Isotropic Conductivity Research Articles

Effect of interface density, quality and period on the lattice thermal conductivity of nanocomposite materials

We examine the effects of interface density, quality, and period size on the lattice thermal conductivity of nanocomposite materials within the framework of a recently developed extended modified effective medium approach. A density functional theory and Boltzmann equation based semi-ab initio approach is used to calculate the constituent thermal conductivities, and the effective thermal boundary conductance is computed by modeling interface roughness based on a realistic combination of acoustic mismatch and diffuse mismatch contributions, for systems with anisotropic (directionally dependent) and isotropic thermal conductivities. Results obtained for Si/Ge and MoS2/WS2 systems indicate that the effective cross-planar thermal conductivity of planar superlattice systems is closely related to the thermal boundary resistance of the system for small superlattice periods, whereas in nanodot superlattices, the effective thermal conductivity for small particles is primarily regulated through the effective scattering lengths used in the calculation of the insert and matrix conductivities.

Динамический изгиб бесконечного электромагнитоупругого стержня

The problem of non-stationary bending of an infinite electromagnetoelastic rod is considered. It is assumed that the material of the rod is a homogeneous isotropic conductor. The closed-form system of process equations is constructed under the assumption that the desired functions depend only on the longitudinal coordinate and time using the corresponding relations for shells which take into account the initial electromagnetic field, the Lorentz force, Maxwell’s equations, and the generalized Ohm’s law. The desired functions are assumed to be bounded, and the initial conditions are assumed to be null. The solution of the problem is constructed in an integral form with kernels in the form of influence functions. Images of kernel are found in the space of Laplace transformations in time and Fourier transformations in spatial coordinates. It is noted that the images are rational functions of the Laplace transform parameter, which makes it quite easy to find the originals. However, for a general model that takes into account shear deformations, the subsequent inversion of the Fourier transform can be carried out only numerically, which leads to computational problems associated with the presence of rapidly oscillating integrals. Therefore, the transition to simplified equations corresponding to the Bernoulli – Euler rod and the quasistationary electromagnetic field is carried out. The method of a small parameter is used for which a coefficient is selected that relates the mechanical and electromagnetic fields. In the linear approximation, influence functions are found for which images and originals are constructed. In this case, the zeroth approximation corresponds to a purely elastic solution. Originals are found explicitly using transform properties and tables. Examples of calculations are given for an aluminum rod with a square cross section. It is shown that for the selected material the quantitative difference from the elastic solution is insignificant. At the same time, taking into account the connectedness of the process leads to additional significant qualitative effects.

Electrical conductivity tensor of β−Ga2O3 analyzed by van der Pauw measurements: Inherent anisotropy, off-diagonal element, and the impact of grain boundaries

The semiconducting oxide $\beta$-Gallium Oxide ($\beta$-Ga$_{2}$O$_{3}$) possesses a monoclinic unit cell whose low symmetry generally leads to anisotropic physical properties. For example, its electrical conductivity is generally described by a polar symmetrical tensor of second rank consisting of four independent components. Using van der Pauw measurements in a well-defined square geometry on differently-oriented high-quality bulk samples and the comparison to finite element simulations we precisely determine the ratio of all elements of the $\beta$-Ga$_{2}$O$_{3}$ 3-dimensional electrical conductivity tensor. Despite the structural anisotropy a nearly isotropic conductivity at and above room temperature was found with the principal conductivities deviating from each other by less than 6% and the off-diagonal element being $\approx3$% of the diagonal ones. Analysis of the temperature dependence of the anisotropy and mobility of differently doped samples allows us to compare the anisotropy for dominant phonon-scattering to that for dominant ionized-impurity scattering. For both scattering mechanisms, the conductivites along the $a$ and $b$-direction agree within 2%. In contrast, the conductivity along $c$-direction amounts to $0.96\times$ and up to $1.12\times$ that along the $b$-direction for phonon and ionized impurity scattering, respectively. The determined transport anisotropies are larger than the theoretically predicted effective mass anisotropy, suggesting slightly anisotropic scattering mechanisms. We demonstrate that significantly higher anisotropies can be caused by oriented extended structural defects in the form of low-angle grain boundaries for which we determined energy barriers of multiple 10 meV.

