Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python framework. There a
re libraries for Julia that cover the majority of scientific and engineering computations demands. The aim of this paper is to combine the usage of the Julia framework for numerical computations and for symbolic computations in mathematical modeling problems. The main functional domains determining various variants of the application of computer algebra systems are described. In each of these domains, generic representatives of computer algebra systems in Julia are distinguished. The conclusion is that it is possible (and even convenient) to use computer algebra systems within the Julia framework.
In research problems that involve the use of numerical methods for solving systems of ordinary differential equations (ODEs), it is often required to select the most efficient method for a particular problem. To solve a Cauchy problem for a system of
ODEs, Runge-Kutta methods (explicit or implicit ones, with or without step-size control, etc.) are employed. In that case, it is required to search through many implementations of the numerical method and select coefficients or other parameters of its numerical scheme. This paper proposes a library and scripts for automated generation of routine functions in the Julia programming language for a set of numerical schemes of Runge-Kutta methods. For symbolic manipulations, we use a template substitution tool. The proposed approach to automated generation of program code allows us to use a single template for editing, instead of modifying each individual function to be compared. On the one hand, this provides universality in the implementation of a numerical scheme and, on the other hand, makes it possible to minimize the number of errors in the process of modifying the compared implementations of the numerical method. We consider Runge-Kutta methods without step-size control, embedded methods with step-size control, and Rosenbrock methods with step-size control. The program codes for the numerical schemes, which are generated automatically using the proposed library, are tested by numerical solution of several well-known problems.
The enormous structural and chemical diversity of metal-organic frameworks (MOFs) forces researchers to actively use simulation techniques on an equal footing with experiments. MOFs are widely known for outstanding adsorption properties, so precise d
escription of host-guest interactions is essential for high-throughput screening aimed at ranking the most promising candidates. However, highly accurate ab initio calculations cannot be routinely applied to model thousands of structures due to the demanding computational costs. On the other side, methods based on force field (FF) parametrization suffer from low transferability. To resolve this accuracy-efficiency dilemma, we apply the machine learning (ML) approach. The trained models reproduce atom-in-material quantities, including partial charges, polarizabilities, dispersion coefficients, quantum Drude oscillator and electron cloud parameters within the accuracy of underlying density functional theory method. The aforementioned FF precursors make it possible to thoroughly describe non-covalent interactions typical for MOF-adsorbate systems: electrostatic, dispersion, polarization, and short-range repulsion. The presented approach can also significantly facilitate hybrid atomistic simulations/ML workflows.
The unprecedented structural flexibility and diversity of inorganic frameworks of layered hybrid halide perovskites (LHHPs) rise up a wide range of useful optoelectronic properties thus predetermining the extraordinary high interest to this family of
materials. Nevertheless, the influence of different types of distortions of their inorganic framework on key physical properties such as band gap has not yet been quantitatively identified. We provided a systematic study of the relationships between LHHPs band gaps and six main structural descriptors of inorganic framework, including interlayer distances (dint), in-plane and out-of-plane distortion angles in layers of octahedra ({theta}in,{theta}out), layer shift factor (LSF), axial and equatorial Pb-I bond distances (dax,deq). Using the set on the selected structural distortions we realized the inverse materials design based on multi-step DFT and machine learning approach to search LHHPs with target values of the band gap. The analysis of calculated descriptors band gap dependences for the wide range of generated model structures of (100) single-layered LHHPs results in the following descending order of their importance:dint > {theta}in > dax > LSFmin > {theta}out > deq > LSFmax, and also implies a strong interaction value for some pairs of structural descriptors. Moreover,we found that the structures with completely different distortions of inorganic framework can have similar band gap, as illustrated by a number of both experimental and model structures.
Different kinds of models are used to study various natural and technical phenomena. Usually, the researcher is limited to using a certain kind of model approach, not using others (or even not realizing the existence of other model approaches). The a
uthors believe that a complete study of a certain phenomenon should cover several model approaches. The paper describes several model approaches which we used in the study of the random early detection algorithm for active queue management. Both the model approaches themselves and their implementation and the results obtained are described.
Asceding interest of the scientific community in layered hybrid halide perovskites (LHHPs) as materials for innovative photovoltaic and optoelectronic applications led to unprecedented expansion of this family of compounds, reaching now several hundr
ed refined structures. Despite the unique structural diversity of LHHPs, traditional approaches of describing their structures, such as dividing into Dion-Jacobson (DJ) or Ruddlesden-Popper (RP) phases for mostt structures are ambiguous and unquantifiable. Here, we introduced a quantitative layer shift factor (LSF) for a univocal classification and quantitative comparison of the structures. We also developed an algorithm for automatic calculation of the LSF for such structures. We demonstrate the application of the proposed approach for an analysis of correlations between LSF and band gap to reveal structure-property relationships. Our study gives a simple and useful approach to classify of either the layered perovskite-like structures or other layered compounds composed of layers of vertex-connected octahedra as a structural unit.
