Conductivity Tensor Research Articles

Study of anisotropy in polydispersed 2D micro and nano-composites by Elbow and K-Means clustering methods

A new two-dimensional polydisperse model for testing multiphase composites is developed. The verification of the model is carried out based on the microstructure of two composites obtained in the ex-situ and in-situ techniques produced in the Friction Stir Processing (Al–Si–Cu/SiCp) and the Self-propagating High temperature Synthesis (Al/nano-TiCp). The examined microstructure is considered on macro-, meso- and micro- levels. Besides the reinforcement phase distribution concentration, an anisotropy coefficient κ is calculated for every meso-cell. It is the cumulative vector parameter that characterizes the spatial two-point correlation of inclusions. In particular, κ determines the principal axes of the effective conductivity tensor over a meso-cell. The anisotropy spatial distribution ϰ(x) is introduced as the discrete function of values κ calculated over meso-cells centered at the point x. This new distribution ϰ(x) accumulates the geometrical information of the considered microstructure. A computational experiment is designed and carried out in order to study the influence of the reinforcement phase redistribution on the anisotropy. Therefore, it adequately describes the anisotropy of fields in composites modeling thermal and electric conductivity, diffusion, and elastic antiplane deformation. The results of the computational experiments are analyzed using the Elbow and K-Means clustering machine learning algorithm. The detailed analysis is carried out to divide the data set into up to 5 clusters. A research hypothesis concerning the criterion of isotropy of the distribution of reinforcing phase particles in the composite structure is formulated

Quantum kinetic equation and thermal conductivity tensor for bosons

Quantum kinetic equation and thermal conductivity tensor for bosons

Enormous and Tunable Bulk Charge/Spin Photovoltaic Effect in Piezoelectric Binary Materials T-IV-VI and T-V-V.

Understanding the nonlinear response of light and materials is crucial for fundamental physics and next-generation electronic devices. In this work, we have investigated the second-order nonlinear bulk photovoltaic (BPV) and bulk spin photovoltaic (BSPV) effects in the piezoelectric binary materials T-IV-VI and T-V-V (IV = Ge, Sn; VI = S, Se; and V = P, As, Sb, Bi). The independent nonzero conductivity tensors of charge current are derived for these binaries through the symmetry analysis, along with the mechanism for generating pure spin current. These binaries, with their unique folded structure, exhibit significant charge and spin currents under illumination. Furthermore, we find that strain engineering can effectively modulate charge/spin currents by influencing charge density distribution and built-in electric field due to the piezoelectric effect. Our research suggests that the piezoelectric binary materials possess enormous and tunable charge/spin currents, underscoring their potential for applications in nonlinear flexible optoelectronics and spintronics.

The Impact of a Strong Electromagnetic Wave on the Quantum Hall Effect in Cylindrical Quantum Wires

The impact of strong electromagnetic waves Hall effect is studied theoretically in a Cylindrical Quantum Wire (CQW) with infinitely high potential inside the wire and elsewhere subjected to a dc electric field , a magnetic field and a laser radiation . By using the quantum kinetic equation method for electrons interacting with Acoustic Phonon (AP) at low temperatures, we obtain analytical expressions for the conductivity tensor and the Hall Coefficient (HC), which are different from in comparison to those obtained for a rectangular quantum wire (RQW) or two-dimensional (2D) electron systems. Numerical calculations are also applied for GaAs/GaAsAl CQW to show the nonlinear dependence of the HC on the electromagnetic wave (EMW) frequency, and the radius, the length characteristic parameters of CQW. Wave function and energy spectrum in a CQW are dissiminar to those in Quantum Wires (QWs). Therefore, all numerical results are different from those in the case of QWs. The most important result is that the HC reaches saturation as the radius, the length of CQW or the EMW frequency increases.

Effect of shear flow on the transverse thermal conductivity of polymer melts.

