Components Of Tensor Research Articles

The Influence of Blood and Serum Microenvironment on Spin-Labeled Magnetic Nanoparticles

The investigation and clarification of the properties of surface-functionalized superparamagnetic nanoparticles in a biological environment are key challenges prior to their medical applications. In the present work, electron paramagnetic resonance spectroscopy (EPR) combined with the spin labeling technique was utilized to better understand the behavior of nitroxides attached to magnetite nanoparticles dispersed in body fluid. EPR spectra of spin-labeled, silane-coated Fe3O4 nanoparticles in human serum and whole blood were recorded and analyzed for both room- and low-temperature values. In all cases, the obtained EPR signal consisted of a broad line from magnetite cores and a characteristic signal from the attached 4-Amino-2,2,6,6-tetramethylpiperidine-1-oxyl (4-amino-TEMPO). Even for liquid samples, the anisotropic components of magnetic tensors did not fully average out, which was reflected in the differences in the intensity of three narrow hyperfine lines from nitroxide. At 230 K the irregular slow-motion signal from the attached radical was also simulated using the EasySpin toolbox, which allowed to determine the parameters related to magnetic tensors and the dynamics of the spin label. The study showed that the anisotropy of the motion of the spin label 4-amino-TEMPO reflects its interactions with the surrounding medium and the manner of the attachment of the nitroxide to the surface of nanoparticles.

Dimensionality reduction beyond neural subspaces with slice tensor component analysis.

Recent work has argued that large-scale neural recordings are often well described by patterns of coactivation across neurons. Yet the view that neural variability is constrained to a fixed, low-dimensional subspace may overlook higher-dimensional structure, including stereotyped neural sequences or slowly evolving latent spaces. Here we argue that task-relevant variability in neural data can also cofluctuate over trials or time, defining distinct 'covariability classes' that may co-occur within the same dataset. To demix these covariability classes, we develop sliceTCA (slice tensor component analysis), a new unsupervised dimensionality reduction method for neural data tensors. In three example datasets, including motor cortical activity during a classic reaching task in primates and recent multiregion recordings in mice, we show that sliceTCA can capture more task-relevant structure in neural data using fewer components than traditional methods. Overall, our theoretical framework extends the classic view of low-dimensional population activity by incorporating additional classes of latent variables capturing higher-dimensional structure.

Full-waveform reconstruction of micro-seismic events via topological derivative approach

Micro-seismic events, naturally occurring within geological formations and quasi-brittle engineered systems, provide a powerful window into the evolving processes of material degradation and failure. Accurate characterization of these events is critical for a comprehensive understanding of the underpinning fracturing mechanisms and potential implications. In this work, we present an algorithm for the spatial reconstruction and characterization of micro-seismic events in a three-dimensional bounded elastic body (with known geometry and nominal material properties) via combined source location and moment tensor inversion. Assuming availability of the full-waveform “acoustic emission” traces whose spectral content can be exposed via Fourier transform, the inverse solution is based on (i) a time-harmonic (forward) elastodynamic model and (ii) the concept of topological derivative as a framework for robust event reconstruction. On exploiting an equivalence between the elastic wavefield generated by the creation of a new micro-surface and that stemming from a suitable set of dipoles and double-couples (whose strengths are synthesized via the seismic moment tensor), we formulate the inverse problem as that for the real (in-phase) and imaginary (out-of-phase) components of the moment tensor at trial grid locations. In this way the optimal solution is obtained via a combinatorial search over a prescribed grid, inherently allowing for successive refinements of event reconstruction over the region(s) of interest. The analysis is illustrated by numerical experiments highlighting the key features of the inversion scheme including the reconstruction of multiple (i.e. contemporaneous) events, localization of the “off-grid” micro-seismic events, and the ability to handle noisy data. The results in particular highlight the utility of multi-frequency event reconstruction toward reducing the demand on the number of sensing locations.

