Isotropic Form Research Articles

Impact of nanosilver surface electronic distributions on serum protein interaction and hemocompatibility.

Translation of silver-based nanotechnology "from bench to bedside" requires a deep understanding of the molecular aspects of its biological action, which remains controversial at low concentrations and non-spherical morphologies. Here, we present a hemocompatibility approach based on the effect of the distinctive electronic charge distribution in silver nanoparticles (nanosilver) on blood components. On basis of spectroscopic, volumetric, microscopic, dynamic light scattering measurements, pro-coagulant activity tests and cellular inspection we determine that, at extremely low nanosilver concentrations (0.125 - 2.5 μg mL-1) there is a relevant interaction effect on serum albumin and on red blood cells. The explanation has its origin in the surface charge distribution of nanosilver and their electron-mediated energy transfer mechanism. Prism-shaped nanoparticles, with anisotropic charge distributions, act at the surface level generating a compaction of the native protein molecule, while the spherical nanosilver, by exhibiting isotropic surface charge, generates a polar environment comparable to the solvent. Both morphologies induce aggregation at NPs / BSA ≅ 0.044 molar ratio values without altering the coagulation cascade tests, although the spherical-shaped nanosilver has a negative impact on red blood cells. Overall, our results suggest that the electron distributions of nanosilver, even at extremely low concentrations, are a critical factor influencing the molecular structure of blood proteins and red blood cells' membranes. Isotropic forms of nanosilver should be considered with caution, as they are not always the least harmful.

Weak magnetohydrodynamic turbulence theory revisited

Two recent papers, P. H. Yoon and G. Choe, Phys. Plasmas 28, 082306 (2021) and Yoon et al., Phys. Plasmas 29, 112303 (2022), utilized in the derivation of the kinetic equation for the intensity of turbulent fluctuations the assumption that the wave spectra are isotropic, that is, the ensemble-averaged magnetic field tensorial fluctuation intensity is given by the isotropic diagonal form, ⟨δBiδBj⟩k=⟨δB2⟩kδij. However, it is more appropriate to describe the incompressible magnetohydrodynamic turbulence involving shear Alfvénic waves by modeling the turbulence spectrum as being anisotropic. That is, the tensorial fluctuation intensity should be different in diagonal elements across and along the direction of the wave vector, ⟨δBiδBj⟩k=12 ⟨δB⊥2⟩k(δij−kikj/k2)+⟨δB∥2⟩k(kikj/k2). In the present paper, we thus reformulate the weak magnetohydrodynamic turbulence theory under the assumption of anisotropy and work out the form of nonlinear wave kinetic equation.

A-priori evaluation of data-driven models for large-eddy simulations in Rayleigh–Bénard convection

Natural convection is a commonly occurring heat-transfer problem in many industrial flows and its prediction with conventional large eddy simulations (LES) at higher Rayleigh numbers using progressively coarser grids leads to increasingly inaccurate estimates of important performance indicators, such as Nusselt number (Nu). Thus, to improve the heat transfer predictions, we utilize Gene Expression Programming (GEP) to develop sub-grid scale (SGS) stress and SGS heat-flux models simultaneously for LES. The models’ development is performed using reference direct numerical simulation data of a typical natural convection case, i.e. the Rayleigh–Bénard convection (RBC). The training frameworks are built by using alignment as the evaluation metrics of the basis functions when comparing to the Gaussian-filtered SGS stress and SGS heat-flux. The trained models in isotropic form, by utilizing the L2 norm of the grid cell ΔL2 as the length scale, demonstrate good performance in the bulk region, but less improved performance in the near wall region. It is shown, that for LES of wall-bounded flow, the GEP models in anisotropic form, i.e. using different grid length scale for the different spatial directions, are required to obtain generalized models suitable for different regions. Consequently, the a-priori results demonstrate a significant improvement in the prediction of both instantaneous and mean quantities for a wide range of filter widths.

Structure and role of the pressure Hessian in regions of strong vorticity in turbulence

Amplification of velocity gradients, a key feature of turbulent flows, is affected by the non-local character of the incompressible fluid equations expressed by the second derivative (Hessian) of the pressure field. By analysing the structure of the flow in regions where the vorticity is the highest, we propose an approximate expression for the pressure Hessian in terms of the local vorticity, consistent with the existence of intense vortex tubes. Contrary to the often used simplification of an isotropic form for the pressure Hessian, which in effect inhibits vortex stretching, the proposed approximate form of the pressure Hessian enables much stronger vortex stretching. The prediction of the approximation proposed here is validated with results of direct numerical simulations of turbulent flows.

