Multipole Model Research Articles

Completely Multipolar Model as a General Framework for Many-Body Interactions as Illustrated for Water.

We introduce a general framework for many-body force fields, the Completely Multipolar Model (CMM), that utilizes multipolar electrical moments modulated by exponential decay of electron density as a common functional form for all terms of an energy decomposition analysis of intermolecular interactions. With this common functional form, the CMM model establishes well-formulated damped tensors that reach the correct asymptotes at both long- and short-range while formally ensuring no short-range catastrophes. CMM describes the separable EDA terms of dispersion, exchange polarization, and Pauli repulsion with short-ranged anisotropy, polarization as intramolecular charge fluctuations and induced dipoles, while charge transfer describes explicit movement of charge between molecules, and naturally describes many-body charge transfer by coupling into the polarization equations. We also utilize a new one-body potential that accounts for intramolecular polarization by including an electric field-dependent correction to the Morse potential to ensure that CMM reproduces all physically relevant monomer properties including the dipole moment, molecular polarizability, and dipole and polarizability derivatives. The quality of CMM is illustrated through agreement of individual terms of the EDA and excellent extrapolation to energies and geometries of an extensive validation set of water cluster data.

ANALYSIS OF THE “EAST” IMAGE IN THE WORKS OF THE BEIJING SPIRITUAL MISSION LEADERS OF THE XVIII - EARLY XX CENTURIES

The purpose of the study. The article is devoted to the problem of forming ideas about the East in the representative writings of the Beijing Spiritual Mission. Special attention is paid to the ideas contributed to the formation of the socio-cultural construct “East”, which is important for the formation of the Russian state identity today, in the context of the formation of a multipolar world model. Conclusions. As a result of the research, we traced the evolution of the East images as “alien” and “other” in the intercultural interaction context through the activities of the Russian Ecclesiastical Mission in Beijing, which created the foundations for an effective intercultural dialogue of the period previously considered.

Crystal structure and characterization of monascin from the extracts of Monascus purpureus-fermented rice.

We present a novel solid form of monascin, an azaphilonoid derivative extracted from Monascus purpureus-fermented rice. The crystal structure, C21H26O5, was characterized by single-crystal X-ray diffraction and belongs to the orthorhombic space group P212121. To gain insight into the electronic properties of the short contacts in the crystalline state of monascin, we utilized the Experimental Library of Multipolar Atom Model 2 (ELMAM2) database to transfer the electron density of monascin in its crystalline state. Hirshfeld surface analysis, fingerprint analysis, electronic properties and energetic characterization reveal that intermolecular C-H...O hydrogen bonds play a crucial role in the noncovalent bonding interactions by connecting molecules into two- and three-dimensional networks. The molecular electrostatic potential (MEP) map of the monascin molecule demonstrates that negatively charged regions located at four O atoms are favoured binding sites for more positively charged amino acid residues during molecular recognition. In addition, powder X-ray diffraction confirms that no transformation occurs during the crystallization of monascin.

Current developments and trends in quantum crystallography.

Quantum crystallography is an emerging research field of science that has its origin in the early days of quantum physics and modern crystallography when it was almost immediately envisaged that X-ray radiation could be somehow exploited to determine the electron distribution of atoms and molecules. Today it can be seen as a composite research area at the intersection of crystallography, quantum chemistry, solid-state physics, applied mathematics and computer science, with the goal of investigating quantum problems, phenomena and features of the crystalline state. In this article, the state-of-the-art of quantum crystallography will be described by presenting developments and applications of novel techniques that have been introduced in the last 15 years. The focus will be on advances in the framework of multipole model strategies, wavefunction-/density matrix-based approaches and quantum chemical topological techniques. Finally, possible future improvements and expansions in the field will be discussed, also considering new emerging experimental and computational technologies.

