Multipole Model Research Articles

Russian economy in the conditions of institutional transformation of moving towards a multipolar world

Aim. To identify the key institutional characteristics of the transition to a multipolar world and to substantiate the directions of development of the Russian economy during this transition, contributing to the restoration of Russia’s position as an economic and political center of power in the new model of the world order.Objectives. To consider the institutional foundations of the world order to determine the place of multipolarity among other types of world order; to trace the features of the transition to a multipolar world as an institutional transformation from the point of counteraction to the dominance of one superpower; to formulate the directions of transformation of the Russian economy during the transition to a multipolar world.Methods. Using general methods of scientific cognition, as well as institutional and civilizational approaches, the paper considers the transition to a multipolar world as a natural stage of transition to a new model of world order, reflecting the evolution of world economic patterns and their corresponding world orders.Results. The regulatory functions of formal and value-ethical institutions in the institutional environment of the world order, as well as the role of states and civilizations as their sources and guarantors are determined. Institutional gaps in the models of unipolar and multipolar worlds are revealed. The thesis that the movement to the multipolar world model implies institutional transformation in economic, socio-spiritual and political aspects is substantiated. The role of values and conscious efforts of states in the transition to a multipolar world is shown. The main challenges and threats in the transition to a multipolar world for the Russian economy are identified and the directions of efforts necessary for its strengthening are formulated.Conclusions. The transition to a multipolar world is a complex process of transformation of the institutions of the world order and the world economic order on the basis of taking into account the national interests and values of a large number of global actors. During the period of institutional transformation of the transition, the Russian state faces new challenges in the sociovalue, economic and political spheres. The development of the Russian economy in the transition period should become the basis for strengthening the economic and political power of the country, its national sovereignty and provide a worthy place for Russia in the new model of the world order.

Multipole couplings and resonance shifts in an array of dielectric particles at oblique incidence

In the present paper, we propose a coupled multipole model to treat the mutual interactions between nanoparticles aligned in a periodic array, which may be frequently encountered in designing metasurfaces and other functional electromagnetic structures. Our model is comprehensive in that it takes into account the electric and magnetic multipoles both up to the quadrupole order. Working under Cartesian coordinates, this model can readily give the multipole responses of the particles in an infinite array at both normal and oblique incidence. In particular, we work out the analytical expressions of the cross-multipole coupling tensors, which are much more complicated for oblique incidence than normal incidence. We invoke the Ewald method to efficiently and accurately calculate the involved lattice sum whose convergence is otherwise very slow. By quantifying the contributions from the various couplings, we are able to analyze the mechanisms of new resonances that emerge only at oblique incidence. As a prototypical example, we use this method to give physically clear explanations of and show flexible control on the resonance shifts of the multipoles of an array of silicon spheres. The power of this model makes it very promising for dealing with metasurfaces with extended areas or working at large numerical apertures.

Streamlining and Optimizing Strategies of Electrostatic Parameterization.

Accurate characterization of electrostatic interactions is crucial in molecular simulation. Various methods and programs have been developed to obtain electrostatic parameters for additive or polarizable models to replicate electrostatic properties obtained from experimental measurements or theoretical calculations. Electrostatic potentials (ESPs), a set of physically well-defined observables from quantum mechanical (QM) calculations, are well suited for optimization efforts due to the ease of collecting a large amount of conformation-dependent data. However, a reliable set of QM ESP computed at an appropriate level of theory and atomic basis set is necessary. In addition, despite the recent development of the PyRESP program for electrostatic parameterizations of induced dipole-polarizable models, the time-consuming and error-prone input file preparation process has limited the widespread use of these protocols. This work aims to comprehensively evaluate the quality of QM ESPs derived by eight methods, including wave function methods such as Hartree-Fock (HF), second-order Møller-Plesset (MP2), and coupled cluster-singles and doubles (CCSD), as well as five hybrid density functional theory (DFT) methods, used in conjunction with 13 different basis sets. The highest theory levels CCSD/aug-cc-pV5Z (a5z) and MP2/aug-cc-pV5Z (a5z) were selected as benchmark data over two homemade data sets. The results show that the hybrid DFT method, ωB97X-D, combined with the aug-cc-pVTZ (a3z) basis set, performs well in reproducing ESPs while taking both accuracy and efficiency into consideration. Moreover, a flexible and user-friendly program called PyRESP_GEN was developed to streamline input file preparation. The restraining strengths, along with strategies for polarizable Gaussian multipole (pGM) model parameterizations, were also optimized. These findings and the program presented in this work facilitate the development and application of induced dipole-polarizable models, such as pGM models, for molecular simulations of both chemical and biological significance.