Anisotropic quasi-static permittivity of rare-earth scandate single crystals measured by terahertz spectroscopy

We report the real-valued static and complex-valued quasi-static anisotropic permittivity parameters of rare-earth scandate orthorhombic single crystal GdScO3 (GSO), TbScO3 (TSO), and DyScO3 (DSO). Employing continuous-wave terahertz spectroscopy (0.2–1 THz), the complex permittivity was extracted using an anisotropic ambient-film-ambient model. Data obtained from multiple samples of the same oxides and different surface cuts were analyzed simultaneously. The zero-frequency limit of the modeled data indicates that at room temperature the real part of the dielectric tensor components for GSO are ɛa = 22.7, ɛb = 19.3, and ɛc = 28.1; for DSO, ɛa = 20.3, ɛb = 17.4, and ɛc = 31.1; and for TSO, ɛa = 21.6, ɛb = 18.1, and ɛc = 30.3, with a, b, and c crystallographic axes constituting the principal directions for the permittivity tensor. These results are in excellent agreement with expectations from theoretical computations and with scarcely available data from previous experimental studies. Furthermore, our results evidence a noticeable attenuation, which increases with frequency, and are very significant especially at the higher frequency end of the measurement and along the c-direction in all samples. We suggest the attenuation is most likely caused by the onset of absorption due to long-wavelength active optical phonon modes. These results are important for electronic and potential sub-terahertz applications (e.g., quarter-wave plate) benefiting from the large index contrast along different directions in these materials.

Iterative removal of sources to model the turbulent electromotive force

Abstract We describe a novel method to compute the components of dynamo tensors from direct magnetohydrodynamic (MHD) simulations. Our method relies upon an extension and generalisation of the standard Högbom CLEAN algorithm widely used in radio astronomy to systematically remove the impact of the strongest beams onto the corresponding image. This generalisation, called the Iterative Removal of Sources (IROS) method, has been adopted here to model the turbulent electromotive force (EMF) in terms of the mean magnetic fields and currents. Analogous to the CLEAN algorithm, IROS treats the time series of the mean magnetic field and current as beams that convolve with the dynamo coefficients which are treated as (clean) images to produce the EMF time series ( the dirty image). We apply this method to MHD simulations of galactic dynamos, to which we have previously employed other methods of computing dynamo coefficients such as the test-field method, the regression method, as well as local and non-local versions of the singular value decomposition (SVD) method. We show that our new method reliably recovers the dynamo coefficients from the MHD simulations. It also allows priors on the dynamo coefficients to be incorporated easily during the inversion, unlike in earlier methods. Moreover, using synthetic data, we demonstrate that it may serve as a viable post-processing tool in determining the dynamo coefficients, even when the power of additive noise to the EMF is twice as much the actual EMF.

Surface tension of aqueous electrolyte solutions. A thermomechanical approach.

We determine the surface tension of aqueous electrolyte solutions in contact with non-polar dielectric media using a thermomechanical approach, which involves deriving the stress tensor from the thermodynamic potential of an inhomogeneous fluid. To obtain the surface tension, we calculate both the normal and tangential pressures using the components of the stress tensor, recently derived by us [Y. A. Budkov and P. E. Brandyshev, J. Chem. Phys. 159, 174103 (2023)] within the framework of Wang's variational field theory. Using this approach, we derive an analytical expression for the surface tension in the linear approximation. At low ionic concentrations, this expression represents the classical Onsager-Samaras limiting law. By utilizing only one fitting parameter, which is related to the affinity of anions to the dielectric boundary, we successfully approximated experimental data on the surface tension of several aqueous electrolyte solutions. This approximation applies to both the solution-air and solution-dodecane interfaces, covering a wide range of electrolyte concentrations.

Physical properties and maximum allowable mass-radius relation of complexity-free compact stellar objects within modified $f(R,T)$ gravity formalism