Energetic particle activity in AD Leo: Detection of a solar-like type-IV burst

Context. AD Leo is a young and active M dwarf with high flaring rates across the X-ray-to-radio bands. Flares accelerate particles in the outer coronal layers and often impact exo-space weather. Wide-band radio dynamic spectra let us explore the evolution of particle acceleration activity across the corona. Identifying the emission features and modelling the mechanisms can provide insights into the possible physical scenarios driving the particle acceleration processes. Aims. We performed an 8 h monitoring of AD Leo across the 550-850 MHz band using upgraded-Giant Metrewave Radio Telescope (uGMRT). The possible flare and post-flare emission mechanisms are explored based on the evolution of flux density and polarisation. Methods. The python-based module, Visibility Averaged Dynamic spectrum (VISAD), was developed to obtain the visibility-averaged wide-band dynamic spectra. Direct imaging was also performed with different frequency-time averaging. Based on existing observational results on AD Leo and on solar active region models, radial profiles of electron density and magnetic fields were derived. Applying these models, we explored the possible emission mechanisms and magnetic field profile of the flaring active region. Results. The star displayed a high brightness temperature (TB≈ 1010−1011 K) throughout the observation. The emission was also nearly 100% left circularly polarised during bursts. The post-flare phase was characterised by a highly polarised (60–80%) solar-like type IV burst confined above 700 MHz. Conclusions. The flare emission favours a Z-mode or a higher harmonic X-mode electron cyclotron maser emission mechanism. The >700 MHz post-flare activity is consistent with a type-IV radio burst from flare-accelerated particles trapped in magnetic loops, which could be a coronal mass ejection (CME) signature. This is the first solar-like type-IV burst reported on a young active M dwarf belonging to a different age-related activity population (‘C’ branch) compared to the Sun (‘I’ branch). We also find that a multipole expansion model of the active region magnetic field better accounts for the observed radio emission than a solar-like active region profile.

Excellent energy storage properties in ZrO2 toughened Ba0.55Sr0.45TiO3-based relaxor ferroelectric ceramics via multi-scale synergic regulation

Lead-free ceramic capacitors offer ultrahigh power density and ultrafast discharging rates, making them critical energy storage components for advanced pulsed power systems. However, the greatest obstacle to broader applications remains the relatively low energy storage density. In this study, a relaxor ferroelectric ceramic based on (0.6-x)Ba0.55Sr0.45TiO3-0.4Bi0.5Na0.5TiO3-xSrZrO3 ((0.6-x)BST-0.4BNT-xSZ) is prepared using the tape casting method, resulting in an excellent energy density (Wrec ≈ 10.0 J cm−3) and high energy storage efficiency (η ≈ 91 %). The solid solution of linear dielectrics SrZrO3 synergistically regulates both relaxor properties and breakdown strength. The variation of relaxor property was explored utilizing New Glass model and the multi-polarization model, with confirmation provided by piezoresponse force microscopy. Furthermore, the breakdown strength could be attributed to improvements in electric insulation and the widening of the bandgap. As SrZrO3 content increases, the in-situ emergence of the second phase ZrO2, accompanied by a martensitic transformation, not only improves the fracture toughness of ceramics but also serves to elongate the breakdown path. Encouragingly, x = 0.20 ceramics also achieve excellent temperature stability (−95–125 ℃), frequency stability (1–1000 Hz), cycling reliability (1–106 cycles), and great charging-discharging properties. This multiscale synergic regulation strategy plays a guiding role in the screening of high-performance energy storage dielectric materials.

Multi-objective optimization strategy for multipolar magnesium electrolysis cell based on thermal-electric model

In the operation of industrial multipolar magnesium electrolysis cell, cell voltage and current density are important indicators of the production performance of the cell, while thermal balance is a key factor for normal operation. This paper utilizes the finite element method to establish a three-dimensional full cell thermal-electric model, studying the thermal field distribution and current density distribution in a 165kA multipolar magnesium electrolysis cell. Based on the heat balance of the multipolar cell, the influence of structural parameters on current intensity, average current density at the anode surface and resistance voltage is assessed. Dimensionless analysis yielded optimization criteria, and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was employed for multi-objective optimization problems. When stringent optimization is executed, significant performance improvements can be achieved in terms of the electrolysis cell's resistance voltage and current density. Moreover, under the optimization criteria, the relative error of the 265kA multipolar magnesium electrolysis cell model is less than 1 %. The results indicate that the workflow combining the finite element method with multi-objective optimization algorithms can be applied to the optimization and scale-up design of high-current multipolar magnesium electrolysis cell.

