Isotropic Case Research Articles

Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection

We study the large-time behaviour of nonnegative solutions to the Cauchy problem for a nonlocal heat equation with a nonlinear convection term. The diffusion operator is the infinitesimal generator of a stable Lévy process, which may be highly anisotropic. The initial data are assumed to be bounded and integrable. The mass of the solution is conserved along the evolution, and the large-time behaviour is given by the source-type solution, with the same mass, of a limit equation that depends on the relative strength of convection and diffusion. When diffusion is stronger than convection the original equation simplifies asymptotically to the purely diffusive nonlocal heat equation. When convection dominates, it does so only in the direction of convection, and the limit equation is still diffusive in the subspace orthogonal to this direction, with a diffusion operator that is a “projection” of the original one onto the subspace. The determination of this projection is one of the main issues of the paper. When convection and diffusion are of the same order the limit equation coincides with the original one.Most of our results are new even in the isotropic case in which the diffusion operator is the fractional Laplacian. We are able to cover both the cases of slow and fast convection, as long as the mass is preserved. Fast convection, which corresponds to convection nonlinearities that are not locally Lipschitz, but only locally Hölder, has not been considered before in the nonlocal diffusion setting.

THE ANEURISMAL ABDOMINAL AORTA WALL MECHANICAL RESISTANCE LOSS AND COLLAGEN FIBRE PATHOLOGICAL REORIENTATION. A NUMERICAL STUDY

The biomechanical properties’ changes of the abdominal aortic aneurysms’ (AAA) walls are closely related to the pathological degeneration of the smooth muscle cells and the main fibrous components (collagen and elastin). In this study, the passive mechanical response of the aneurysmal aortic wall is computationally investigated as a function of the dispersion and orientation of collagen. So, to better understand how the ultimate resistance of the diseased wall varies, several numerical simulations on models of AAA specimens have been performed, using the Gasser-Ogden-Holzapfel anisotropic hyperplastic constitutive model where the dispersion and orientation parameters are explicitly introduced. The simulations were carried out for a variation of the average orientation of the collagen from 0° to 90° with a dispersion that varies from 0 (orthotropic case) to 1/3 (isotropic case). The results of the numerical simulations show that an increase in the dispersion and the angle of orientation in the aneurysm leads to a decrease in the circumferential resistance of the diseased artery. Such results can help to better understand the negative effects of the disease on the arterial wall and to target the necessary therapy.

Anisotropic Segre [(11)(1,1)] dark energy following a particular equation of state

A generally anisotropic equation of state originally derived in the context of Newman-Janis rotating systems allows for vacuum energy at a specific density. In this paper we examine the possibility of using that equation of state for cosmological dark energy. We treat the case of large scale ordering of the directions of the energy-momentum tensor eigenvectors with a Bianchi cosmological model, and treat the case where the ordering is random on small scales with an effectively isotropic FLRW system. We find particular spacetimes which evolve towards a vacuum energy/ de Sitter like configuration in either case. In the anisotropic Bianchi case, the system can have behavior reminiscent of big bounce cosmologies, in which the matter content approaches vacuum energy at large scale factor and can behave in a variety of ways at small scale factor. For particular conditions in the effectively isotropic case, we can evolve between true and false vacuum configurations, or between radiation like and vacuum energy configurations. We also show how some simpler equations of state behave under the same assumptions to elucidate the methods for analysis.

Tunability of Half Cycle Cutoff Harmonics with Inhomogeneously Enhanced Laser Pulse

For homogeneous driving, half cycle harmonics and its corresponding half cycle cutoff (HCO) show prominent spectral features, allowing one to produce an isolated attosecond pulse with suitable filtering, or vice versa the retrieval of the driving pulse itself. The temporal profile and spatial dependence of the inhomogeneously enhanced field are two important factors that determine the high harmonic generation (HHG) near a plasmonic nanostructure. This leads us to the question of how the HHG spectra and, in particular, the corresponding half cycle harmonics modify with different types of inhomogeneously enhanced fields. To elucidate this, we have made a comparative study of the HHG in three different types of inhomogeneously enhanced laser pulses by employing the time-dependent Schrödinger equation in one dimension. Within our chosen parameter range, the HCO in cutoff and mid-plateau regimes shift towards higher order with the increase of strength of the inhomogeneity in isotropic case. In anisotropic inhomogeneity, the cutoff HCO shifts towards the higher order but the mid-plateau HCO shifts towards lower order with the increase of strength of inhomogeneity. With increasing carrier envelope phase (CEP), the enhanced HCO in the lower-order harmonic region shifts towards higher orders. This shift is nearly linear from near the above threshold to mid-plateau region and becomes saturated in the near cutoff region. The harmonic spectra is modulo-π periodic for the isotropic inhomogeneity and it is modulo-2π periodic for the anisotropic inhomogeneity. This extension of periodicity increases the tunability of the enhanced HCO harmonics with CEP in the anisotropic inhomogeneity than the CEP tuning of the HCO harmonics in the isotropic inhomogeneity or vice versa the retrieval of CEP.

