Isotropic Situation Research Articles

Thermal enhancement of couple stress fluid flow through anisotropic porous media

This study examines forced convective heat transfer via an anisotropic porous channel in a couple stress flow. The flow field is assumed to be fully developed and governed by the Darcy Brinkman Forchheimer equation. The thermal field is assumed to be developing. The channel walls are subjected to constant heat flux. Since the momentum equation is non-linear and the thermal energy equation is linear, coupled equations are solved numerically using the finite difference method. The variation in the bulk mean temperature is linear with the axial distance for all values of the couple stress parameter and Darcy number. In the absence of axial conduction and heat sources or sinks in the flow field, it is easy to see that the energy gained by the fluid up to an axial distance is twice the axial distance. The parameters, anisotropic permeability ratio, and anisotropic angle enhance the heat transfer. The couple stress parameter lessens the enhancement in heat transfer. Anisotropy is critical in heat transmission for Darcy number, DaH≤0.8. The heat transfer rate decreases by more than 40% due to couple stress fluid and anisotropic effects in the channel, as opposed to the Newtonian isotropic situation. This investigation's findings have been compared with previous experimental and numerical research.

Combining three sources of optical anisotropy in a tunable open-access microcavity: From theory to experiment

Photonic spin–orbit (SO) coupling is an important physical mechanism leading to numerous interesting phenomena in the systems of microcavity photons and exciton-polaritons. We report the effect of SO coupling in a tunable open-access microcavity embedded with anisotropic active media. The SO coupling associated with the TE–TM splitting results in an emergent anisotropy, which further leads to fine energy splittings allowing clear observation of the full set of eigenstates, in sharp contrast with the isotropic situation which leads to the isotropic eigenstates of spin vortices. We show that the photonic potential can be engineered by playing with the relation between the emergent anisotropy and the cavity ellipticity. All the experimental results are well reproduced by the degenerate perturbation theory. Our results constitute a significant extension to the research field of microcavity spinoptronics, with potential applications in polarization control and optical property measurement of photonic devices and materials.

Wellbore stability analysis of inclined wells in transversely isotropic formations accounting for hydraulic-mechanical coupling

As the main hydrocarbon reservoirs, sedimentary formations are usually anisotropic in elasticity, strength, and permeability. Traditional wellbore stability analysis assumes that the surrounding rocks are isotropic and elastic, whereas some analytical and numerical methods assume that the surrounding rocks are anisotropic in both elasticity and strength. Since the anisotropy of permeability is usually ignored, the wellbore instability mechanism in anisotropic formations may not be identified. Therefore, based on the poroelasticity theory and the assumption of generalized plane strain, this study proposed a pseudo-3D coupled hydraulic-mechanical finite element model by considering the anisotropies of elasticity, strength, and permeability. Taking the L203-x well as an example, the elastic and permeability anisotropies and the wellbore trajectory and stability in any bedding plane directions were analyzed parametrically. Results showed that the model simultaneously considering the strength and elastic anisotropies was in line with the actual hole enlargement rate of the L203-x well. With the increased anisotropy index of the elastic parameters, the anisotropic induced pore pressure is opposite to that of isotropic situation on the 2D cross-sectional plane of the wellbore, and the effective stress increased and was deflected at a certain angle. The effective hoop stress was biased toward the direction of higher stiffness, and the shear failure area that grew smaller gradually decreased. With the increased anisotropy index of permeability, the pore pressure rapidly increased along the direction parallel to the bedding plane, the effective radial stress of shape became rectangular along the bedding direction, the high-stress concentration zone of effective hoop stress changed from four to two, and the shear failure area grew smaller. The relative importance order of the anisotropy influences on the wellbore stability was thus: strength anisotropy > elastic parameter anisotropy > permeability anisotropy. A comparison of the well inclination and bedding plane orientation showed that, when the relative angle between the well axis and bedding normal was small, the influence of the bedding plane declined. In practical drilling engineering, avoiding drilling parallel to bedding planes is conducive to borehole stability.

Stochastic Intermittency Fields in a von Kármán Experiment

We discuss the application of stochastic intermittency fields to describe and analyse the statistical properties of time series of the generalised turbulence intensity in an anisotropic and inhomogeneous turbulent flow and provide a parsimonious description of the one-, two-, and three-point statistics. In particular, we show that the three-point correlations can be predicted from observed two-point statistics. Our analysis is motivated by observed stylised features of the energy dissipation in homogeneous and isotropic situations where these statistical properties are well represented within the framework of stochastic intermittency fields. We find a close resemblance and conclude that stochastic intermittency fields may be relevant in more general situations.