Electron density changes accompanying high-pressure phase transition in AlOOH

Abstract An attempt to compare and describe the differences in the electron density distribution between two phase structures of AlOOH has been made. High-resolution, high-pressure experiments with α-AlOOH diaspore were conducted using single-crystal synchrotron X-ray diffraction data. A multipole model of experimental electron density in the α-AlOOH single crystal was refined. Simultaneously, similar multipole refinement was conducted for another phase of diaspore (δ-AlOOH), this time based on a previously published data set. Both results were compared and supported by density functional theory (DFT) calculations. Although the results are affected by the limited quality of the data, it is clear that the phase transition caused significant changes in the shape and arrangement of the atomic basins. Atomic basins are a much better tool to present subtle electron density distribution changes than traditional polyhedra. Straightforward comparison of datasets available in older scientific papers and current datasets is challenging because of differences in data quality and collection parameters. However, augmenting experimental data with computational results can help reveal important information in even incomplete datasets.

The Eurasian Economic Union and Multipolar Globalization

The article discusses ways to resolve the contradiction between globalization and national sovereignty in the context of the transition to a multipolar world order. The main features of the emerging multipolar model of globalization are shown. Through the prism of Eurasian integration, the differences between Russia’s partnership with the countries of the West and its partnership with the countries of the Global East and the Global South are analyzed. The special role of the Eurasian Economic Union and Russia in the formation of a just multipolar world is revealed.Aim. To substantiate Russia’s integration policy in the context of its global confrontation with the West. Tasks. To study the role of mega-regulators and regionalization in resolving the contradictions between the global nature of the economy and national sovereignty in the context of the transition to a multipolar world order. Analysis of the development of the EAEU, its bodies and institutions as a factor in resolving the contradiction between the old and new leaders of globalization.Methods. A systematic approach to the study of Eurasian integration in the process of formation and development of multipolar globalization. Many years of practical experience in participating in specific processes of Eurasian integration.Results. The ways of strengthening the economic sovereignty of the EAEU countries based on the institutional development of Eurasian integration and the formation of new mega-regulators within the framework of the SCO and BRICS are shown.Conclusions. Multipolar globalization is irreversible. At the same time, the EAEU, SCO and BRICS are gaining a leading role in this process. The Russian Federation needs to critically review its partnership with Western countries and organizations, taking into account their threefold role in relation to our country: opponents, rivals, partn.

Interactions Between Alumina Inclusions at the Liquid Iron/Argon Gas Interface: Role of Contact Line Undulation

A deep understanding of the behavior of nonmetallic inclusions is essential for steel cleanliness control. The behavior of alumina inclusions at the liquid iron/argon gas interface is investigated using a high‐temperature confocal scanning laser microscope. The obtained images are used to determine the moving velocity of the inclusions on the interface. The obtained experimental data are quantitatively evaluated using the lateral capillary interaction model for multipole orders established by Danov–Kralchevsky while taking into account the resistive drag force. The attraction forces calculated from these data are in the range between ≈10−13 and ≈10−11 N. The best‐fitting model is assigned for each case. The multipole models almost counterbalance the drag force, indicating a good interpretation of the interaction between the inclusions. Moreover, the acting length of this interaction is examined and compared to the previous work on Ce2O3 inclusions. It is found that alumina inclusions generally exhibit a larger acting length at a large critical radius and a smaller acting length at a small critical radius when comparing them to their counterpart cerium oxide inclusions. Considering the particle shapes, high shape irregularity is better interpreted by higher orders of the multipoles.

Globalization in the format of multipolarity: philosophical and worldview foundation of globopolycentrism

The subject is multipolar globalization formed in the context of globomonocentrism and globopolycentrism confrontation. The aim is to study the process of globalization in its main (current and potential) manifestations, including bipolar, unipolar and multipolar models. Their essence and specificity are considered, their effectiveness is assessed, philosophical and worldview foundation is found. F. Fukuyama’s, S. Huntington’s, Z. Brzezinski’s conceptions are analyzed as a philosophical and worldview foundation of globomonocentrism; philosophical ideas of N. Y. Danilevsky, K. N. Trubetskoy, P. N. Savitsky — of globopolycentrism. It’s concluded that there’s a need to revise the global world order from a unipolar to a multipolar format. The importance of globopolycentrism as an alternative development strategy opposing neocolonialism is emphasized. Constructing a multipolar world is necessary to strengthen the civilizational sovereignty of modern Russia and other countries of the world. The article uses historical, logical and comparative methods of analysis, the civilizational approach as a methodological instrument to substantiate the multipolarity. The main conclusions are the following: globalization as a form of interaction between civilizations isn’t identical to globomonocentrism. It’s one of the forms (not the only and not the most perfect) of constructing the interaction of civilizations. Modern globomonocentrism (in fact, americanocentrism) tries to reconstruct the world in the interests of a neocolonial regime. An alternative form of civilizational coexistence, providing protection from neocolonialism, is a multipolar world. Today we can’t talk about abandoning globalization as a whole, only about changing its format from unipolar to multipolar globalization. Multipolarity basing on the worldview principle of globopolycentrism perceives other (not only highly developed) countries as equal partners. The globopolycentric model of a multipolar world has flaws as well as the bipolar and unipolar models, but it’s much more connected with objective reality and, therefore, gives humanity a chance to overcome global geopolitical crises.