Bilinear magnetoresistance in 2DEG with isotropic cubic Rashba spin–orbit interaction

Bilinear magnetoresistance has been studied theoretically in 2D systems with isotropic cubic form of Rashba spin–orbit interaction. We have derived the effective spin–orbital field due to current-induced spin polarization and discussed its contribution to the unidirectional system response. The analyzed model can be applied to the semiconductor quantum wells as well as 2DEG at the surfaces and interfaces of perovskite oxides.

On the analytic theory of isotropic ternary quadratic forms

A new local-global result about the primitive representations of zero by integral ternary quadratic forms is proven. By an extension of a result of Kneser (given in the Appendix), it yields a quantitative supplement to the Hasse principle on the number of automorphic orbits of primitive zeros of a genus of forms. One ingredient in its proof is an asymptotic formula for a count of the zeros of a given form in such an orbit.

A novel and fully automated coordinate system transformation scheme for near optimal surrogate construction

This work develops a novel coordinate system transformation scheme to improve the performance of common radial basis function surrogate models. This coordinate system transformation scheme is based on the fact that commonly used basis functions are isotropic.Three main empirical findings are established in this study. Firstly, in general isotropic functions are inadequate to describe anisotropic data manifolds due to a mismatch between the functional form and the form of the data manifold resulting in poor generative performance. Counter-intuitively, utilising additional gradients during surrogate training often worsens the generative capability.Secondly, component-wise scaling of isotropic model forms during cross-validation is inadequate to enhance the functional form of the data manifold form as anisotropic coupling in the data manifold remains coupled. Improving the match between the functional form and the data manifold form requires both rotation and scaling.Thirdly, the coordinate system transformation scheme should predominantly be based on a collection of local curvature estimations and not on global curvature approximations. Gradients are critical to estimating the local curvature for identifying a near-optimal reference frame for surrogate construction, which then translates to additional benefits of gradients in gradient-enhanced surrogates.Based on the above observations, this paper proposes an isotropic transformation for the data coordinate system that performs near-optimal transformations on lower dimensional data without requiring any cross-validation. The method is compared against commonly applied component-wise cross-validation data coordinate system scaling as well as the more modern Active Subspace Method on a carefully crafted decomposable test problem, which has a known optimal coordinate system, that varies between 2 and 16 dimensions.The paper concludes after demonstrating that the developed transformation scheme, as well as the other common methods, will offer little benefit on non-decompose problems and offers some suggestions on future work to create a more general isotropic transformation.

Energy transfer and third-order law in forced anisotropic magneto-hydrodynamic turbulence with hyper-viscosity

The third-order law links energy transfer rates in the inertial range of magneto- hydrodynamic (MHD) turbulence with third-order structure functions. Anisotropy, a typical property in the solar wind, challenges the applicability of the third-order law with the isotropic assumption. To shed light on the energy transfer process in the presence of anisotropy, we conducted direct numerical simulations of forced MHD turbulence with normal and hyper-viscosity under various strengths of the external magnetic field ( $B_0$ ), and calculated three forms of third-order structure function with or without averaging of the azimuthal or polar angles with respect to $B_0$ direction. Correspondingly, three estimated energy transfer rates were obtained. The result shows that the peak of normalized third-order structure function occurs at larger scales closer to the $B_0$ direction, and the maximum of longitudinal transfer rates shifts away from the $B_0$ direction at larger $B_0$ . Compared with normal viscous cases, hyper-viscous cases can attain better separated inertial range, thus facilitating the estimation of the energy cascade rates. We find that the widespread use of the isotropic form of the third-order law in estimating the energy transfer rates is questionable in some cases, especially when the anisotropy arising from the mean magnetic field is inevitable. In contrast, the direction-averaged third-order structure function properly accounts for the effect of anisotropy and predicts the energy transfer rates and inertial range accurately, even at very high $B_0$ . With limited statistics, the third-order structure function shows a stronger dependence on averaging of azimuthal angles than the time, especially for high $B_0$ cases. These findings provide insights into the anisotropic effect on the estimation of energy transfer rates.