Monte Carlo study of the phase transitions in the classical XY ferromagnets with random anisotropy

ABSTRACT The three-dimensional anisotropic classical XY ferromagnet has been investigated by extensive Monte Carlo simulation using the Metropolis single spin flip algorithm. The magnetisation (M) and the susceptibility (χ) are measured and studied as functions of the temperature of the system. For constant anisotropy, the ferro-para phase transition has been found to take place at a higher temperature than that observed in the isotropic case. The system gets ordered at higher temperatures for higher values of the strength of anisotropy. The opposite scenario is observed in the case of random anisotropy. For all three different kinds of statistical distributions (uniform, Gaussian, and bimodal) of random anisotropy, the system gets ordered at lower temperatures for higher values of the width of the distribution of anisotropy. We have provided the phase boundaries in the case of random anisotropy. The critical exponents for the scaling laws and are estimated through the finite size analysis.

The proportion of triangles in a class of anisotropic Poisson line tessellations

AbstractStationary Poisson processes of lines in the plane are studied, whose directional distributions are concentrated on $k\geq 3$ equally spread directions. The random lines of such processes decompose the plane into a collection of random polygons, which form a so-called Poisson line tessellation. The focus of this paper is to determine the proportion of triangles in such tessellations, or equivalently, the probability that the typical cell is a triangle. As a by-product, a new deviation of Miles’s classical result for the isotropic case is obtained by an approximation argument.

Three-Dimensional Separate and Joint Inversions of Multi-Component Frequency-Domain Airborne Electromagnetic Data: Synthetic Model Studies.

Airborne electromagnetic (AEM) surveys using airborne mobile platforms enable rapid and efficient exploration of areas where groundwork is difficult. They have been widely used in fields such as shallow resource exploration and environmental engineering. Three-dimensional AEM inversion is the main technique used in fine structural interpretation. However, most current methods focus on separate component data inversions, which limit the kinds of structures that can be recovered in the inversion results. To address this issue, a method for the robust 3D joint inversion of multicomponent frequency-domain AEM data was developed in this study. First, a finite element method based on unstructured tetrahedral grids was used to solve the forward problem of frequency-domain AEM data for both isotropic and anisotropic media. During inversion, a limited-memory quasi-Newton (L-BFGS) method was used to reduce the memory requirements and enable the joint inversion of large-scale multicomponent AEM data. The effectiveness of our algorithm was demonstrated using synthetic models for both isotropic and anisotropic cases, with 5% Gaussian noise added to the modeling data to simulate the measured data for separate and joint inversions. The results of the synthetic models show that joint inversion has advantages over separate inversion in that it enables the recovery of finer underground structures and provides a novel approach for the fine interpretation of frequency-domain AEM data.

Static traversable wormhole solutions in f(R,ℒm) gravity

In this study, we explore the new wormhole solutions in the framework of new modified $f(R,L_m)$ gravity. To obtain a characteristic wormhole solution, we use anisotropic matter distribution and a specific form of energy density. As second adopt the isotropic case with a linear EoS relation as a general technique for the system and discuss several physical attributes of the system under the wormhole geometry. Detailed analytical and graphical discussion about the matter contents via energy conditions is discussed. In both cases, the shape function of wormhole geometry satisfies the required conditions. Several interesting points have evolved from the entire investigation along with the features of the exotic matter within the wormhole geometry. Finally, we have concluding remarks.

