Properties Of Tensor Research Articles

A simple approach to rotationally invariant machine learning of a vector quantity.

Unlike with the energy, which is a scalar property, machine learning (ML) prediction of vector or tensor properties poses the additional challenge of achieving proper invariance (covariance) with respect to molecular rotation. For the energy gradients needed in molecular dynamics (MD), this symmetry is automatically fulfilled when taking analytic derivative of the energy, which is a scalar invariant (using properly invariant molecular descriptors). However, if the properties cannot be obtained by differentiation, other appropriate methods should be applied to retain the covariance. Several approaches have been suggested to properly treat this issue. For nonadiabatic couplings and polarizabilities, for example, it was possible to construct virtual quantities from which the above tensorial properties are obtained by differentiation and thus guarantee the covariance. Another possible solution is to build the rotational equivariance into the design of a neural network employed in the model. Here, we propose a simpler alternative technique, which does not require construction of auxiliary properties or application of special equivariant ML techniques. We suggest a three-step approach, using the molecular tensor of inertia. In the first step, the molecule is rotated using the eigenvectors of this tensor to its principal axes. In the second step, the ML procedure predicts the vector property relative to this orientation, based on a training set where all vector properties were in this same coordinate system. As the third step, it remains to transform the ML estimate of the vector property back to the original orientation. This rotate-predict-rotate (RPR) procedure should thus guarantee proper covariance of a vector property and is trivially extensible also to tensors such as polarizability. The RPR procedure has an advantage that the accurate models can be trained very fast for thousands of molecular configurations, which might be beneficial where many training sets are required (e.g., in active learning). We have implemented the RPR technique, using the MLatom and Newton-X programs for ML and MD, and performed its assessment on the dipole moment along MD trajectories of 1,2-dichloroethane.

A Bond-Based Machine Learning Model for Molecular Polarizabilities and A Priori Raman Spectra.

The use of machine learning (ML) algorithms in molecular simulations has become commonplace in recent years. There now exists, for instance, a multitude of ML force field algorithms that have enabled simulations approaching ab initio level accuracy at time scales and system sizes that significantly exceed what is otherwise possible with traditional methods. Far fewer algorithms exist for predicting rotationally equivariant, tensorial properties such as the electric polarizability. Here, we introduce a kernel ridge regression algorithm for machine learning of the polarizability tensor. This algorithm is based on the bond polarizability model and allows prediction of the tensor components at the cost similar to that of scalar quantities. We subsequently show the utility of this algorithm by simulating gas phase Raman spectra of biphenyl and malonaldehyde using classical molecular dynamics simulations of these systems performed with the recently developed MACE-OFF23 potential. The calculated spectra are shown to agree very well with the experiments and thus confirm the expediency of our algorithm as well as the accuracy of the used force field. More generally, this work demonstrates the potential of physics-informed approaches to yield simple yet effective machine learning algorithms for molecular properties.

Modified crystal plasticity constitutive model considering tensorial properties of microstructural evolution and creep life prediction model for Ni-based single crystal superalloy with film cooling hole

Accurate assessment of the creep life of film cooling hole structures is critical for long-life design and safe operation of aero engines and gas turbines. Firstly, through the high temperature creep experiment of nickel-based single crystal superalloy with film cooling hole, the microstructure evolution process under multiaxial stress state around film hole is characterized. Then, considering the directional effect of rafting structure and the influence of multiaxial stress, a fourth-order tensor is used to describe the evolution of γ phase width, and the microstructure evolution model accounting for multi-axial stress states is established. The microstructure evolution is coupled into the crystal plasticity constitutive model by Orowan stress. Meanwhile, based on continuous damage mechanics, a new multiaxial damage evolution law is established by introducing a multiaxial ductility factor into the constitutive model. The improved crystal plasticity constitutive model can effectively predict the microstructural evolution under multiaxial stress conditions. Furthermore, the combination of the modified crystal plasticity constitutive model and the critical distance method considering stress gradients is used for life prediction of film cooling hole structures. The prediction results show the effectiveness and necessity of considering the microstructure evolution in the life prediction.

