Dorodnitsyn Computing Centre

Mass spectra of heavy baryons are calculated in the heavy-quark--light-diquark picture in the framework of the QCD-motivated relativistic quark model. The dynamics of light quarks in the diquark as well as the dynamics of the heavy quark and light diquark in the baryon are treated completely relativistically without application of nonrelativistic $v/c$ and heavy quark $1/{m}_{Q}$ expansions. Such an approach allows us to get predictions for the heavy baryon masses for rather high orbital and radial excitations. On this basis the Regge trajectories of heavy baryons for orbital and radial excitations are constructed, and their linearity, parallelism, and equidistance are verified. The relations between the slopes and intercepts of heavy baryons are considered and a comparison of the slopes of Regge trajectories for heavy baryons and heavy-light mesons is performed. All available experimental data on heavy baryons fit nicely to the constructed Regge trajectories. The possible assignment of the quantum numbers to the observed excited charmed baryons is discussed.

Many clustering algorithms, including cluster ensembles, rely on a random component. Stability of the results across different runs is considered to be an asset of the algorithm. The cluster ensembles considered here are based on k-means clusterers. Each clusterer is assigned a random target number of clusters, k and is started from a random initialization. Here, we use 10 artificial and 10 real data sets to study ensemble stability with respect to random k, and random initialization. The data sets were chosen to have a small number of clusters (two to seven) and a moderate number of data points (up to a few hundred). Pairwise stability is defined as the adjusted Rand index between pairs of clusterers in the ensemble, averaged across all pairs. Nonpairwise stability is defined as the entropy of the consensus matrix of the ensemble. An experimental comparison with the stability of the standard k-means algorithm was carried out for k from 2 to 20. The results revealed that ensembles are generally more stable, markedly so for larger k. To establish whether stability can serve as a cluster validity index, we first looked at the relationship between stability and accuracy with respect to the number of clusters, k. We found that such a relationship strongly depends on the data set, varying from almost perfect positive correlation (0.97, for the glass data) to almost perfect negative correlation (-0.93, for the crabs data). We propose a new combined stability index to be the sum of the pairwise individual and ensemble stabilities. This index was found to correlate better with the ensemble accuracy. Following the hypothesis that a point of stability of a clustering algorithm corresponds to a structure found in the data, we used the stability measures to pick the number of clusters. The combined stability index gave best results.

Natural neighbour co-ordinates (Sibson co-ordinates) is a well-known interpolation scheme for multivariate data fitting and smoothing. The numerical implementation of natural neighbour co-ordinates in a Galerkin method is known as the natural element method (NEM). In the natural element method, natural neighbour co-ordinates are used to construct the trial and test functions. Recent studies on NEM have shown that natural neighbour co-ordinates, which are based on the Voronoi tessellation of a set of nodes, are an appealing choice to construct meshless interpolants for the solution of partial differential equations. In Belikov et al. (Computational Mathematics and Mathematical Physics 1997; 37(1) : 9–15), a new interpolation scheme (non-Sibsonian interpolation) based on natural neighbours was proposed. In the present paper, the non-Sibsonian interpolation scheme is reviewed and its performance in a Galerkin method for the solution of elliptic partial differential equations that arise in linear elasticity is studied. A methodology to couple finite elements to NEM is also described. Two significant advantages of the non-Sibson interpolant over the Sibson interpolant are revealed and numerically verified: the computational efficiency of the non-Sibson algorithm in 2-dimensions, which is expected to carry over to 3-dimensions, and the ability to exactly impose essential boundary conditions on the boundaries of convex and non-convex domains. Copyright © 2001 John Wiley & Sons, Ltd.

Masses of the ground state and the orbitally and radially excited states of quark-antiquark mesons composed of light $(u,d,s)$ quarks are calculated within the framework of the relativistic quark model based on the quasipotential approach. The relativistic treatment of the light quark dynamics results in mass spectra which agree well with available experimental data for the masses of the most well-established states. The Regge trajectories for angular and radial excitations are constructed, and their linearity, parallelism, and equidistance are verified. The assignment of experimentally observed light mesons to particular Regge trajectories is based on their masses and quantum numbers.