A machine learning approach to support deep brain stimulation programming

Adjusting the stimulation parameters is a challenge in deep brain stimulation (DBS) therapy due to the vast number of different configurations available. As a result, systems based on the visualization of the volume of tissue activated (VTA) produced by a particular stimulation setting have been developed. However, the medical specialist still has to search, by trial and error, for a DBS set-up that generates the desired VTA. Therefore, our goal is developing a DBS parameter tuning strategy for current clinical devices that allows defining a target VTA under biophysically viable constraints. We propose a machine learning approach that allows estimating the DBS parameter values for a given VTA, which comprises two main stages: i) A K-nearest neighbors-based deformation to define a target VTA preserving biophysically viable constraints. ii) A parameter estimation stage that consists of a data projection using metric learning to highlight relevant VTA properties, and a regression/classification algorithm to estimate the DBS parameters that generate the target VTA. Our methodology allows setting a biophysically compliant target VTA and accurately predicts the required configuration of stimulation parameters. Also, the performance of our approach is stable for both isotropic and anisotropic tissue conductivities. Furthermore, the computational cost of the trained system is acceptable for real-world implementations.

Quasi-bonding driven abnormal isotropic thermal transport in intrinsically anisotropic nanostructure: a case of study of a phosphorus nanotube array

Thermal anisotropy/isotropy is one of the fundamental characteristics of the thermal properties of a material, playing a significant role in the high-performance thermal management in micro-/nanoelectronics. It has been well documented in the literature that the symmetry of geometric structures governs the anisotropy/isotropy of thermal transport. However, the fundamental correlation and the underlying mechanism remain unclear. In this paper, using a new two-dimensional (2D) van der Waals (vdW) phosphorus nanotube array as a case study, we show that the lattice thermal conductivity can be abnormally almost isotropic although the geometric structure presents remarkable anisotropy, which contradicts the previous consensus. The key factor for the abnormal isotropic thermal conductivity is mainly the essentially analogous group velocities along the intratube and intertube directions. Compared with a carbon-nanotube array, a traditional vdW system, a microscopic picture is established to underpin the underlying mechanism. The quasi-bond (non-covalent bonding, but far stronger than the vdW interatomic interaction) between the phosphorus nanotubes is found to be responsible for such diverse isotropic transport phenomena. The findings in this paper are expected to deepen our understanding of the anisotropy/isotropy thermal transport of materials and are also helpful for future thermal management technology.

Computer simulation of polarization rotation characteristics of graphene

The magnetically biased graphene has the polarization rotation characteristics which is useful to design the polarizer. But this characteristic is difficult to simulate by using the finite-difference time-domain (FDTD) method, not only due to the graphene's thin layer which confines the time step size, but also because of graphene's isotropic surface conductivity when it is biased by static magnetic field. To solve this problem, this study presents an anisotropic hybrid implicit-explicit FDTD method. This method uses auxiliary difference equations to represent graphene's conductivity, and removes the confinement of graphene's thickness on time step size by using hybrid implicit-explicit technique. So, compared with FDTD method, the presented method can save a large number of computational time, which are validated by numerical examples.

Investigation of borehole effects on azimuthal resistivity measurements using novel pseudo‐analytic formulas

ABSTRACTDownhole resistivity measurements provide valuable information for geosteering and formation evaluation. It is important to understand and correct the environmental effects, such as the borehole, the tool eccentricity and the resistivity anisotropy effects, of the measurements based on fast and accurate modelling methods. A new pseudo‐analytic solution for eccentric coaxial and tilted‐coil antennas in the cylindrically multilayered medium with transverse isotropic conductivity was developed. This method can take the eccentric tool, the borehole, the mud invasion and the resistivity anisotropy into account. These formulas enable us to simulate the responses of the downhole induction logging tools, including induction wireline and azimuthal propagation logging‐while‐drilling measurements. Instead of using the prior fictitious boundary, the generalized reflection coefficients are proposed to construct the linear matrix functions to deal with the tool eccentricity. The cylindrical functions are reorganized and presented in forms of ratios. Thus, the proposed formulas obviate the overflow issue in the computation and are more stable and efficient. The proposed approach is compared and validated with other well‐established methods. Simulations and case studies show that: (1) the responses of azimuthal resistivity logging‐while‐drilling tool are affected by the tool's eccentricity in both isotropic and anisotropic medium; (2) sine curve behaviours exist for the phase difference and amplitude ratio of azimuthal resistivity measurements along with different eccentricity azimuth.