A finite element modeling for anisotropic dielectric elastomer energy harvesters with inhomogeneous displacement fields

In this paper, we are to investigate the effects of imparting anisotropy to dielectric elastomers (DEs) to evaluate the promising capabilities of this phenomenon in energy harvesting (EH) enhancement. To this end, we employ the principle of virtual work to obtain the governing equations and the boundary conditions of dielectric elastomers at finite strains. As for the material law, it incorporates three parts, including an isotropic, an anisotropic, and an electric one with no modes of dissipation. Having to deal with inhomogeneous displacement fields necessitates the employment of finite element (FE) simulations. Moreover, a staggered algorithm has been put into use which is capable of reducing computational expense while producing the same results as that of a fully coupled solution. Further, F-bar method has been selected to alleviate the issue of volumetric locking. The aforementioned finite element implementation is conducted through a computer program. It is noteworthy that all the terms involved in FE modeling, particularly electroelastic moduli and the terms originated from the follower load assumption are fully derived. Three energy harvesting applications, including a cylindrical tube, a diaphragm, and an annular membrane which satisfy the axisymmetric assumptions, are investigated. In the interest of verifying the developed axisymmetric element, the finite element results have been compared with that of analytical ones for a one-dimensional homogenous actuation problem. Intended to reveal the efficacy of imparting anisotropy to DEs in EH, we fix all the other contributing factors in the energy harvesting cycle for each application. As a result, corresponding isotropic and anisotropic cases become possible whose only difference is in the existence or absence of anisotropic fibers. Eventually, through numerical simulations it is proved that imparting anisotropy to dielectric elastomers in most cases culminates in favor of energy harvesting. Particularly, the maximum amount of relative energy harvesting difference of corresponding isotropic and anisotropic cases for the cylindrical tube, the diaphragm, and the annular membrane is achieved to be 27.75%, 10.61%, and 19.76%, respectively, in favor of the anisotropic cases.

High-dimensional approximation with kernel-based multilevel methods on sparse grids

Moderately high-dimensional approximation problems can successfully be solved by combining univariate approximation processes using an intelligent combination technique. While this has so far predominantly been done with either polynomials or splines, we suggest to employ a multilevel kernel-based approximation scheme. In contrast to those schemes built upon polynomials and splines, this new method is capable of combining arbitrary low-dimensional domains instead of just intervals and arbitrarily distributed points in these low-dimensional domains. We introduce the method and analyse its convergence in the so-called isotropic and anisotropic cases.

Three-dimensional nonlocal models of deformable ferroelectrics: A thermodynamically consistent approach

Within the framework of continuum thermodynamics, the paper develops a scheme for the study of piezo-ferroelectric materials undergoing large deformations. The ferroelectric polarization is decomposed into the sum of a reversible and a residual part which is considered as an independent variable. The modeling of the constitutive properties is made simpler by using referential, Euclidean invariant quantities. Constitutive functions depend on a set of variables that includes their time derivatives and gradients, and therefore must be consistent with a nonlocal statement of the second law of thermodynamics where the entropy production is represented as the sum of a non-negative supply and a flux. Both terms are also assigned by means of constitutive functions. A new and quite general model relating the residual-polarization rate and the ‘electric Gibbs free entropy’ is established. This thermodynamic potential is modeled according to the Landau-Devonshire approach and appropriate explicit expressions are proposed for anisotropic materials. Consequently, a new explicit evolution equation for the polarization vector is obtained for both high and low temperatures. In particular, the Landau-Devonshire scalar model is recovered in the isotropic case. Under the assumption of small strains and small polarization gradients, hysteresis and electromechanical coupling are described for a simple one-dimensional model. The advantage of our original approach is that a few constitutive parameters provide a good fit of material behavior.

Microwave backscatter enhancement using radial anisotropy in biomimetic core-shell spheres

Enhanced backscattering of microwave radiation is demonstrated experimentally in a biomimetic radially anisotropic spherical metamaterial component. The core-shell device replicates the optical function of nanospheres observed in the tapetum reflector of the compound eye of the shrimp Litopenaeus vannamei (Boone, 1931) and translates the effect from the optical domain to microwave frequencies. Analytical Mie theory calculations and numerical-method simulations are used to describe the origin of the observed scattering from a single dielectric sphere in terms of its multipolar Mie resonances. The fabrication of components using additive manufacture and their experimental characterization are described. The results show that the introduction of radial anisotropy in the shell more than doubles the monostatic radar cross section compared to the equivalent isotropic case. This work represents a practical demonstration of a synthetic bio-inspired structure, harnessing performance-enhancing adaptations that have evolved in nature. The results augment the range of techniques available for the control of electromagnetic scattering with relevance to applications in the manipulation of radar return signals.

