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For a quasilinear p -form defined over a field F of characteristic p > 0 , we prove that its defect over the field F ( a 1 p n 1 , ... , a r p n r ) is equal to its defect over the field F ( a 1 p , ... , a r p) , strengthening a result of Hoffmann from 2004. We also compute the full splitting pattern of some families of quasilinear p -forms. [ABSTRACT FROM AUTHOR]

It is known that an incident bulk P wave propagating in a homogeneous isotropic halfspace, being reflected from the plane boundary, may exhibit a mode conversion into shear S wave without the formation of reflected P waves. The mode conversion takes place, when the incident wave hits the boundary at some critical angles, which depend upon Poisson's ratio. Herein, it is revealed that the Jeffreys solution for the mode conversion angles needs in in corrections, mainly because of spurious roots, appeared at solving a specially constructed eighth-order polynomial for the P wave reflection coefficient. The developed approach allowed us to construct a bi-cubic polynomial and obtain analytical expressions for its roots, and to find correct values for angles of incidence, at which the mode conversion occurs. [ABSTRACT FROM AUTHOR]

Compressed and stabilized earth block (CSEB) masonry is a locally appropriate alternative for low-rise dwellings that offers attractive affordability, sustainability, and durability features. From a designer's perspective, the availability of standards for material characterization and design codes is essential for CSEB masonry to be accepted and adopted. However, current standards and codes are limited—this is certainly the case in North America—and largely rely on empirical and prescriptive provisions that are adapted from those for conventional masonry (e.g., fired-clay or cinder-block). Advancing standardization and codification calls for advances in the fundamental understanding of material and structural behavior as a function of constituents and manufacturing methods. For CSEBs that are customarily compacted using metallic molds and hydraulic presses, a fundamental gap lies in the understanding of whether the heterogeneity of stabilized soil mixtures, together with their manufacturing process, result in block materials that can be approximated as homogeneous and isotropic at the scale of specimens used for physicomechanical characterization. This paper reports on an investigation of a CSEB material whose constituent properties and manufacturing process are representative of those frequently encountered in North America. Homogeneity and isotropy are established based on empirical evidence from microscopic and chemical analysis, and on the statistical analysis of uniaxial compressive strength and stiffness data obtained from samples that were extracted from different areas of different source blocks, and then tested by applying loads parallel or perpendicular to the compaction direction. [ABSTRACT FROM AUTHOR]

Anisotropic hyperelastic distortion energies are used to solve many problems in fields like computer graphics and engineering with applications in shape analysis, deformation, design, mesh parameterization, biomechanics, and more. However, formulating a robust anisotropic energy that is low order and yet sufficiently non-linear remains a challenging problem for achieving the convergence promised by Newton-type methods in numerical optimization. In this article, we propose a novel analytic formulation of an anisotropic energy that is smooth everywhere, low order, rotationally invariant, and at least twice differentiable. At its core, our approach utilizes implicit rotation factorizations with invariants of the Cauchy-Green tensor that arises from the deformation gradient. The versatility and generality of our analysis is demonstrated through a variety of examples, where we also show that the constitutive law suggested by the anisotropic version of the well-known As-Rigid-As-Possible energy is the foundational parametric description of both passive and active elastic materials. The generality of our approach means that we can systematically derive the force and force-Jacobian expressions for use in implicit and quasistatic numerical optimization schemes, and we can also use our analysis to rewrite, simplify, and speed up several existing anisotropic and isotropic distortion energies with guaranteed inversion safety. [ABSTRACT FROM AUTHOR]

While the theory of random isotropic scalar fields on the sphere is well established, it has not been fully extended to the case of vector fields yet. In this contribution, several theoretical results are thus generalized to random isotropic vector fields on the sphere, including an equivalent of the Wiener–Khinchin theorem, which relates the distance-dependent covariance of the field’s components in a particular rotationally invariant basis to the covariance of the vector spherical harmonic coefficients of the field, i.e., its angular power spectrum. A parametric model, based on a stochastic partial differential equation, is proposed to represent the spatial covariance and angular power spectrum of such fields. Such a model is adjusted, with minor modifications, to empirical spatial correlations of the white noise and flicker noise components of 3D displacement time series of ground global navigation satellite system (GNSS) tracking stations. The obtained spatial correlation model may find several applications such as enhanced detection of offsets in GNSS station position time series, enhanced estimation of long-term ground deformation (i.e., station velocities), enhanced isolation of station-specific displacements (i.e., spatial filtering) and more realistic assessment of uncertainties in all GNSS network-based applications (e.g., estimation of crustal strain rates, of glacial isostatic adjustment models or of tectonic plate motion models). [ABSTRACT FROM AUTHOR]