Macroscopic thermal profile of heterogeneous cancerous breasts. A three-dimensional multiscale analysis

The present work focuses on a multiscale analysis of temperature maps for cancerous breasts. A three-dimensional model is proposed based on a system of bioheat transfer equations for the healthy and cancerous breast regions, which are characterized by different microstructure and thermophysical properties. The geometrical model of the cancerous breast is identified by the presence of muscle, glandular and fat tissues, as well as the heterogeneous tumorous tissue. The latter is assumed to be a two-phase periodic composite with spherical inclusions. A cubic lattice distribution is chosen, wherein the constituents exhibit isotropic thermal conductivity behavior. The tissue effective thermal conductivities are computed by means of the asymptotic homogenization approach, i.e. by solving relevant periodic problems on the cell which is representative of the malignant tissue microstructure. These are then exploited to solve the macroscale homogenized model by finite elements. The obtained results, in terms of temperature maps, are successfully compared with relevant experiments and could pave the way towards the development of a robust multiscale mathematical framework featuring microstructural information which can be useful in cancer diagnosis. This approach could provide qualitative and quantitative hints that can be used to improve tumor detection based on temperature maps of the breast tissue.

Explicit Splitting Scheme for Maxwell’s Equations

A new explicit scheme for the numerical integration of Maxwell’s equations in isotropic and anisotropic dielectrics and conductors is presented. In this scheme, the electric and magnetic fields are calculated at the same instants and at the same nodes of the spatial grid with splitting by spatial directions and physical processes. The scheme is conservative, monotonic, second-order accurate in time, and third-order accurate in spatial variables. In the course of simulating the propagation of low-frequency signals in the Earth-ionosphere waveguide, the scheme allows using a significantly bigger time integration step than the widely used finite-difference time domain method for the same accuracy.

Parallel 3-D marine controlled-source electromagnetic modelling using high-order tetrahedral Nédélec elements

SUMMARY We present a parallel and high-order Nédélec finite element solution for the marine controlled-source electromagnetic (CSEM) forward problem in 3-D media with isotropic conductivity. Our parallel Python code is implemented on unstructured tetrahedral meshes, which support multiple-scale structures and bathymetry for general marine 3-D CSEM modelling applications. Based on a primary/secondary field approach, we solve the diffusive form of Maxwell’s equations in the low-frequency domain. We investigate the accuracy and performance advantages of our new high-order algorithm against a low-order implementation proposed in our previous work. The numerical precision of our high-order method has been successfully verified by comparisons against previously published results that are relevant in terms of scale and geological properties. A convergence study confirms that high-order polynomials offer a better trade-off between accuracy and computation time. However, the optimum choice of the polynomial order depends on both the input model and the required accuracy as revealed by our tests. Also, we extend our adaptive-meshing strategy to high-order tetrahedral elements. Using adapted meshes to both physical parameters and high-order schemes, we are able to achieve a significant reduction in computational cost without sacrificing accuracy in the modelling. Furthermore, we demonstrate the excellent performance and quasi-linear scaling of our implementation in a state-of-the-art high-performance computing architecture.

High intrinsic ZT in InP3 monolayer at room temperature

Two-dimensional thermoelectric (TE) materials which have the figure of merit ZT that is greater than 1.5 at room temperature would be highly desirable in energy conversion since the efficiency is competitive to conventional energy conversion techniques. Here, we report that the indium triphosphide (InP3) monolayer shows a large ZT of 1.92 at 300 K, based on the quantum calculations within the ballistic thermal transport region. A remarkably low and isotropic phononic thermal conductivity is found due to the flat lattice vibration modes, which takes a major responsibility for the impressively high ZT at room temperature. Moreover, a large ZT of 1.67 can still be achieved even under a 1% mechanical tension on the lattice. These results suggest that the InP3 monolayer is a promising candidate for low dimensional TE applications.