Theoretical Study of the Effect of Permeability Tensor upon Drainage of Soils

the influence of permeability tensor upon drainage of anisotropic soils under ponded water and steady recharge (rainfall) is theoretically investigated. Tensorial permeability has led to the formulation of mixed type partial differential equations. Since there is no analytical solution to this problem, the formulation is therefore solved numerically by the method of finite elements. The finite element formulation is implemented into a computer model which can be applied to any problem of seepage under steady state conditions. Two different example problems representing two different flow conditions under full anisotropy have been studied. Results of the model for the isotropic case were checked against exact mathematical solutions derived analytically for isotropic soils and found to be accurate which indicates that using this model for anisotropic soils is safe and sound

Anisotropic Behavior of S-Wave and P-Wave States of Heavy Quarkonia at Finite Magnetic Field

We studied the effect of momentum space anisotropy on heavy quarkonium states using an extended magnetized effective fugacity quasiparticle model (EQPM). Both the real and imaginary part of the potential has been modified through the dielectric function by including the anisotropic parameter ξ. The real part of the medium-modified potential becomes more attractive in the presence of the anisotropy and constant magnetic field. The binding energy of the 1S, 2S, and 1P quarkonium states including anisotropy effects for both the oblate and the isotropic case were studied. We find that the binding energy of QQ¯ states becomes stronger in the presence of anisotropy. However, the magnetic field is found to reduce the binding energy. The thermal width of the charmonium and bottomonium 1S states has been studied at constant magnetic field eB=0.3 GeV2 for isotropic and prolate cases. The effect of magnetic field on the mass spectra of the 1P state for the oblate case was also examined. The dissociation temperature for the 1S, 2S, and 1P states of charmonium and bottomonium has been determined to be higher for the oblate case with respect to the isotropic case.

Wormhole solutions in [formula omitted] gravity

In this work, we intend to explore wormhole geometries in the framework of f(R,Lm) gravity. We derive the field equations for the generic f(R,Lm) function by assuming the static and spherically symmetric Morris–Thorne wormhole metric. Then we consider two non-linear f(R,Lm) model, specifically, f(R,Lm)=R2+Lmα and f(R,Lm)=R2+(1+λR)Lm, where α and λ are free model parameters. We obtain the wormhole solutions by assuming three cases, namely, a linear barotropic EoS, anisotropic EoS, and isotropic EoS corresponding to model I. We observe that for both barotropic and anisotropic cases, the corresponding wormhole solutions obey the flaring-out condition under asymptotic background, while for the isotropic case, the shape function does not follow the flatness condition. Also, we find that the null energy condition exhibits negative behavior in the vicinity of the throat. Further, we consider two different shape functions to investigate the behavior of model II. We find some constraints on the model parameter for which the violation of the null energy condition exhibits. Finally, we employ the volume integral quantifier to calculate the amount of exotic matter required near the wormhole throat for both models. We conclude that the modification of standard GR can efficiently minimize the use of exotic matter and provide stable traversable wormhole solutions.

Computation of minimal covariants bases for 2D coupled constitutive laws

We produce minimal integrity bases for both isotropic and hemitropic invariant algebras (and more generally covariant algebras) of most common bidimensional constitutive tensors and — possibly coupled — laws, including piezoelectricity law, photoelasticity, Eshelby and elasticity tensors, complex viscoelasticity tensor, Hill elasto-plasticity, and (totally symmetric) fabric tensors up to twelfth-order. The concept of covariant, which extends that of invariant is explained and motivated. It appears to be much more useful for applications. All the tools required to obtain these results are explained in detail and a cleaning algorithm is formulated to achieve minimality in the isotropic case. The invariants and covariants are first expressed in complex forms and then in tensorial forms, thanks to explicit translation formulas which are provided. The proposed approach also applies to any n-uplet of bidimensional constitutive tensors.

Energy Equivalence Based Estimation of Hybrid Composites Mechanical Properties.

Hybrid composites, usually combining natural and synthetic reinforcing filaments, have gained a lot of attention due to their better properties than traditional two-component materials. For structural applications of hybrid composites, there is a need to precisely determine their mechanical properties on the basis of the mechanical properties, volume fractions, and geometrical distributions of constituent materials. The most common methods, such as the rule of mixture, are inaccurate. More advanced methods, giving better results in the case of classic composites, are difficult to apply in the case of several types of reinforcement. In the present research, a new estimation method is considered, which is simple and accurate. The approach is based on the definition of two configurations: the real, heterogeneous, multi-phase hybrid composite configuration, and the fictitious, quasi-homogeneous one, in which the inclusions are "smeared out" over a representative volume. A hypothesis of the internal strain energy equivalence between the two configurations is formulated. The effect of reinforcing inclusions on the mechanical properties of a matrix material is expressed by functions of constituent properties, their volume fractions, and geometrical distribution. The analytical formulas are derived for an isotropic case of a hybrid composite reinforced with randomly distributed particles. The validation of the proposed approach is performed by comparing the estimated hybrid composite properties with the results of other methods, and with experimental data available in the literature. It is shown that a very good agreement is obtained between experimentally measured hybrid composite properties and their predictions resulting from the proposed estimation method. The estimation errors are much lower than the errors of other methods.