Observational consequences of Bianchi I spacetimes in loop quantum cosmology

Anisotropies generically dominate the earliest stages of expansion of a homogeneous universe. They are particularly relevant in bouncing models, since shears grow in the contracting phase of the cosmos, making the isotropic situation unstable. This paper extends the study of cosmological perturbations in loop quantum cosmology (LQC) to anisotropic Bianchi I models that contain a bounce followed by a phase of slow-roll inflation. We show that, although the shear tensor dilutes and the universe isotropizes soon after the bounce, cosmic perturbations retain memory of this short anisotropic phase. We develop the formalism needed to describe perturbations in anisotropic, effective LQC, and apply it to make predictions for the cosmic microwave background (CMB), while respecting current observational constraints. We show that the anisotropic bounce induces: (i) anisotropic features in all angular correlation functions in the CMB, and in particular a quadrupolar modulation that can account for a similar feature observed in the temperature map by the Planck satellite, and (ii) quantum entanglement between scalar and tensor modes, that manifests itself in temperature-polarization (T-B and E-B) correlations in the CMB.

Photoluminescence mapping of the strain induced in InP and GaAs substrates by SiNx stripes etched from thin films grown under controlled mechanical stress

We measured details of the strain/stress fields produced in GaAs(100) and InP(100) substrates by the presence of narrow dielectric stripes processed from thin films obtained by plasma-enhanced chemical vapor deposition with a residual and controlled built-in compressive or tensile stress. Micro-photoluminescence techniques were used, measuring either the spectral shift of the luminescence peak or the degree of polarization (DOP) of the spectrally integrated signal. These techniques provide information on different parts of the strain tensor (isotropic and anisotropic). The anisotropic deformation was found to change with the magnitude and sign of the initial built-in stress, and also with the stripe width. Using an analytical model, we were able to determine accurately several physical parameters which describe the stress/strain situation. The localized stress at the edges, expressed within an edge force concept, is shown to follow the expected initial built-in stress and also a stress reduction when the stripe width is decreased. This is interpreted as an evidence of some strain relaxation occuring near the stripe edges. This relaxation also impacts the shape of the DOP curves near the edges. The other important conclusion is the observation that the strain does not return to an isotropic situation (as in the case of an infinite thin film) in the central part of the stripes, even if the widths of these stripes are large (100 µm). The analytical model is developpeddeveloped and explained step-by-step. This analytical model produces quantitative data that describe the different effects observed. These data can be very helpful in the design and optimization of photonic devices when the photo-elastic effect can be significant, such as waveguides. The μPL measurements coupled with the model can also provide feedback to allow better control of the processing of such thin film devices.

Forced convection in a fluid saturated anisotropic porous channel with isoflux boundaries

Fully developed forced convective flow inside a channel filled with a porous material bounded by two impermeable walls subject to a constant heat flux is considered. We consider the Brinkman-Forchheimer equation to govern the flow inside the porous medium, which accounts for the presence of the inertial term. We assume that the porous medium is anisotropic in nature and the permeability is varying along all the directions so that it appears as a positive semidefinite matrix in the momentum equation. We have obtained velocity, temperature, and Nusselt number numerically due to the presence of the nonlinear quadratic term in the momentum equation. Asymptotic solutions for small Darcy number (∼10−3) and high Darcy number (∼10) are obtained. The asymptotic behavior of the Nusselt number is discussed. The key purpose of this paper is to study the effect of anisotropic permeability ratio, anisotropic angle, and inertial parameter on the hydrodynamic quantities and heat transfer for the configuration considered. In particular, we observe that for the moderate range of Darcy number, 10−2 to 102, inertia plays a significant role in the Nusselt number. We observe that inclusion of anisotropic permeability enhances the relative heat transfer rate by almost 20% compared to the corresponding isotropic situation. We present a detailed analysis about the inclusion of the permeability matrix in the Brinkman-Forchheimer extended Darcy momentum equation.