Abstract This paper focuses on investigating the physical properties and predicted radii of compact stars generated by Tolman--IV complexity-free model within the background of modified gravity theory, especially $f(\mathcal{R},T)$-gravity theory, under complexity formalism for a spherically symmetric spacetime proposed by L. Herrera [Phys Rev D 97: 044010, 2018]. By solving the resulting set of differential equations, the explicit forms of the energy-momentum (EM) tensor components, including the density, radial pressure and tangential pressure, are obtained. The influence of the parameter $\chi$ on various physical properties of the star has been thoroughly investigated. The model undergoes a series of rigorous tests to determine its physical relevance. The findings indicate that the model exhibits regularity, stability and features a surface with vanishing pressure. The boundary of this surface is determined by carefully selecting the parameter space. The complexity method employed in $f(\mathcal{R},T)$ gravity offers an interesting approach for developing astrophysical models that are consistent with observable events as demonstrated by recent experiments. In this regard, we present a study that uses observational data from the GW190814 event, detected by the LIGO and Virgo observatories, to investigate the validity of the Tolman-IV model in $f(R, T)$ gravity. The analysis includes comparing the model's predictions with the observed characteristics of the compact object involved in the merger. In addition, data from two-millisecond pulsars, PSR J1614-2230 and PSR J0952-0607, are incorporated to further constrain theoretical theories. However, we present a diagram illustrating the relationship between the total mass and radius of the compact object candidates for different values of a parameter $\chi$.

Anisotropy ansatz for the axisymmetric Jeans equations

Abstract The Jeans equations do not form a closed system, and to solve them a parametrization relating the velocity moments is often adopted. For axisymmetric models, a phenomenological choice (the “b-ansatz”) is widely used for the relation between the vertical ($\sigma _z^2$) and radial ($\sigma _R^2$) components of the velocity dispersion tensor, thus breaking their identity present in two-integral systems. However, the way in which the ansatz affects the resulting kinematical fields can be quite complicated, so that the analysis of these fields is usually performed only after numerically computing them. We present here a general procedure to study the properties of the ansatz-dependent fields $\overline{v_{\varphi }^2}$, $\Delta =\overline{v_{\varphi }^2}- \sigma _z^2$ and $\Delta _R= \overline{v_{\varphi }^2}- \sigma _R^2$. Specifically, the effects of the b-ansatz can be determined before solving the Jeans equations once the behaviour over the (R, z)-plane of three easy-to-build ansatz-independent functions is known. The procedure also constrains the ansatz to exclude unphysical results (as a negative $\overline{v_{\varphi }^2}$). The method is illustrated by discussing the cases of three well-known galaxy models: the Miyamoto & Nagai and Satoh disks, and the Binney logarithmic halo, for which the regions and the constraints on the ansatz values can be determined analytically; a two-component (Miyamoto & Nagai plus logarithmic halo) model is also discussed.

Experimental study of DC Kerr effect of chalcogenide glass film by free space coupling method

Chalcogenide glass is an important nonlinear optical material that has attracted much attention in the areas of integrated photonics, supercontinuum sources, and all-optical switches in recent years. However, the current research mainly focuses on the nonlinear effect excited by light, and the research on its properties under the action of a DC field is still deficient. Here, a metal-cladding optical waveguide, which is composed of a chalcogenide glass film coated on a glass substrate, is presented to analyze the quadratic electro-optic (QEO) effect of the chalcogenide glass film. The DC Kerr coefficient and the whole components of the QEO tensor of the sample were experimentally determined by the free space coupling method.

High-speed photoelastic tomography for axisymmetric stress fields in a soft material: Temporal evolution of all stress components

This study presents a novel approach for reconstructing all stress components of the dynamic axisymmetric fields of a soft material using photoelastic tomography (PT) and a high-speed polarization camera. This study focuses on static and dynamic Hertzian contact as an example of transient stress field reconstructions. For the static Hertzian contact (a solid sphere pressed against a gel block), all stress components in the urethane gel, which has an elastic modulus of 47.4 kPa, were reconstructed by PT using the measured photoelastic parameters. The results were compared with theoretical solutions and showed good agreement. For the dynamic Hertzian contact (a sphere impacting gel), a high-speed polarization camera was used to reconstruct the transient stress field within the gel. PT was used to quantitatively measure the shear and axial stress waves and showed different propagation speeds on the substrate. The technique allowed the simultaneous measurement of stress fields ranging from O(10−1) to O(101) kPa during large deformations, demonstrating its accuracy in capturing rapidly changing stress tensor components in dynamic scenarios. The scaling laws of the calculated impact force agreed with theoretical predictions, validating the accuracy of PT for measuring dynamic axisymmetric stress fields in soft materials.