Intelligence thermotics: Correlated self-fixing behavior of thermal metamaterials

It is a challenge to design intelligent thermal metamaterials due to the lack of suitable theories. Here we propose a kind of intelligent thermal metamaterials by investigating a core-shell structure, where both the core and shell have an anisotropic thermal conductivity. We solve Laplace's equation for deriving the equivalent thermal conductivity of the core-shell structure. Amazingly, the solution gives two coupling relations of conductivity tensors between the core and the shell, which cause the whole core-shell structure to counterintuitively self-fix a constant isotropic conductivity even when the area or volume fraction of the core changes within the full range in two or three dimensions. The theoretical findings on fraction-independent properties are in sharp contrast with those predicted by the well-known effective medium theories, and they are further confirmed by our laboratory experiments and computer simulations. This work offers two coupling relations for designing intelligent thermal metamaterials, and they are not only helpful for thermal stabilization or camouflage/illusion, but they also offer hints on how to achieve similar metamaterials in other fields.

Effect of Heart Structure on Ventricular Fibrillation in the Rabbit: A Simulation Study.

Ventricular fibrillation (VF) is a lethal condition that affects millions worldwide. The mechanism underlying VF is unstable reentrant electrical waves rotating around lines called filaments. These complex spatio-temporal patterns can be studied using both experimental and numerical methods. Computer simulations provide unique insights including high resolution dynamics throughout the heart and systematic control of quantities such as fiber orientation and cellular kinetics that are not feasible experimentally. Here we study filament dynamics using two bi-ventricular 3-D high-resolution rabbit heart geometries, one with detailed fine structure and another without fine structure. We studied filament dynamics using anisotropic and isotropic conductivities, and with four cellular action potential models with different recovery kinetics. Spiral wave dynamics observed in isotropic two-dimensional sheets were not predictive of the behavior in the whole heart. In 2-D the four cell models exhibited stable reentry, meandering spiral waves, and spiral-wave breakup. In the whole heart with fine structure, all simulation results exhibited complex dynamics reminiscent of fibrillation observed experimentally. In the whole heart without fine structure, anisotropy acted to destabilize filament dynamics although the number of filaments was reduced compared to the heart with structure. In addition, in isotropic hearts without structure the two cell models that exhibited meandering spiral waves in 2-D, stabilized into figure-of-eight surface patterns. We also studied the sensitivity of filament dynamics to computer system configuration and initial conditions. After large simulation times, different macroscopic results sometimes occurred across different system configurations, likely due to a lack of bitwise reproducibility. The study conclusions were insensitive to initial condition perturbations, however, the exact number of filaments over time and their trends were altered by these changes. In summary, we present the following new results. First, we provide a new cell model that resembles the surface patterns of VF in the rabbit heart both qualitatively and quantitatively. Second, filament dynamics in the whole heart cannot be predicted from spiral wave dynamics in 2-D and we identified anisotropy as one destabilizing factor. Third, the exact dynamics of filaments are sensitive to a variety of factors, so we suggest caution in their interpretation and their quantitative analyses.

Accurate Prediction of Melt Pool Shapes in Laser Powder Bed Fusion by the Non-Linear Temperature Equation Including Phase Changes

In this contribution, we validate a physical model based on a transient temperature equation (including latent heat) w.r.t. the experimental set AMB2018-02 provided within the additive manufacturing benchmark series, established at the National Institute of Standards and Technology, USA. We aim at predicting the following quantities of interest: width, depth, and length of the melt pool by numerical simulation and report also on the obtainable numerical results of the cooling rate. We first assume the laser to posses a double ellipsoidal shape and demonstrate that a well calibrated, purely thermal model based on isotropic thermal conductivity is able to predict all the quantities of interest, up to a deviation of maximum 7.3\% from the experimentally measured values. However, it is interesting to observe that if we directly introduce, whenever available, the measured laser profile in the model (instead of the double ellipsoidal shape) the investigated model returns a deviation of 19.3\% from the experimental values. This motivates a model update by introducing anisotropic conductivity, which is intended to be a simplistic model for heat material convection inside the melt pool. Such an anisotropic model enables the prediction of all quantities of interest mentioned above with a maximum deviation from the experimental values of 6.5\%. We note that, although more predictive, the anisotropic model induces only a marginal increase in computational complexity.