Fracture-initiation pressure prediction for transversely isotropic formations

Fracture-initiation pressure (FIP) is one of the most important considerations for the exploitation of petroleum and geothermal energy as well as the storage of hydrogen energy, CO2 and hydrocarbon. Wellbore pressures above the FIP maybe lead to formation fracturing, gas leakage and mud lost circulation. The effect of rock anisotropy on FIP is significant, but has not received enough attention. In this paper, the rock mechanical properties were investigated for transverse isotropic rock. Taking into account the anisotropic deformation, modulus, tensile strength and in-situ stress, a FIP prediction model was developed. The FIP models with isotropic situation, anisotropic modulus, anisotropic strength, and fully anisotropic situation were compared. The influence of anisotropic mechanical parameters, horizontal stress ratio (HSR) and pore pressure (PP) on the FIP were also analyzed. The results suggested that the transversely isotropic rock exhibits a distinct anisotropic characteristic. When the anisotropy of rock mechanical parameters was taken into account, the FIP may be higher or lower than that of isotropic model, and the amplitude of variation was about ±10%. Poisson's ratio anisotropy had a slight impact on the maximum and minimum FIPs. While the more significant the tensile strength anisotropy means the lower FIP. In addition, the influence of anisotropy on the FIP becomes increasingly pronounced with larger HSR and higher PP. The present paper can provide effective guidance to improve the drilling and hydraulic fracturing.

Floquet engineering of Haldane Chern insulators and chiral bosonic phase transitions

The realization of synthetic gauge fields has attracted a lot of attention recently in relation with periodically driven systems and the Floquet theory. In ultra-cold atom systems in optical lattices and photonic networks, this allows to simulate exotic phases of matter such as quantum Hall phases, anomalous quantum Hall phases and analogs of topological insulators. In this paper, we apply the Floquet theory to engineer anisotropic Haldane models on the honeycomb lattice and two-leg ladder systems. We show that these anisotropic Haldane models still possess a topologically non-trivial band structure associated with chiral edge modes (without the presence of a net unit flux in a unit cell), then referring to the quantum anomalous Hall effect. Focusing on (interacting) boson systems in s-wave bands of the lattice, we show how to engineer through the Floquet theory, a quantum phase transition between a uniform superfluid and a BEC (Bose-Einstein Condensate) analog of FFLO (Fulde-Ferrell-Larkin-Ovchinnikov) states, where bosons condense at non-zero wave-vectors. We perform a Ginzburg-Landau analysis of the quantum phase transition on the graphene lattice, and compute observables such as chiral currents and the momentum distribution. The results are supported by exact diagonalization calculations and compared with those of the isotropic situation. The validity of high-frequency expansion in the Floquet theory is also tested using time-dependent simulations for various parameters of the model. Last, we show that the anisotropic choice for the effective vector potential allows a bosonization approach in equivalent ladder (strip) geometries.

재순환유동 예측을 위한 κ-ε 난류모델 개선에 대한 연구

The standard <TEX>${\kappa}-{\varepsilon}$</TEX> and realizable <TEX>${\kappa}-{\varepsilon}$</TEX> models are adopted to improve the prediction performance on the recirculating flow. In this paper, the backward facing step flows are used to assess the prediction performance of the recirculation zone. The model constants of turbulence model are obtained by the experimental results and they have a different value according to the flow. In the case of an isotropic flow situation, decaying of turbulent kinetic energy should follow a power law behavior. In accordance with the power law, the coefficients for the dissipation rate of turbulent kinetic energy are not universal. Also, the other coefficients as well as the dissipation coefficient are not constant. As a result, a suitable coefficients can be varied according to each of the flow. The changes of flow over the backward facing step in accordance with model constants of the <TEX>${\kappa}-{\varepsilon}$</TEX> models show that the reattachment length is dependent on the growth rate(<TEX>${\lambda}$</TEX>) and the <TEX>${\kappa}-{\varepsilon}$</TEX> models can be improved the prediction performance by changing the model constants about the recirculating flow. In addition, it was investigated for the curvature correction effect of the <TEX>${\kappa}-{\varepsilon}$</TEX> models in the recirculating flow. Overall, the curvature corrected <TEX>${\kappa}-{\varepsilon}$</TEX> models showed an excellent prediction performance.

Spherical confinement of coulombic systems inside an impenetrable box: H atom and the Hulthén potential

The generalized pseudospectral method is used to study spherical confinement in two simple Coulombic systems: (i) well celebrated and heavily studied H atom (ii) relatively less explored Hulthén potential. In both instances, arbitrary cavity size as well as low and higher states are considered. Apart from bound state eigenvalues, eigenfunctions, expectation values, quite accurate estimates of the critical cage radius for H atom for all the 55 states corresponding to , are also examined. Some of the latter are better than previously reported values. Degeneracy and energy ordering under the isotropic confinement situation are discussed as well. The method produces consistently high‐quality results for both potentials for small as well as large cavity size. For the H atom, present results are comparable to best theoretical values, while for the latter, this work gives considerably better estimates than all existing work so far. © 2014 Wiley Periodicals, Inc.

