Conductivity Tensor Research Articles

Automatic generation of high-fidelity representative volume elements and computational homogenization for the determination of thermal conductivity in foamed concretes

Foamed concretes are highly porous materials with excellent insulation properties. Their thermal conductivity is strongly dependent on the pore structure, characterized by the porosity as well as the shape and size distribution of pores. To define the representative volume element (RVE) of foamed concretes with high fidelity, we develop NRGene, an automatic generator of cubic samples with spherical air inclusions whose number and size obey a given distribution. We compute the effective thermal conductivity tensor for a given RVE using finite-element-based computational homogenization. The hi-fi RVE of foamed concretes may contain hundreds of millions of finite elements, making it better suited for benchmarking than for everyday engineering applications. Then, having the hi-fi model as benchmark, we propose a simplified model consisting of the hi-fi model called with a truncated histogram as input, which is largely cheaper while keeping a satisfactory accuracy. We model 21 different foamed concretes with a wide range of porosities and different compositions of the cement paste. Further, we demonstrate that it is the volume of all the pores of a given size, and not its quantity, what affects the effective thermal conductivity of foamed concretes.

Using transducerless time-domain thermoreflectance technique to measure in- and cross-plane thermal conductivity of nanofilms

Time-domain thermoreflectance (TDTR) and frequency-domain thermoreflectance techniques have been widely used to measure thermal properties. However, the existence of the metal sensor brings some limitations to the experimental measurement, such as temperature limits, disability to measure low in-plane thermal conductivity, in situ measurement cannot be achieved, etc. This paper proposes a transducerless time-domain thermoreflectance method to measure in- and cross-plane thermal conductivity of nanofilms, in which the optical absorption depth and thermal conductivity tensor are considered to establish a new differential equation that can describe the heat conduction process in multilayer structures. This thermal model can also calculate the effects of spot ellipticity and spot offset distance. Then, the analytical solution and relative deviation of this new model and the surface heat flow boundary model used in conventional TDTR are compared by calculating the phase signals. In terms of experimental measurement, this model is successfully used to derive cross- and in-plane thermal conductivity of PdSi and IrNiTa amorphous alloy nanofilms without a metal sensor.

Graphene-based terahertz antenna with polarization reconfiguration

This article presents the design of a terahertz antenna with the ability to reconfigure its polarization using graphene’s anisotropic properties. By applying a DC magnetic flux, the graphene conductivity tensor can be transformed into a non-diagonal tensor. Conversely, the magnetic bias can be switched off to revert the tensor to a diagonal state. This approach allows the antenna to switch between linear and circular polarizations, making it highly versatile for terahertz applications. Additionally, by altering the direction of the applied DC magnetic bias, one can select the rotation direction of circular polarization between left and right hand. The feeding line and ground plane of the antenna are made of silver metal, and its behavior in the terahertz band is described using the Modified Relaxation-Effect model, which is more accurate than the skin effect model for this band. The finite element numerical method is utilized to analyze the antenna, which yields results consistent with the design predictions. The antenna’s impedance bandwidth spans 2.8 to 3.22 terahertz for linear polarization and 2.9 to 3.18 THz for circular polarization. The antenna’s maximum gain is 6 dB for linear polarization and 5 dB for circular polarization. The axial ratio for circular polarization is 1.36 in the middle of the band, which is below the 3 dB threshold for circular polarization. The antenna produces directive patterns for both linear and circular polarizations. The key innovation of this antenna design lies in its unique utilization of a magnetostatic field to achieve reconfiguration in the terahertz graphene dielectric resonator antenna, a method that has not been previously documented in literature.