The effect of shear flows on the thermal conductivity of polymer melts is investigated using a reversed nonequilibrium molecular-dynamics (RNEMD) method. We extended the original RNEMD method to simultaneously produce spatial gradients of temperature and flow velocity in a single direction. This method enables accurate measurement of the thermal conductivity in the direction transverse to shear flow. The Weissenberg number defined with the shear rate and the relaxation time of the polymer conformation can uniformly differentiate the occurrence of shear rate dependence of the thermal conductivity across different chain lengths. The stress-thermal rule (STR) (i.e., the linear relationship between anisotropic parts of the stress tensor and the thermal conductivity tensor) holds for entangled polymer melts even under shear flows but not for unentangled polymer melts. Furthermore, once entanglements form in polymer chains, the stress-thermal coefficient in the STR remains independent of the polymer chain length. These observations align with the theoretical foundation of the STR, which focuses on energy transmission along the network structure of entangled polymer chains [B. van den Brule, Rheol. Acta 28, 257 (1989)0035-451110.1007/BF01329335]. However, under driven shear flows, the stress-thermal coefficient is notably smaller than that measured in the literature for a quasiquiescent state without external forces. Although the mechanism of the STR in shear flows has yet to be fully elucidated, our study confirmed the validity of the STR in shear flows. This allows us to use the STR as a constitutive equationfor computational thermofluid dynamics of polymer melts, thus having broad engineering applications.

An Electrical Parameter Characterizing Solute Heterogeneity: The Mixing Factor M

AbstractQuantitative estimates of hydrological state variables using electrical or electromagnetic geophysical methods are systematically biased by overlooked heterogeneity below the spatial scale resolved by the method. We generalize the high‐salinity asymptotic limit of electrical conduction in porous media at the continuous (e.g., Darcy) scale, by introducing a new petrophysical parameter, the mixing factor M, which accounts for the effect of fluid conductivity heterogeneity on the equivalent electrical conductivity tensor; it is expressed in terms of the volume‐average of the product of mean‐removed fluid conductivity and electric fields. We investigate the behavior of M for static and evolving fluid conductivity scenarios. Considering 2‐D ergodic log‐normal random fields of fluid conductivity, we demonstrate, in absence of surface conductivity, that observing the components of the M‐tensor allows univocally determining the variance and anisotropy of the field. Further, time‐series of the M‐tensor under diffusion‐limited mixing allows distinguishing between different characteristic temporal scales of diffusion, which are directly related to the initial integral scales of the salinity field. Under advective‐diffusive transport and for a pulse injection, the time‐series of M have a strong dependence on the Péclet number. Since M is defined in the absence of surface conductivity, we investigate how to correct measurements for surface conductivity effects. The parameter M provides conceptual understanding about the impact of saline heterogeneity on electrical measurements. Further work will investigate how it can be incorporated into hydrogeophysical inverse formulations and interpretative frameworks.

Tailored plasmon polariton landscape in graphene/boron nitride patterned heterostructures

Surface plasmon polaritons (SPPs), which are electromagnetic modes representing collective oscillations of charge density coupled with photons, have been extensively studied in graphene. This has provided a solid foundation for understanding SPPs in 2D materials. However, the emergence of wafer-transfer techniques has led to the creation of various quasi-2D van der Waals heterostructures, highlighting certain gaps in our understanding of their optical properties in relation to SPPs. To address this, we analyzed electromagnetic modes in graphene/hexagonal-boron-nitride/graphene heterostructures on a dielectric Al2O3 substrate using the full ab initio RPA optical conductivity tensor. Our theoretical model was validated through comparison with recent experiments measuring evanescent in-phase Dirac and out-of-phase acoustic SPP branches. Furthermore, we investigate how the number of plasmon branches and their dispersion are sensitive to variables such as layer count and charge doping. Notably, we demonstrate that patterning of the topmost graphene into nanoribbons provides efficient Umklapp scattering of the bottommost Dirac plasmon polariton (DP) into the radiative region, resulting in the conversion of the DP into a robust infrared-active plasmon. Additionally, we show that the optical activity of the DP and its hybridization with inherent plasmon resonances in graphene nanoribbons are highly sensitive to the doping of both the topmost and bottommost graphene layers. By elucidating these optical characteristics, we aspire to catalyze further advancements and create new opportunities for innovative applications in photonics and optoelectronic integration.

Revised Enskog theory and molecular dynamics simulations of the viscosities and thermal conductivity of the hard-sphere fluid and crystal.