Indium Kα radiation from a MetalJet X-ray source: the long way to a successful charge-density investigation.

The MetalJet X-ray source provides indium Kα radiation with a wavelength even shorter than Ag radiation. This paper reports on problematic spectral impurities and presents possible countermeasures so that collection of data with excellent quality up to a high resolution is possible. It is demonstrated that these data can be used in the refinement of a multipole model, the results of which are used for a topological analysis to assess the bonding situation in a sulfur ylide compound.

Comparative study of conventional and synchrotron X-ray electron densities on molecular crystals.

Five different electron density datasets obtained from conventional and synchrotron single crystal X-ray diffraction experiments are compared. The general aim of the study is to investigate the quality of data for electron density analysis from current state-of-the-art conventional sources, and to see how the data perform in comparison with high-quality synchrotron data. A molecular crystal of melamine was selected as the test compound due to its ability to form excellent single crystals, the light atom content, and an advantageous suitability factor of 3.6 for electron density modeling. These features make melamine an optimal system for conventional X-ray diffractometers since the inherent advantages of synchrotron sources such as short wavelength and high intensity are less critical in this case. Data were obtained at 100 K from new in-house diffractometers Rigaku Synergy-S (Mo and Ag source, HyPix100 detector) and Stoe Stadivari (Mo source, EIGER2 1M CdTe detector), and an older Oxford Diffraction Supernova (Mo source, Atlas CCD detector). The synchrotron data were obtained at 25 K from BL02B1 beamline at SPring-8 in Japan (λ = 0.2480 Å, Pilatus3 X 1M CdTe detector). The five datasets were compared on general quality parameters such as resolution, ⟨I/σ⟩, redundancy and R factors, as well as the more model specific fractal dimension plot and residual density maps. Comparison of the extracted electron densities reveals that all datasets can provide reliable multipole models, which overall convey similar chemical information. However, the new laboratory X-ray diffractometers with advanced pixel detector technology clearly measure data with significantly less noise and much higher reliability giving densities of higher quality, compared to the older instrument. The synchrotron data have higher resolution and lower measurement temperature, and they allow for finer details to be modeled (e.g. hydrogen κ parameters).

Non-invasive glucose sensing via the fingernail bed using THz radiation

Abstract The possibility of establishing a novel technique for reliably accessing glycemic information in a non-invasive, easy to implement method at THz frequencies via the fingernail bed is investigated. The nail bed’s major content is blood at its various glucose levels and is also partially protected from environmental conditions by the nail plate, making it a desirable platform for non-invasive glucose sensing. The study is based on a 2D computational electromagnetics (EM) model of the layered fingernail in COMSOL Multiphysics, where the required dielectric function (i.e. permittivity and conductivity) of the fingernail plate is measured using THz-Time-Domain- Spectroscopy (THz-TDS), and the glucose-dependend dielectric functions of the fingernail bed are taken from available experimental data in the literature. From this data a material model using a multipole Cole-Cole model is established for both, the nail plate and the nail bed, where the glucose content in the latter is varied from 3.0-19.0 mmol/l. A numerical analysis of the THz reflectometry at the fingernail in the frequency range of 0.1-2.0 THz revealed that the reflectance spectra are sensitive to the glucose content in the nail bed proving that accurate glucose sensing via the fingernail bed may become feasible around 0.2-0.4 THz.