Thermal conductivity of Portlandite: Molecular dynamics based approach

Energy storage provides a greener path of efficient energy utilization. Recent trends of research suggest concrete as a potential thermal energy storage (TES) material. Its cheap commercial availability makes it one of the most deserving candidates. Cement paste is the key glue of concrete, hence performance of its major components in thermal conduction seeks thorough scientific study. Portlandite or calcium hydroxide is the second major component of cement paste, microscopically visible at a scale length of <10−4 m. Molecular dynamics (MD) simulation has been utilized to investigate the thermal transport mechanism of portlandite at an atomistic scale. The thermal conductivity of this component has been computed using three major force fields which are compared with the experimental outcome using modulated differential scanning calorimetry (MDSC). It has been observed that the simulation outcomes are in order with the experimental value but the results are sensitive to the choice of force fields. Excitation of molecules during thermal transport is predominantly governed by lower-frequency molecular vibration indicating the existence of Boson Peaks. This manuscript presents the full thermal conductivity tensor of portlandite along with the possible mechanism associated with thermal transport.

Electromagnetic Force on an Aluminum Honeycomb Sandwich Panel Moving in a Magnetic Field.

This paper reports a method for calculating the electromagnetic force acting on an aluminum honeycomb sandwich panel moving in a magnetic field. This research is motivated by the non-contact electromagnetic detumbling technology for space non-cooperative targets. Past modeling of the electromagnetic forces and torques generally assumes that the target is homogeneous. However, aluminum honeycomb sandwich panels are extensively used in spacecraft structures to reduce weight without sacrificing structural strength and stiffness, which are so inhomogeneous and complicated that it is difficult to obtain the induced electromagnetic force even by numerical methods. An equivalent conductivity tensor of an aluminum honeycomb sandwich panel is proposed, which allows the aluminum honeycomb sandwich panel to be treated as a homogeneous structure when calculating the induced electromagnetic forces. The advantage of the equivalent conductivity tensor in the calculation of induced electromagnetic forces is verified by finite element simulations. The proposed method makes it possible to evaluate the electromagnetic force of a large aluminum honeycomb sandwich structure moving in a magnetic field.

Bilayer thermal metadevices that mold transient heat flows

Thermal manipulation has been widely researched due to its potential in novel functions, such as cloaking, illusion and sensing. To avoid the spatially inhomogeneous and anisotropic heat conductivity tensors (introduced by transformation thermodynamics), several thermal cloaks based on scattering cancellation (SC) approach are designed and experimentally demonstrated. However, the current SC cloak is only effective in the steady-state heat transfer condition as the heat capacity terms are neglected by the requirement of constant external fields. In order to expand the SC cloak to the transient regime, a bilayer scheme is introduced to achieve the accurate solutions of the camouflage equations considering time factors. Indeed, there are two equations to solve with two unknown quantities: first the thermal conductivity and second the product of specific heat capacity by the density. We construct thermal camouflage devices and verify their ability to mold dynamic heat flows both by simulations and experiments. Our proposed method paves an efficient avenue to extend SC approach to dynamic heat transfer regime.

High-frequency transport properties of a 2D electron gas with spin-orbit interaction under magnetic field driven topological transition

We study the transport properties of a two-dimensional electron system with an essential spin-orbit interaction under topological phase transition due to changing in-plane magnetic field. We have analyzed the contribution of diagonal and off-diagonal components of density matrix with respect to number of spin zone in the high-frequency conductivity. Analytical formulas for the conductivity tensor have been obtained. A numerical analysis giving full enough representation about the dependence of the conductivity on frequency and magnetic field is presented. We have shown that the contribution of the off-diagonal elements of density matrix is the greater than the higher the frequency of the alternating electromagnetic field. It has been established that for magnetic field value at which the minimum electron energy of upper spin zone exceeds the Fermi energy, the conductivity as a function of magnetic field change in discrete step.

A novel method for depolarization tensor and average form of an arbitrarily shaped inclusion: Extension to different physical fields and their effective transport properties of composites