Hard-sphere (HS) shear, longitudinal, cross, and bulk viscosities and the thermal conductivity are obtained by molecular dynamics (MD) simulations, covering the entire density range from the dilute fluid to the solid crystal near close-packing. The transport coefficient data for the HS crystal are largely new and display, unlike for the fluid, a surprisingly simple behavior in that they can be represented well by a simple function of the density compressibility factor. In contrast to the other four transport coefficients (which diverge), the bulk viscosity in the solid is quite small and decreases rapidly with increasing density, tending to zero in the close-packed limit. The so-called cross viscosity exhibits a different behavior to the other viscosities, in being negative over the entire solid range, and changes sign from negative to positive on increasing the density in the fluid phase. The extent to which the viscosity tensor and thermal conductivity of the HS crystal can be represented by revised Enskog theory (RET) is investigated. The RET expressions are sums of an instantaneous (I), a kinetic (K), and a so-called α part. The I part of the transport coefficients evaluated directly by MD are statistically indistinguishable from those of the corresponding kinetic theory (Enskog and RET) expressions. For the K part the integral over the spatial two-particle distribution function at contact was determined and the α part was estimated using the direct correlation function and density functional theory approximations. All three parts were determined in this work which allowed the accuracy of RET for solid systems to be assessed rigorously. It is found that in the case of the thermal conductivity the predictions of RET are in excellent agreement with the MD results. Also, for the shear viscosity the agreement over the entire solid phase is quite good but is considerably worse for the three remaining viscosities in the solid phase.

Prediction of giant anomalous Nernst effect in Sm(Co,Ni)5

Sm-Co bulk alloys are well-known permanent magnets having large remanent magnetizations and coercive forces and are widely used in many industrial products. Recently, a large transverse thermoelectric conversion was observed for SmCo5 over a wide temperature range in the absence of magnetic fields. The large thermoelectric conductivity tensors (αxy) was also confirmed by the first-principles density functional theory (DFT) calculations. In this study, we predicted further enhancement of the αxy by including Ni in Co site of SmCo5. We showed that the αxy of Sm(Co1−xNix)5 increases with increasing the Ni ratio and takes the maximum value αxy = 11.3 A K−1 m−1 around x = 0.08 at 300 K, which is about 77% enhancement of αxy = 6.4 A K−1 m−1 in SmCo5. We clarified that the band proximity points near the nodal line of Sm(Co0.92Ni0.08)5 are the main contributing factor to the large Berry curvature, providing the steep slope of the energy dependence in the anomalous Hall conductivity around the Fermi energy.

On quantification of equivalent permeability tensor in sparsely fractured rock masses

The work presented in this paper is focused on the assessment of hydraulic conductivity in sparsely fractured rocks. Different simplified methodologies are used, including Oda's notion of permeability tensor as well as pipe network models, and the results are compared with those generated by a more accurate approach, which incorporates a constitutive law with embedded discontinuity (CLED). Several numerical examples involving fluid flow in the presence of discrete fracture networks are provided, and the estimates of principal values as well as eigenvectors of the equivalent conductivity tensor are compared for all methodologies employed. It is demonstrated that the predictions corresponding to pipe-network model, enhanced by the graph theory algorithm, are fairly consistent with CLED approach, particularly in terms of assessing the orientation of principal directions of permeability. A simple pragmatic procedure is therefore suggested for defining the anisotropic equivalent hydraulic conductivity operator.

Magneto-transport in the monolayer MoS2 material system for high-performance field-effect transistor applications

Electronic transport in monolayer MoS2 is significantly constrained by several extrinsic factors despite showing good prospects as a transistor channel material. Our paper aims to unveil the underlying mechanisms of the electrical and magneto-transport in monolayer MoS2. In order to quantitatively interpret the magneto-transport behavior of monolayer MoS2 on different substrate materials, identify the underlying bottlenecks, and provide guidelines for subsequent improvements, we present a deep analysis of the magneto-transport properties in the diffusive limit. Our calculations are performed on suspended monolayer MoS2 and MoS2 on different substrate materials taking into account remote impurity and the intrinsic and extrinsic phonon scattering mechanisms. We calculate the crucial transport parameters such as the Hall mobility, the conductivity tensor elements, the Hall factor, and the magnetoresistance over a wide range of temperatures, carrier concentrations, and magnetic fields. The Hall factor being a key quantity for calculating the carrier concentration and drift mobility, we show that for suspended monolayer MoS2 at room temperature, the Hall factor value is around 1.43 for magnetic fields ranging from 0.001 to 1 Tesla, which deviates significantly from the usual value of unity. In contrast, the Hall factor for various substrates approaches the ideal value of unity and remains stable in response to the magnetic field and temperature. We also show that the MoS2 over an Al2O3 substrate is a good choice for the Hall effect detector. Moreover, the magnetoresistance increases with an increase in magnetic field strength for smaller magnetic fields before reaching saturation at higher magnetic fields. The presented theoretical model quantitatively captures the scaling of mobility and various magnetoresistance coefficients with temperature, carrier densities, and magnetic fields.