Optimal method for reconstructing polychromatic maps from broadband observations with an asymmetric antenna pattern

Broadband time-ordered data obtained from telescopes with a wavelength-dependent, asymmetric beam pattern can be used to extract maps at multiple wavelengths from a single scan. This technique is especially useful when collecting data on cosmic phenomena such as the cosmic microwave background (CMB) radiation, as it provides the ability to separate the CMB signal from foreground contaminants. We develop a method to determine the optimal linear combinations of wavelengths (``colors'') that can be reconstructed for a given telescope design and the number of colors that are measurable with high signal-to-noise ratio. The optimal colors are found as eigenvectors of a matrix derived from the inverse noise covariance matrix. When the telescope is able to scan the sky isotropically, it is useful to transform to a spherical harmonic basis, in which this matrix has a particularly simple form. We propose using the optimal colors determined from the isotropic case even when the actual scanning pattern is not isotropic (e.g., covers only part of the sky). We perform simulations showing that maps in multiple colors can be reconstructed accurately from both full-sky and partial-sky scans. Although the original motivation for this research comes from mapping the CMB, this method of polychromatic mapmaking will have broader applications throughout astrophysics.

Bias in the Representative Volume Element method: Periodize the Ensemble Instead of Its Realizations

We study the representative volume element (RVE) method, which is a method to approximately infer the effective behavior ahom\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_{\ extrm{hom}}$$\\end{document} of a stationary random medium. The latter is described by a coefficient field a(x) generated from a given ensemble ⟨·⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle \\cdot \\rangle $$\\end{document} and the corresponding linear elliptic operator -∇·a∇\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\ abla \\cdot a\ abla $$\\end{document}. In line with the theory of homogenization, the method proceeds by computing d=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=3$$\\end{document} correctors (d denoting the space dimension). To be numerically tractable, this computation has to be done on a finite domain: the so-called representative volume element, i.e., a large box with, say, periodic boundary conditions. The main message of this article is: Periodize the ensemble instead of its realizations. By this, we mean that it is better to sample from a suitably periodized ensemble than to periodically extend the restriction of a realization a(x) from the whole-space ensemble ⟨·⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle \\cdot \\rangle $$\\end{document}. We make this point by investigating the bias (or systematic error), i.e., the difference between ahom\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a_{\ extrm{hom}}$$\\end{document} and the expected value of the RVE method, in terms of its scaling w.r.t. the lateral size L of the box. In case of periodizing a(x), we heuristically argue that this error is generically O(L-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(L^{-1})$$\\end{document}. In case of a suitable periodization of ⟨·⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle \\cdot \\rangle $$\\end{document}, we rigorously show that it is O(L-d)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(L^{-d})$$\\end{document}. In fact, we give a characterization of the leading-order error term for both strategies and argue that even in the isotropic case it is generically non-degenerate. We carry out the rigorous analysis in the convenient setting of ensembles ⟨·⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle \\cdot \\rangle $$\\end{document} of Gaussian type, which allow for a straightforward periodization, passing via the (integrable) covariance function. This setting has also the advantage of making the Price theorem and the Malliavin calculus available for optimal stochastic estimates of correctors. We actually need control of second-order correctors to capture the leading-order error term. This is due to inversion symmetry when applying the two-scale expansion to the Green function. As a bonus, we present a stream-lined strategy to estimate the error in a higher-order two-scale expansion of the Green function.

Roughness-Resolved Large-Eddy Simulation of Additive Manufacturing-Like Channel Flows

Abstract In the last decade, progresses in additive manufacturing (AM) have paved the way for optimized heat exchangers whose disruptive design will heavily rely on predictive numerical simulations. However, due to typical roughness induced by AM, current wall models used in steady and unsteady 3D Navier–Stokes simulations do not take into account such characteristics. For the development and assessment of novel wall models for AM, a high-fidelity roughness-resolved large-eddy simulation (RRLES) database is built. This article describes the numerical setup and the methodology used for conducting RRLES, from surface generation to postprocessing. In addition, three different cases representing two printing directions plus a streamwise and spanwise isotropic case are investigated. While the roughness distributions are the same in the three cases, the effective slope (ES) is very different, and the impact of this parameter on turbulence and heat transfer is analyzed at different Reynolds numbers.