Depolarization tensor (DT), exclusively controlled by the inclusion shape, is crucial in assessing composite transport behavior. However, the solution of DT for a non-ellipsoidal inclusion exhibits nonuniformity and lacks a closed-form expression. Average DT is then introduced to ensure uniformity and seamlessly integrate the evaluation of effective transport properties of composites. In this work, we devise a novel method to obtain DT and average DT of an arbitrarily shaped inclusion by leveraging mathematical similarity from Greenʼs function to degenerate the Eshelby tensor and average Eshelby tensor in an elastic field. The method circumvents singularity and complexity in direct integration and successfully extracts all tensor components. As natural extensions, we also derive the Eshelby conduction tensor, polarizability tensor, and their averages. The accuracy of the method is validated by comparing the average polarizabilities of Platonic solids and stem cells with existing literature data. Furthermore, we incorporate average DT into a developed homogenization model to predict effective transport properties of two-phase composites comprising randomly distributed congruent irregular inclusions. Comparisons with finite element simulations demonstrate accurate predictions of the effective transport properties like effective permeability, diffusivity, conductivity, and permittivity. The proposed framework offers valuable guidance for tailoring inclusion shapes to design particulate/fibrous/porous/biological composites.

On multiphysics concurrent multiscale topology optimization for designing porous heat-activated compliant mechanism under convection for additive manufacture

In this research, we investigated the use of concurrent multiscale topology optimization to design additively manufacturable lightweight porous compliant mechanisms that enable harnessing heat energy as the energy source to perform mechanical actions. By establishing two independent dimensionless representations of the design problem, i.e., macro and microscale domains, a concurrent multiscale topology optimization framework is implemented, and the effective properties of the microscale (i.e., elastic and heat conductivity tensors, as well as the thermal expansion coefficient) are calculated and used as the thermo-elastic modeling effective properties of the macroscale. For heat transfer physics, heat transport in solids, as well as heat convection, are simultaneously considered in this study. Sensitivity analysis on the suggested concurrent optimization scheme was derived to address the macro and microstructure coupling as well as the thermo-elastic physics coupling. Several numerical cases are studied with single and multiple microstructure systems. To investigate the macrostructure dependency on the microstructure systems, a study was performed for multiple microstructure subsystems. Incorporating several microstructures into a single macro design domain increased design freedom and improved the performance-to-weight ratio. Furthermore, and for achieving good additive manufacturability we investigated the connectivity of the multi-microstructure optimization and implement boundary competitivity technique to attain fully connected design for attaining good additive manufacturability.

Energy loss of charged particles in anisotropic 2D materials using the oscillator model

We apply the oscillator model to study the energy loss processes of external charged particles interacting with a 2D material characterized by an anisotropic conductivity tensor. We model the material as a monolayer of harmonic oscillators, with anisotropic electronic vibration modes. We focus on the cases of parallel and perpendicular trajectories of the external particle, and we obtain analytical expressions for the stopping power and total energy loss in terms of reduced variables. This allows us to analyze in detail the interaction and to adapt the model to the considered material using adequate values for the physical parameters involved.

Electromagnetism of one-component plasmas of massless fermions

We present a theoretical study of two- and three-dimensional massless Dirac one-component plasmas embedded in a constant uniform magnetic field. We determine the wavefunctions and Landau energy levels of a massless Dirac fermion in a constant magnetic field. On this basis we consider magnetism of Fermi fluids of massless charged particles. We show that such a three-dimensional Dirac plasma consisting of fermions with the same helicity has its own magnetic moment. We also consider the limit of strong magnetic fields and investigate the De Haas–van Alphen effect. We derive the Kubo formula for the electrical conductivity tensor of massless Dirac plasmas and consider the Shubnikov–de Haas effect. In addition, we propose a model of the static conductivity tensor and employ the matrix version of the classical method of moments to derive a Drude-like formula for the dynamic conductivity tensor for massless Dirac plasmas. We find that the electrical conductivity tensor for Dirac fermions with the right helicity is not isotropic in the plane perpendicular to the magnetic field.

A semi-analytic method for the computation of the effective properties of composites of two isotropic constituent materials

We develop a computational framework for the semi-analytic representation of the effective transport properties of two-component composite materials, in the spirit of Bergman’s spectral representation. The components of the effective permittivity (or conductivity) tensor are expanded as power series in a contrast parameter between the two phases. The coefficients (the moments of a spectral measure) of these expansions are determined recursively through the numerical evaluations of integrals defined solely on the boundary between the constituent phases, and discretized by high-order (possibly exponentially converging) quadrature schemes. The high precision reached by these coefficients allows the series representation to be recast into Padé approximants (or continued fractions) to provide analytical expressions valid over large (possibly infinite) regions of the parameter complex plane. Examples, thus far limited to two-dimensional rhombic unit cells, demonstrate that the method is reliable for microgeometries and material parameters for which other methods are far less dependable. The analytical representations are particularly useful to study the optical or electrostatic resonant behaviour of some composite materials.