PCMRESP: A Method for Polarizable Force Field Parameter Development and Transferability of the Polarizable Gaussian Multipole Models Across Multiple Solvents.

The transferability of force field parameters is a crucial aspect of high-quality force fields. Previous investigations have affirmed the transferability of electrostatic parameters derived from polarizable Gaussian multipole models (pGMs) when applied to water oligomer clusters, polypeptides across various conformations, and different sequences. In this study, we introduce PCMRESP, a novel method for electrostatic parametrization in solution, intended for the development of polarizable force fields. We utilized this method to assess the transferability of three models: a fixed charge model and two variants of pGM models. Our analysis involved testing these models on 377 small molecules and 100 tetra-peptides in five representative dielectric environments: gas, diethyl ether, dichloroethane, acetone, and water. Our findings reveal that the inclusion of atomic polarization significantly enhances transferability and the incorporation of permanent atomic dipoles, in the form of covalent bond dipoles, leads to further improvements. Moreover, our tests on dual-solvent strategies demonstrate consistent transferability for all three models, underscoring the robustness of the dual-solvent approach. In contrast, an evaluation of the traditional HF/6-31G* method indicates poor transferability for the pGM-ind and pGM-perm models, suggesting the limitations of this conventional approach.

Adaptive multipole models of optically pumped magnetometer data.

Multipole expansions have been used extensively in the Magnetoencephalography (MEG) literature for mitigating environmental interference and modelling brain signal. However, their application to Optically Pumped Magnetometer (OPM) data is challenging due to the wide variety of existing OPM sensor and array designs. We therefore explore how such multipole models can be adapted to provide stable models of brain signal and interference across OPM systems. Firstly, we demonstrate how prolate spheroidal (rather than spherical) harmonics can provide a compact representation of brain signal when sampling on the scalp surface with as few as 100 channels. We then introduce a type of orthogonal projection incorporating this basis set. The Adaptive Multipole Models (AMM), which provides robust interference rejection across systems, even in the presence of spatially structured nonlinearity errors (shielding factor is the reciprocal of the maximum fractional nonlinearity error). Furthermore, this projection is always stable, as it is an orthogonal projection, and will only ever decrease the white noise in the data. However, for array designs that are suboptimal for spatially separating brain signal and interference, this method can remove brain signal components. We contrast these properties with the more typically used multipole expansion, Signal Space Separation (SSS), which never reduces brain signal amplitude but is less robust to the effect of sensor nonlinearity errors on interference rejection and can increase noise in the data if the system is sub-optimally designed (as it is an oblique projection). We conclude with an empirical example utilizing AMM to maximize signal to noise ratio (SNR) for the stimulus locked neuronal response to a flickering visual checkerboard in a 128-channel OPM system and demonstrate up to 40 dB software shielding in real data.

Transferable Hirshfeld atom model for rapid evaluation of aspherical atomic form factors.

Form factors based on aspherical models of atomic electron density have brought great improvement in the accuracies of hydrogen atom parameters derived from X-ray crystal structure refinement. Today, two main groups of such models are available, the banks of transferable atomic densities parametrized using the Hansen-Coppens multipole model which allows for rapid evaluation of atomic form factors and Hirshfeld atom refinement (HAR)-related methods which are usually more accurate but also slower. In this work, a model that combines the ideas utilized in the two approaches is tested. It uses atomic electron densities based on Hirshfeld partitions of electron densities, which are precalculated and stored in a databank. This model was also applied during the refinement of the structures of five small molecules. A comparison of the resulting hydrogen atom parameters with those derived from neutron diffraction data indicates that they are more accurate than those obtained with the Hansen-Coppens based databank, and only slightly less accurate than those obtained with a version of HAR that neglects the crystal environment. The advantage of using HAR becomes more noticeable when the effects of the environment are included. To speed up calculations, atomic densities were represented by multipole expansion with spherical harmonics up to l = 7, which used numerical radial functions (a different approach to that applied in the Hansen-Coppens model). Calculations of atomic form factors for the small protein crambin (at 0.73 Å resolution) took only 68 s using 12 CPU cores.

