Isotropic Constants Research Articles

Small perturbations of polytopes

Motivated by first-order conditions for extremal bodies of geometric functionals, we study a functional analytic notion of infinitesimal perturbations of convex bodies and give a full characterization of the set of realizable perturbations if the perturbed body is a polytope. As an application, we derive a necessary condition for polytopal maximizers of the isotropic constant.

Indirect interaction of 13C nuclear spins in diamond with NV centers: simulation of the full J-coupling tensors

Recent experiments on the detection, imaging, characterization and control of multiple 13C nuclear spins, as well as of individual 13C–13C dimers in diamond using a single nitrogen-vacancy (NV) center as a sensor, along with the impressive progress in increasing the spectral resolution of such sensor (up to sub-Hertz), have created a request for detailed knowledge of all possible spin interactions in the studied systems. Here, we focus on the indirect interaction (J-coupling) of 13C nuclear spins in diamond, which was not previously taken into account in studies of NV centers. Using two different levels of the density functional theory (DFT), we simulated the full tensors nJKL (K, L = X, Y,Z), describing n-bond J-coupling of nuclear spins 13C in H-terminated diamond-like clusters C10H16 (adamantane) and C35H36, as well as in the cluster C33[NV−]H36 hosting the negatively charged NV− center. We found that, in addition to the usually considered isotropic scalar nJ-coupling constant, the anisotropic contributions to the nJ-coupling tensor are essential. We also showed that the presence of the NV center affects the J-coupling characteristics, especially in the case of 13C–13C pairs located near the vacancy of the NV center.

Giant anisotropic Gilbert damping and spin wave propagations in single-crystal magnetic insulator

Gilbert damping in magnetic systems describes the relaxation of magnetization. This term was phenomenologically introduced into the Landau–Lifschitz–Gilbert (LLG) equation to describe spin dynamics. In most studies, such as magnetic random access memory, spin-wave propagations, and microwave devices, it has been assumed that the Gilbert damping is an isotropic constant. In this study, we uncover a giant anisotropic Gilbert damping parameter of up to 431% in single-crystal thin films of epitaxial [100]-oriented yttrium iron garnet (YIG) using angle-dependent ferromagnetic resonance. In contrast, the Gilbert damping parameter of a [111]-oriented YIG film is almost isotropic. The observed anisotropic damping is shown to have a similar fourfold symmetry with magneto-crystalline anisotropy. The anisotropic spin-wave group velocity (vg), relaxation time (τ), and decay length (ld) were also experimentally evaluated through spin-wave spectra of [100]-oriented YIG thin film. We developed the LLG equation with the introduction of an anisotropic orbital Gilbert damping term. This anisotropic orbital damping originates from the crystal-field dominated anisotropic spin–orbit coupling and orbital-related magnon–phonon coupling. Our results extend the understanding of the mechanism of anisotropic Gilbert damping in single-crystal magnetic insulators with strong magneto-crystalline anisotropy.

Elastic Behavior of Transversely Isotropic Cylindrical Rock Samples under Uniaxial Compression Considering Ideal and Frictional Boundary Conditions

Conceptualizing sophisticated measurement set-ups as well as testing and evaluation procedures for laboratory experiments on anisotropic rocks requires a basic understanding of the potential specimen behavior. The focus of the present work was therefore to investigate the influence of different transversely isotropic parameters and their ratios on the elastic behavior of cylindrical rock samples in uniaxial compression tests. Parameter sets corresponding to soft anisotropic rocks were chosen based on naturally observed ranges for the five elastic transversely isotropic constants. Analytical results for the radial and vertical strain distributions around the sample circumference and a comparison with finite element simulations are presented. Further, the effect of interface friction between samples and loading platens was analyzed within the numerical models. The results suggest that radial strains around cylindrical anisotropic samples are rarely uniform except for specific combinations of parameters and isotropy plane inclinations. The effect of interface friction was found to have a clear influence on the developing elastic stress and strain distributions for samples with inclined isotropy planes. Nevertheless, no significant influence of frictional boundary conditions on the back-calibrated values of the elastic parameters could be identified, suggesting that friction-reducing measures in uniaxial compression tests on transversely isotropic samples with predominantly linear behavior are not required.