Shielding Effectiveness of Magnetostatically-Biased Anisotropic Graphene by the Method of Auxiliary Sources With a Surface Current Boundary Condition

Extensive experimental data and numerical simulations show that graphene is an ideal shielding material in the RF/microwave region. In most cases, it is considered to be isotropic with its scalar surface conductivity given by the Kubo formula. However, when it is electrostatically- and magnetostatically-biased, it exhibits anisotropy described by a surface conductivity tensor. The main objective of this work is to evaluate the shielding effectiveness of anisotropic graphene in the RF/microwave region. Since graphene’s thickness is many orders of magnitude smaller than the shortest wavelength in the considered regime, it does not affect substantially the computation of the fields. For this reason, we replace the graphene layer with a Surface Current Boundary Condition (SCBC), hence its effect is equivalent to a surface electric current density. We employ the Method of Auxiliary Sources (MAS) to analyze a planar and a cylindrical shielding configuration. For the cylindrical shield, the derived MAS results are compared with the exact solutions, which are also extracted. For the planar shield, the results are compared to those obtained by FEM-based commercial software. In both cases, excellent agreement is observed.

Advances in Automated Eddy-Current Characterisation of Carbon Fibre Composites

Ply wrinkles in CFRP laminates are common and can lead to significant failure in composite structures if not properly assessed during the design, manufacturing, and service phases. Evaluating wrinkle geometries can be difficult as they are influenced by multiple factors, such as asymmetry, wavelength, and amplitude, which impact the structure's mechanical performance. High-frequency eddy current testing has proven effective for detecting in-plane waviness and out-of-plane wrinkles. However, the complex nature of CFRP structures and electrical anisotropy may hinder the effectiveness of an eddy current in-line monitoring system if not taken into account. In this study, an advanced modelling approach is employed to simulate the structural variation of the conductivity tensor. A designated wrinkle area, characterized by reduced electrical conductivity, is integrated with structural modelling to replicate a realistic coupon sample containing a wrinkle defect. Four proposed configurations are used to virtually test the samples, and their detection capabilities are analyzed quantitatively.

Determination of heat transfer representative element volume and three-dimensional thermal conductivity tensor of fractured rock masses

The natural fracture system exerts a significant influence on the physical and mechanical properties of rock masses. The heat transfer in fractured rock masses is much more complicated than that of intact rock due to the thermal contact resistance induced by natural fractures with varying size, aperture, roughness, and orientation. This work describes a method for determining the representative element volume (REV) of heat transfer and the 3D thermal conductivity tensor of fractured rock masses. The method is based on the element-wise averaging of temperature and heat flux, which can be obtained from a finite element solution to a steady state heat transfer problem with specific boundary conditions. A case study was conducted based on the geological data of a potential area for high level radioactive waste disposal in China. The results indicate that the size of heat transfer REV of the rock masses in the study area is approximately 18 m × 18 m × 18 m. 3D thermal conductivity tensor, the magnitudes and directions of the three principal thermal conductivities, and anisotropy of the fractured rock masses were obtained. Influences of main fracture parameters including density, disc diameter, and thermal contact resistance on the heat transfer characteristics were investigated. The research results in this work can provide a better understanding of the discontinuous heat transfer processes in fractured rock masses and their homogenization methods.

The free material design problem for the stationary heat equation on low dimensional structure

For a given balanced distribution of heat sources and sinks, Q, we find an optimal conductivity tensor field, , minimizing the thermal compliance. We present in a rather explicit form in terms of the datum. Our solution is a Borel measure taking values in a cone of non-negative tensors. We present a series of examples with explicit solutions.