A microstructure-based parameterization of the effective anisotropic elasticity tensor of snow, firn, and bubbly ice

Abstract. Quantifying the link between microstructure and effective elastic properties of snow, firn, and bubbly ice is essential for many applications in cryospheric sciences. The microstructure of snow and ice can be characterized by different types of fabrics (crystallographic and geometrical), which give rise to macroscopically anisotropic elastic behavior. While the impact of the crystallographic fabric has been extensively studied in deep firn, the present work investigates the influence of the geometrical fabric over the entire range of possible volume fractions. To this end, we have computed the effective elasticity tensor of snow, firn, and ice by finite-element simulations based on 391 X-ray tomography images comprising samples from the laboratory, the Alps, Greenland, and Antarctica. We employed a variant of Eshelby's tensor that has been previously utilized for the parameterization of thermal and dielectric properties of snow and utilized Hashin–Shtrikman bounds to capture the nonlinear interplay between density and geometrical anisotropy. From that we derive a closed-form parameterization for all components of the (transverse isotropic) elasticity tensor for all volume fractions using two fit parameters per tensor component. Finally, we used the Thomsen parameter to compare the geometrical anisotropy to the maximal theoretical crystallographic anisotropy in bubbly ice. While the geometrical anisotropy clearly dominates up to ice volume fractions of ϕ≈0.7, a thorough understanding of elasticity in bubbly ice may require a coupled elastic theory that includes geometrical and crystallographic anisotropy.

Friction tensor for an ellipsoid enclosed in a rarefied gas

This research renders calculations of rotranslational friction and diffusion tensors in a rarefied gas, considering both specular and diffuse reflection off ellipsoidal particles. Calculations were conducted in a spherical polar coordinate system, revealing the dynamic nature of these off-diagonal tensors. The tensor elements were determined analytically, intending to compute the surface integrals. All diagrams, and pictures of two-dimensional surfaces were obtained by the numerical integration process in MATLAB. Additionally, we performed calculations without using the time parameter and time derivatives in the relevant relations. Deviations from the state of spherical symmetry were observed in the results for an ellipsoid and show that the tensors are dynamic quantities. Therefore, it is necessary to provide average values. We established that the non-zero elements of the friction tensor for an ellipsoid represent the directions of linear momentum transfer. Also, the non-zero components of the diffusion tensor signify the extent of fluctuations in relevant momentum transfers in corresponding directions.

Uniaxially drawn poly (L-lactic acid)/ poly (vinylidene fluoride) polymer blend as a promising piezoelectric material: Hysteresis and resonance spectroscopy study

This study explores the potential for piezoelectricity in a blend of polyvinylidene fluoride (PVDF) and poly-L-lactic acid (PLLA) prepared using the solution casting method. Dielectric frequency measurements across a range of 102 to 106 Hz revealed piezoelectric resonance within a broader dielectric relaxation regime. Analysis of the resonance spectra for length and width vibrational modes enabled the determination of the piezoelectric tensor components of the PVDF/PLLA blend. The blend exhibited enhanced ferroelectric polarization reversal, remnant polarization, and coercive field compared to pristine PVDF samples. The piezoelectric constants d31 and d14 (d36 of the blend) were determined. Mechanical drawing and poling techniques were employed to generate multiple piezoelectric constants, allowing for efficient energy harvesting from various directions. This flexible blend offers promising prospects for versatile energy conversion applications.

Surface crack effect on frequency and vibration mode switching of solar-powered aerospace structures