Оптические свойства сверхтонких пленок Pd и Pt на кварцевой подложке и на пленках триоксида вольфрама

Based on ellipsometry and transmission spectra, optical parameters of palladium and platinum films were determined. The Pd and Pt films had a thickness of 5 – 7 nm and were studied both on a SiO2 and WO3 substrates. Despite the extremely small thicknesses, the parameters of most films were well described by isotropic dielectric constant. An interesting feature was that films deposited directly on a SiO2 substrate had a positive (rather than negative, characteristic of a metal) real part of the effective dielectric constant, while the films deposited on WO3 exhibited metallic properties for unannealed films and properties characteristic of metal-dielectric composites for films that have been annealed (some of the films annealed at 300°C in argon retained their metallic properties).

Study of factors affecting some properties of hydrophilic suppository base

The aim. To study the effect of the composition of hydrophilic suppository bases on the physicochemical and osmotic properties of suppositories made from them.
 Materials and methods. The bases were studied with varying compositions of excipients. The microstructure of the bases was evaluated, and the disintegration time and resistance to rupture of suppositories made from them were determined. The kinetics of water absorption and solvent release were studied by dialysis. The content of propylene glycol (PG) and macrogol 400 (M400) in the receptor medium was determined by gas chromatography. The melted bases were studied by rotational viscometry. The electron paramagnetic resonance spectra of spin probes in hydrophilic solvents and bases were obtained; the type of spectrum, isotropic constant (AN), rotational correlation times (τ), and anisotropy parameter (ε) were determined.
 Results. The disintegration times and resistance to rupture of suppositories were determined depending on such factors as the content and grade of poloxamers, the ratio between high molecular weight macrogols and the mixed solvent PG-M400 (60 : 40 % m/m), the ratio of nonionic surfactant and cetostearyl alcohol (CSA) and their total content, water and hard fat content. The introduction of solid fat and a mixture of surfactants and CSA provides the uniform structure of the bases. The mass ratio between surfactants and CSA and their total content are important factors that provide acceptable resistance to rupture and disintegration times for suppositories and reduce water absorption and solvent release. As the temperature decreases from 45 °C to 20 °C, the bases transform from Newtonian liquids to solids. At that time, the microviscosity of the environment of the spin probes increased by about 5 times, but the parameters of their rotational diffusion in solid bases and the mixed solvent PG-M400 are comparable. This indicates the dissolved state of the spin probes in the bases and the absence of the formation of mixed associates from molecules of surfactant and CSA.
 Conclusions. By varying the composition of excipients, the properties of hydrophilic suppository bases can be controlled, significantly reducing their osmotic properties. The active substances in these bases may be in a dissolved state due to the high content of non-aqueous solvents

Automated calculations of exchange magnetostriction

We present a methodology based on deformations of the unit cell that allows to compute the isotropic magnetoelastic constants, isotropic magnetostrictive coefficients and spontaneous volume magnetostriction associated to the exchange magnetostriction. This method is implemented in the python package MAELAS (v3.0), so that it can be used to obtain these quantities by first–principles calculations and classical spin–lattice models in an automated way. We show that the required reference state to obtain the spontaneous volume magnetostriction combines the equilibrium volume of the paramagnetic state and magnetic order of the ground state. In the framework of a classical spin–lattice model, we find that the analysis of volume dependence of this method jointly to the knowledge of the spatial derivative of the exchange interactions can reveal the equilibrium volume of the paramagnetic state and spontaneous volume magnetostriction unambiguously without involving any calculation of the paramagnetic state. We identify an error in the theoretical expression of the isotropic magnetostrictive coefficient λα1,0 for uniaxial crystals given in previous publications, which is corrected in this work. The presented computational tool may be helpful to provide a better understanding and characterization of the relationship between the exchange interaction and magnetoelasticity.

A note on the reduction of the slicing problem to centrally symmetric convex bodies

In this paper, we obtain the best possible value of the absolute constant C such that for every isotropic convex body K⊆Rn the following inequality (which was proved by Klartag and reduces the hyperplane conjecture to centrally symmetric convex bodies) is satisfied:LK≤CLKn+2(gK). Here LK denotes the isotropic constant of K, gK its covariogram function, which is log-concave, and, for any log-concave function g, Kn+2(g) is a convex body associated to the log-concave function g, which belongs to a uniparametric family introduced by Ball. In order to obtain this inequality, sharp inclusion results between the convex bodies in this family are obtained whenever g satisfies a better type of concavity than the log-concavity, as gK is, indeed 1n-concave.

