ephemeris, along with its underlying dynamical model and software, was used to obtain the presented results. All available observations were processed, since the earliest made at the end of 1969 at the McDonald observatory till the end of July 2019 (Matera, Grasse and also Wettzell observatory which began to provide data in 2018). The results and some open questions are discussed.

astro-ph.EP↗

arXiv2019

Exploring the Asymmetry of the Solar Corona Electron Density with Very Long Baseline Interferometry

The Sun's corona has interested researchers for multiple reasons, including the search for solution for the famous coronal heating problem and a purely practical consideration of predicting geomagnetic storms on Earth. There exist numerous different theories regarding the solar corona; therefore, it is important to be able to perform comparative analysis and validation of those theories. One way that could help us move towards the answers to those problems is the search for observational methods that could obtain information about the physical properties of the solar corona and provide means for comparing different solar corona models. In this work we present evidence that VLBI observations are, in certain conditions, sensitive to the electron density of the solar corona and are able to distinguish between different electron density models, which makes the technique of VLBI valuable for solar corona investigations. Recent works on the subject used a symmetric power-law model of the electron density in solar plasma; in this work, an improvement is proposed based on a 3D numerical model.

astro-ph.SR↗

arXiv2019

A Comparative Evaluation of Visual and Natural Language Question Answering Over Linked Data

With the growing number and size of Linked Data datasets, it is crucial to make the data accessible and useful for users without knowledge of formal query languages. Two approaches towards this goal are knowledge graph visualization and natural language interfaces. Here, we investigate specifically question answering (QA) over Linked Data by comparing a diagrammatic visual approach with existing natural language-based systems. Given a QA benchmark (QALD7), we evaluate a visual method which is based on iteratively creating diagrams until the answer is found, against four QA systems that have natural language queries as input. Besides other benefits, the visual approach provides higher performance, but also requires more manual input. The results indicate that the methods can be used complementary, and that such a combination has a large positive impact on QA performance, and also facilitates additional features such as data exploration.

cs.IR↗

arXiv2019

Landau: language for dynamical systems with automatic differentiation

Most numerical solvers used to determine free variables of dynamical systems rely on first-order derivatives of the state of the system w.r.t. the free variables. The number of the free variables can be fairly large. One of the approaches of obtaining those derivatives is the integration of the derivatives simultaneously with the dynamical equations, which is best done with the automatic differentiation technique. Even though there exist many automatic differentiation tools, none have been found to be scalable and usable for practical purposes of dynamic systems modeling. Landau is a Turing incomplete statically typed domain-specific language aimed to fill this gap. The Turing incompleteness provides the ability of sophisticated source code analysis and, as a result, a highly optimized compiled code. Among other things, the language syntax supports functions, compile-time ranged for loops, if/else branching constructions, real variables and arrays, and the ability to manually discard calculation where the automatic derivatives values are expected to be negligibly small. In spite of reasonable restrictions, the language is rich enough to express and differentiate any cumbersome paper-equation with practically no effort.

cs.MS↗

arXiv2019

On the Extension of Adams--Bashforth--Moulton Methods for Numerical Integration of Delay Differential Equations and Application to the Moon's Orbit

One of the problems arising in modern celestial mechanics is the need of precise numerical integration of dynamical equations of motion of the Moon. The action of tidal forces is modeled with a time delay and the motion of the Moon is therefore described by a functional differential equation (FDE) called delay differential equation (DDE). Numerical integration of the orbit is normally being performed in both directions (forwards and backwards in time) starting from some epoch (moment in time). While the theory of normal forwards-in-time numerical integration of DDEs is developed and well-known, integrating a DDE backwards in time is equivalent to solving a different kind of FDE called advanced differential equation, where the derivative of the function depends on not yet known future states of the function. We examine a modification of Adams--Bashforth--Moulton method allowing to perform integration of the Moon's DDE forwards and backwards in time and the results of such integration.

math.NA↗

arXiv2019

Using Word Embeddings for Visual Data Exploration with Ontodia and Wikidata

One of the big challenges in Linked Data consumption is to create visual and natural language interfaces to the data usable for non-technical users. Ontodia provides support for diagrammatic data exploration, showcased in this publication in combination with the Wikidata dataset. We present improvements to the natural language interface regarding exploring and querying Linked Data entities. The method uses models of distributional semantics to find and rank entity properties related to user input in Ontodia. Various word embedding types and model settings are evaluated, and the results show that user experience in visual data exploration benefits from the proposed approach.

cs.CL↗

arXiv2017

Are numerical theories irreplaceable? A computational complexity analysis

It is widely known that numerically integrated orbits are more precise than analytical theories for celestial bodies. However, calculation of the positions of celestial bodies via numerical integration at time $t$ requires the amount of computer time proportional to $t$, while calculation by analytical series is usually asymptotically faster. The following question then arises: can the precision of numerical theories be combined with the computational speed of analytical ones? We give a negative answer to that question for a particular three-body problem known as Sitnikov problem. A formal problem statement is given for the the initial value problem (IVP) for a system of ordinary dynamical equations. The computational complexity of this problem is analyzed. The analysis is based on the result of Alexeyev (1968-1969) about the oscillatory solutions of the Sitnikov problem that have chaotic behavior. We prove that any algorithm calculating the state of the dynamical system in the Sitnikov problem needs to read the initial conditions with precision proportional to the required point in time (i.e. exponential in the length of the point's representation). That contradicts the existence of an algorithm that solves the IVP in polynomial time of the length of the input.