In the engineering design of modern wing panels and their optimal control system, the first step is to find and predict their dynamic characteristics. These characteristics are dependent on material properties, panel geometry, and boundary conditions. In addition, possible fracture existence, imperfections and environmental conditions may unpredictably change the frequency and modes shape of the panel and then the parameters of a control system. In the present paper, the effect of surface fracture depth and orientation on frequency and vibration mode switching of perovskite solar cells-based aircraft wing panels is investigated for the first time. The PSC (perovskite solar cell) panel is made of a polymer substrate reinforced with even-distributed graphene platelets (GPLs) and thin solar layers to enhance the overall electromechanical performance of the whole structure. Equations of motion of the panel are obtained by the Hamilton approach based on the properties of Reddy's third-order shear deformation theory and linear components of the Green-Lagrange strain tensor. The novel aspect is a line-spring model of surface crack by Cartmell et al. adapted to the model of the PSC panel under consideration. The discretization of the established equations of motion for the cracked panel is carried out by the element-free IMLS-Ritz method with mesh-free features. Validation of the obtained solutions is carried out by comparisons with results from previous studies for cracked laminated plates.First, material and geometric properties effect on vibration characteristics of the PSC structure was investigated. Next, partial surface crack depth and orientation angle are examined to show changes in frequency and vibration modes shape of the panel. It is shown, that there is a mode swapping between the second and third modes when transitioning from an intact panel to a cracked one. As the crack length increases, higher-order mode variations become more noticeable, potentially leading to their swapping or the excitation of new ones. Additionally, the findings demonstrate that the surface crack orientation angle significantly impacts the higher-order modes of the panel. When the orientation angle is 90°, the first six modes align with those of the intact plate. Mode shapes and frequency shifts are significant for crack orientation angles between 0° and 90°.

HYSCORE and QM/MM Studies of Second Sphere Variants of the Type 1 Copper Site in Azurin: Influence of Mutations on the Hyperfine Couplings of Remote Nitrogens.

Secondary coordination sphere (SCS) interactions have been shown to play important roles in tuning reduction potentials and electron transfer (ET) properties of the Type 1 copper proteins, but the precise roles of these interactions are not fully understood. In this work, we examined the influence of F114P, F114N, and N47S mutations in the SCS on the electronic structure of the T1 copper center in azurin (Az) by studying the hyperfine couplings of (i) histidine remote Nε nitrogens and (ii) the amide Np using the two-dimensional (2D) pulsed electron paramagnetic resonance (EPR) technique HYSCORE (hyperfine sublevel correlation) combined with quantum mechanics/molecular mechanics (QM/MM) and DLPNO-CCSD calculations. Our data show that some components of hyperfine tensor and isotropic coupling in N47SAz and F114PAz (but not F114NAz) deviate by up to ∼±20% from WTAz, indicating that these mutations significantly influence the spin density distribution between the CuII site and coordinating ligands. Furthermore, our calculations support the assignment of Np to the backbone amide of residue 47 (both in Asn and Ser variants). Since the spin density distributions play an important role in tuning the covalency of the Cu-Scys bond of Type 1 copper center that has been shown to be crucial in controlling the reduction potentials, this study provides additional insights into the electron spin factor in tuning the reduction potentials and ET properties.

Relations between Reynolds stresses and their dissipation rates during premixed flame–wall interaction within turbulent boundary layers

A direct numerical simulation (DNS) database for head-on quenching of premixed flames propagating across turbulent boundary layers representative of friction Reynolds numbers, Reτ, of 110 and 180 has been utilized to analyze the interrelation between Reynolds stresses and their dissipation rates during flame–wall interaction. The Reynolds stresses and their dissipation rates exhibit significant deviations from the corresponding non-reacting flow profiles within the flame brush and in the burned gas region. This behavior is prominent for the components in the wall-normal direction because the mean direction of flame normal acceleration due to thermal expansion aligns with the wall-normal direction in this configuration. The anisotropy of Reynolds stresses and their dissipation rate tensors have been found to be qualitatively similar, but the anisotropic behavior weakens with increasing Reτ. However, the components of the anisotropy tensors of Reynolds stresses and viscous dissipation rate are not related according to a linear scaling, and thus, the models based on this assumption do not successfully capture the viscous dissipation rate components obtained from the DNS data. By contrast, a model, which includes the invariants of the anisotropy tensor of Reynolds stresses and satisfies the limiting conditions, has been found to capture especially the diagonal components of the viscous dissipation rate tensor more successfully for both non-reacting and reacting cases considered in this work. However, the quantitative prediction of this model suffers for the components in the wall-normal direction for lower values of Reτ, but the performance of this model improves with an increase in Reτ.