Applicability of transferable multipole pseudo-atoms for restoring inner-crystal electronic force density fields. Chemical bonding and binding features in the crystal and dimer of 1,3-bis(2-hydroxyethyl)-6-methyluracil.

We considered it timely to test the applicability of transferable multipole pseudo-atoms for restoring inner-crystal electronic force density fields. The procedure was carried out on the crystal of 1,3-bis(2-hydroxyethyl)-6-methyluracil, and some derived properties of the scalar potential and vector force fields were compared with those obtained from the experimental multipole model and from the aspherical pseudo-atom model with parameters fitted to the calculated structure factors. The procedure was shown to accurately replicate the general vector-field behavior, the peculiarities of the quantum potentials and the characteristics of the force-field pseudoatoms, such as charge, shape and volume, as well as to reproduce the relative arrangement of atomic and pseudoatomic zero-flux surfaces along internuclear regions. It was found that, in addition to the quantum-topological atoms, the force-field pseudoatoms are spatially reproduced within a single structural fragment and similar environment. In addition, the classical and nonclassical hydrogen bonds in the uracil derivative crystal, as well as the H...O, N...O and N...C interactions in the free π-stacked dimer of the uracil derivative molecules, were studied using the potential and force fields within the concepts of interatomic charge transfer and electron lone pair donation-acceptance. Remarkably, the nitrogen atoms in the N...O and N...C interactions behave rather like a Lewis base and an electron contributor. At the same time, the hydrogen atom in the H...O interaction, being a Lewis acid, also participates in the interatomic electron transfer by acting as a contributor. Thus, it has been argued that, when describing polar interatomic interactions within orbital-free considerations, it makes more physical sense to identify electronegative (electron occupier) and electropositive (electron contributor) atoms or subatomic fragments rather than nucleophilic and electrophilic sites.

An advanced multipole model of the (130) Elektra quadruple system

Context. The Ch-type asteroid (130) Elektra is orbited by three moons, making it the first quadruple system in the main asteroid belt. Aims. We aim to characterise the irregular shape of Elektra and construct a complete orbital model of its unique moon system. Methods. We applied the All-Data Asteroid Modelling (ADAM) algorithm to 60 light curves of Elektra, including our new measurements, 46 adaptive-optics (AO) images obtained by the VLT/SPHERE and Keck/Nirc2 instruments, and two stellar occultation profiles. For the orbital model, we used an advanced N-body integrator, which includes a multipole expansion of the central body (with terms up to the order ℓ = 6), mutual perturbations, internal tides, and the external tide of the Sun acting on the orbits. We fitted the astrometry measured with respect to the central body and also relatively, with respect to the moons themselves. Results. We obtained a revised shape model of Elektra with the volume-equivalent diameter (201 ± 2) km. Of two possible pole solutions, (λ,β) = (189; −88) deg is preferred, because the other one leads to an incorrect orbital evolution of the moons. We also identified the true orbital period of the third moon S/2014 (130) 2 as P2 = (1.642112 ± 0.000400) days, which is in between the other periods, P1 ≃ 1.212days, P3 = 5.300 days, of S/2014 (130) 1 and S/2003 (130) 1, respectively. The resulting mass of Elektra, (6.606-0.013+0.007) ×1018 kg, is precisely constrained by all three orbits. Its bulk density is then (1.536 ± 0.038) g cm−3. The expansion with the assumption of homogeneous interior leads to the oblateness J2 = −C20 ≃ 0.16. However, the best-fit precession rates indicate a slightly higher value, ≃0.18. The number of nodal precession cycles over the observation time span 2014–2019 is 14, 7, and 0.5 for the inner, middle, and outer orbits. Conclusions. Future astrometric or interferometric observations of Elektra’s moons should constrain these precession rates even more precisely, allowing the identification of possible inhomogeneities in primitive asteroids.