Thermal properties of nanoporous materials, large scale modelling with the use of Monte Carlo phonon transport autocorrelation

In the present work, we demonstrate the ability of a technique based on Monte Carlo resolution of the Boltzmann transport equation associated to the Green–Kubo autocorrelation of the phonon heat flux to predict, at thermal equilibrium, the thermal conductivity tensor of nanoporous structures. This methodology, which is derived from a former work [D. Lacroix, M. Isaiev, G. Pernot, Phys. Rev. B 104, 165 202 (2021)] developed in the case of bulk systems, is used to predict thermal transport properties of Si porous matrices and Si phononic membranes at room temperature. A broad range of porosities and different pore network organizations are considered. Our results are compared to available experimental data and former modeling techniques. In addition, analytical models based on the phonon mean free path are detailed and compared to numerical simulations.

Electromagnetic Monitoring of Modern Geodynamic Processes: An Approach for Micro-Inhomogeneous Rock through Effective Parameters

This study focuses on microscale anisotropy in rock structure and texture, exploring its influence on the macro anisotropic electromagnetic parameters of the geological media, specifically electric conductivity (σ), relative permittivity (ε), and magnetic permeability (μ). The novelty of this research lies in the advancement of geophysical monitoring methods for calculating cross properties through the estimation of effective parameters—a kind of integral macroscopic characteristic of media mostly used for composite materials with inclusions. To achieve this, we approximate real geological media with layered bianisotropic media, employing the effective media approximation (EMA) averaging technique to simplify the retrieval of the effective electromagnetic parameters (e.g., apparent resistivity–inversely proportional to electrical conductivity). Additionally, we investigate the correlation between effective electromagnetic parameters and geodynamic processes, which is supported by the experimental data obtained during monitoring studies in the Tien Shan region. The observed decrease and increase in apparent electrical resistivity values of ρk over time in orthogonal azimuths leads to further ρk deviations of up to 80%. We demonstrate that transitioning to another coordinate system is equivalent to considering gradient anisotropic media. Building upon the developed method, we derive the effective electric conductivity tensor for gradient anisotropic media by modeling the process of fracturing in a rock mass. Research findings validate the concept that continuous electromagnetic monitoring can aid in identifying natural geodynamic disasters based on variations in integral macroscopic parameters such as electrical conductivity. The geodynamic processes are closely related to seismicity and stress regimes with provided constraints. Therefore, disasters such as earthquakes are damaging and seismically hazardous.

Microwave Flux-flow Hall Effect in a Multi-band Superconductor FeSe

We have measured the flux-flow Hall effect in a multi-band superconductor FeSe pure single crystal to investigate the nature of the vortex core state by means of the cross-shaped bimodal cavity technique. We found that the flux-flow Hall angle of FeSe at low temperatures is about 0.5, which is equal to or smaller than that evaluated by the effective viscous drag coefficient measurements. This feature is in contrast to the cuprate superconductors. The conductivity tensor of multi-band superconductors that are contributed from holes and electrons shows partial cancellation of the flux-flow Hall voltage by the electrons and holes, which can explain the observed feature. Therefore, our study suggests the appearance of the multi-band nature in the vortex dynamics.

Thermal metamaterials with nonconformal geometry

Thermal metamaterials have garnered significant attention for their potential to manipulate heat flow, leading to the development of various thermal metadevices such as thermal cloaks, concentrators, and rotators. However, the theoretical study of thermal metadevices with nonconformal geometry remains limited due to design and fabrication challenges. This letter proposes a method for designing and manufacturing nonconformal thermal metamaterials using the conformal discrete theory to simplify the anisotropic thermal conductivity tensors. The method involves 3D printing three thermal metadevices (a thermal cloak, concentrator, and rotator) with complex nonconformal geometry. Simulation and experimental results demonstrate the successful implementation of cloaking, concentrating, and rotating functionalities. Moreover, the thermal metadevices still maintained thermal functionality well under the condition of omnidirectional heat flow. This work provides guidance for the design and manufacture of nonconformal thermal metamaterials, as well as their potential applications in other fields such as electrics/magnetics, electromagnetics/optics, and acoustics.