With the rise in carbon fiber-reinforced plastic (CFRP) usage, there is a growing occurrence of waste disposal, prompting the exploration of different recycling methods. The primary methods of recycling include separating carbon fibers and resin from discarded CFRP products or reusing scraps generated during CFRP production, such as dry fabric or prepreg. Recycling leftover dry fabric is essential for waste management in the automotive industry. Current research is centered on utilizing recycled materials to produce anisotropic mats, presenting difficulties in managing variations in properties. Moreover, isotropic mats are the preferred choice for practical automotive component design. Our research aimed to solve this problem by creating recycled carbon fiber (rCF) mats with isotropic characteristics through a wet method to enhance even fiber spreading. Conditions to minimize property changes in the fabric based on direction were identified, and the mats were tailored accordingly. Then, the resin was impregnated into the mats using compression resin transfer molding to form CFRP. The static properties of the CFRP specimens produced were evaluated to identify conditions that maximize isotropy. Furthermore, observations of oil injection into rCF mats showed that resin track formation was reduced when CFRP was fabricated using isotropic mats. [ABSTRACT FROM AUTHOR]

The isotropy is one of the important performance indexes of the six-axis acceleration sensing mechanism, which determines the measurement accuracy of the sensor. In order to obtain the complete isotropy of the sensing mechanism, a new configuration synthesis method is proposed. Firstly, based on the Newton-Euler method and the inherent scale constraint relationship between the branches, the forward decoupling equation of the Stewart-type six-axis acceleration sensing mechanism is constructed. Secondly, the relationship between the isotropy of the sensing mechanism and the condition number of the input matrix in the forward decoupling equation is analyzed, and the mapping relationship between the branch pose and the input matrix is analyzed. Then, the configuration synthesis steps of the fully isotropic sensing mechanism are created. Finally, following this step, a "12-6" Stewart-type six-axis acceleration sensing mechanism is synthesized and a virtual experiment is carried out. The two cases of adding 0.100% random disturbance and zero disturbance are compared, and the results show that the maximum reference error of six-dimensional acceleration is 0.169%, that is, the magnification of the input and output errors is only 1.69. This shows that the new configuration has excellent isotropic properties. [ABSTRACT FROM AUTHOR]

We establish that, for ideal unconstrained uniaxial nematic elastomers described by a homogeneous isotropic strain-energy density function, the only smooth deformations that can be controlled by the application of surface tractions only and are universal in the sense that they are independent of the strain-energy density are those for which the deformation gradient is constant and the liquid crystal director is either aligned uniformly or oriented randomly in Cartesian coordinates. This result generalizes the classical Ericksen's theorem for nonlinear homogeneous isotropic hyperelastic materials. While Ericksen's theorem is directly applicable to liquid crystal elastomers in an isotropic phase where the director is oriented randomly, in a nematic phase, the constitutive strain-energy density must account also for the liquid crystal orientation which leads to significant differences in the analysis compared to the purely elastic counterpart. [ABSTRACT FROM AUTHOR]

Let F be a field of characteristic 2. Our aim in this paper is to prove that the extension given by the function field of a singular conic is excellent for bilinear forms. We also give examples showing that in general this extension is not excellent for quadratic forms of arbitrary dimension. [ABSTRACT FROM AUTHOR]

We obtain discrete mixture representations for parametric families of probability distributions on Euclidean spheres, such as the von Mises–Fisher, the Watson and the angular Gaussian families. In addition to several special results we present a general approach to isotropic distribution families that is based on density expansions in terms of special surface harmonics. We discuss the connections to stochastic processes on spheres, in particular random walks, discrete mixture representations derived from spherical diffusions, and the use of Markov representations for the mixing base to obtain representations for families of spherical distributions. [ABSTRACT FROM AUTHOR]

The increasing use of finite element analysis in modern infrastructure design emphasizes the importance of determining soil stiffness at small strains. This is usually represented by the normalized shear modulus degradation curve, which is crucial for accurate design. In the absence of specific measurements on the local soil, engineers often rely on empirical correlations and assume comparable behavior of soils with similar intrinsic properties. However, the application of this approach leads to uncertainties, especially for unique geological formations such as the soft cohesive soils of the Ljubljana Marsh. The main objective of this study was to determine the small strain shear modulus of Ljubljana Marsh soil with a plasticity index between 11 and 35%. Isotropic and anisotropic stress conditions were investigated as part of an extensive laboratory test program that included 45 bender element and 89 resonant column tests on 20 soil samples. By emphasizing the importance of measuring soil stiffness at small strains, this study not only provides reliable data for the development of the built environment in the Ljubljana Marsh and similar areas, but also underlines its necessity. [ABSTRACT FROM AUTHOR]