Ultra-high-resolution structure of crambin – experimental peculiarities, importance of data processing, influence on multipolar model

Ultra-high-resolution structure of crambin – experimental peculiarities, importance of data processing, influence on multipolar model

Resonant elastic scattering treatment by multipolar oscillator model revisited

Resonant elastic scattering treatment by multipolar oscillator model revisited

Elucidating the nature of chemical bonds in a coordination compound through quantum crystallographic techniques.

Investigations simultaneously involving multiple techniques of quantum crystallography could be very useful to prove the consistency of obtained results or to highlight different facets of the same scientific phenomenon or problem. Pinto et al. [Acta Cryst. (2023), B79, 282-296] exploit three different quantum crystallographic techniques (Hansen & Coppens multipole model refinement, QTAIM analysis of the electron density, and Hirshfeld atom refinement) to characterize the nature of chemical bonds and of intra/intermolecular interactions in an organometallic compound.

New Crystal Form of Human Neuropilin-1 b1 Fragment with Six Electrostatic Mutations Complexed with KDKPPR Peptide Ligand.

Neuropilin 1 (NRP1), a cell-surface co-receptor of a number of growth factors and other signaling molecules, has long been the focus of attention due to its association with the development and the progression of several types of cancer. For example, the KDKPPR peptide has recently been combined with a photosensitizer and a contrast agent to bind NRP1 for the detection and treatment by photodynamic therapy of glioblastoma, an aggressive brain cancer. The main therapeutic target is a pocket of the fragment b1 of NRP1 (NRP1-b1), in which vascular endothelial growth factors (VEGFs) bind. In the crystal packing of native human NRP1-b1, the VEGF-binding site is obstructed by a crystallographic symmetry neighbor protein, which prevents the binding of ligands. Six charged amino acids located at the protein surface were mutated to allow the protein to form a new crystal packing. The structure of the mutated fragment b1 complexed with the KDKPPR peptide was determined by X-ray crystallography. The variant crystallized in a new crystal form with the VEGF-binding cleft exposed to the solvent and, as expected, filled by the C-terminal moiety of the peptide. The atomic interactions were analyzed using new approaches based on a multipolar electron density model. Among other things, these methods indicated the role played by Asp320 and Glu348 in the electrostatic steering of the ligand in its binding site. Molecular dynamics simulations were carried out to further analyze the peptide binding and motion of the wild-type and mutant proteins. The simulations revealed that specific loops interacting with the peptide exhibited mobility in both the unbound and bound forms.

Quantum criticality enabled by intertwined degrees of freedom

Strange metals appear in a wide range of correlated materials. Electronic localization-delocalization and the expected loss of quasiparticles characterize beyond-Landau metallic quantum critical points and the associated strange metals. Typical settings involve local spins. Systems that contain entwined degrees of freedom offer new platforms to realize unusual forms of quantum criticality. Here, we study the fate of an SU(4) spin-orbital Kondo state in a multipolar Bose-Fermi Kondo model, which provides an effective description of a multipolar Kondo lattice, using a renormalization-group method. We show that at zero temperature, a generic trajectory in the model's parameter space contains two quantum critical points, which are associated with the destruction of Kondo entanglement in the orbital and spin channels, respectively. Our asymptotically exact results reveal an overall phase diagram, provide the theoretical basis to understand puzzling recent experiments of a multipolar heavy fermion metal, and point to a means of designing different forms of quantum criticality and strange metallicity in a variety of strongly correlated systems.