The mass spectra of the excited heavy baryons consisting of two light (u,d,s) and one heavy (c,b) quarks are calculated in the heavy-quark–light-diquark approximation within the constituent quark model. The light quarks, forming the diquark, and the light diquark in the baryon are treated completely relativistically. The expansion in v/c up to the second order is used only for the heavy (b and c) quarks. The internal structure of the diquark is taken into account by inserting the diquark–gluon interaction form factor. An overall good agreement of the obtained predictions with available experimental data is found.

Abstract. Soil organic matter (SOM) is key to maintaining soil fertility, mitigating climate change, combatting land degradation, and conserving above- and below-ground biodiversity and associated soil processes and ecosystem services. In order to derive management options for maintaining these essential services provided by soils, policy makers depend on robust, predictive models identifying key drivers of SOM dynamics. Existing SOM models and suggested guidelines for future SOM modelling are defined mostly in terms of plant residue quality and input and microbial decomposition, overlooking the significant regulation provided by soil fauna. The fauna controls almost any aspect of organic matter turnover, foremost by regulating the activity and functional composition of soil microorganisms and their physical–chemical connectivity with soil organic matter. We demonstrate a very strong impact of soil animals on carbon turnover, increasing or decreasing it by several dozen percent, sometimes even turning C sinks into C sources or vice versa. This is demonstrated not only for earthworms and other larger invertebrates but also for smaller fauna such as Collembola. We suggest that inclusion of soil animal activities (plant residue consumption and bioturbation altering the formation, depth, hydraulic properties and physical heterogeneity of soils) can fundamentally affect the predictive outcome of SOM models. Understanding direct and indirect impacts of soil fauna on nutrient availability, carbon sequestration, greenhouse gas emissions and plant growth is key to the understanding of SOM dynamics in the context of global carbon cycling models. We argue that explicit consideration of soil fauna is essential to make realistic modelling predictions on SOM dynamics and to detect expected non-linear responses of SOM dynamics to global change. We present a decision framework, to be further developed through the activities of KEYSOM, a European COST Action, for when mechanistic SOM models include soil fauna. The research activities of KEYSOM, such as field experiments and literature reviews, together with dialogue between empiricists and modellers, will inform how this is to be done.

The masses of the ground state heavy baryons consisting of two light ($u,d,s$) and one heavy ($c,b$) quarks are calculated in the heavy-quark--light-diquark approximation within the constituent quark model. The light quarks, forming the diquark, and the light diquark in the baryon are treated completely relativistically. The expansion in $v/c$ up to the second order is used only for the heavy ($b$ and $c$) quarks. The diquark-gluon interaction is taken modified by the form factor describing the light diquark structure in terms of the diquark wave functions. An overall reasonable agreement of the obtained predictions with available experimental data and previous theoretical results is found.

The Boltzmann kinetic equation is solved by a finite-difference method on a fixed coordinate-velocity grid. The projection method is applied that was developed previously by the author for evaluating the Boltzmann collision integral. The method ensures that the mass, momentum, and energy conservation laws are strictly satisfied and that the collision integral vanishes in thermodynamic equilibrium. The last property prevents the emergence of the numerical error when the collision integral of the principal part of the solution is evaluated outside Knudsen layers or shock waves, which considerably improves the accuracy and efficiency of the method. The differential part is approximated by a second-order accurate explicit conservative scheme. The resulting system of difference equations is solved by applying symmetric splitting into collision relaxation and free molecular flow. The steady-state solution is found by the relaxation method.

Rubella viruses (RV) have been found in an association with granulomas in children with primary immune deficiencies (PID). Here, we report the recovery and characterization of infectious immunodeficiency-related vaccine-derived rubella viruses (iVDRV) from diagnostic skin biopsies of four patients. Sequence evolution within PID hosts was studied by comparison of the complete genomic sequences of the iVDRVs with the genome of the vaccine virus RA27/3. The degree of divergence of each iVDRV correlated with the duration of persistence indicating continuous intrahost evolution. The evolution rates for synonymous and nonsynonymous substitutions were estimated to be 5.7 x 10-3 subs/site/year and 8.9 x 10-4 subs/site/year, respectively. Mutational spectra and signatures indicated a major role for APOBEC cytidine deaminases and a secondary role for ADAR adenosine deaminases in generating diversity of iVDRVs. The distributions of mutations across the genes and 3D hotspots for amino acid substitutions in the E1 glycoprotein identified regions that may be under positive selective pressure. Quasispecies diversity was higher in granulomas than in recovered infectious iVDRVs. Growth properties of iVDRVs were assessed in WI-38 fibroblast cultures. None of the iVDRV isolates showed complete reversion to wild type phenotype but the replicative and persistence characteristics of iVDRVs were different from those of the RA27/3 vaccine strain, making predictions of iVDRV transmissibility and teratogenicity difficult. However, detection of iVDRV RNA in nasopharyngeal specimen and poor neutralization of some iVDRV strains by sera from vaccinated persons suggests possible public health risks associated with iVDRV carriers. Detection of IgM antibody to RV in sera of two out of three patients may be a marker of virus persistence, potentially useful for identifying patients with iVDRV before development of lesions. Studies of the evolutionary dynamics of iVDRV during persistence will contribute to development of infection control strategies and antiviral therapies.