Let O (3) denote the group of orthogonal 3 × 3 real matrices, and M the 5-dimensional real vector space of all 3 × 3 real symmetric matrices with trace zero. Let λ 1 (A) ≤ λ 2 (A) ≤ λ 3 (A) be the eigenvalues of A ∈ M and Ξ - = { A ∈ M ∣ λ 1 (A) = λ 2 (A) } . M is an inner product space with the inner product ⟨ A , B ⟩ = trace (A B) . Let G 3 (M) be the set of all 3-dimensional subspaces of M , a 6-dimensional Grassman manifold. O (3) acts on M on the left by conjugation via inner product preserving linear isomorphisms, which map any 3-dimensional subspace into another 3-dimensional subspace; thus G 3 (M) also has a left action of O (3) . G 3 (M) becomes a category, an action groupoid, with morphisms (V , M , W) ∈ G 3 (M) × O (3) × G 3 (M) , where W = M V M T . Composition of morphisms is (V 1 , N , V 2) ∘ (V 0 , M , V 1) = (V 0 , N M , V 2) . Let C be a category whose objects (V, S) consist of a real inner product space V and S ⊂ V , and whose arrows (V , S) → (W , T) consist of f : V → W , an inner product preserving real linear mapping such that f (S) ⊂ T . We have the functor V ↓ (V , M , W) W G 3 (M) ⟶ F - (V , Ξ - ∩ V) ↓ F - (M) (W , Ξ - ∩ W) C where F - (M) : V → W : A ↦ M A M T . Suppose further that S 3 denotes the group of permutations of { 1 , 2 , 3 } , and ρ : S 3 → O (3) denotes a group homomorphism which is isomorphic as a group representation to the natural representation of S 3 on R 3 (which permutes the coordinates). Let Obj (L S) denote the set of all V ∈ G 3 (M) whose isotropy subgroup contains S = ρ (S 3) as a subgroup. This paper completely describes the full subcategory L S of G 3 (M) with object set Obj (L S) , as well as the details of the above functor restricted to L S . Thus all the members V ∈ Obj (L S) are determined, as well as the smooth manifold structure on Obj (L S) ; it is embedded as a one-dimensional submanifold of G 3 (M) . The isotropy subgroups of all V ∈ Obj (L S) are computed and all pairs V , W ∈ Obj (L S) which are isomorphic via some M ∈ O (3) are determined. The sets Ξ - ∩ V are all determined, and the functorial mappings on morphism sets are computed. However, L S is not a Lie groupoid. The image of Obj (L S) under the functor π 1 F - is the collection of fibres of the smooth manifold ∐ V ∈ Obj (L S) V , which is the total space of the canonical vector bundle over the base manifold Obj (L S) . The bifurcation points of the family of subsets Ξ - ∩ V as V ranges over Obj (L S) (within this total space) are seen to be the points of Obj (L S) with infinite isotropy subgroups. We also show how this mathematical problem arises naturally from a problem in mathematical chemistry. Hence certain features of numerical calculations of energy eigenvalue intersection patterns of the simple chemical system H3 are rationalized through linearization about the triple intersection point. [ABSTRACT FROM AUTHOR]

The paper is devoted to problems related to two-dimensional Nye figures for micropolar continua. The representation technique known from studies on crystallography for 4th, 3rd and 2nd rank tensors is employed by two-dimensional matrices, supplied by relationships between their elements. Such representations are commonly used to simplify a script of the equations of athermic micropolar elastic solids. This method allows us to graphically represent micropolar constitutive tensors and pseudotensors in the form of specific two-dimensional blocks. The Nye figures for the micropolar elastic solids are obtained. The Nye figures enables us to discriminate anisotropic solids and figure out general anisotropic, hemitropic, isotropic, and ultraisotropic continua. [ABSTRACT FROM AUTHOR]

The article refines the axiomatic foundation of central place theory (CPT) and identifies the possibilities and limitations of a logical transition in research from real settlement systems to central place (CP) systems. The necessity of relying on the CPT axioms in the following form is determined: (1) the space of a CP system is not infinite, but finite: the basis of each system is formed by an isolated lattice; the theory deals with physical space, not mathematical or geographical; (2) the space is homogeneous and isotropic in all respects, except for the distribution of not only the urban, but also the rural population; (3) a hexagonal lattice corresponds to the equilibrium state of an isolated CP system as an attractor; deviations from a hexagonal shape result only from external impact on the system; (4) CP systems are polymorphic: they can exist in modifications with both the same and different values for all levels of the hierarchy and not necessarily an integer value K ∈ (1, 7]. The axiom about a consumer's "rational" behavior is accepted when establishing the CP hierarchy in terms of the volume of functions performed; when establishing their hierarchy in terms of population, it is redundant. In contrast to the foreign approach to CPT, which presupposes the transfer of properties of an ideal CP system to a real settlement system, in the approach of the Russian school, they are compared. The possibility of the latter is due to the equivalence principle in the relativistic version of the theory, according to which settlement systems form in the geographic space similarly to how CP systems form in the physical space. In both cases, if the gravitational effects are compensated, it is impossible to distinguish a settlement system from a CP system; i.e., a heterogeneous and anisotropic geographical space cannot be distinguished from a homogeneous and isotropic physical one. The immediate consequence of this is equivalence, on the one hand, of the population of settlements and CP, and, on the other, the distances between them in real settlement systems and CP systems. [ABSTRACT FROM AUTHOR]

This paper is concerned with sample path properties of real-valued isotropic Gaussian fields on compact two-point homogeneous spaces. In particular, we establish the property of strong local nondeterminism of an isotropic Gaussian field and then exploit this result to establish an exact uniform modulus of continuity for its sample paths. [ABSTRACT FROM AUTHOR]