Self-consistent modelling of radio frequency sheath in 3D with realistic ICRF antennas

Abstract Ion Cyclotron Resonant Frequency (ICRF) induced impurity production has raised many concerns since ITER proposed to change the first wall material from beryllium to tungsten. Enhanced DC plasma potential (VDC) due to RF sheath rectification is well known as one of the most important mechanisms behind the RF induced impurities. Our previous work (L. Lu et.al, Plasma Phys. Control. Fusion 60 (2018) 035003) considered the impact of both the slow wave and the fast wave on the RF sheath rectification in a 2D geometry. It can barely recover the double-hump structure of the VDC poloidal distribution observed in various machines when only the slow wave is modelled using the multi-2D approach which intrinsically assumes the poloidal wavenumber kz is zero. The fast wave on the other hand is found to be more sensitive to a finite kz and may need to be tackled in 3D. This work reports our recent progress on the 3D RF sheath modelling. In this new code, the latest RF sheath boundary conditions (J. R. Myra, J. Plasma Phys. 87 (2021) 905870504) and the realistic 3D ICRF antennas are implemented. Compared to the 2D results, the 3D code could well recover the double-hump poloidal distribution of VDC even with the fast wave included, which confirms our speculation on the necessity of treating the fast wave in 3D. While the double-hump pattern is robust in the simulation, the amplitude of VDC is found to be affected by the magnetic tilt angle and the antenna geometry. This emphasizes the importance of adopting a realistic antenna geometry in the RF sheath modelling. The double-hump VDC poloidal structure breaks as the magnetic tilt angle increases. This is explained by the gyrotropic property of the cold plasma dielectric tensor. The spatial proximity effect we identified in the previous 2D simulations is still valid in 3D. Finally, simulation shows the slow wave dominates the RF sheath excitation in the private SOL, while the fast wave gradually takes over when moving to the far SOL region. This code could be a new tool to provide numerical support for ITER impurity assessment and ICRF antenna design.

Quarter-symmetric connection on an almost Hermitian manifold and on a Kähler manifold

The paper observes an almost Hermitian manifold as an example of a generalized Riemannian manifold and examines the application of a quarter-symmetric connection on the almost Hermitian manifold. The almost Hermitian manifold with quarter-symmetric connection preserving the generalized Riemannian metric is actually the Kähler manifold. Observing the six linearly independent curvature tensors with respect to the quarter-symmetric connection, we construct tensors that do not depend on the quarter-symmetric connection generator. One of them coincides with the Weyl projective curvature tensor of symmetric metric $g$. Also, we obtain the relations between the Weyl projective curvature tensor and the holomorphically projective curvature tensor. Moreover, we examine the properties of curvature tensors when some tensors are hybrid.

Subsurface structural trends in Central-Western India: Inferences from magnetotelluric data using the complex MT apparent resistivity tensor

The central-western part of the Indian subcontinent exhibits significant geological diversity and possesses a rich record of different tectonothermal events in the earth's evolutionary history, spanning from the Archean to the present. Precambrian geology in the region is mostly obscured by Cretaceous-Tertiary/Paleocene volcanic eruptions and Proterozoic to Quaternary/recent sedimentary cover. Magnetotelluric (MT) impedance and tipper responses from 146 stations, covering central-western India in a grid fashion with a spacing of ∼55 km, were analyzed to evaluate the subsurface structural trends, dimensionalities, and qualitative characteristics of the electric lithosphere in the region. An advanced Complex Apparent Resistivity Tensor (CART) approach, along with the popular Phase Tensor (PT) approach and induction arrows are utilized to achieve the above goals. The analysis revealed a high degree of 3D induction effects in the data at almost every station and period. The directionality information retrieved from the tensor properties showed that the structural trends in the deep crust and upper mantle of the major geologic domains correlate with the known surface tectonic trend of the respective geologic domain. This study provides vital evidence to support the suspected bifurcation of the Precambrian Aravalli-Delhi Mobile Belt (ADMB) tectonic trend and its extensions into neighboring Kutch, Saurashtra, and Central Indian Tectonic Zone (CITZ) domains. The analysis results indicate a lithospheric scale enhanced conductivity beneath the Malwa plateau, which marks the first major phase of the Reunion mantle plume eruption in India. A critical finding of this study is that the Resistivity Phase Tensor better defines the subsurface resistivity structure and provides much clearer structural information than the conventional Phase Tensor.

Bulk photovoltaic effect in ferroelectric nematic liquid crystals.