Manipulation of optical coherence of quantum-well excitons by transverse magnetic field

We have studied experimentally spin-dependent photon echoes from excitons in an InGaAs/GaAs quantum well subject to a transverse magnetic field (Voigt geometry). Larmor precession of the spins of the electron and heavy hole in an exciton leads to a periodic transfer of coherence between bright and dark exciton states. The increase in dephasing time due to the transition to the dark states could be useful for coherent control development. A comprehensive analysis shows a good agreement between a four-wave mixing experiment and the predictions of a theoretical treatment based on a five-level exciton model comprising a ground state and two pairs of bright and dark states. The extracted optical dephasing time of bright and dark excitons is equal to 30 and 130 ps, respectively. Exploiting the photon echo reveals evidence of electron Larmor precession with in-plane $g$ factor $|{g}_{e,\ensuremath{\perp}}|=0.44\ifmmode\pm\else\textpm\fi{}0.05$ and heavy hole precession as well. The precession frequency of the latter depends nonlinearly on the applied magnetic field, and the corresponding $g$ factor reaches a value of $|{g}_{h,\ensuremath{\perp}}|\ensuremath{\approx}0.3$ at $B=6$ T. Estimates for the heavy hole $g$-factor spreading as well as the isotropic exchange interaction constant are provided.

From two- to three-dimensional continuum-kinematics-inspired peridynamics: More than just another dimension

Continuum-kinematics-inspired Peridynamics (CPD) has been recently proposed as a geometrically exact formulation of peridynamics that is also thermodynamically and variationally consistent. Unlike the original formulation of peridynamics (PD), CPD can accurately capture the Poisson effect. For a three-dimensional analysis, CPD builds upon one-, two- and three-neighbor interactions. The isotropic three-dimensional CPD formulation of non-local elasticity therefore involves three material constants associated with length, area and volume. This manuscript aims to establish the relationships between the material parameters of CPD and isotropic linear elasticity for three-dimensional problems. In addition to addressing significant technical difficulties that arise when advancing from two- to three-dimensional problems, this contribution unravels several key features that are entirely absent in a two-dimensional analysis (Ekiz et al., 2022). It is shown that the three material parameters of CPD reduce to two independent parameters in the linearized framework, and can be expressed in terms of any pairs of isotropic linear elasticity constants, such as Lamé parameters. The analysis here provides a physical interpretation for the first Lamé constant, for the first time. Finally, we establish the admissible ranges for CPD material parameters.

Crossdipole Sonic Data Analyzed To Target Stack Pay in the Permian Basin

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 209327, “Analysis of Crossdipole Sonic Data for an Intelligent Targeting of Stack Pay in the Permian Basin,” by Bikash Sinha, Farid Mohamed, and Lili Xu, SPE, Schlumberger, et al. The paper has not been peer reviewed. The preferred placement of a producer well in unconventional reservoirs is based on available information about the presence of natural fractures and formation stresses. Identifying the depth intervals with natural fractures and the relative magnitudes of the maximum and minimum horizontal stresses enables placement of a producer well that will support effective hydraulic fractures. In the complete paper, the authors apply a work flow to crossdipole sonic data acquired in a vertical pilot well drilled in the Permian Basin. Introduction The authors describe processing, analysis, and interpretation of sonic data acquired in a vertical pilot well with the goal of identifying optimal depth intervals and azimuths for drilling a lateral producer well with a potential for enhanced hydrocarbon productivity. The preferred placement of a lateral producer well requires drilling through an oil-rich layer that exhibits higher fracturability. Theory Borehole sonic data consist of monopole headwave slownesses and borehole Stoneley dispersions together with dipole headwave slownesses and borehole flexural dispersions. While monopole data provide azimuthally averaged formation properties, crossdipole data probe the formation in two opposite quadrants and discriminate formation properties in the two orthogonal directions in the borehole cross-sectional plane. Compressional and shear headwave slownesses can be transformed into compressional and shear moduli of the formation. Borehole Stoneley and flexural dispersions can be inverted to obtain formation transversely isotropic (TI) constants. One can invert for TI constants when the fast- and slow-dipole flexural dispersions overlay, and a subset of orthorhombic constants when the fast- and slow-dipole dispersions are different. Both the borehole flexural and Stoneley dispersions exhibit frequency-dependent sensitivities to changes in the formation anisotropic constants. It is possible to invert for those formation anisotropic constants that show sufficient sensitivities to such measured flexural dispersions. This section of the complete paper is devoted to inversion of borehole Stoneley and flexural dispersions for formation anisotropic constants and associated equations and discusses determination of Young’s moduli and Poisson’s ratio for a transversely isotropic with vertical axis of symmetry (TIV) formation.