On the elastic wave equation in weakly anisotropic VTI media

The knowledge of the wave equation is of fundamental importance for a good and satisfying understanding of the phenomena of wave propagation. However, it is unsatisfactory and inefficient to work with the full anisotropic wave equation in media that exhibit certain symmetries. We derive a specific elastic wave equation for weakly anisotropic VTI media by linearizing the expression of the stiffness tensor in terms of the Thomsen parameters. The resulting wave equation is a system of three coupled differential equations for the three components of the displacement vector. For δ = 0, the third equation becomes an independent equation for the third component of the particle displacement, identical to the isotropic situation, and the first two equations remain coupled. Using zero-order ray theory, we derive the associated eikonal and transport equations for q-P, q-SV and q-SH waves. These are finally reduced to the pseudo-acoustic case where the vertical S-wave velocity is zero. This allows for a better understanding of the pseudo-S-wave artefact in such media.

Crustal shear (S) velocity and Poisson's ratio structure along the INDEPTH IV profile in northeast Tibet as derived from wide-angle seismic data

SUMMARY From the S-wave data collected along a 270-km-long profile spanning the Kunlun mountains in NE Tibet, 14595 Sg phase arrivals and 21 SmS phase arrivals were utilized to derive a whole-crustal S velocity model and, together with a previously derived P velocity model, a Poisson's ratio (σ) model beneath the profile. The final tomogram for the upper 10–15 km of the crust reveals the lower velocities associated with the predominantly Neogene-Quaternary sediments of the Qaidam basin to the north and the higher velocities associated with the predominantly Palaeozoic and Mesozoic upper crustal sequences of the Songpan-Ganzi terrane and Kunlun mountains to the south. This study finds no evidence that the Kunlun mountains are involved in large-scale northward overriding of the Qaidam basin along a shallow south-dipping thrust. The σ in the upper 10–15 km of the crust are often lower than 0.25, indicating a preponderance of quartz-rich rocks in the upper crust beneath the profile. Below 10–15 km depth, the remainder of the crust down to the Moho has an average σ of 0.24 beneath the Songpan-Ganzi terrane and Kunlun mountains and 0.25 below the Qaidam basin. These low σ are similar to other low σ found along other profiles in the northeastern part of the plateau. Assuming an isotropic situation and no significant variation in σ between 10–15 km depth and the Moho, then the lower crust between 25–30 km depth below sea level and the Moho with P velocities varying from 6.6 km s−1 at the top to around 6.9 km s−1 at the base and σ of 0.24–0.25 should comprise intermediate granulites in the upper part transitioning to granulite facies metapelites in the lower part. As the pre-Cenozoic Qaidam basin crust has probably not lost any of its lower crust during the present Himalayan orogenic cycle in the Cenozoic and only has a σ of 0.245–0.25, then it appears that the pre-Cenozoic Qaidam basin crust involved in the collision is more felsic and thus weaker and more easily deformable than normal continental crust with a global average σ of 0.265–0.27 and the Tarim and Sichuan basin crusts. This situation then probably facilitates the collision and promotes the formation of new high plateau crust at the NE margin of Tibet. South of the Qaidam basin, the crust of the Songpan-Ganzi terrane and Kunlun mountains has an even lower average crustal σ of 0.23–0.24 and is thus presumably even weaker and more easily deformable than the crust beneath the Qaidam basin. This then supports the hypothesis of Karplus et al. that ‘the high Tibetan Plateau may be thickening northward into south Qaidam as its weak, thickened lower crust is injected beneath stronger Qaidam crust'.