The work is focused on creating a method for accounting of internal friction, which provides frequency independence, considers the dependence of internal friction on the level of the stress state, and is suitable for physically nonlinear tasks at large and small displacements. The authors consider an approximated method of accounting the damping in plates using the rod approximation according to A.R. Rzhanitsyn. An analysis of the discrete Rzhanitsyn medium with a square cell is given in terms of isotropy of its damping properties. The exact fulfillment of the isotropic damping properties is shown for the eight specific directions in the orientation of the deformations. The solution for a test example is given, where a rod oscillating in tension is calculated according to two computational schemes. One of these schemes is a real rod, the other is a rectangular plate experiencing uniaxial tension, and for its dynamic modeling, in turn, the discrete model by A.R. Rzhanitsyn is applied. The use of the same damping parameters for the real rod and rods in the Rzhanitsyn approximation leads to close damping. An approximate approach has been developed to account for internal friction during vibrations of a two-dimensional continuous medium, as well as a variant of clarifying the damping forces in the plate. A numerical example of damping modeling is given in the case of considering geometrically and physically nonlinear oscillations.

The uniform grid, a tool commonly used to generate homogeneous and isotropic turbulence, has been the subject of many studies. Many studies have primarily focused on how initial conditions of uniform square grids, including the Reynolds number, mesh size, bar size, cross-section of bar, and solidities, affect the statistical characteristics of grid turbulence. However, the influence of mesh shape has not been studied extensively. This study deviates from the norm by examining the influence of different mesh shapes, specifically the uniform nonsquare grid, on grid turbulence. This variation in mesh shape can be easily achieved based on the traditional uniform square grid. The findings reveal that when a uniform nonsquare grid is used, the distance required for turbulence to fully develop decreases. Additionally, there is an increase in the low-frequency components of fluctuating velocity, while high-frequency components decrease. This shift leads to a difference in energy distribution. Moreover, using a uniform nonsquare grid reduces the anisotropies of decaying turbulence to a certain extent. The skewness approaches theoretical value of 0 more closely, while the flatness remains largely unchanged. The mesh shape also affects the decay exponents and power-law coefficients obtained, with the decay exponent potentially getting much closer to 1. Furthermore, larger integral length scales can be achieved at the same downstream position, without significantly modifying the turbulence intensity, by using the uniform nonsquare grid. This could better meet the requirements of large-scale turbulence in certain engineering fields, such as wind engineering, compared to the traditional uniform square grid. [ABSTRACT FROM AUTHOR]

Selective laser melting (SLM) can effectively replace traditional processing methods to prepare parts with arbitrary complex shapes through layer-by-layer accumulation. However, SLM Ti-6Al-4V alloy typically exhibits low ductility and significant mechanical properties anisotropy due to the presence of acicular α′ martensite and columnar prior β grains. Post-heat treatment is frequently used to obtain superior mechanical properties by decomposing acicular α′ martensite into an equilibrium α + β phase. In this study, the microstructure and tensile properties of SLM Ti-6Al-4V alloy before and after various heat treatments were systematically investigated. The microstructure of the as-fabricated Ti-6Al-4V sample was composed of columnar prior β grains and acicular α′ martensite, which led to high strength (~1400 MPa) but low ductility (~5%) as well as significantly tensile anisotropy. The single heat treatment samples with lamellar α + β microstructure exhibited improved elongation to 6.8–13.1% with a sacrifice of strength of 100–200 MPa, while the tensile anisotropy was weakened. A trimodal microstructure was achieved through multi-step high-to-low-temperature (HLT) heat treatment, resulting in an excellent combination of strength (~1090 MPa) and ductility (~17%), while the tensile anisotropy was almost eliminated. The comprehensive mechanical properties of the HLT samples were superior to that of the conventional manufactured Ti-6Al-4V alloy. [ABSTRACT FROM AUTHOR]

In this paper we derive the linear elastic Cosserat shell model incorporating in the variational problem effects up to order O (h 5) in the shell thickness h as a particular case of the recently introduced geometrically nonlinear elastic Cosserat shell model. The existence and uniqueness of the solution is proven in suitable admissible sets. To this end, inequalities of Korn-type for shells are established which allow to show coercivity in the Lax-Milgram theorem. We are also showing an existence and uniqueness result for a truncated O (h 3) model. Main issue is the suitable treatment of the curved reference configuration of the shell. Some connections to the classical Koiter membrane-bending model are highlighted. [ABSTRACT FROM AUTHOR]

Let F be a field of characteristic 2 and K a purely inseparable extension of F. When K is modular, we give a complete classification of anisotropic semisingular F -quadratic forms that have over K a maximal Witt index and a defect index at least equal to the half of the dimension of the quasilinear part. The case of totally singular quadratic forms will be also treated. Moreover, without the modularity hypothesis, we give necessary and sufficient conditions under which an anisotropic semisingular F -quadratic form has a given Witt index over K. The quasi-hyperbolicity of semisingular F -quadratic forms over function fields of certain irreducible polynomials will be treated, extending to such forms many results established by the first author in [11]. [ABSTRACT FROM AUTHOR]