High-Frequency Hall Effect and Transverse Electric Galvanomagnetic Waves in Current-Biased 2D Electron Systems

We derive the electrodynamic conductivity tensor for 2DESs with dc drift with account for the high-frequency Hall effect (interaction of dc current with ac magnetic field). We demonstrate the limitations of the quasistatic approach which neglects this effect. With the help of electrodynamic conductivity we find a novel two-dimensional transverse electric (TE) electromagnetic mode. This mode is non-reciprocal with dispersion \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega = {\\mathbf{k}}{{{\\mathbf{u}}}_{0}}$$\\end{document} and manifests itself in lowering the reflection coefficient of 2DES at the resonance frequency. In addition, we predict birefringence of an incident evanescent TE wave on a 2DES system with drift and find hints of Cerenkov amplification in the low frequency limit. We discuss the limiting cases when the quasistatic approach is suitable.

Spatially resolved lock-in micro-thermography (SR-LIT): A tensor analysis-enhanced method for anisotropic thermal characterization

While high-throughput (HT) computations have streamlined the discovery of promising new materials, experimental characterization remains challenging and time-consuming. One significant bottleneck is the lack of an HT thermal characterization technique capable of analyzing advanced materials exhibiting varying surface roughness and in-plane anisotropy. To tackle these challenges, we introduce spatially resolved lock-in micro-thermography, an innovative technique enhanced by tensor analysis for optical thermal characterization. Our comprehensive analysis and experimental findings showcase notable advancements: We present a novel tensor-based methodology that surpasses the limitations of vector-based analysis prevalent in existing techniques, significantly enhancing the characterization of arbitrary in-plane anisotropic thermal conductivity tensors. On the instrumental side, we introduce a straightforward camera-based detection system that, when combined with the tensor-based methodology, enables HT thermal measurements. This technique requires minimal sample preparation and enables the determination of the entire in-plane thermal conductivity tensor with a single data acquisition lasting under 40 s, demonstrating a time efficiency over 90 times superior to state-of-the-art HT thermology. Additionally, our method accommodates millimeter-sized samples with poor surface finish, tolerating surface roughness up to 3.5 μm. These features highlight an innovative approach to realizing HT and accurate thermal characterization across various research areas and real-world applications.

Guiding infrared electromagnetic waves through TI nanowires with extremely large wavenumber and azimuthal index.

In this paper, the dispersion relations of the surface plasmon polaritons (SPPs) in TI nanowires have been investigated. For simplicity, TI nanowire has been modeled as a dielectric cylinder with a conductive surface, the conductivity of which is an anti-symmetric tensor. The off-diagonal terms of the conductivity tensor only slightly change the dispersion relations. Due to small conductivities, these SPPs have extremely large wavenumbers and azimuthal indices; the electric fields are tightly confined near the conductive surface. For high-order modes, cut-off phenomena have been observed. In the end, the effects of losses and much larger bulk permittivities on the dispersion relations of surface plasmons have been discussed. The simple model proposed in this paper can be directly applied to other materials with arbitrary surface conductivity. Our investigations show that TI nanostructures are promising platforms for nanophotonic applications in the future.

Direction-dependent conductivity in planar Hall set-ups with tilted Weyl/multi-Weyl semimetals.

We compute the magnetoelectric conductivity tensors in planar Hall set-ups, which are built with tilted Weyl semimetals (WSMs) and multi-Weyl semimetals (mWSMs), considering all possible relative orientations of the electromagnetic fields (EandB) and the direction of the tilt. The non-Drude part of the response arises from a nonzero Berry curvature in the vicinity of the WSM/mWSM node under consideration. Only in the presence of a nonzero tilt do we find linear-in-|B|terms in set-ups where the tilt-axis is not perpendicular to the plane spanned byEandB. The advantage of the emergence of the linear-in-|B|terms is that, unlike the various|B|2-dependent terms that can contribute to experimental observations, they have purely a topological origin, and they dominate the overall response-characteristics in the realistic parameter regimes. The important signatures of these terms are that they (1) change the periodicity of the response fromπto 2π, when we consider their dependence on the angleθbetweenEandB; and (2) lead to an overall change in sign of the conductivity depending onθ, when measured with respect to theB=0case.