The bulk photovoltaic (BPV) effect in ferroelectric liquid crystals is of increasing scientific interest owing to its great potential for light-energy conversion. The ferroelectric nematic phase exhibits a huge spontaneous polarization that can be aligned to a preferred direction. In this Letter, we investigate the tensorial properties of the BPV effect in the planarly aligned ferroelectric nematic phase of the liquid crystalline material RM734. A steady-state short-circuit photocurrent of ~160 pA and an open-circuit photovoltage of ~50 mV were observed in a cell with a thickness of 5.5 µm under the illumination of ultraviolet light without any bias voltage. Based on the photocurrent measurements in different electrode configurations, the non-zero elements of the BPV tensor were obtained. The BPV effect is attributed to the combination of the spontaneous polarization and the asymmetric distribution of photoinduced charge carriers. This study not only provides an understanding of the bulk PV mechanism in soft ferroelectrics but also promises a wide range of unprecedented, to the best of our knowledge, benefits for light harvesting to engineer marketable photovoltaic devices.

(Digital Presentation) Multiscale Modeling of Two-Phase Transport in the Membrane Electrode Assembly of Polymer Electrolyte Membrane Fuel Cells: Effect of Relative Humidity and Temperature

Water management plays an important role in the performance and durability of polymer electrolyte membrane fuel cells (PEMFCs). Achieving enhanced water removal at high current density without membrane dehydration requires an optimal design of the membrane electrode assembly (MEA) and MEA-channel interaction depending on operating conditions. The analysis of two-phase transport is challenged by the wide range of pore sizes found in porous layer assemblies, varying from 1-100 nm in the catalyst layer (CL), 50-1000 nm in the microporous layer (MPL) and 10 µm in the gas diffusion layer (GDL), up to the millimeter-sized channel. In this work, a hybrid multiscale model is presented to describe two-phase transport and performance of a representative unit cell as a function of relative humidity (RH) and temperature [1-3]. A control volume (CV) decomposition is used to represent the multiscale pore space of the GDL, MPL and CL in terms of local effective transport properties (porosity, effective diffusivity, permeability, thermal/electrical conductivity and entry capillary pressure) [4]. The model incorporates a macroscopic continuum formulation for gas flow and species, energy, liquid-phase pressure, water dissolved in ionomer, and electronic and ionic potentials [5]. Liquid water transport is modeled by means of a multi-cluster invasion-percolation algorithm, which is coupled to the macroscopic continuum formulation by the phase-change source term of water (evaporation/condensation). Water clusters with a net condensation rate grow by invading the adjacent dry CV with the lowest entry capillary pressure, while clusters with a net evaporation rate shrink by drying the wet CV of the cluster with the lowest entry capillary pressure. An all-or-nothing invasion law is adopted for saturation in the GDL (one pore per CV), while a macroscopic description in terms of capillary pressure curve at the representative elementary volume scale (REV) is used for the MPL and the GDL (thousands to millions of pores per CV). An example of the saturation distribution in the cathode MEA is shown in Figure 1. Local saturation remains between 0.1-0.4 in REVs of the CL and the MPL, increasing up to 1 in macropores of the GDL. Water condenses preferentially under the ribs and transport by capillary action to the GDL/channel interface, where the water flow is released to the channel. The channel saturation remains low, around 0.1, due to the large gas flow velocity used in the differential cell.[1] P.A. García-Salaberri, Modeling diffusion and convection in thin porous transport layers using a composite continuum-network model: Application to gas diffusion layers in polymer electrolyte fuel cells, 167 (2021) 120824.[2] D. Zapardiel, P.A. García-Salaberri, Modeling the interplay between water capillary transport and species diffusion in gas diffusion layers of proton exchange fuel cells using a hybrid computational fluid dynamics formulation, J. Power Sources 520 (2022) 230735.[3] P.A. García-Salaberri, Effect of thickness and outlet area fraction of macroporous gas diffusion layers on oxygen transport resistance in water injection simulations, Transp. Porous Media 145 (2022) 413-440.[4] P.A. García-Salaberri, I.V. Zenyuk, A General-Purpose Tool for Modeling Multifunctional Thin Porous Media (POREnet): From Pore Network To Effective Property Tensors, Heliyon (2023), submitted.[5] P.A. García-Salaberri, A. Sánchez-Ramos, A numerical analysis of the effect of layer-scale and microscopic parameters of membrane electrode assembly in proton exchange fuel cells under two-phase conditions, J. Power Sources (2023), accepted. Figure 1. Saturation distribution in the cathode MEA of a PEMFC operated at 70 oC and RH=0.95 at high stoichiometric conditions. The current density is I=0.5 A cm-2.- Figure 1