The construction of fundamental solutions in R3 for the equations of harmonic vibrations in the theory of elasticity of anisotropic elastic media is carried out. Solutions are constructed in the form of multipole series. Theorems on the convergence of series in the topology of compact convergence in are proved. The problems on constructing some singular solutions of the theory of vibrations of an anisotropic body are discussed. The fundamental solution of the oscillation equations for an isotropic medium is obtained in a closed form. [ABSTRACT FROM AUTHOR]

We study the asymptotic behaviour of a stationnary shot noise random field. We use the notion of association to prove the asymptotic normality of the moments and a multidimensional version for the correlation functions. The variance of the moment estimates is detailed as well as their correlation. When the field is isotropic, the estimators are improved by reducing the variance. These results will be applied to the estimation of the model parameters in the case of a Gaussian kernel, with a focus on the correlation parameter. The asymptotic normality is proved and a simulation study is carried out. [ABSTRACT FROM AUTHOR]

In this work, stability analysis of plane wave solutions of the cubic-quintic complex Ginzburg–Landau equation for isotropic and anisotropic systems is carried out. In this regard, we perform extensive numerical simulations based on a two-dimensional spatial Fourier discretization and an explicit scheme for temporal differentiation to find the domain of existence of the space-time dynamical behavior of the two-dimensional complex Ginzburg–Landau equation with cubic and quintic nonlinearities. One of the nonlinearity parameters is fixed and the others are varied one by one to determine the regimes in which plane wave solutions exist as stable/instable structures. Moreover, the stability criterion which has been plotted with the state diagram and the different dynamic structures obtained in space parameters has been established. Energy function was also used to characterize spatiotemporal dynamics observed in our system. By performing long simulations for the different parameters of the equation, we found the existence of stable (plane wave, localized defect), intermittent (intermittency state), and unstable (bichaos, phase turbulence, and defect turbulence) structures. [ABSTRACT FROM AUTHOR]

This paper constructs a class of isotropic vector random fields on the probability simplex via infinite series expansions involving the ultraspherical polynomials, whose covariance matrix functions are functions of the metric (distance function) on the probability simplex, and introduces the scalar and vector fractional, bifractional, and trifractional Brownian motions over the probability simplex, while the metric is shown to be conditionally negative definite. [ABSTRACT FROM AUTHOR]

Copyright of World Nuclear Geoscience is the property of World Nuclear Geoscience Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the present work, the issues of isotropic/anisotropic character of adsorption-induced deformation of carbon adsorbents were addressed. A simple model of microporous zones of carbon adsorbents was developed in terms of their structure determined by a raw material and activation conditions. The model made it possible to evaluate the number of micropores (~ 1020 g−1) and the number of microporous nanocrystals with micropores (denoted as an elementary microporous zone, EMZ) ~ 1011 g−1 for four carbon adsorbents differing in raw material and activation conditions. The equiprobable orientation of the EMZ in activated carbons nullifies the influence of the anisotropic structure of nanocrystallites on the changes in macroscopic dimensions of the adsorbents stimulated by adsorption. The assumption was confirmed by the dilatometry measurements of the CO2 adsorption-induced deformation for the commercial activated carbon Sorbonorit-4 granules, which were deposited parallel and perpendicular to the vertical axis of the dilatometer. The adsorption-induced strain isotherms did not depend on the orientation of the Sorbonorit-4 granules and exhibited the non-monotonic character. The initial contraction of the adsorbent was followed by its expansion with increasing pore filling. The contraction–expansion transition, as well as the contraction magnitude, were found to be temperature-dependent within the temperature range from 216.6 to 393 K. The compressibility and triaxial compression modulus of Sorbonorit-4 were evaluated over the temperature range from 216.6 to 293 K. The temperature dependences of both parameters were approximated by exponential functions. The triaxial compression modulus of Sorbonorit-4 decreased from 42 to 10 GPa and the compressibility increased by five times with a rise in temperature from 216.6 to 293 K. [ABSTRACT FROM AUTHOR]

Embeddings, i.e., vector representations of objects, such as texts, images, or graphs, play a key role in deep learning methodologies nowadays. Prior research has shown the importance of analyzing the isotropy of textual embeddings for transformer-based text encoders, such as the BERT model. Anisotropic word embeddings do not use the entire space, instead concentrating on a narrow cone in such a pretrained vector space, negatively affecting the performance of applications, such as textual semantic similarity. Transforming a vector space to optimize isotropy has been shown to be beneficial for improving performance in text processing tasks. This paper is the first comprehensive investigation of the distribution of multimodal embeddings using the example of OpenAI's CLIP pretrained model. We aimed to deepen the understanding of the embedding space of multimodal embeddings, which has previously been unexplored in this respect, and study the impact on various end tasks. Our initial efforts were focused on measuring the alignment of image and text embedding distributions, with an emphasis on their isotropic properties. In addition, we evaluated several gradient-free approaches to enhance these properties, establishing their efficiency in improving the isotropy/alignment of the embeddings and, in certain cases, the zero-shot classification accuracy. Significantly, our analysis revealed that both CLIP and BERT models yielded embeddings situated within a cone immediately after initialization and preceding training. However, they were mostly isotropic in the local sense. We further extended our investigation to the structure of multilingual CLIP text embeddings, confirming that the observed characteristics were language-independent. By computing the few-shot classification accuracy and point-cloud metrics, we provide evidence of a strong correlation among multilingual embeddings. Embeddings transformation using the methods described in this article makes it easier to visualize embeddings. At the same time, multiple experiments that we conducted showed that, in regard to the transformed embeddings, the downstream tasks performance does not drop substantially (and sometimes is even improved). This means that one could obtain an easily visualizable embedding space, without substantially losing the quality of downstream tasks. [ABSTRACT FROM AUTHOR]