Multiscale topology optimization of cellular structures with high thermal conductivity and large convective surface area

Cellular structures have excellent thermal performance due to their high specific surface areas and porosities. This paper proposes a multiscale topology optimization (MTO) method of cellular structures with high thermal conductivity and large convective surface area, which enables them to have rapid cooling capability. In the MTO of a cellular structure, the triply periodic minimal surface (TPMS) lattices are adopted and Kriging metamodels are constructed to predict their effective thermal conductivity tensors and surface areas. The thermal compliance of the cellular structure is firstly minimized under the given volume constraint by topology optimization. Then, maximizing the convective surface area of the cellular structure is considered as the objective to when imposing the optimized thermal compliance as the constraint. After conducting topology optimization, the cellular structure with high thermal conductivity and large convective surface area is achieved. Additionally, in the above MTO, isogeometric analysis (IGA) is employed to improve the accuracy of numerical analysis. A numerical example is provided to verify the effectiveness of the proposed method. By both simulation and experiment, the high thermal conductivity, large convective surface area and rapid cooling capability of the optimized cellular structure are verified.

Anisotropic Klemens model for the thermal conductivity tensor and its size effect

With the constraint from Onsager reciprocity relations, here we generalize the Klemens model for intrinsic phonon-phonon scattering from isotropic to anisotropic. Combined with the anisotropic Debye dispersion, this anisotropic Klemens model leads to analytical expressions for heat transfer along both ab-plane (κab) and c-axis (κc), suitable for both layered and chainlike materials with any anisotropy ratio of the dispersion and the scattering. This combination of dispersion and scattering is further applied to the equation of phonon radiative transfer to model heat conduction across anisotropic thin films. The model is compared to experimental κab and κc of bulk graphite at high temperatures (T≥0.1×max(θD,ab,θD,c), where θD,ab and θD,c are the two Debye temperatures), leading to best-fit scattering parameters that capture the harmonic and anharmonic nature of the intra- and inter-layer bonding of graphite. With no further adjusting of these parameters, the anisotropic scattering model performs at least 9 times better than the isotropic one at explaining the experimental κc of graphite thin films. This size effect is further justified by comparing the accumulation function of κc.

Hydraulic conductivity tensor of anisotropic soils: the impact on seepage flow

Natural or artificial changes in soil stratigraphic-plane (i.e., the deposition of soil and sediments into distinct layers) orientation can cause variations in hydraulic conductivity in different direction. Hydraulic conductivity must, therefore, be considered – in this case – as a nondiagonal, full tensor to appropriately represent the effect of the orientation of soil stratigraphic planes on the seepage flow pattern. This paper introduces the derivation of the formula for the three-dimensional nondiagonal hydraulic conductivity full tensor calculation in terms of azimuth and vertical angles. Furthermore, two-dimensional numerical simulations of the seepage flow beneath a concrete dam are presented to demonstrate the need to account for the nondiagonal elements of the hydraulic conductivity tensor in anisotropic soils of varying degrees of stratigraphic tilt with respect to the coordinate system.

Inverse design method of thermal devices with thermal Hall effect

Efficient thermal management is important for both performance and efficiency improvements of thermal devices. For designing reasonable materials and structures of such devices, various design methods were proposed where the material thermal conductivity tensors were positive definite and symmetric based on the physical requirements. Here, we propose an inverse design method for thermal devices considering the thermal Hall effect, which makes the material thermal conductivity tensor asymmetric. Enlarging the design space consisting of the symmetric constitutive tensors to that of the asymmetric ones, there is a possibility of improving the theoretical performance limit of thermal devices. We formulate an inverse problem based on the free material optimization formalism, parameterizing the design space so that the physically available property could be naturally satisfied. Several numerical experiments are provided to show the validity and the utility of the proposed method.

A differential scheme for the effective conductivity of microinhomogeneous materials with the Hall effect

A differential scheme is proposed for the calculation of the components of the effective electrical conductivity tensor of a microinhomogeneous material taking into account the Hall effect. The presence of the Hall effect results in an appearance of asymmetry of the components of the conductivity tensor and a dependence of these components on the magnitude of the magnetic field applied to the material. In this case, the differential scheme leads to a system of matrix differential equations that were solved numerically in the current work. This solution was obtained for materials containing spherical or cylindrical inclusions. In the case of cylindrical inclusions, the results were obtained for inclusions with the symmetry axes parallel or orthogonal to the magnetic field. A comparison of the results obtained by the proposed methodology to the low concentration approximation was carried out.