Milky Way dwarf satellites are unique objects that encode the early structure formation and therefore represent a window into the high redshift Universe. So far, their study was conducted using electromagnetic waves only. The future Laser Interferome
ter Space Antenna (LISA) has the potential to reveal Milky Way satellites in gravitational waves emitted by double white dwarf (DWD) binaries. We investigate gravitational wave (GW) signals detectable by LISA as a possible tool for the identification and characterisation of the Milky Way satellites. We use the binary population synthesis technique to model the population of DWDs in dwarf satellites and we assess the impact on the number of LISA detections when making changes to the total stellar mass, distance, star formation history and metallicity of satellites. We calibrate predictions for the known Milky Way satellites on their observed properties. We find that DWDs emitting at frequencies $gtrsim 3,$mHz can be detected in Milky Way satellites at large galactocentric distances. The number of these high frequency DWDs per satellite primarily depends on its mass, distance, age and star formation history, and only mildly depends on the other assumptions regarding their evolution such as metallicity. We find that dwarf galaxies with $M_star>10^6,$M$_{odot}$ can host detectable LISA sources with a number of detections that scales linearly with the satellites mass. We forecast that out of the known satellites, Sagittarius, Fornax, Sculptor and the Magellanic Clouds can be detected with LISA. As an all-sky survey that does not suffer from contamination and dust extinction, LISA will provide observations of the Milky Way and dwarf satellites galaxies valuable for Galactic archaeology and near-field cosmology.
In this work an exactly solvable model of N two-level systems interacting with a single bosonic dephasing reservoir is considered to unravel the role played by collective non-Markovian dephasing. We show that phase estimation with entangled states fo
r this model can exceed the standard quantum limit and demonstrate Heisenberg scaling with the number of atoms for an arbitrary temperature. For a certain class of reservoir densities of states decoherence can be suppressed in the limit of large number of atoms and the Heisenberg limit can be restored for arbitrary interrogation times. We identify the second class of densities when the Heisenberg scaling can be restored for any finite interrogation time. We also find the third class of densities when the standard quantum limit can be exceeded only on the initial stage of dynamics in the Zeno-regime.
Double white dwarf binaries with merger timescales smaller than the Hubble time and with a total mass near the Chandrasekhar limit (i.e. classical Chandrasekhar population) or with high-mass primaries (i.e. sub-Chandrasekhar population) are potential
supernova type Ia (SNIa) progenitors. However, we have not yet unambiguously confirmed the existence of these objects observationally, a fact that has been often used to criticise the relevance of double white dwarfs for producing SNIa. We analyse whether this lack of detections is due to observational effects. To that end we simulate the double white dwarf binary population in the Galaxy and obtain synthetic spectra for the SNIa progenitors. We demonstrate that their identification, based on the detection of Halpha double-lined profiles arising from the two white dwarfs in the synthetic spectra, is extremely challenging due to their intrinsic faintness. This translates into an observational probability of finding double white dwarf SNIa progenitors in the Galaxy of (2.1+-1.0)x10^{-5} and (0.8+-0.4)x10^{-5} for the classical Chandrasekhar and the sub-Chandrasekhar progenitor populations, respectively. Eclipsing double white dwarf SNIa progenitors are found to suffer from the same observational effect. The next generation of large-aperture telescopes are expected to help in increasing the probability for detection by ~1 order of magnitude. However, it is only with forthcoming observations such as those provided by LISA that we expect to unambiguously confirm or disprove the existence of double white dwarf SNIa progenitors and to test their importance for producing SNIa.
We have investigated the influence of the substrate on the fluorescence of adsorbed organic molecules. Monolayer films of perylene-3,4,9,10-tetracarboxylic-3,4,9,10-diimide (PTCDI), a supramolecular network formed from PTCDI and melamine, and perylen
e-3,4,9,10-tetracarboxylic-3,4,9,10-dianhydride (PTCDA) have been deposited on hexagonal boron nitride (hBN). The principal peaks in the fluorescence spectra of these films were red-shifted by up to 0.37 eV relative to published measurements for molecules in helium droplets. Smaller shifts (~0.03 eV) arising from interactions between neighbouring molecules are investigated by comparing the fluorescence of distinct arrangements of PTCDI, which are templated by supramolecular self-assembly and determined with molecular resolution using atomic force microscopy under ambient conditions. We compare our experimental results with red-shifts calculated using a combination of a perturbative model and density functional theory which account for, respectively, resonant and non-resonant effects of a dielectric hBN substrate. We show that the substrate gives rise to a red-shift in the fluorescence of an adsorbed molecule and also screens the interactions between neighbouring transition dipole moments; both these effects depend on the refractive index of the substrate.