Convexification of electrical impedance tomography with restricted Dirichlet-to-Neumann map data

We propose a new numerical method to reconstruct the isotropic electrical conductivity from measured restricted Dirichlet-to-Neumann map data in electrical impedance tomography (EIT). ‘Restricted Dirichlet-to-Neumann (DtN) map data’ means that the Dirichlet and Neumann boundary data for EIT are generated by a point source running either along an interval of a straight line or along a curve located outside of the domain of interest. We ‘convexify’ the problem via constructing a globally strictly convex Tikhonov-like functional using a Carleman weight function. In particular, two new Carleman estimates are established. Global convergence to the correct solution of the gradient projection method for this functional is proven. Numerical examples demonstrate a good performance of this numerical procedure.

Drywell infiltration and hydraulic properties in heterogeneous soil profiles

Drywells are increasingly used to capture stormwater runoff for surface infiltration and aquifer recharge, but little research has examined the role of ubiquitous subsurface heterogeneity in hydraulic properties on drywell performance. Numerical experiments were therefore conducted using the HYDRUS (2D/3D) software to systematically study the influence of subsurface heterogeneity on drywell infiltration. Subsurface heterogeneity was described deterministically by defining soil layers or lenses, or by generating stochastic realizations of soil hydraulic properties with selected variance (σ) and horizontal (X) and vertical (Z) correlation lengths. The infiltration rate increased when a high permeability layer/lens was located at the bottom of the drywell, and had larger vertical and especially horizontal dimensions. Furthermore, the average cumulative infiltration (I) for 100 stochastic realizations of a given subsurface heterogeneity increased with σ and X, but decreased with Z. This indicates that the presence of many highly permeable, laterally extending lenses provides a larger surface area for enhanced infiltration than the presence of isolated, highly permeable lenses. The ability to inversely determine soil hydraulic properties from numerical drywell infiltration results was also investigated. The hydraulic properties and the lateral extension of a highly permeable lens could be accurately determined for certain idealized situations (e.g., simple layered profiles) using constant head tests. However, variability in soil hydraulic properties could not be accurately determined for systems that exhibited more realistic stochastic heterogeneity. In this case, the heterogeneous profile could be replaced with an equivalent homogeneous profile and values of an effective isotropic saturated conductivity (Ks) and the shape parameter in the soil water retention function (α) could be inversely determined. The average value of Ksfor 100 stochastic realizations showed a similar dependency to I on σ, X, and Z. Whereas, the average value of α had large confidence interval for soil heterogeneity parameters and played a secondary role in drywell infiltration. This research provides valuable insight on the selection of site, design, installation, and long-term performance of a drywell.

Fabrication of thermally conductive and electrically insulating polymer composites with isotropic thermal conductivity by constructing a three-dimensional interconnected network.

Efficient heat removal via thermal management materials has become one of the most critical challenges in the development of modern microelectronic devices. However, the conventional polymer-based thermally conductive composites with randomly distributed filler particles usually yield an undesired value because of the lack of efficient heat transfer pathways. Therefore, constructing a three-dimensional interconnected filler structure is greatly desirable for realizing high thermal conductivity enhancement in composites. Herein, graphene oxide (GO) was used as a thermally conductive filler due to its excellent thermal conductivity and coated with polydopamine (PDA) to enhance its electric insulation performance. A unique "particle-constructing" method was adopted for fabricating highly ordered three-dimensional GO-based polymer composites, throughout which the GO-PDA formed an intact, uniform and well-defined network structure. The composite, even with a very low GO-PDA loading of 0.96 vol%, exhibited both high in-plane (4.13 W m-1 K-1) and through-plane (4.56 W m-1 K-1) thermal conductivities and also presented excellent electrically insulating properties (>1014Ω cm). These composites have promising applications in heat dissipation of next-generation portable and collapsible electronic devices.