Molecular Insights into Water-Chloride and Water-Water Interactions in the Supramolecular Architecture of Aconine Hydrochloride Dihydrate.

Despite the previous preparation of aconine hydrochloride monohydrate (AHM), accurate determination of the crystal's composition was hindered by severely disordered water molecules within the crystal. In this study, we successfully prepared a new dihydrate form of the aconine hydrochloride [C25H42NO9+Cl-·2(H2O), aconine hydrochloride dihydrate (AHD)] and accurately refined all water molecules within the AHD crystal. Our objective is to elucidate both water-chloride and water-water interactions in the AHD crystal. The crystal structure of AHD was determined at 136 K using X-ray diffraction and a multipolar atom model was constructed by transferring charge-density parameters to explore the topological features of key short contacts. By comparing the crystal structures of dihydrate and monohydrate forms, we have observed that both AHD and AHM exhibit identical aconine cations, except for variations in the number of water molecules present. In the AHD crystal, chloride anions and water molecules serve as pivotal connecting hubs to establish three-dimensional hydrogen bonding networks and one-dimensional hydrogen bonding chain; both water-chloride and water-water interactions assemble supramolecular architectures. The crystal packing of AHD exhibits a complete reversal in the stacking order compared to AHM, thereby emphasizing distinct disparities between them. Hirshfeld surface analysis reveals that H···Cl- and H···O contacts play a significant role in constructing the hydrogen bonding network and chain within these supramolecular architectures. Furthermore, topological analysis and electrostatic interaction energy confirm that both water-chloride and water-water interactions stabilize supramolecular architectures through electrostatic attraction facilitated by H···Cl- and H···O contacts. Importantly, these findings are strongly supported by the existing literature evidence. Consequently, navigating these water-chloride and water-water interactions is imperative for ensuring storage and safe processing of this pharmaceutical compound.

Assessment of Amino Acid Electrostatic Parametrizations of the Polarizable Gaussian Multipole Model.

Accurate parametrization of amino acids is pivotal for the development of reliable force fields for molecular modeling of biomolecules such as proteins. This study aims to assess amino acid electrostatic parametrizations with the polarizable Gaussian Multipole (pGM) model by evaluating the performance of the pGM-perm (with atomic permanent dipoles) and pGM-ind (without atomic permanent dipoles) variants compared to the traditional RESP model. The 100-conf-combterm fitting strategy on tetrapeptides was adopted, in which (1) all peptide bond atoms (-CO-NH-) share identical set of parameters and (2) the total charges of the two terminal N-acetyl (ACE) and N-methylamide (NME) groups were set to neutral. The accuracy and transferability of electrostatic parameters across peptides with varying lengths and real-world examples were examined. The results demonstrate the enhanced performance of the pGM-perm model in accurately representing the electrostatic properties of amino acids. This insight underscores the potential of the pGM-perm model and the 100-conf-combterm strategy for the future development of the pGM force field.

Cole-Cole Model for the Dielectric Characterization of Healthy Skin and Basal Cell Carcinoma at THz Frequencies.

THz radiationeffectively probes biological tissue water content due to its high sensibility to polar molecules. Skin and basal cell carcinoma (BCC), both rich in water, have been extensively studied in the THz range. Typically, the Double Debye model is used to study their dielectric permittivity. This work focuses on the viability of the multipole Cole-Cole model as an alternative dielectric model. To determine the best fit parameters, we used a genetic algorithm-based approach, solving a least squares problem. Compared with the Double Debye model, a maximum reduction of the RMSE value up to more than 50% and maximum relative percentage errors of 2.8% have been measured for both second and third order Cole-Cole models. Since the errors of the second and third order Cole-Cole models are similar, a two-poles model is enough to describe the behaviour both tissues from 0.2 THz to 2 THz.