Aspherical scattering factors from multipole model for X-ray and electron crystallography

Aspherical scattering factors from multipole model for X-ray and electron crystallography

Integrated multipole acoustic modeling and processing in general stressed formations, Part 1: An effective approach study

Velocity variation around the borehole due to stress is widely important for borehole stability, hydraulic fracturing and sanding prevention during hydrocarbon production. Theoretical formulation of the acoustic velocity variation around the borehole under stress condition is derived. The formation around the borehole is considered as an rock with two orthogonal crack sets caused by the drilling operation. The relationship between fracture shape and near-borehole stress is established. The effective modulus of elasticity of the above media is derived. The finite difference method is then used to model the acoustic properties. The modeling results show that in a stressed formation, shear wave splitting and dispersion crossover would occur for a monopole and dipole source, respectively. It also explains that the dipole wave-dispersion crossover may not be clear which is more suitable for the field data observation. The modeling results can be used as a guide to understand and interpret the acoustic measurements in stressed formations.

MATHEMATICAL MODELING OF THE OPERATION OF AUDIO FREQUENCY (NO JUNCTION) AND JUNCTION RAIL CIRCUITS

Rail circuits are the basic elements of modern railway automation and telemechanics systems, performing the functions of track sensors and telemechanical channels. It is shown that the calculation of their operating boundary conditions becomes more complicated with the application of junctionless audio frequency rail circuits. The analysis of track circuits consists of studying the changes in their operation in various modes when the circuit parameters are changed. During the analysis, the optimal values of the parameters of the circuit elements and the frequency of the power source are determined for the given operating conditions. An analysis of the factors affecting the operating currents and voltages of such rail circuit schemes has been carried out. When analyzing and calculating a track circuit, it is assumed that the track line and equipment elements are linear, that is, their parameters do not depend on the flowing currents. To simplify the calculations, the track circuit is represented by the corresponding mathematical model (equivalent circuit) for each mode. Depending on the type of equivalent circuit used, four-pole and multi-pole models are distinguished. At the same time, the analysis and reporting of jointed rail circuits are carried out. Based on their results, the directions that allow for more accurate modeling of the operating modes of the circuits of the non-joint audio frequency rail circuits have been determined. Keywords: Rail circuits, train traffic safety, audio frequency (no junction) track circuits, junction rail circuits, signaling system, track sensors, mathematical model, remote conditioning monitoring.

Fourier-synthesis approach for static charge-density reconstruction from theoretical structure factors of CaB6.

In a pilot study, electron-density (ED) and ED Laplacian distributions were reconstructed for the challenging case of CaB6 (Pearson symbol cP7) with conceptually fractional B-B bonds from quantum-chemically calculated structure-factor sets with resolutions 0.5 Å-1 ≤ [sin(θ)/λ]max ≤ 5.0 Å-1 by means of Fourier-synthesis techniques. Convergence of norm deviations of the distributions obtained with respect to the reference ones was obtained in the valence region of the unit cell. The QTAIM (quantum theory of atoms in molecules) atomic charges, and the ED and ED Laplacian values at the characteristic critical points of the Fourier-synthesized distributions have been analysed for each resolution and found to display a convergent behaviour with increasing resolution. The presented method(exponent) (ME) type of Fourier-synthesis approach can qualitatively reconstruct all characteristic chemical bonding features of the ED from valence-electron structure-factor sets with resolutions of about 1.2 Å-1 and beyond, and from all-electron structure-factor sets with resolutions of about 2.0 Å-1 and beyond. Application of the ME type of Fourier-synthesis approach for reconstruction of ED and ED Laplacian distributions at experimental resolution is proposed to complement the usual extrapolation to infinite resolution in Hansen-Coppens multipole model derived static ED distributions.