Natural convection and anisotropic heat transfer in a ferro-nanofluid under magnetic field

In this paper, effects of anisotropic thermal conductivity and the Lorentz force in a ferro-nanofluid induced by external magnetic fields are investigated. The nanofluid is modeled as a non-linear single-phase fluid, where the viscosity is considered to depend on the nanoparticle concentration; the thermal conductivity shows anisotropy due to the existence of the magnetic field. The anisotropic thermal conductivity tensor, which depends on the magnetic field vector, is derived by considering the principle of material frame indifference of Continuum Mechanics. Numerical simulations are performed in a horizontal annulus enclosure. Effects of the nanoparticle concentration, magnetic distribution, and the dimensionless parameters, such as the Rayleigh number and the Hartmann number, are studied. The numerical results indicate that due to the anisotropic thermal conductivity, the isotherms become elliptic and deviate significantly from a circle which is a typical distribution with isotropic thermal conductivity; furthermore the elliptic shape changes as the direction of the magnetic field varies while the heat transfer is always much faster in the direction parallel to the magnetic field. For the range of the dimensionless parameters studied here, the Nusselt number increases significantly as the Rayleigh number (ranging from 2500 to 50,000) increases; depending on the situation, the magnetic field (the Hartmann number which ranges from 0 to 1) may enhance or diminish the thermal performance. In addition, the streamlines are more organized and less wavy when there exists a magnetic field; this could be attributed to the suppressive effect of the Lorentz force.

Isotropic thermal conductivity in rolled large-sized W-Y2O3 bulk material prepared by powder metallurgy route and rolling deformation technology

Tungsten (W) or W alloys are the main candidates for plasma-facing materials of future fusion reactors. Large-sized W-Y2O3 bulk material has been successfully produced in this study for future engineering applications. Wet chemical method and continuous hydrogen (H2) reduction were applied to achieve mass preparation of W-Y2O3 composite powder. The final bulk material was obtained using the H2 atmosphere sintering technique and rolling deformation process. Conventional X-ray diffraction patterns were used to characterize the different surfaces of the rolled specimen, which coincide with the results of electron backscatter diffraction detection, to evaluate the texture information. The 50% rolled W-Y2O3 bulk material have three types of textures, namely, θ-fiber, α-fiber, and γ-fiber. Notably, the thermal conductivity exhibits no obvious difference between sintered bulk at the original state and rolled bulk along various directions. After rolling deformation of the W-Y2O3 bulk material, the effect of the anisotropic microstructure on the thermal conductivity can be offset by the effect of the fiber geometric structure. For the body-centered cubic structure of W, the thermal conductivity versus the crystal orientation should be λ[100] >λ[110].

Optimizing the design of composite phase change materials for high thermal power density

Phase change materials (PCMs) provide a high energy density for thermal storage systems but often suffer from limited power densities due to the low PCM thermal conductivity. Much like their electrochemical analogs, an ideal thermal energy storage medium combines the energy density of a thermal battery with the power density of a thermal capacitor. Here, we define the design rules and identify the performance limits for rationally-designed composites that combine an energy dense PCM with a thermally conductive material. Beginning with the Stefan-Neumann model, we establish the material design space using a Ragone framework and identify regimes where hybrid conductive-capacitive composites have thermal power densities exceeding that of copper and other high conductivity materials. We invoke the mathematical bounds on isotropic conductivity to optimize and define the theoretical limits for transient cooling using PCM composites. We then demonstrate the impact of power density on thermal transients using copper inverse opals infiltrated with paraffin wax to suppress the temperature rise in kW cm−2 hotspots by ∼10% compared to equivalent copper thin film heat spreaders. These design rules and performance limits illuminate a path toward the rational design of composite phase change materials capable of buffering extreme transient thermal loads.