Weak antiferromagnetic interaction in Cu(ii) complex with semi-coordination exchange pathway

We present structural and magnetic studies of complex [Cu(dpt)(NCS)2], 1a, dpt = bis(3-aminopropyl)amine. A weak antiferromagnetic interaction mediated by a Cu⋯ π non-covalent interaction was identified by magnetometry measurements, and the exchange magnitude (J = -2.24 cm−1, J stands for isotropic magnetic exchange constant) was determined. These results were supported by theoretical calculations (DFT) and the nature of the Cu⋯ π interaction was studied by QT-AIM. It was confirmed that the Cu⋯ π non-covalent interaction could be described as semi-coordination. The obtained results were compared to those previously reported for the isomorphous complex [Co(dpt)(NCS)2].

Characterization of Cuban and Brazilian natural zeolites by photoacoustic spectroscopy and electron paramagnetic resonance.

This report describes the photoacoustic and electron paramagnetic resonance investigations of Brazilian and Cuban zeolites. Photoacoustic optical absorption measurements indicate the presence of iron (Fe3+) ions with their respective transition bands for both zeolites. Two species of manganese (Mn2+ and Mn3+) were identified in the Cuban sample and the electronic transitions assigned. Iron and manganese ions were confirmed through nonradiative relaxation (τ) and characteristic diffusion (τβ) times evaluation, whose values were found to be τBRA = 5.40 ms, τCUB = 4.60 ms, τβBRA = 387 μs and τβCUB = 305 μs. Crystal field (Dq-BRA/Dq-CUB = 1048 cm-1/945 cm-1) plus Racah (B-BRA/B-CUB = 457 cm-1/813 cm-1 and C-BRA/C-CUB = 3655 cm-1/2496 cm-1) parameters were assessed as well. Paramagnetic resonance corroborated Fe3+ ions present in the Brazilian zeolite occupying sites showing axial and/or rhombic symmetry distortions. For the Cuban sample, results reveal the characteristic hyperfine sextet lines of Mn2+ overlapping the Fe3+ line. Values of Landé factor and isotropic hyperfine splitting constant were found to be 2.0 and 9.7 mT, respectively. This tells us that the Mn2+ lies in octahedral symmetry probably replacing calcium ions and point towards an ionic bonding character of the Mn2+ and its surroundings.

Interaction of surfactants with poloxamers 338 and its effect on some properties of cream base

The aim. Study of the interaction of surfactants with poloxamer 338 (P338) and the effect of P338 on the properties of cream bases.
 Materials and methods. Solutions of the surfactants and P338 as well as cream bases were under study. The average hydrodynamic diameter (Dh) and zeta potential (ζ‑potential) were determined by the light scattering intensity and electrophoretic mobility of micelles. The electron paramagnetic resonance (EPR) spectra of spin probes in micelles, solvents and bases were obtained; the type of spectrum, isotropic constant (AN), rotational correlation times (τ) and anisotropy parameter (ε) were determined. Liquids and cream bases were studied by capillary and rotational viscometry; the flow behaviour and yield stress (t0), dynamic and apparent viscosity (η) as well as the hysteresis (thixotropic) area (AH) were determined. The microstructure of the bases was examined by optical microscopy. The strength of adhesion (Sm) was assessed by the pull-off test, and the absorption of water was studied by dialysis.
 Results. Under the impact of P338 the hydrodynamic diameters of micelles formed by cationic, anionic and nonionic surfactants decreased as well as the absolute values of their ζ‑potential became lower, but the microviscosity of the micelle nuclei increased. There was also a change in the structure of the aggregates of surfactant with fatty alcohols; EPR spectra, which were superpositions characteristic for the lateral phase separation, converted into triplets that indicated the uniform distribution of lipophilic probes in the surfactant phase. When the content of P338 increased to 17 %, the rheological parameters of the bases increased drastically, the flow behaviour and the microstructure changed. The bases had the consistency of cream within temperature range from 25 °C to 70 °C and completely restored their apparent viscosity, which had decreased under shear stress. P338 enhances the adhesive properties of the bases. Due to their microstructure, cream bases have a lower ability to absorb water compared to a solution and gel containing 17 % and 20 % P338, respectively.
 Conclusions. The structure of surfactant micelles and aggregates of surfactants with fatty alcohols changed under impact of P338 due to the interaction of surfactants with P338. As a result of this interaction, at a sufficiently high concentration of P338, the microstructure and flow behaviour of bases changed, their rheological parameters, which remain high at temperatures from 25 °C to 70 °C, increased significantly, and water absorption parameters decreased. The bases with P338 were more adhesive