A Numerical Study of Lossy Multipole Debye Dispersive Media Using a Recursive Integral-FDTD Method

A dispersive finite-difference time-domain (FDTD) method based on the recursive integration (RI) technique for the modeling of the lossy multipole Debye dispersive media is described in this article. The interaction between the electromagnetic (EM) field and the human tissues is simulated by means of the RI method, and the frequency-dependent formulations which possess good compatibility with the main FDTD algorithm are achieved. Next, the expression of the multipole Debye dispersion model is similar to the multipole complex frequency shift (CFS) stretching function which is utilized to build the multipole perfectly matched layer (MPML). Therefore, a significant feature of using the RI method is its overall modeling of both multipole Debye dispersive media and MPML boundary conditions. Furthermore, the stability analysis of the RI method in solving the lossy multipole Debye dispersive model indicates that the Courant–Friedrich–Levy (CFL) stability limit of the regular FDTD can be maintained. At last, the numerical cases performed in this work demonstrate the correctness of the RI method in modeling dispersive media.

Transferability of the Electrostatic Parameters of the Polarizable Gaussian Multipole Model.

Accuracy and transferability are the two highly desirable properties of molecular mechanical force fields. Compared with the extensively used point-charge additive force fields that apply fixed atom-centered point partial charges to model electrostatic interactions, polarizable force fields are thought to have the advantage of modeling the atomic polarization effects. Previous works have demonstrated the accuracy of the recently developed polarizable Gaussian multipole (pGM) models. In this work, we assessed the transferability of the electrostatic parameters of the pGM models with (pGM-perm) and without (pGM-ind) atomic permanent dipoles in terms of reproducing the electrostatic potentials surrounding molecules/oligomers absent from electrostatic parameterizations. Encouragingly, both the pGM-perm and pGM-ind models show significantly improved transferability than the additive model in the tests (1) from water monomer to water oligomer clusters; (2) across different conformations of amino acid dipeptides and tetrapeptides; (3) from amino acid tetrapeptides to longer polypeptides; and (4) from nucleobase monomers to Watson-Crick base pair dimers and tetramers. Furthermore, we demonstrated that the double-conformation fittings using amino acid tetrapeptides in the αR and β conformations can result in good transferability not only across different tetrapeptide conformations but also from tetrapeptides to polypeptides with lengths ranging from 1 to 20 repetitive residues for both the pGM-ind and pGM-perm models. In addition, the observation that the pGM-ind model has significantly better accuracy and transferability than the point-charge additive model, even though they have an identical number of parameters, strongly suggest the importance of intramolecular polarization effects. In summary, this and previous works together show that the pGM models possess both accuracy and transferability, which are expected to serve as foundations for the development of next-generation polarizable force fields for modeling various polarization-sensitive biological systems and processes.

From unipolarity to G-Zero and beyond: Political economy of the world without superpowers

The erosion of the unipolar system of international relations, accelerated as a result of the turbulent events of 2022, is returning experts in the field of international relations to discuss the phenomenon of the balance of power and its embodiment in various models. During the thirty-year period, following the end of the Cold War (1991–2021), the system of interstate relations went through periods when unipolar, bipolar and multipolar models were considered optimal. This article, based on the author’s address at the plenary session of the First Saint-Petersburg Congress of International Studies, proposes a political and economic interpretation of the consequences that the member states of the world community will face at a new stage in the transformation of the modern architecture of international relations in the 21st century through the mechanism of the balance of power. The trend of reducing state power in comparison with the growing economic power of market institutions and business structures in the modern era has been replaced by a reverse trend. It is characterized by the “return of the state” against the backdrop of a global system in crisis. The absence of a hegemonic state in the new system leads to the destruction of the foundations of the international liberal order, the formation of a decentralized system of alliances of states, an increase in the number and scale of economic conflicts, expressed both in the formation of regional trade blocks and in the expansion of the practice of applying economic sanctions as a substitute for armed conflicts of the past. A new era in the political and economic development of the planet, in which new actors will replace the superpowers of the past, should be characterized as a period of competitive interdependence. The coming years will show what will prevail — competition, extolled by representatives of the realistic school of the theory of international relations, i. e. inter-country/inter-bloc rivalry, or interdependence raised to the shield by the liberals.