Influence of Capillary Flow on Self-Organization of Water Droplets in Nematic Liquid Crystal

The results of studying the motion of isotropic liquid drops in a homeotropic layer of liquid crystal Е7 with long-lived instabilities induced by a damped shear flow that occurs when a flat capillary is filled due to the action of capillary forces (capillary flow). An intense flow of nematics with initial homeotropic orientation leads to the appearance of orientational instabilities. In the experiments, a liquid-crystal cell with a variable gap (from 60 to 100 μm) was used. The object of the study was a 10:1 emulsion "liquid crystal – isotropic liquid". It was found that drops of isotropic liquid form various types of spatial structures. In particular, chains of drops in the region of strong deformations of LC orientation (for example, at the boundaries of the existence of long-lived regions with a changed orientation) were observed. In addition, an increased concentration of isotropic droplets occurred in the region separating the sections of the liquid crystal under the action of an electric field and in the absence of its action. Based on the analysis of microscopic images, the velocity of mutual motion of two isolated drops was determined. It made possible to estimate the interaction force between the drops (Fa = 5.6 pN) that was caused by the distortions of orientational structure in the vicinity of the drops. The results obtained are discussed within the existing theory of liquid crystals.

Dark energy on astrophysical scales and its detection in the Milky Way

The origin and nature of dark energy is one of the most significant challenges in modern science. This research aims to investigate dark energy on astrophysical scales and provide a cosmology-independent method to measure its equation-of-state parameter w. To accomplish this, we introduce the concept of a perfect fluid in any static, curved spacetime, and express the energy-momentum tensor of the perfect fluid in a general isotropic form, namely Weinberg's isotropic form. This enables us to define an equation-of-state parameter in a physical and global manner. Within this theoretical framework, we demonstrate that the energy-momentum tensor of dark energy on different scales can take the general isotropic form. Furthermore, we explore the SdS w spacetime and establish its connection with dark energy in cosmology through the equation-of-state parameter w. In the SdS w spacetime, a repulsive dark force can be induced by dark energy locally. We then apply the concept of the dark force to realistic astrophysical systems using the Poisson equation. Finally, we find that an anomaly in the Milky Way rotation curve can be quantitatively interpreted by the dark force. By fitting the galactic curve, we are able to obtain the value of the equation-of-state parameter of dark energy, independently of specific dark energy models.

Tuning the physicochemical properties of axitinib by crystallization: Preparation, calculation and Structure-property relationship

Crystal engineering is a radical method to modulate the physicochemical properties of the drugs to meet the needs of the pharmaceutical industry. Examined herein are six axitinib solid-state forms, including anhydrous forms (Ⅳ and XLI), solvates (acetic acid, nitromethane and n-propanol), and cocrystal (nicotinamide). Comprehensive characterization containing morphology, hygroscopicity, solubility, fluorescence and powder tabletability were performed. Calculations of lattice energy, packing coefficient and energy framework rationalized the structure–property relationship of these six forms from the packing landscape. This system illustrates that form IV and cocrystal improve the solubility of axitinib, but the humidity stability is also decreased. Six crystal forms show polychromatic solid-state luminescence ranging from violet to indigo to green. Form IV and cocrystal with slip plane structures exhibited superior tensile strength and compactibility than isotropic form XLI. Elusive form VI can be obtained by controlling the humidity levels during desolvation of the solvate. This work not only realizes the regulation of better physicochemical properties of axtinnib for industrial manufacturing, but also provides a detailed understanding of the structure–property relationship of drugs in complex polymorphic systems.

Phenotyping the Histopathological Subtypes of Non-Small-Cell Lung Carcinoma: How Beneficial Is Radiomics?

The aim of this study was to investigate the usefulness of radiomics in the absence of well-defined standard guidelines. Specifically, we extracted radiomics features from multicenter computed tomography (CT) images to differentiate between the four histopathological subtypes of non-small-cell lung carcinoma (NSCLC). In addition, the results that varied with the radiomics model were compared. We investigated the presence of the batch effects and the impact of feature harmonization on the models' performance. Moreover, the question on how the training dataset composition influenced the selected feature subsets and, consequently, the model's performance was also investigated. Therefore, through combining data from the two publicly available datasets, this study involves a total of 152 squamous cell carcinoma (SCC), 106 large cell carcinoma (LCC), 150 adenocarcinoma (ADC), and 58 no other specified (NOS). Through the matRadiomics tool, which is an example of Image Biomarker Standardization Initiative (IBSI) compliant software, 1781 radiomics features were extracted from each of the malignant lesions that were identified in CT images. After batch analysis and feature harmonization, which were based on the ComBat tool and were integrated in matRadiomics, the datasets (the harmonized and the non-harmonized) were given as an input to a machine learning modeling pipeline. The following steps were articulated: (i) training-set/test-set splitting (80/20); (ii) a Kruskal-Wallis analysis and LASSO linear regression for the feature selection; (iii) model training; (iv) a model validation and hyperparameter optimization; and (v) model testing. Model optimization consisted of a 5-fold cross-validated Bayesian optimization, repeated ten times (inner loop). The whole pipeline was repeated 10 times (outer loop) with six different machine learning classification algorithms. Moreover, the stability of the feature selection was evaluated. Results showed that the batch effects were present even if the voxels were resampled to an isotropic form and whether feature harmonization correctly removed them, even though the models' performances decreased. Moreover, the results showed that a low accuracy (61.41%) was reached when differentiating between the four subtypes, even though a high average area under curve (AUC) was reached (0.831). Further, a NOS subtype was classified as almost completely correct (true positive rate ~90%). The accuracy increased (77.25%) when only the SCC and ADC subtypes were considered, as well as when a high AUC (0.821) was obtained-although harmonization decreased the accuracy to 58%. Moreover, the features that contributed the most to models' performance were those extracted from wavelet decomposed and Laplacian of Gaussian (LoG) filtered images and they belonged to the texture feature class.. In conclusion, we showed that our multicenter data were affected by batch effects, that they could significantly alter the models' performance, and that feature harmonization correctly removed them. Although wavelet features seemed to be the most informative features, an absolute subset could not be identified since it changed depending on the training/testing splitting. Moreover, performance was influenced by the chosen dataset and by the machine learning methods, which could reach a high accuracy in binary classification tasks, but could underperform in multiclass problems. It is, therefore, essential that the scientific community propose a more systematic radiomics approach, focusing on multicenter studies, with clear and solid guidelines to facilitate the translation of radiomics to clinical practice.