Relationships between the material parameters of continuum-kinematics-inspired peridynamics and isotropic linear elasticity for two-dimensional problems

Continuum-kinematics-inspired Peridynamics (CPD) has been recently proposed as a geometrically exact formulation of peridynamics that is also thermodynamically and variationally consistent. CPD can capture the Poisson effect exactly, unlike the original formulation of peridynamics (PD). Due to its geometrically exact nature, CPD does not suffer from zero-energy modes and displacement oscillations that may be observed in state-based PD formulations. For a two-dimensional analysis, CPD builds upon one-neighbor and two-neighbor interactions. The one-neighbor interactions of CPD are equivalent to the bond-based interactions of the original PD formalism. Two-neighbor interactions, however, are key in CPD since the basic notions of classical continuum kinematics, namely length and area, are preserved exactly. The isotropic two-dimensional CPD formulation of non-local elasticity therefore involves two material constants, namely C1 and C2, associated with length and area, respectively. This manuscript aims to establish relationships between the material parameters of CPD and isotropic linear elasticity for an affine deformation in a two-dimensional setting. It is shown that each of the CPD material parameters can be expressed in terms of any pairs of isotropic linear elasticity constants, such as Lamé parameters. Finally, we establish the admissible ranges for CPD material parameters.

Thin-shell concentration for random vectors in Orlicz balls via moderate deviations and Gibbs measures

In this paper, we study the asymptotic thin-shell width concentration for random vectors uniformly distributed in Orlicz balls. We provide both asymptotic upper and lower bounds on the probability of such a random vector Xn being in a thin shell of radius n times the asymptotic value of n−1/2(E[‖Xn‖22])1/2 (as n→∞), showing that in certain ranges our estimates are optimal. In particular, our estimates significantly improve upon the currently best known general Lee-Vempala bound when the deviation parameter t=tn goes down to zero as the dimension n of the ambient space increases. We shall also determine in this work the precise asymptotic value of the isotropic constant for Orlicz balls. Our approach is based on moderate deviation principles and a connection between the uniform distribution on Orlicz balls and Gibbs measures at certain critical inverse temperatures with potentials given by Orlicz functions, an idea recently presented by Kabluchko and Prochno (2021) [32].

Relativistic study of parity-violating nuclear spin-rotation tensors.

We present a four-component relativistic approach to describe the effects of the nuclear spin-dependent parity-violating (PV) weak nuclear forces on nuclear spin-rotation (NSR) tensors. The formalism is derived within the four-component polarization propagator theory based on the Dirac-Coulomb Hamiltonian. Such calculations are important for planning and interpretation of possible future experiments aimed at stringent tests of the standard model through the observation of PV effects in NSR spectroscopy. An exploratory application of this theory to the chiral molecules H2X2 (X = 17O, 33S, 77Se, 125Te, and 209Po) illustrates the dramatic effect of relativity on these contributions. In particular, spin-free and spin-orbit effects are even of opposite signs for some dihedral angles, and the latter fully dominate for the heavier nuclei. Relativistic four-component calculations of isotropic nuclear spin-rotation constants, including parity-violating electroweak interactions, give frequency differences of up to 4.2 mHz between the H2Po2 enantiomers; on the nonrelativistic level of theory, this energy difference is 0.1 mHz only.