Progress in computer hardware and improvement of numerical methods made solution of the Boltzmann equation for rather complex gas dynamic problems real. The method developed by the author is based on a projection technique for evaluation of the collision operator. The computed collision integral is conservative by density, impulse, and energy, and became equal to zero when the solution has a form of the Maxwellian distribution. The later feature sharply increases its efficiency, especially for the near equilibrium flows. The method is extended on a mixture of gases and the gases with internal degrees of freedom, where it can incorporate real physical parameters of molecular potential and of internal energy spectrum. Examples of computations for a range of Mach and Knudsen numbers are presented.

Mass spectra of strange baryons are calculated in the framework of the relativistic quark model based on the quasipotential approach. Baryons are treated as relativistic quark-diquark bound systems. It is assumed that two quarks with equal constituent masses form a diquark. The diquark excitations and its internal structure are consistently taken into account. Calculations are performed up to rather high orbital and radial excitations of strange baryons. On this basis the Regge trajectories are constructed. The obtained results are compared with available experimental data and previous predictions. It is found that all masses of the 4- and 3-star states of strange baryons with established quantum numbers, as well as most of the 2- and 1-star states, are well reproduced. The developed relativistic quark-diquark model predicts less excited states than three-quark models of strange baryons.

Abstract The paper is devoted to the development of an efficient deterministic framework for modelling of three-dimensional rarefied gas flows on the basis of the numerical solution of the Boltzmann kinetic equation with the model collision integrals. The framework consists of a high-order accurate implicit advection scheme on arbitrary unstructured meshes, the conservative procedure for the calculation of the model collision integral and efficient implementation on parallel machines. The main application area of the suggested methods is micro-scale flows. Performance of the proposed approach is demonstrated on a rarefied gas flow through the finite-length circular pipe. The results show good accuracy of the proposed algorithm across all flow regimes and its high efficiency and excellent parallel scalability for up to 512 cores.

An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration ($r$) and velocity ($v$) spaces is produced using a ``tree of trees'' (ToT) data structure. The $r$ mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The $v$ mesh is created on-the-fly in each $r$ cell. Mappings between neighboring $v$-space trees is implemented for the advection operator in $r$ space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive $v$ mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems.

The form factors of weak decays of ${B}_{s}$ mesons to ground state ${D}_{s}^{(*)}$ mesons as well as to their radial ${D}_{s}^{(*)}(2S)$ and orbital ${D}_{sJ}^{(*)}$ excitations are calculated in the framework of the relativistic quark model based on the quasipotential approach. All relativistic effects, including contributions of intermediate negative-energy states and boosts of the meson wave functions, are consistently taken into account. As a result, the form factors are determined in the whole kinematical range without additional phenomenological parametrizations and extrapolations. On this basis, semileptonic decay branching fractions are calculated. Two-body nonleptonic ${B}_{s}$ decays are considered within the factorization approximation. The obtained results agree well with available experimental data.

Abstract In this work we present a methodology for the mapping of Snow Water Equivalent (SWE) temporal variations based on the Synthetic Aperture Radar (SAR) Interferometry technique and Sentinel-1 data. The shift in the interferometric phase caused by the refraction of the microwave signal penetrating the snow layer is isolated and exploited to generate maps of temporal variation of SWE from coherent SAR interferograms. The main advantage of the proposed methodology with respect to those based on the inversion of microwave SAR backscattering models is its simplicity and the reduced number of required in-situ SWE measurements. The maps, updated up to every 6 days, can attain a spatial resolution up to 20 m with sub-centimetre ΔSWE measurement accuracy in any weather and sun illumination condition. We present results obtained using the proposed methodology over a study area in Finland. These results are compared with in-situ measurements of ΔSWE, showing a reasonable match with a mean accuracy of about 6 mm.