Crustal and uppermost mantle velocity structure along a profile across the Pamir and southern Tien Shan as derived from project TIPAGE wide-angle seismic data

SUMMARY Utilizing seismic refraction/wide-angle reflection data from 11 approximately in-line earthquakes, 2-D P- and S-velocity models and a Poisson's ratio model of the crust and uppermost mantle beneath the southern Tien Shan and the Pamir have been derived along the 400-km long main profile of the TIPAGE (TIen shan—PAmir GEodynamic program) project. These models show that the crustal thickness varies from about 65.5 km close to the southern end of the profile beneath the South Pamir through about 73.6 km under Lake Karakul in the North Pamir, to about 57.7 km, 50 km south of the northern end of the profile in the southern Tien Shan. Average crustal P velocities are low with respect to the global average, varying from 6.26 to 6.30 km s−1. The average crustal S velocity varies from 3.54 to 3.70 km s−1 along the profile and thus average crustal Poisson's ratio (σ) varies from 0.23 beneath the central Pamir in the south central part of the profile to 0.265 towards the northern end of the profile beneath the southern Tien Shan. The main layer of the upper crust extending from about 2 km below the Earth's surface to 27 km depth below sea level (b.s.l.) has average P velocities of about 6.05–6.1 km s−1, except beneath the south central part of the profile where they decrease to around 5.95 km s−1. This is in contrast to the S velocities which range from 3.4 to 3.6 km s−1 and exhibit the highest values of 3.55–3.6 km s−1 where the P velocity is lowest. Thus, σ for the main layer of the upper crust is 0.26 beneath the profile except beneath the south central part of the profile where it decreases to 0.22. The low value of 0.22 for σ under the central Pamir, the along-strike equivalent of the Qiangtang terrane in Tibet, is similar to that within the corresponding layer beneath the northern Lhasa and southern Qiangtang terranes in central Tibet and is indicative of felsic rocks rich in quartz in the α state. The lower crust below 27 km b.s.l. has P velocities ranging from 6.1 km s−1 at the top to 7.1 km s−1 at the base. Further, σ for this layer is 0.27–0.28 towards the northern end of the profile but is low at about 0.24 beneath the central and southern parts of the profile, which is similar to the situation found in the northeast Tibetan plateau. The low values can be explained by felsic schists and gneisses in the upper part of the lower crust transitioning to granulite-facies and possibly also eclogite-facies metapelites in the lower part. Within the uppermost mantle, the average P velocity is about 8.10–8.15 km s−1 and σ is about 0.26. Assuming an isotropic situation, then a relatively cool (700–800°C) uppermost mantle beneath the profile is indicated. This would in turn indicate an intact mantle lid beneath the profile. An upper mantle reflector dipping from 104 km b.s.l., 120 km from the southern end of the profile to 86 km b.s.l., 155 km from the northern end of the profile has also been identified. The preferred model presented here for the crustal and lithospheric mantle structure beneath the Pamir calls for nearly horizontal underthrusting of relatively cool Indian mantle lithosphere, the leading edge of which is outlined by the Pamir seismic zone. This cool Indian mantle lithosphere is overlain by significantly shortening, warm Asian crust. The Moho trough that is a feature seen beneath some other orogenic belts, for example the Alps and the Urals, beneath the northern Pamir may mark the southern tip of the actively underthrusting Tien Shan crust along the Main Pamir thrust.

Parametric approximation of isotropic and anisotropic elastic flow for closed and open curves

Deckelnick and Dziuk (Math. Comput. 78(266):645–671, 2009) proved a stability bound for a continuous-in-time semidiscrete parametric finite element approximation of the elastic flow of closed curves in $${\mathbb{R}^d, d\geq2}$$ . We extend these ideas in considering an alternative finite element approximation of the same flow that retains some of the features of the formulations in Barrett et al. (J Comput Phys 222(1): 441–462, 2007; SIAM J Sci Comput 31(1):225–253, 2008; IMA J Numer Anal 30(1):4–60, 2010), in particular an equidistribution mesh property. For this new approximation, we obtain also a stability bound for a continuous-in-time semidiscrete scheme. Apart from the isotropic situation, we also consider the case of an anisotropic elastic energy. In addition to the evolution of closed curves, we also consider the isotropic and anisotropic elastic flow of a single open curve in the plane and in higher codimension that satisfies various boundary conditions.

Analysis of elastic functionally graded materials under large displacements via high-order tetrahedral elements

The purpose of this study is to present a position based tetrahedral finite element method of any order to accurately predict the mechanical behavior of solids constituted by functionally graded elastic materials and subjected to large displacements. The application of high-order elements makes it possible to overcome the volumetric and shear locking that appears in usual homogeneous isotropic situations or even in non-homogeneous cases developing small or large displacements. The use of parallel processing to improve the computational efficiency, allows employing high-order elements instead of low-order ones with reduced integration techniques or strain enhancements. The Green–Lagrange strain is adopted and the constitutive relation is the functionally graded Saint Venant–Kirchhoff law. The equilibrium is achieved by the minimum total potential energy principle. Examples of large displacement problems are presented and results confirm the locking free behavior of high-order elements for non-homogeneous materials.

