Recently, a novel type of a multiscale simulation, called Relative Resolution (RelRes), was introduced. In a single system, molecules switch their resolution in terms of their relative separation, with near neighbors interacting via fine-grained pote
ntials yet far neighbors interacting via coarse-grained potentials; notably, these two potentials are analytically parameterized by a multipole approximation. This multiscale approach is consequently able to correctly retrieve across state space, the structural and thermal, as well as static and dynamic, behavior of various nonpolar mixtures. Our current work focuses on the practical implementation of RelRes in LAMMPS, specifically for the commonly used Lennard-Jones potential. By examining various correlations and properties of several alkane liquids, including complex solutions of alternate cooligomers and block copolymers, we confirm the validity of this automated LAMMPS algorithm. Most importantly, we demonstrate that this RelRes implementation gains almost an order of magnitude in computational efficiency, as compared with conventional simulations. We thus recommend this novel LAMMPS algorithm for anyone studying systems governed by Lennard-Jones interactions.
With the example of the 229Th nucleus, which is the most likely candidate for the creation frequency standard of a future, the dynamics of the interplay and the relationship of various resonance conversion mechanisms is analyzed. As a result, a solut
ion is proposed for the so-called thorium puzzle, which consisted of a contradiction between the experimental and theoretical lifetimes of Th+ ions. First, the solution demonstrates the dependence of the lifetime of the nuclear isomer on the ambient conditions. Second, it demonstrates the leveling role of the fragmentation of the single-electron levels, which makes the resonance amplification of the electron-nuclear interaction more likely. Both of these trends lead to a probable decrease of the theoretical lifetime towards agreement with experiment.
We study resource similarity and resource bisimilarity -- congruent restrictions of the bisimulation equivalence for the (P,P)-class of Process Rewrite Systems (PRS). Both these equivalences coincide with the bisimulation equivalence for (1,P)-subcla
ss of (P,P)-PRS, which is known to be decidable. While it has been shown in the literature that resource similarity is undecidable for (P,P)-PRS, decidability of resource bisimilarity for (P,P)-PRS remained an open question. In this paper, we present an algorithm for checking resource bisimilarity for (P,P)-PRS. We show that although both resource similarity and resource bisimilarity are congruences and have a finite semi-linear basis, only the latter is decidable.
If not properly accounted for, unresolved binary stars can induce a bias in the photometric determination of star cluster masses inferred from star counts and the luminosity function. A correction factor close to 1.15 (for a binary fraction of 0.35)
was found in citep{Boro19}, which needs to be applied to blind photometric mass estimates. This value for the correction factor was found to be smaller than literature values. In an attempt to lift this discrepancy, in this work the focus is on higher order multiple stars with the goal of investigating the effect of triple and quadruple systems adopting the same methodology and data-set as in the quoted work. Then the result is found that when triple and quadruple together with binary systems are properly accounted for, the actual cluster mass (computed as all stars were single) should be incremented by a factor of 1.18$-$1.27, depending on the cluster and when the binary fraction $alpha$ is 0.35. Fitting formulae are provided to derive the increment factor for different binary star percentages.
It is known that hyperedge replacement grammars are similar to string context-free grammars in the sense of definitions and properties. Therefore, we expect that there is a generalization of the well-known Greibach normal form from string grammars to
hypergraph grammars. Such generalized normal forms are presented in several papers; however, they do not cover a large class of hypergraph languages (e.g. languages consisting of star graphs). In this paper, we introduce a weak Greibach normal form, whose definition corresponds to the lexicalized normal form for string grammars, and prove that every context-free hypergraph language (with nonsubstantial exceptions) can be generated by a grammar in this normal form. The proof presented in this paper generalizes a corresponding one for string grammars with a few more technicalities.
The energy spectrum of primary cosmic rays at energies between at 2x10$^{13}$ - 3x10$^{17}$ eV is presented according to data from the Tien Shan array on the basis of the detection of the number of electrons in extensive air showers. In the energy ra
nge 5x10$^{15}$ - 3x10$^{17}$ eV, the spectrum was obtained by means of the HADRON array and was extended to the region of lower energies from 2x10$^{13}$ eV on the basis of the results of an individual experiment. The changes in the slope of the spectrum in the energy range of 10$^{16}$ - 3x10$^{17}$ eV and a feature of this spectrum at about 1017 eV are analyzed in detail and are described. The spectrum in question is compared with the results obtained at some other arrays.