Turbulence Closure With Small, Local Neural Networks: Forced Two‐Dimensional and β‐Plane Flows

AbstractWe parameterize sub‐grid scale (SGS) fluxes in sinusoidally forced two‐dimensional turbulence on the β‐plane at high Reynolds numbers (Re ∼25,000) using simple 2‐layer convolutional neural networks (CNN) having only O(1000) parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8–10 layers; we obtain stable, accurate, and long‐term online or a posteriori solutions at 16× downscaling factors. Our methodology significantly improves training efficiency and speed of online large eddy simulations runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor, Sd. We minimize a loss between the SGS vorticity flux divergence (computed from the high‐resolution solver) and that obtained from the CNN‐modeled Sd, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non‐local dependence on coarse fields; it also aligns with our physical conception that small‐scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2‐layer CNN‐parameterizations are more likely to be interpretable.

First principles study on the elastic properties of two-dimensional Janus ZrXY (X/Y = Cl, Br, and I, X ≠ Y)

In recent years, a novel two-dimensional semiconductor ZrX2 (X = Cl, Br, and I) has been found to have excellent optoelectronic properties and has attracted much attention. In this paper, the elastic properties of two-dimensional Janus ZrXY (X/Y = Cl, Br, and I, X ≠ Y) are studied by first principles, including elastic parameters, such as elastic tensor components, Young’s modulus, Poisson’s ratio, and stability. Research has found that the lattice parameters of two-dimensional Janus ZrXY are still influenced by the atomic radius. The Janus structure shows excellent dynamic stability both before and after its construction. Based on the elastic theory, the mechanical stability of the two-dimensional Janus ZrXY was proved indirectly. After constructing the two-dimensional Janus ZrXY structure with different planes, the elastic tensor component increases to a certain extent, and Young’s modulus and Poisson’s ratio increase, but the anisotropy of Young’s modulus and Poisson’s ratio decreases significantly.

On Generalized Kenmotsu Manifolds as Hypersurfaces of Vaisman-Gray Manifolds

In this paper, we conclude that the hypersurfaces of Vaisman-Gray manifolds have generalized Kenmotsu structures under some conditions for the Lee form, Kirichenko's tensors and the second fundamental form of the immersion of the hypersurface into the manifold of Vaisman-Gray class. Moreover, the components of the second fundamental form are determined when the foregoing hypersurfaces have generalized Kenmotsu structures or any special kind of it or Kenmotsu structures, such that some of these components are vanish. Also, some components of Lee form and some components of some Kirichenko's tensors in the Vaisman--Gray class are equal to zero. On the other hand, the minimality of totally umbilical, totally geodesic hypersurfaces of Vaisman--Gray manifolds with generalized Kenmotsu structures are investigated. In addition, we deduced that the hypersurface of Vaisman--Gray manifold that have generalized Kenmotsu structure is totally geodesic if and only if it is totally umbilical and some components of Lee form are constants.

Study of the distribution of residual stresses across the surface layer depth following machining through probing hole drilling and digital image correlation

The article aims to study the distribution of residual stresses across the surface layer depth following the machining of test specimens (free orthogonal cutting and burnishing). The machining by cutting and burnishing of 45 steel specimens was carried out using a milling machine with numerical control under varying machining factors. For a comparative analysis, the processes were also modeled via the finite element method using identical experimental values of geometric parameters and machining modes. In order to obtain residual stress distributions across the surface layer depth, probe holes having depths of 0.5; 0.75; 1; 1.5; and 2 mm were drilled. By differentiating the displacement of specimen surface particles, measured using digital image correlation, radial strains around the probe holes were determined. Then, these values were used to determine the residual stress components for each probe hole, and the averaged values of each residual stress component were calculated using the calculation algorithm presented in this article. After burnishing the specimen with a force of 3400 N, the test value of the σx component within the depth range (from the surface) of 0.5–0.75 mm amounted to -250 MPa. Model and experimental distributions of residual stress tensor components across the surface layer depth were obtained following machining via two methods. The experimental values of residual stresses were found to have good convergence with each other and with model distributions at depths up to 1 mm from the machined surface at a drill diameter of 1.7 mm. The proposed approach provides a means to obtain the residual stress distribution across the surface layer depth by drilling probe holes of different depths and estimating radial strains on the specimen surface using the digital image correlation method.