Selective Smoothed Finite Element Method

The paper examines three selective schemes for the smoothed finite element method (SFEM) which was formulated by incorporating a cell-wise strain smoothing operation into the standard compatible finite element method (FEM). These selective SFEM schemes were formulated based on three selective integration FEM schemes with similar properties found between the number of smoothing cells in the SFEM and the number of Gaussian integration points in the FEM. Both scheme 1 and scheme 2 are free of nearly incompressible locking, but scheme 2 is more general and gives better results than scheme 1. In addition, scheme 2 can be applied to anisotropic and nonlinear situations, while scheme 1 can only be applied to isotropic and linear situations. Scheme 3 is free of shear locking. This scheme can be applied to plate and shell problems. Results of the numerical study show that the selective SFEM schemes give more accurate results than the FEM schemes.

Mode-coupling of low-frequency electromagnetic waves in dusty plasmas with temperature anisotropy

This paper studies the effects of the presence of dust particles with variable charge, in fully ionized, homogeneous, magnetized plasma of electrons and ions, with the electrons and ions described by bi-Maxwellian distributions in the equilibrium. The dispersion relation and the absorption rate are obtained for low frequency waves, with frequencies much lower than the ion cyclotron frequency. Two branches are obtained, identified as the whistler branch and the branch of circularly polarized waves, featuring damping due to the Landau damping process and to the collisional charging of the dust particles. The effects of the anisotropy of temperature on the damping rate of low frequency waves, and on the mode coupling which was demonstrated to occur in the isotropic situation, are numerically investigated. The results obtained show that in the anisotropic case the point of mode coupling is displaced to different values of dust density, and that a new point of mode coupling may appear from the effect of the temperature anisotropy.

Spontaneous Symmetry-Breaking Vortex Lattice Transitions in Pure Niobium

We report an extensive investigation of magnetic vortex lattice (VL) structures in single crystals of pure niobium with the magnetic field applied parallel to a fourfold symmetry axis, so as to induce frustration between the cubic crystal symmetry and hexagonal VL coordination expected in an isotropic situation. We observe new VL structures and phase transitions; all the VL phases observed (including those with an exactly square unit cell) spontaneously break some crystal symmetry. One phase even has the lowest possible symmetry of a two-dimensional Bravais lattice. This is quite unlike the situation in high-Tc or borocarbide superconductors, where VL structures orient along particular directions of high crystal symmetry. The causes of this behavior are discussed.

Practical modelling of porous media from second‐order statistics: the phase‐retrieval problem and the interpretation of the covariance

SummaryIn many disciplines, binary numerical porous media are commonly generated as realizations of a random process characterized by a limited set of morphological measurements, e.g. the conditioning and truncated Gaussian random field (GRF) model or the Monte Carlo simulated annealing (SA) reconstruction. Whether the output microstructures of a model are quantitative or qualitative depends largely on the information carried by the constraints that are implemented. We focus on the standard two‐point correlation function, also referred to as the covariance. The isotropic situation has been previously extensively studied. Here, we concentrate on a vector distance‐dependent covariance. Relying on practical solutions to the phase‐retrieval problem (retrieving an object from its Fourier modulus) encountered in general imaging, we show empirically that a finite binary two‐ or three‐dimensional actual sample can be recovered systematically to within a pixel from its correlation integral (the volume average covariance to within a scale factor). In random modelling, this characteristic, describing uniquely a single sample of finite size, must be simplified, i.e. reduced to its statistical content, prior to be fitted in a random model (GRF, SA) as the characteristic of a series of realizations of a porous medium. We consider a common simplification, i.e. truncation, in which that part of the covariance relating to the small‐scale features of the observed sample is preserved only. This arbitrary simplification is empirically supported by numerous published numerical experiments showing that the small‐scale content of a volume‐averaged covariance can be fairly well reproduced in realizations of various random models: its statistical nature is thus illustrated with the GRF model. The unique solution to the phase‐retrieval problem confers an important sense to this numerical agreement: the correlation integral being the most complete descriptor, the actual sample and the model outputs are considered as true analogues over scales smaller or equal to the cutoff length attached to the truncation. Thus, awareness of the phase‐retrieval problem supports on an empirical basis the generation of synthetic binary objects from a direct measurement on an available sample.