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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., Comment: 22 pages, 12 figures, 6 tables

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.

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., Comment: 10 pages, 7 figures

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.

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., Comment: Accepted for publication in the Astrophysical Journal

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., Comment: KEOD 2019

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.

Modern radio astrometry has reached the limit of the resolution that is determined by the size of the Earth. The only way to overcome that limit is to create the radio telescopes outside our planet. It is proposed to build an autonomous remote-controlled radio observatory on the Moon. Working together with the existing radio telescopes on Earth in the VLBI mode, the new observatory will form an interferometer baseline up to 410000 km, enhancing the present astrometric and geodetic capabilities of VLBI. We perform numerical simulations of Earth-Moon VLBI observations operating simultaneously with the international VLBI network. It is shown that these observations will significantly improve the precision of determination of Moon's orbital motion, libration angles, ICRF, and relativistic parameters.

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.

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.

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., Comment: Presented in a form of a poster at the Seventh International Meeting on Celestial Mechanics (CELMEC VII) on 5 September 2017 at San Martino al Cimino, Italy

The aim of this work is to combine the model of orbital and rotational motion of the Moon developed for DE430 with up-to-date astronomical, geodynamical, and geo- and selenophysical models. The parameters of the orbit and physical libration are determined in this work from LLR observations made at different observatories in 1970-2013. Parameters of other models are taken from solutions that were obtained independently from LLR. A new implementation of the DE430 lunar model, including the liquid core equations, was done within the EPM ephemeris. The postfit residuals of LLR observations make evident that the terrestrial models and solutions recommended by the IERS Conventions are compatible with the lunar theory. That includes: EGM2008 with conventional corrections and variations from solid and ocean tides; displacement of stations due to solid and ocean loading tides; and precession-nutation model. Usage of these models in the solution for LLR observations has allowed us to reduce the number of parameters to be fit. The fixed model of tidal variations of the geopotential has resulted in a lesser value of Moon's extra eccentricity rate, as compared to the original DE430 model with two fit parameters. A mixed model of lunar gravitational potential was used, with some coefficients determined from LLR observations, and other taken from the GL660b solution. Solutions obtain accurate positions for the ranging stations and the 5 retroreflectors. Station motion is derived for sites with long data spans. Dissipation is detected at the lunar fluid core-solid mantle boundary demonstrating that a fluid core is present. Tidal dissipation is strong at both Earth and Moon. Consequently, the lunar semimajor axis is expanding by 38.20 mm/yr, the tidal acceleration in mean longitude is -25.90 "/cy2, and the eccentricity is increasing by 1.48e-11 each year.

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., Comment: IAU working group final report: 41 pages, 11 figures, and 6 tables

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.

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., Comment: 51 pages, 27 figures

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., Comment: 22 pages, 19 pages

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).

Large sparse sets of binary transaction data with millions of records and thousands of attributes occur in various domains: customers purchasing products, users visiting web pages, and documents containing words are just three typical examples. Real-time query selectivity estimation (the problem of estimating the number of rows in the data satisfying a given predicate) is an important practical problem for such databases. We investigate the application of probabilistic models to this problem. In particular, we study a Markov random field (MRF) approach based on frequent sets and maximum entropy, and compare it to the independence model and the Chow-Liu tree model. We find that the MRF model provides substantially more accurate probability estimates than the other methods but is more expensive from a computational and memory viewpoint. To alleviate the computational requirements we show how one can apply bucket elimination and clique tree approaches to take advantage of structure in the models and in the queries. We provide experimental results on two large real-world transaction datasets., Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000)

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-Poincar\'{e} 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.

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., Comment: 16 pp, 12 fig

The geometric nature of Euler fluids has been clearly identified and extensively studied over the years, culminating with Lagrangian and Hamiltonian descriptions of fluid dynamics where the configuration space is defined as the volume-preserving diffeomorphisms, and Kelvin's circulation theorem is viewed as a consequence of Noether's theorem associated with the particle relabeling symmetry of fluid mechanics. However computational approaches to fluid mechanics have been largely derived from a numerical-analytic point of view, and are rarely designed with structure preservation in mind, and often suffer from spurious numerical artifacts such as energy and circulation drift. In contrast, this paper geometrically derives discrete equations of motion for fluid dynamics from first principles in a purely Eulerian form. Our approach approximates the group of volume-preserving diffeomorphisms using a finite dimensional Lie group, and associated discrete Euler equations are derived from a variational principle with non-holonomic constraints. The resulting discrete equations of motion yield a structure-preserving time integrator with good long-term energy behavior and for which an exact discrete Kelvin's circulation theorem holds.