Substructures of the Weyl group and their physical applications

We study substructures of the Weyl group of conformal transformations of the metric of (pseudo)Riemannian manifolds. These substructures are identified by differential constraints on the conformal factors of the transformations which are chosen such that their composition is associative. Mathematically, apart from rare exceptions, they are partial associative groupoids, not groups, so they do not have an algebra of infinitesimal transformations, but this limitation can be partially circumvented using some of their properties cleverly. We classify and discuss the substructures with two-derivatives differential constraints, the most famous of which being known as the harmonic or restricted Weyl group in the physics literature, but we also show the existence of a lightcone constraint which realizes a proper subgroup of the Weyl group. We then show the physical implications that come from invariance under the two most important substructures, concentrating on classical properties of the energy-momentum tensor and a generalization of the quantum trace anomaly. We also elaborate further on the harmonic substructure, which can be interpreted as partial gauge fixing of full Weyl invariance using BRST methods. Finally, we discuss how to construct differential constraints of arbitrary higher-derivative order and present, as examples, generalizations involving scalar constraints with four and six derivatives.

Joint Probability Densities on Riemannian Manifolds are Symmetric Tensor Densities

This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially, we develop a binary data matrix to record the values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle-oriented coordinate and the generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar fields in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of the cumulative probability function defined on Riemannian manifolds also give the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and give the formal definition of joint probabilities by partial derivatives of the cumulative distribution function. The equivalence between the symmetrized covariant derivative and the generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.

A type of nearly parallel G-structures

We study properties of a certain symmetric tensor r induced by the intrinsic torsion of a Riemannian G–structure. This tensor naturally arises in the context of nearly Kähler manifolds and is parallel with respect to the canonical Hermitian connection. In general, we call a G-structure a second order parallel if ∇Gr=0 for a minimal G–connection ∇G. We show correlation with harmonicity of a G–structure and with G–structures with parallel torsion. An example of second order parallel G–structure is, apart from nearly Kähler manifolds and nearly parallel G2 structures, an α-Kenmotsu manifold.

London Dispersion Effects on the Structure and Properties of Nonlinear Optical BiB3O6 Crystal.

α-BiB3O6 (BiBO) is an important nonlinear optical (NLO) material with high efficiency for applications in harmonic generations and quantum technology. Owing to its low symmetry and cooperative Bi3+ lone pair arrangement, it has also exceptional large piezoelectric and electro-optic coefficients and strong anisotropies on other material characteristics. Previous theoretical calculations on its physical (mainly optical) properties often gave confusing results. It is found here that London dispersion (LD) tends to stabilize structures with closer pack entities like lone pair heavy ion Bi3+ with large polarizabilities, which is ignored in most previous density functional theory (DFT) calculations. Present study shows that without considering the LD effect, the structure of α-BiB3O6 (BiBO) was predicted with an over-estimated (by over 10 %) unique b-axis while underestimates a and overestimates c in a less amount. Consequently it is not possible to use the calculated structure to obtain meaningful properties of this important material. By applying a modified post-DFT LD correction based on linear combination of atomic orbitals (LCAO) and B3LYP functional, the experimental structure is well reproduced with the theoretical optimized one. Many important material property tensors of BiBO crystal are calculated in unprecedented precisions, including: dielectric constants (static and in THz range), elastic and elasto-optic constants, piezoelectric constants, refractive indices, NLO and electro-optic (EO) coefficients. Among them, theoretical calculation of the refractive indices in the THz range by diagonalizing the clamped-ion dielectric constants was firstly achieved at least for BiBO crystal. The calculation also confirms that BiBO has an exceptional large piezoelectric constant d22=40 pC/N and largest free EO coefficients , , on the order of 10 pm/V among borate crystals. The calculation also reveals that the large free EO coefficients are largely originated from the piezoelectric induced photo-elastic effect and for practical high speed applications only the clamped-ion EO coefficients take effect. The clamped ion EO coefficient of =-4.17 pm/V, =-2.61 pm/V are obtained for the first time and may be consulted if one seeks to design BiBO crystal as a high-speed EO modulator. Furthermore, full tensor matrix of the elasto-optic constants was obtained on the first time. Together with the calculated elastic constants, it can help to design acoustic optic modulating devices with preferable figure of merits 10 times that of traditional quartz crystal.