Fully linear band crossings at high symmetry points in layers: classification and role of spin–orbit coupling and time reversal

Symmetry imposed restrictions to the Hamiltonian are systematized and applied to all of 80 clusters of single/double ordinary/gray groups (320 groups in total), to single out linear (in all directions) band crossings and corresponding effective Hamiltonians in high-symmetry Brillouin zone points of layered materials. The resulting dispersion types are isotropic or anisotropic forms of: single cone (with double degenerate crossing point and non-degenerate branches, or four-fold degenerate crossing point with double degenerate conical branches), poppy-flower (four-fold degenerate crossing point with two pairs of non-degenerate mutually rotated conical branches), and fortune teller (with nodal lines). Further, we describe the nontrivial patterns of dispersions’ behavior in high symmetry points when symmetry is varied within a cluster. Namely, Clebsch–Gordan series of the products of spin representation with the integer ones are relevant when spin–orbit coupling is included, and clarify observed scenarios (gap closing, gap opening, cone preserving, cone splitting etc). Analogously, analysis of behavior of dispersions in transition from ordinary to gray group enlightens the role of time reversal symmetry. The results refine and expand data existing in literature, and interesting or even unexpected cases are singled out in discussion.

Angular dependence of the upper critical induction of clean s- and d x 2−y 2 -wave superconductors with self-consistent ellipsoidal effective mass and Zeeman anisotropies

We employ the Schrödinger-Dirac method generalized to an ellipsoidal effective mass anisotropy in order to treat the spin and orbital effective mass anisotropies self consistently, which is important when Pauli-limiting effects on the upper critical field characteristic of singlet superconductivity are present. By employing the Klemm–Clem transformations to map the equations of motion into isotropic form, we then calculate the upper critical magnetic induction at arbitrary directions and temperatures T for isotropic s-wave and for anisotropic -wave superconducting order parameters. As for anisotropic s-wave superconductors, is largest in the direction of the lowest effective mass, and is proportional to the universal orientation factor . However, for -wave pairing and vanishing planar effective mass anisotropy, exhibits a four-fold azimuthal pattern with C 4 symmetry the maxima of which are along the crystal axes just below the transition temperature T c , but these maxima are rotated by about the z axis as T is lowered to 0. However for -wave pairing with weak planar effective mass anisotropy, exhibits a two-fold pattern with C 2 symmetry for all , which also rotates by about the z axis as T is lowered to 0. These low planar effective mass anisotropy cases provide a new method to distinguish s-wave and -wave pairing symmetries in clean unconventional superconductors.

Perturbative model for the second-order velocity structure function tensor in turbulent shear flows

A model for the second order velocity structure function tensor, based on Kolmogorov's theory and valid for the inertial range, is proposed, incorporating the effect of anisotropy as a linear perturbation to the standard isotropic form. Structure functions measured from direct numerical simulations of channel flow and from experimental measurements in turbulent boundary layers are compared with predicted behavior and reasonable agreement is found.

In Situ Optical and X-ray Spectroscopy Reveals Evolution toward Mature CdSe Nanoplatelets by Synergetic Action of Myristate and Acetate Ligands.