НЕЙРО-ЭКОНОМИЧЕСКИЕ И КОГНИТИВНО-ПСИХОЛОГИЧЕСКИЕ АСПЕКТЫ ТЕХНОЛОГИЙ МЕРЧАНДАЙЗИНГА

This article is of a review and analytical nature and is devoted to the problems of applying modern discoveries of neuroscience (neurobiology, neurophysiology, neuroeconomics) in managing customer behavior. In particular, a multipolar model of customer behavior is proposed, combining the emotional-sensory and cognitive-psychological fields of irrationally rational consumer behavior. The authors found that purchasing decisions by visitors to points of sale can be made at three levels: 1) at the emotional and sensory level, dictated by neurobiological processes and being irrational, which are taken unconsciously during the direct neuro-communication interaction of the product and the visitor in the trading halls; 2) at the level of automatic decisions based on empirical experience that are rational – consciously reflective (objective experience) or irrational - unconsciously reflective (subjective experience), while the constancy of the product’s place in the space of the trading floor is a necessary condition for the formation of experience and the manifestation of such behavior; c) at a high cognitive level based on complex cognitive-psychological processes caused by the need to think about and justify rational decisions. They are aimed at reducing the qualitative, financial or other risk that can cause cognitive dissonance, and visitors are characterized by resistance to merchandising tools used at points of sale. The obtained results make a definite contribution to the development of the theory of neuromarketing and contribute to the formation of the neuro-cognitive concept of merchandising. The main provisions of the article may be of practical importance in applied research in the development of new neuromarketing and merchandising tools.

Analyzing Earth's Position based on the Anisotropic Characteristics of Cosmic Microwave Background Radiation

This paper elaborates on the results of an exhaustive study regarding the Earth's position in the universe based on the Cosmic Microwave Background (CMB) radiation map, which is the latest discovery in modern astronomy. CMB radiation provides crucial insights into the early distribution of mass and energy in the universe. The aim of this research is to understand the theory and mechanisms behind the formation of polarity structures in the CMB and analyze their correlation with Earth's position in the overall structure of the universe. Intensity measurement data of CMB radiation published by COBE, WMAP, and Planck present temperature distribution data in coordinates in FITS (Flexible Image Transport System) format files. Subsequently, a spherical harmonic transformation is performed to obtain spherical harmonic coefficients a_lm as equations that represent dipole, quadrupole, octupole models, and various other multipole models. The analysis of the correlation in the temperature distribution of CMB radiation involves detailing various patterns found in the dipole, quadrupole, and octopole models, demonstrating quasi-symmetry characteristics with Earth at its center. An analysis of anisotropic CMB data yields an interesting hypothesis that the Earth's position plays a role in shaping the structure of the universe on a certain scale. Even more extremely, it can be said that Earth is at the center of the universe. This finding prompts profound contemplation about Earth's position in the structure of the cosmos, opening the door for further research in this field.

Integrated multipole acoustic modeling and processing in general stressed formations, Part 2: A well case study

Stress-induced borehole multipole waveform characterization and processing interpretation are critical for borehole stabilization and hydraulic fracturing development. In the first paper (Part 1), an effective approach was presented to simulate the multipole acoustic responses of a stressed formation. In this second paper (Part 2), the objective is to analyze the shear (S)-wave slowness and anisotropy processing methods for stressed formations using the borehole acoustic logging data from the Mesopotamia Basin, Iraq. An integrated approach for evaluating acoustic slowness and anisotropy is presented. This approach combines a time-domain controlled slowness-time-coherence (TCSTC) method for the monopole logging, waveform inversion and frequency-domain processing methods for the four-component (4C) data from the cross-dipole acoustic logging measurement, to provide an overall assessment of acoustic characteristics around borehole under stress. The results of single depth point and interval data processing demonstrate that the proposed TCSTC can be well applied to the slowness extraction of monopole fast and slow shear waves, especially in the case of fast formation where the slowness of fast and slow transverse waves is difficult to distinguish. Meanwhile, the anisotropy results show that stress-induced S-wave anisotropy results from dipole logging data based on frequency domain processing methods are generally larger than those from dipole and monopole logging data based on time domain methods. Integrating the slowness results of the fast and slow shear waves extracted from the monopole and dipole measurements allows us to assess the velocity variations at radial distances along the borehole under stress, which can be well interpreted using the radial shear-wave velocity profile. A potential limitation of this integration approach is the need for analysis of acoustic multipole logging data, which can be available as part of routine logging measurements. The processing and analysis results can be used as a guideline for understanding and interpreting acoustic measurements in stressed formations.