Mathematical modeling of the elastic properties of cubic crystals at small scales based on the Toupin\u2013Mindlin anisotropic first strain gradient elasticity

In this work, a mathematical modeling of the elastic properties of cubic crystals with centrosymmetry at small scales by means of the Toupin–Mindlin anisotropic first strain gradient elasticity theory is presented. In this framework, two constitutive tensors are involved, a constitutive tensor of fourth-rank of the elastic constants and a constitutive tensor of sixth-rank of the gradient-elastic constants. First, 3+11 material parameters (3 elastic and 11 gradient-elastic constants), 3 characteristic lengths and 1+6 isotropy conditions are derived. The 11 gradient-elastic constants are given in terms of the 11 gradient-elastic constants in Voigt notation. Second, the numerical values of the obtained quantities are computed for four representative cubic materials, namely aluminum (Al), copper (Cu), iron (Fe) and tungsten (W) using an interatomic potential (MEAM). The positive definiteness of the strain energy density is examined leading to 3 necessary and sufficient conditions for the elastic constants and 7 ones for the gradient-elastic constants in Voigt notation. Moreover, 5 lattice relations as well as 8 generalized Cauchy relations for the gradient-elastic constants are derived. Furthermore, using the normalized Voigt notation, a tensor equivalent matrix representation of the two constitutive tensors is given. A generalization of the Voigt average toward the sixth-rank constitutive tensor of the gradient-elastic constants is given in order to determine isotropic gradient-elastic constants. In addition, Mindlin’s isotropic first strain gradient elasticity theory is also considered offering through comparisons a deeper understanding of the influence of the anisotropy in a crystal as well as the increased complexity of the mathematical modeling.

Aminoxyl (nitroxyl or nitroxide) radical formation by the action of ozone on squalene containing secondary aromatic amine antioxidants

AbstractSqualene, a model compound of polyisoprene or natural rubber, was employed as solvent to study the reaction between ozone and a series of N,N′‐substituted‐p‐phenylenediamines (PPDs) and other secondary aromatic amines. In all cases, it was found that nitroxyl radicals were formed nearly quantitatively by the action of ozone on the squalene solutions containing dissolved the selected additives. The resulting nitroxyl radicals from PPDs or from other secondary aromatic amines were easily detected by electron spin resonance spectroscopy at room temperature and the isotropic and anisotropic hyperfine interaction constants of the said nitroxides were determined. The FT‐IR spectroscopy was employed to show the easy oxidation of unprotected squalene when exposed to an ozone stream, while in presence of PPDs, ozone is quantitatively scavenged by the PPDs forming the resulting nitroxides and protecting completely squalene from ozonolysis reactions. The nitroxyl radicals formed by PPDs or secondary aromatic amine ozonation exert a permanent antioxidant activity entering in a redox cycle already known to ensure a long flex fatigue life or the given rubber compound.

Inverse Hooke's law and complementary strain energy in coupled strain gradient elasticity

AbstractThe inverse Hooke's law and complementary strain energy density has been examined in the context of the theory of coupled gradient elasticity for second gradient materials. To this end, it was assumed that the potential energy density is a quadratic form of the strain and of the second gradient of displacement. Existence of the coupling term significantly complicates the problem. To avoid this complication the equation for the potential energy density was transformed in order to present it as an uncoupled quadratic form of a modified strain and the second gradient of displacement or of the strain and a modified second gradient of displacement. These transformations, which is in essence a block matrix diagonalization, lead to a decoupling of strains and strain gradient in the potential energy density and makes it possible to determine tensorial relations for the compliance tensors of fourth‐, fifth‐ , and sixth‐rank. Both modifications result in the same compliance tensors and are valid for an arbitrary material symmetry class. In the case of hemitropic materials, the compliance tensors have the same symmetry and the same form as the stiffness tensors and are characterized by eight independent constants, namely the two classical isotropic constants, five constants in the strain gradient part and one constant in the coupling term. Explicit expressions for these eight parameters are obtained from the tensorial relations for the compliance tensors and are compared with the direct solution of a linear system for the compliance's. All three solutions are identical, what we consider as a verification of the presented results.