The growth of two-dimensional platelets of the CdX family (X = S, Se, or Te) in an organic solvent requires the presence of both long- and short-chain ligands. This results in nanoplatelets of atomically precise thickness and long-chain ligand-stabilized Cd top and bottom surfaces. The platelets show a bright and spectrally pure luminescence. Despite the enormous interest in CdX platelets for optoelectronics, the growth mechanism is not fully understood. Riedinger et al. studied the reaction without a solvent and showed the favorable role for short-chain carboxylates for growth in two dimensions. Their model, based on the total energy of island nucleation, shows favored side facet growth versus growth on the top and bottom surfaces. However, several aspects of the synthesis under realistic conditions are not yet understood: Why are both short- and long-chain ligands required to obtain platelets? Why does the synthesis result in both isotropic nanocrystals and platelets? At which stage of the reaction is there bifurcation between isotropic and 2D growth? Here, we report an in situ study of the CdSe nanoplatelet reaction under practical synthesis conditions. We show that without short-chain ligands, both isotropic and mini-nanoplatelets form in the early stage of the process. However, most remaining precursors are consumed in isotropic growth. Addition of acetate induces a dramatic shift toward nearly exclusive 2D growth of already existing mini-nanoplatelets. Hence, although myristate stabilizes mini-nanoplatelets, mature nanoplatelets only grow by a subtle interplay between myristate and acetate, the latter catalyzes fast lateral growth of the side facets of the mini-nanoplatelets.

Thermal stability of quasi-isotropic strands with different cross-sections and with/without metal sheaths

This paper mainly focuses on the thermal stability performance, such as minimum quench energy (MQE) and normal zone propagation velocity (NZPV), of a quasi-isotropic strand (Q-IS) with three different configurations made from 2G high-temperature superconducting (HTS) tapes in the adiabatic approximation. Due to the anisotropic performance of thermal conductivity in 2G HTS tapes, the tensor form of the heat conduction equation was used instead of conventional isotropic forms. We first measured the MQE and NZPV of three strands in the adiabatic approximation. Subsequently, the experimental results were verified by finite element analysis and compared with the values of MQE and NZPV in a liquid nitrogen (LN2) bath. Finally, the effect of a metal sheath on the current distribution and generation of Joule heat during the quench process were analyzed through simulation. The results show that the arc-shaped aluminum filler brings slightly higher thermal stability of Q-IS while the copper sheath largely improves stability. Moreover, compared with the thermal stability of the strand fully exposed to the LN2 bath, for the strand in the adiabatic approximation, the MQE decreases a lot while the maximum of NZPV is increased by 2–3 times.

Preparation and Characterization of Gelatin-Based Films Cross-Linked by Two Essential Oils at Different Concentrations and Plasticized with Glycerol

Gelatin cross-linking has recently been discovered to be a very appealing method of producing gelatin-based films. The current research looks at various commercial gelatin (type B) films to improve their physical qualities. Bunium alpinum and bunium incrassatum essential oils (EOs) in two quantities (5% and 25%) were added to the films, which showed substantial biological activity (antibacterial, antioxidant, antihemolytic, and anti-inflammatory). According to electronic scanning microscopy, the basic gelatin matrix had changed and there were multiple dense spots on the cross-linked films. The particles appear to be more bonded in an isotropic form. Infrared spectroscopy cannot provide substantial accuracy on the new characteristics and chemical interactions formed due to the complex system of both gelatin and EOs. According to the UV transmission test results, adding EOs to gelatin films improves the barrier properties against UV rays and prevents UV light transmission. Finally, the swelling water test revealed that included EOs in the film composition reduce the film's swelling.

Casimir effect nearby and through a cosmological wormhole

In this letter, we investigate the changes in the quantum vacuum energy of the massless scalar field inside a Casimir cavity that orbits a wormhole. We consider a cosmological model with the isotropic form of the Morris-Thorne wormhole, embedded in the FLRW Universe. In this sense, we examine the effects of global curvature and scale factor in an instant of the cosmic history, besides the influences of the local geometry and inertial forces, on the Casimir energy density. We also study the behavior of this quantity when each plate is positioned without rotation at opposite sides of the wormhole throat, at zero and finite temperatures, taking into account the effective distance between the plates through the wormhole throat.

Uniqueness of Curvature Measures in Pseudo-Riemannian Geometry

The recently introduced Lipschitz–Killing curvature measures on pseudo-Riemannian manifolds satisfy a Weyl principle, i.e. are invariant under isometric embeddings. We show that they are uniquely characterized by this property. We apply this characterization to prove a Künneth-type formula for Lipschitz–Killing curvature measures, and to classify the invariant generalized valuations and curvature measures on all isotropic pseudo-Riemannian space forms.