We describe the fall of Annama meteorite occurred in the remote Kola Peninsula (Russia) close to Finnish border on 2014 April 19 (local time). The fireball was instrumentally observed by the Finnish Fireball Network. From these observations the strewnfield was computed and two first meteorites were found only a few hundred metres from the predicted landing site on 2014 May 29 and 30, so that the meteorite (an H5 chondrite) experienced only minimal terrestrial alteration. The accuracy of the observations allowed a precise geocentric radiant to be obtained, and the heliocentric orbit for the progenitor meteoroid to be calculated. Backward integrations of the orbits of selected near-Earth asteroids and the Annama meteoroid showed that they rapidly diverged so that the Annama meteorites are unlikely related to them. The only exception seems to be the recently discovered 2014UR116 that shows a plausible dynamic relationship. Instead, analysis of the heliocentric orbit of the meteoroid suggests that the delivery of Annama onto an Earth-crossing Apollo-type orbit occurred via the 3:1 mean motion resonance with Jupiter or the nu6 secular resonance, dynamic mechanisms that are responsible for delivering to Earth most meteorites studied so far.

In many fields of modern science, there are problems adequate formalization of which is indispensable for obtaining practically and theoretically important results. In the terminology of the scientific school of academician Yu.I. Zhuravlev, a formalized problem is uniquely defined by the matrix of information and the information matrix. In the present paper, a whole class of issues related to the formalization of recognition/classification problems is considered, and a universal formalism is proposed for carrying out a metric analysis of poorly formalized problems. Thus, the formalization of a problem can be represented as a successive transition from the set of original descriptions to a particular topology, then to a lattice, and then to a certain metric space. It is shown that the property of Zhuravlev’s regularity is sufficient for the existence of bijective mappings between these mathematical constructs. The possibilities of application of the apparatus developed are illustrated by several issues important for the formalization of the problems: introduction of metrics on the sets of the features and metrics on the sets of objects and analysis of “interactions” between dissimilar feature descriptions.

New relations and transformation formulas for the Appell function F2 (a, b, b′; c, c′; w, z) and confluent Appell functions (Humbert functions) Ψ1, Ψ2 are obtained. These relations include limit formulas, integral representations, differentiation and recurrence formulas. Summation formulas for F2, Ψ1, and Ψ2 are derived.

This paper is devoted to the derivation of novel analytic expressions and bounds for a family of special functions that are useful in wireless communication theory. These functions are the well-known Nuttall Q-function, incomplete Toronto function, Rice Ie-function, and incomplete Lipschitz-Hankel integrals. Capitalizing on the offered results, useful identities are additionally derived between the above functions and Humbert, Φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , function as well as for specific cases of the Kampé de Fériet function. These functions can be considered as useful mathematical tools that can be employed in applications relating to the analytic performance evaluation of modern wireless communication systems, such as cognitive radio, cooperative, and free-space optical communications as well as radar, diversity, and multiantenna systems. As an example, new closed-form expressions are derived for the outage probability over nonlinear generalized fading channels, namely, α-η-μ, α-λ-μ, and α-κ-μ as well as for specific cases of the η-μ and λ-μ fading channels. Furthermore, simple expressions are presented for the channel capacity for the truncated channel inversion with fixed rate and corresponding optimum cutoff signal-to-noise ratio for single-antenna and multiantenna communication systems over Rician fading channels. The accuracy and validity of the derived expressions is justified through extensive comparisons with respective numerical results.

Abstract This paper analyses numerical efforts regarding nanosecond (NS) surface dielectric barrier discharge (SDBD) modelling in atmospheric air. Numerical results of the discharge structure for positive and negative applied voltage pulse polarity, and the features of the physical models and boundary conditions used, are discussed. The results of 2D simulations of the quasi-uniform SDBD mode are presented and compared with the results of other research teams, and with experimental data, to reveal the most appropriate approaches. New results of numerical simulations and analytical estimations of the energy into gas deposition due to NS SDBD driven by a single NS voltage pulse are presented. The problems relating to NS SDBD modelling are discussed.