Problems and related results in algebraic vision and multiview geometry

This article is a survey of results in algebraic vision and multiview geometry. The starting point is the study of projective algebraic varieties which are critical for scene reconstruction. Initially studied for reconstructing static scenes in three-dimensional spaces, these critical loci are later investigated for dynamic and segmented scenes in higher-dimensional projective spaces. The formal analysis of the ideals of critical loci employs Grassmann tensors, introduced as crucial tools for determining these ideals and aiding the reconstruction process away from critical loci. A long-term goal of the authors with other co-authors involves two main aspects: firstly studying properties of Grassmann tensors, as rank, multi-rank and core, along with the varieties that parameterize these tensors; concurrently conducting an analysis of families of critical loci in various scenarios.

Temperature-dependent characterization of full tensor properties of [111]c poled Mn-doped 28PIN-43PMN-29PT single crystals

The temperature-dependent characterization of full tensor properties of single-domain relaxor-based single crystals (SCs) is important for understanding the influence of temperature on the properties of their multidomain SCs. However, no relevant results have been published because characterization is difficult to achieve using the traditional electric resonance method. In this Letter, the temperature-dependent elastic and piezoelectric properties of single-domain [111]c poled Mn-doped 28Pb(In1/2Nb1/2)O3-43Pb(Mg1/3Nb2/3)O3-29PbTiO3 SCs were investigated in the range of 20–80 °C by resonant ultrasound spectroscopy (RUS) using a rectangular parallelepiped sample. The temperature-dependent dielectric constants were calculated from the measured capacitances of the sample. The results are self-consistent because they were obtained from the same sample. The elastic constants obtained using the ultrasonic pulse-echo method agree closely with those obtained using RUS. Moreover, the experimental results of electric impedance spectrum agree closely with those simulated using the material constants characterized herein, indicating that the characterization is reliable.

Defining the geomechanical operating limits for subsurface CO2 storage

Carbon capture and storage (CCS) is a critical component of proposed pathways to limit global warming, though considerable upscaling is required to meet emissions reduction targets. Quantifying and managing the risks of fault reactivation is a leading barrier to scaling global CCS projects from current levels of ~40 million tonnes of carbon dioxide(CO2) per year (to target levels of several gigatonnes of CO2 per year), because CO2 injection into reservoirs can result in increased pore-fluid pressure and temperature changes, which can reduce the strength of rocks and faults and induce brittle failure. This can result in induced seismicity, whilst hydraulic fracturing of seals could provide pathways for CO2 leakage. Consequently, identifying favourable geomechanical conditions (typically determined through data on pre-injection rock stress, mechanical and elastic properties, and pore-fluid pressures) to minimise deformation of reservoirs and seals represents a key challenge in the selection of safe and effective sites for CCS projects. Critically, however, such geomechanical data are typically spatially limited (i.e. restricted to wells) and mainly consist of pre-injection crustal stress orientation measurements, rather than a full 3D description of the stress tensor and related geomechanical properties. This paper reviews some key geomechanical issues and knowledge gaps (particularly those associated with data availability and limitations) that need to be understood to enable successful reservoir and seal management for CCS projects. We also highlight recent advances in multi-scale and dimensional geomechanical modelling approaches that can be used to assess sites for the secure storage of CO2 as well as other gases, including hydrogen.

Second harmonic generation in structures with inhomogeneous magnetization distribution

The study of the interaction of laser radiation with ferromagnetic materials is not only an inexhaustible source of new effects, but also provides an opportunity to study magnetic media at the micro- and macroscale. This is especially important for the development of modern technologies to produce structures with fundamentally new magnetic and optical properties that can’t be observed in natural materials. The review presents the results of studies of nonlinear optical effects in ferromagnetic nano- and microstructures, as well as films of different compositions. The unique capabilities of nonlinear-optical diagnostics of anisotropic, vortex, exchange-biased magnetic structures, visualization of the micromagnetic structure of the surface layers of ferrite garnets, based both on the high sensitivity of the optical second harmonic generation method to the magnetic state of nanostructures and interfaces, and on the symmetry properties of high-order magnetizationinduced susceptibility tensor have been demonstrated.