Three existent states of carbon were introduced in FeOCl, namely graphite carbon, carbon dots and lattice carbon. The excellent photo-Fenton performance of C-FeOCl were attributed to the exposure of CUISs on the inner/outer surfaces of FeOCl and the efficient transportation-separation of photogenerated electrons in the horizontal and vertical directions of FeOCl. [Display omitted] The photo-Fenton process is promising for sincerely treating contaminated water. In this work, carbon-decorated iron oxychloride (C-FeOCl) is synthesized as a photo-Fenton catalyst for removing tetracycline (TC) from water. Three actual states of carbon are identified and their different roles in enhancing photo-Fenton performance are revealed. All carbon on/in FeOCl, including graphite carbon, carbon dots and lattice carbon, enhance visible light adsorption. More importantly, a homogeneous graphite carbon on the outer surface of FeOCl accelerates the transportation-separation of photo-excited electrons along the horizontal direction of FeOCl. Meanwhile, the interlayered carbon dots offer a Fe O C bridge in helping the transportation-separation of photo-excited electrons along the vertical direction of FeOCl. In this way, C-FeOCl acquires isotropy in conduction electrons to ensure an efficient Fe(II)/Fe(III) cycle. These interlayered carbon dots extend the layer spacing (d) of FeOCl to about 1.10 nm, exposing the internal iron centers. The lattice carbon significantly increases the amounts of coordinatively unsaturated iron sites (CUISs) in activating hydrogen peroxide (H 2 O 2) to hydroxyl radical (OH). Density functional theory (DFT) calculations confirm this activation on inner and external CUISs with a significantly low activation energy of about 0.33 eV. [ABSTRACT FROM AUTHOR]

Mechanical processing of cortical bone tissue is one of the most common surgical procedures. A critical issue accompanying this processing is the condition of the surface layer, which can stimulate tissue growth and serve as a drug carrier. A comparison of the surface condition before and after orthogonal and abrasive processing was conducted to validate the influence of bone tissue's processing mechanism and orthotropic properties on the surface topography. A cutting tool with a defined geometry and a custom-made abrasive tool was used. The bone samples were cut in three directions, depending on the orientation of the osteons. The cutting forces, acoustic emission, and surface topography were measured. The level of isotropy and the topography of the grooves showed statistical differences relative to the anisotropy directions. After orthogonal processing, the surface topography parameter Ra was determined from 1.38 ± 0.17 μm to 2.82 ± 0.32. In the case of abrasive processing, no correlation was found between the orientation of osteons and topographical properties. The average groove density for abrasive machining was below 1004 ± 0.7, and for orthogonal, it was above 1156 ± 58. Due to the positive properties of the developed bone surface, it is advisable to cut in the transverse direction and parallel to the axis of the osteons. [ABSTRACT FROM AUTHOR]

Copyright of Acta Materiae Compositae Sinica is the property of Acta Materiea Compositae Sinica Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Excellent mechanical and isotropic optical properties are achieved simultaneously from fully dense polycrystalline advanced alumina ceramics with a hexagonal crystal structure, which are optically anisotropic. A small amount (240 ppm) of ZrO2 additive is used to synthesize the transparent alumina ceramics with an average grain size of 0.7 µm, and locally detected optical distortion (birefringence) is extremely minimized, less than 20 nm/pass. Total transmittance (86%) of the alumina ceramics (thickness = 0.3 mm) in ultraviolet (UV) to infrared (IR) regions is similar to that of commercial c-axis sapphire single crystals produced by Czochralski (CZ) method, while the extinction ratio in the visible wavelength area is over 25 dB. Like glass and the c-axis sapphire single crystals, the alumina ceramics can clearly display texts and images on liquid crystal display (LCD) screens. A grain boundary phase of nano-sized Al2O3–ZrO2 composition (amorphous) is formed at the grain boundary of the advanced alumina ceramics, which enhances four-point bending strength and fracture toughness (KIC) simultaneously to 921 MPa and 6.8 MPa·m0.5, respectively, and hence the mechanical properties are superior to those of the sapphire single crystals.