In this survey, we explore Andrei Nikolayevich Kolmogorovs seminal work in just one of his many facets: its influence Computer Science especially his viewpoint of what herein we call Algorithmic Theory of Informatics. Can a computer file reduce its
size if we add to it new symbols? Do equations of state like second Newton law in Physics exist in Computer Science? Can Leibniz principle of identification by indistinguishability be formalized? In the computer, there are no coordinates, no distances, and no dimensions; most of traditional mathematical approaches do not work. The computer processes finite binary sequences i.e. the sequences of 0 and 1. A natural question arises: Should we continue today, as we have done for many years, to approach Computer Science problems by using classical mathematical apparatus such as mathematical modeling? The first who drew attention to this question and gave insightful answers to it was Kolmogorov in 1960s. Kolmogorovs empirical postulate about existence of a program that translates a natural number into its binary record and the record into the number formulated in 1958 represents a hint of Kolmogorovs approach to Computer Science. Following his ideas, we interpret Kolmogorov algorithm, Kolmogorov machine, and Kolmogorov complexity in the context of modern information technologies showing that they essentially represent fundamental elements of Algorithmic Theory of Informatics, Kolmogorov Programmable Technology, and new Komputer Mathematics i.e. Mathematics of computers.
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V.A.Topchii
, n V.A.Vatutin (Steklov Mathematical Institute of Russian Academy of Sciences
2020
We consider an indecomposable Galton-Watson branching process with countably infinitely many types. Assuming that the process is critical and allowing for infinite variance of the offspring sizes of some (or all) types of particles we describe the as
ymptotic behavior of the survival probability of the process and establish a Yaglom-type conditional limit theorem for the infinite-dimensional vector of the number of particles of all types.
We present the discovery of correlations between the X-ray spectral (photon) index and mass accretion rate observed in active galactic nuclei (AGNs) 3C~454.3 and M87. We analyzed spectral transition episodes observed in these AGNs using Chandra, Swif
t, Suzaku, BeppoSAX, ASCA and RXTE data. We applied a scaling technique for a black hole (BH) mass evaluation which uses a correlation between the photon index (Gamma) and normalization of the seed component which is proportional to a disk mass accretion rate Mdot. We developed an analytical model that shows that Gamma of the BH emergent spectrum undergoes an evolution from lower to higher values depending on Mdot. To estimate a BH mass in 3C~454.3 we consider extra-galactic SMBHs NGC~4051 and NGC~7469 as well as Galactic BHs Cygnus X--1 and GRO~J1550--564 as reference sources for which distances, inclination angles are known and the BH masses are already evaluated. For M87 on the other hand, we provide the BH mass scaling using extra-galactic sources (IMBHs: ESO 243-49 HLX 1 and M 101 ULX--1) and Galactic sources (stellar mass BHs: XTE J1550-564, 4U 1630-472, GRS 1915+105 and H 1743-322) as reference sources. Application of the scaling technique for the photon index-Mdot correlation provides estimates of the BH masses in 3C 454.3 and M87 to be about 3.4x10^9 and 5.6 x10^7 solar masses, respectively. We also compared our scaling BH mass estimates with a recent BH mass estimate of M_{87}=6.5x 10^9 M_{odot} made using the {Event Horizon Telescope} which gives an image at 1.3 mm and is based on the angular size of the `BH event horizon. Our BH mass estimate in M87 is at least two orders of magnitude lower than that made by the EHT team.
This paper examines the transverse momentum spectra of hadrons in the multiparticle production at LHC in the framework of the Quark-Gluon String Model (QGSM). It discusses the dependence of average pt on the masses of mesons and baryons at the LHC en
ergy 7 TeV. The QGSM description of the experimental spectra of various hadrons led to the number of conclusions. I. The average transverse momenta of baryons and mesons are growing with the hadron mass and for beauty hadrons, they are almost equal to the mass. II. By the product of research, a regularity has been detected in the mass gaps between hadron generations. This hypothesis suggests some hidden symmetrical (neither-meson-nor-baryon) neutral hadron states with the masses: 0.251,0.682,1.85,5.04,13.7,37.2,101.,275.,748.... GeV, which is produced by geometrical progression with the mass factor of order delta(ln M)=1. III. The baryon-meson symmetry seems broken until the mass of beauty hadrons, then the hidden states should be more and more stable with the growth of the mass, so the suggested sequence of hadronic states is a proper candidate for the Dark Matter that, you know, contributes the valuable part to the mass of Universe. The growing average transverse momenta are extrapolated with a similar function, as for energy dependence of average baryon pt, < pt > ~ M**0.1.