Tensor schatten-p norm guided incomplete multi-view self-representation clustering

Incomplete multi-view clustering (IMC), which aims to handle incomplete data with missing views, has recently received more attention. According to the investigation of the existing IMC methods, they have at least one of the four limitations. First, some methods do not recover the missing view-specific information. Second, some approaches rely on fixed similarity graphs of incomplete views. Third, some methods need a separate spectral clustering step to produce the final cluster indicator. Last, most works utilize tensor nuclear norm to characterize the low-rank property of multi-view representation. These four limitations degrade the clustering performance. Hence, this paper proposes a tensor schatten-p norm guided incomplete multi-view self-representation clustering (TIMSRC) method to handle these four limitations simultaneously. TIMSRC models the missing instances as a data matrix for each view. And it integrates the missing samples inferring and complete self-representation graph learning into a unified framework. TIMSRC adopts a multi-view spectral clustering with adaptive weights to mine the semantic information while considering the contributions of multiple self-representing graphs. TIMSRC exploits the tensor schatten-p norm to enhance the low-rank property of a three-order tensor constructed with multiple self-representation graphs. We present an optimization algorithm to solve the objective function. The experiments demonstrate that TIMSRC outperforms the state-of-the-art IMC approaches.

Exploring Data Layout for Sparse Tensor Times Dense Matrix on GPUs

An important sparse tensor computation is sparse-tensor-dense-matrix multiplication (SpTM), which is used in tensor decomposition and applications. SpTM is a multi-dimensional analog to sparse-matrix-dense-matrix multiplication (SpMM). In this article, we employ a hierarchical tensor data layout that can unfold a multidimensional tensor to derive a 2D matrix, making it possible to compute SpTM using SpMM kernel implementations for GPUs. We compare two SpMM implementations to the state-of-the-art PASTA sparse tensor contraction implementation using: (1) SpMM with hierarchical tensor data layout; and, (2) unfolding followed by an invocation of cuSPARSE’s SpMM. Results show that SpMM can outperform PASTA 70.9% of the time, but none of the three approaches is best overall. Therefore, we use a decision tree classifier to identify the best performing sparse tensor contraction kernel based on precomputed properties of the sparse tensor.

Comparing local energy cascade rates in isotropic turbulence using structure-function and filtering formulations

Two common definitions of the spatially local rate of kinetic energy cascade at some scale $\ell$ in turbulent flows are (i) the cubic velocity difference term appearing in the ‘scale-integrated local Kolmogorov–Hill’ equation (structure-function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number 1250. While in the past observations of negative subfilter-scale energy flux (backscatter) have led to debates regarding interpretation and relevance of such observations, we argue that the interpretation of the local structure-function-based cascade rate definition is unambiguous since it arises from a divergence term in scale space. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered viscous dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. We find statistically robust evidence of inverse cascade when both the large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ‘vortex compression’ $R>0$ , $Q>0$ quadrant, where $R$ and $Q$ are velocity gradient invariants. Qualitatively similar but quantitatively much weaker trends are observed for the conditionally averaged subfilter-scale energy flux. Flow visualizations show consistent trends, namely that spatially, the inverse cascade events appear to be located within large-scale vortices, specifically in subregions when $R$ is large.

A general-purpose tool for modeling multifunctional thin porous media (POREnet): From pore network to effective property tensors

POREnet, a novel approach to model effective properties of thin porous media, TPM, is presented. The methodology allows the extraction of local effective property tensors by volume averaging from discrete pore networks, PNs, built on the tessellated continuum space of a TPM. The gradient theorem is used to describe 3D transport in bulk tessellated space, providing an appropriate metric to normalize network fluxes. Implemented effective transport properties include diffusivity, permeability, solid-phase conductivity, and entry capillary pressure and contact angle under two-phase conditions, considering multi-component materials with several solid phases and local contact resistances. Calculated property tensors can be saved on 3D image stacks, where interfacial and sub-CV scale features can be added before exporting data to CFD meshes for simulation. Overall, POREnet provides a general-purpose, versatile methodology for modeling TPM in an ample range of conditions within a single CFD framework. Among other advantages, coupling of PN and continuum models at TPM-channel interfaces is simplified, interfacial contact resistances can be included using robin boundary conditions, and transient multiphysics simulations can be implemented more easily using CFD. The code is tested against a miscellaneousness of examples extracted from electrochemical applications.