Strength ductility tradeoff, strain hardenability and in-plane isotropy under tensile loading are big dilemmas in magnesium alloys. In this study, we have fabricated an extruded low alloyed Mg-0.5Zn-0.5Y-0.15Si alloy. Based on bimodal grain size, strong basal texture, Schmidt factor analysis and precipitates (MgZn2, Mg3Zn6Y and Mg3Zn3Y2), the alloy exhibited high mechanical strength, high elongation to fracture, strain hardenability and excellent in-plane tensile isotropy. The underlying deformation mechanisms for excellent symmetric and high yield strength along extruded and transverse directions were synergistic effects of low Schmidt factor values of basal slip due to intense basal texture (c-axes//ND), pre-induce dislocation, grain boundary strengthening and precipitate strengthening. While, the strain hardenability and high elongation to fracture are the combined effect of the interaction of basal and profuse non-basal dislocation with precipitates, dislocation pileup at grain boundaries, dislocation pileup on stacking faults and the signature of extension and contraction twinning activity.

The effect of extrusion parameters on the characteristics of nanocomposites based on polypropylene random copolymer and ethylene–propylene block copolymer with carbon black and aluminum nanoparticles and calcium stearate was studied. Printex XE 2-B carbon black with the nanoparticle size of 18–20 nm was used. Exхelor PO 1020 compatibilizer was used for improving the compatibility of the blend components. Introduction of the above fillers allows obtaining a multifunctional nanocomposite that exhibits high levels of electrical conductivity, adhesion to metals, and thermal conductivity and can be processed by pressure casting and extrusion. The effect of the temperature conditions in the extruder material cylinder on the breaking stress and relative elongation of the nanocomposites was considered. The optimum temperature conditions of the extrusion, ensuring relatively high properties of the composite, were determined. [ABSTRACT FROM AUTHOR]

It has been proven by Schupp and Bergman that the inner automorphisms of groups can be characterized purely categorically as those group automorphisms that can be coherently extended along any outgoing homomorphism. One is thus motivated to define a notion of (categorical) inner automorphism in an arbitrary category, as an automorphism that can be coherently extended along any outgoing morphism, and the theory of such automorphisms forms part of the theory of covariant isotropy. In this paper, we prove that the categorical inner automorphisms in any category Group J of presheaves of groups can be characterized in terms of conjugation-theoretic inner automorphisms of the component groups, together with a natural automorphism of the identity functor on the index category J . In fact, we deduce such a characterization from a much more general result characterizing the categorical inner automorphisms in any category T mod J of presheaves of T -models for a suitable first-order theory T . [ABSTRACT FROM AUTHOR]

In this paper, we linearise the recently introduced geometrically nonlinear constrained Cosserat-shell model. In the framework of the linear constrained Cosserat-shell model, we provide a comparison of our linear models with the classical linear Koiter shell model and the "best" first-order shell model. For all proposed linear models, we show existence and uniqueness based on a Korn's inequality for surfaces. [ABSTRACT FROM AUTHOR]

Amorphous alloys, also known as metallic glasses, are solid metallic materials having long-range disordered atomic structures. Compared to crystalline alloys, amorphous alloys not only have metallic characters, but also possess several distinct properties associated to the amorphous structure, such as isotropy, composition flexibility, unsaturated surface, etc. As a result, amorphous alloys offer a class of highly promising materials for catalyzing electrochemical reactions. In this minireview, the preparation, characterization and electrocatalytic performances of a variety of metallic amorphous alloy materials are summarized. The influences of the amorphous alloy structure on different electrochemical reactions are discussed. Finally, a summary on the advantages and challenges of amorphous alloys in electrocatalysis is provided, along with some perspectives about the future research directions. [ABSTRACT FROM AUTHOR]

It is well known that every non-degenerate quadratic form admits a decomposition into an orthogonal sum of its anisotropic part and a hyperbolic form. This decomposition is unique up to isometry. In this paper we present an algorithm for constructing an anisotropic part of a given form with coefficients in an arbitrary number field. [ABSTRACT FROM AUTHOR]

In the paper, the boundary value problem for the loaded heat equation is solved, and the loaded term is represented as the Riemann-Liouville derivative with respect to the time variable. The domain of the unknown function is the cone. The order of the derivative in the loaded term is less than 1, and the load moves along the lateral surface of the cone, that is in the domain of the desired function. The boundary value problem is studied in the case of the isotropy property in an angular coordinate (case of axial symmetry). The problem is reduced to the Volterra integral equation, which is solved by the method of the Laplace integral transformation. It is also shown by direct verification that the resulting function satisfies the boundary value problem.

The increasing use of finite element analysis in modern infrastructure design emphasizes the importance of determining soil stiffness at small strains. This is usually represented by the normalized shear modulus degradation curve, which is crucial for accurate design. In the absence of specific measurements on the local soil, engineers often rely on empirical correlations and assume comparable behavior of soils with similar intrinsic properties. However, the application of this approach leads to uncertainties, especially for unique geological formations such as the soft cohesive soils of the Ljubljana Marsh. The main objective of this study was to determine the small strain shear modulus of Ljubljana Marsh soil with a plasticity index between 11 and 35%. Isotropic and anisotropic stress conditions were investigated as part of an extensive laboratory test program that included 45 bender element and 89 resonant column tests on 20 soil samples. By emphasizing the importance of measuring soil stiffness at small strains, this study not only provides reliable data for the development of the built environment in the Ljubljana Marsh and similar areas, but also underlines its necessity.