nlin.CD↗

arXiv2015

Report of the IAU Commission 4 Working Group on Standardizing Access to Ephemerides and File Format Specification

The IAU Commission 4 Working Group on Standardizing Access to Ephemerides recommends the use of the Spacecraft and Planet Kernel (SPK) format as a standard format for the position ephemerides of planets and other natural solar system bodies, and the use of the Planetary Constants Kernel (PCK) format for the orientation of these bodies. It further recommends that other supporting data be stored in a text PCK. These formats were developed for use by the SPICE Toolkit by the Navigation and Ancillary Information Facility of NASA's Jet Propulsion Laboratory (JPL). The CALCEPH library developed by the Institut de mecanique celeste de calcul des ephemerides (IMCCE) is also able to make use of these files. High accuracy ephemerides available in files conforming to the SPK and PCK formats include: the Development Ephemerides (DE) from JPL, Integrateur Numerique Planetaire de l'Observatoire de Paris (INPOP) from IMCCE, and the Ephemerides Planets and the Moon (EPM), developed by the Institute for Applied Astronomy (IAA). The bulk of this report is a description of the portion of PCK and SPK formats required for these ephemerides. New SPK and PCK data types, both called Type 20: Chebyshev (Velocity Only), have been added. Other changes to the specification are (i) a new object identification number for coordinate time ephemerides and (ii) a set of three new data types that use the TCB rather than the TDB time scale for the ephemerides, but are otherwise identical to their TDB versions.

astro-ph.IM↗

arXiv2015

Geometric Discretization of the EPDiff Equations

The main objective of this paper is to develop a general method of geometric discretization for infinite-dimensional systems and apply this method to the EPDiff equation. The method described below extends one developed by Pavlov et al. for incompressible Euler fluids. Here this method is presented in a general case applicable to all, not only divergence-free, vector fields. Also, a different (pseudospectral) representation of the velocity field is used. We will apply this method to the one-dimensional EPDiff equation and present numerical results.

math.NA↗

arXiv2015

The hyperbolic field theory on the plane of double variable

By analogy to the theory of harmonic fields on the complex plane, we build the theory of wave-like fields on the plane of double variable. We construct the hyperbolic analogues of point vortices, sources, vortice-sources and their higher-order multipole generalizations. We examine the physical aspects and the possibility of extension to the space of polynumbers of higher dimensions.

math-ph↗

arXiv2015

h-Holomorphic Functions of Double Variable and their Applications

The paper studies the complex differentiable functions of double argument and their properties, which are similar to the properties of the holomorphic functions of complex variable: the Cauchy formula, the hyperbolic harmonicity, the properties of general $h$-conformal mappings and the properties of the mappings, which are hyperbolic analogues of complex elementary functions. We discuss the utility of $h$-conformal mappings to solving 2-dimensional hyperbolic problems of Mathematical Physics.

math.GM↗

arXiv2014

Hyperbolic statics in space-time

Based on the concept of material event as an elementary material source that is concentrated on metric sphere of zero radius --- light-cone of Minkowski space-time, we deduce the analog of Coulomb's law for hyperbolic space-time field universally acting between the events of space-time. Collective field that enables interaction of world lines of a pair of particles at rest contains a standard 3-dimensional Coulomb's part and logarithmic addendum. We've found that the Coulomb's part depends on a fine balance between causal and geometric space-time characteristics (the two regularizations concordance).

physics.gen-ph↗

arXiv2010

Geometric, Variational Discretization of Continuum Theories

This study derives geometric, variational discretizations of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central role in these discretizations is played by the geometric formulation of fluid dynamics, which views solutions to the governing equations for perfect fluid flow as geodesics on the group of volume-preserving diffeomorphisms of the fluid domain. Inspired by this framework, we construct a finite-dimensional approximation to the diffeomorphism group and its Lie algebra, thereby permitting a variational temporal discretization of geodesics on the spatially discretized diffeomorphism group. The extension to MHD and complex fluid flow is then made through an appeal to the theory of Euler-Poincaré systems with advection, which provides a generalization of the variational formulation of ideal fluid flow to fluids with one or more advected parameters. Upon deriving a family of structured integrators for these systems, we test their performance via a numerical implementation of the update schemes on a cartesian grid. Among the hallmarks of these new numerical methods are exact preservation of momenta arising from symmetries, automatic satisfaction of solenoidal constraints on vector fields, good long-term energy behavior, robustness with respect to the spatial and temporal resolution of the discretization, and applicability to irregular meshes.

math-ph↗

arXiv2010

Some numerical and algorithmical probelms in the asymptotic representation theory

The article presents the results of experiments in computation of statistical values related to Young diagrams, including the estimates on maximum and average (by Plancherel distribution) dimension of irreducible representation of symmetric group $S_n$. The computed limit shapes of two-dimensional and three-dimensional diagrams distributed by Richardson statistics are presented as well.

math.RT↗