Here, a detailed mechanical characterization of five important anhydrous microporous aluminophosphate materials (VPI-5, ALPO-8, ALPO-5, ALPO-18, and ALPO-31) is performed using first principles methods based on periodic density functional theory. These materials are characterized by the presence of large empty structural channels expanding along several different crystallographic directions. The elasticity tensors, mechanical properties, and compressibility functions of these materials are determined and analyzed. All of these materials have a common elastic behavior and share many mechanical properties. They are largely incompressible at zero pressure, the compressibilities along the three crystallographic directions being frequently smaller than 5 TPa−1. Notably, the compressibilities of ALPO-5 and ALPO-31 along the three principal directions are smaller than this threshold. Likewise, the compressibilities of ALPO-18 along two directions are smaller than 5 TPa−1. All of the considered materials are shear resistant and ductile due to the large bulk to shear moduli ratio. Furthermore, all of these materials have very small mechanical anisotropies. ALPO-18 exhibits the negative linear compressibility (NLC) phenomenon for external pressures in the range P = 1.21 to P = 2.70 GPa. The minimum value of the compressibility along the [1 0 0] direction, ka=−30.9 TPa−1, is encountered for P = 2.04 GPa. The NLC effect in this material can be rationalized using the empty channel structural mechanism. The effect of water molecule adsorption in the channels of ALPO-18 is assessed by studying the hydrated ALPO-18 material (ALPO-18W). ALPO-18W is much more compressible and less ductile than ALPO-18 and does not present NLC effects. Finally, the effect of aging and pressure polymorphism in the mechanical properties of VPI-5 and ALPO-5 is studied. As hydration, aging leads to significant variations in the elastic properties of VPI-5 and increases substantially its compressibility. For ALPO-5, pressure polymorphism has a small impact in its elasticity at zero pressure but a large influence at high pressure.

Representations from common pre-trained language models have been shown to suffer from the degeneration problem, i.e., they occupy a narrow cone in latent space. This problem can be addressed by enforcing isotropy in latent space. In analogy with variational autoencoders, we suggest applying a token-level variational loss to a Transformer architecture and optimizing the standard deviation of the prior distribution in the loss function as the model parameter to increase isotropy. The resulting latent space is complete and interpretable: any given point is a valid embedding and can be decoded into text again. This allows for text manipulations such as paraphrase generation directly in latent space. Surprisingly, features extracted at the sentence level also show competitive results on benchmark classification tasks.

Tissue-mimicking materials [e.g., polyvinyl alcohol cryogel (PVA-C)] are extensively used in clinical applications such as tissue repair and tissue engineering. Various mechanical testing techniques have been used to assess the biomechanical compatibility of tissue-mimicking materials. This article presents the development of inverse finite element (FE) techniques that are solved using numerical optimization to characterize the mechanical properties of PVA-C specimens. In this study, a numerical analysis where the displacement influence factor was employed in conjunction with a linear elastic model of finite thickness was performed. In the analysis, the effects of Poisson's ratio, specimen aspect ratio, and relative indentation depth were investigated, and a novel mathematical term was introduced to Sneddon's equation. In addition, a robust optimization algorithm was developed in MATLAB that utilized FE modeling for parameter estimation before it was rigorously validated.

Let φ and ψ be quadratic forms over a field K of characteristic different from 2. In this paper, we give a criterion for isotropy of φ over the function field of ψ in terms of representations and we apply it to stably birational equivalence of φ and ψ. Then we use this criterion to investigate the case of stably birational equivalence of multiples of Pfister forms. Finally, we give a criterion of stably birational equivalence of quadratic forms in terms of isomorphisms of quotients of special Clifford groups by the kernel of the spinor norm. [ABSTRACT FROM AUTHOR]

An isogrid is a lattice structure with a high strength to weight ratio making it an ideal structure for spacecraft. Isogrids were originally designed to yield isotropic properties; however, recent finite element analyses show that isogrids do not exhibit isotropic behavior. Isogrids are theorized to be isotropic because of the equal distribution of stresses induced by the structure's geometry. To determine the isotropy of an isogrid, truss and finite element analyses are executed to predict failure among four various isogrid specimens. The isogrid specimens are 3D printed and vary in geometry to determine the effect of geometric parameters on the isotropy of the structure. In addition, experimental tests are conducted by applying compressive loads to the specimens using a universal testing machine (UTM) with digital image correlation (DIC) to measure strain. The analyses indicate that isogrids are not isotropic because of the observed unequal load distributions. • Analytical, FEM, and experimental assessment of isogrid structures. • Isotropy assumption for isogrids is demonstrated to be incorrect. • Four different isogrid sizes tested using 3D printed specimens with DIC. • All techniques indicate that the diagonal stiffeners carry a higher stress than the horizontal stiffeners. [ABSTRACT FROM AUTHOR]