Logarithmic Behavior Research Articles

Dynamical tidal Love numbers of Kerr-like compact objects

We develop a framework to compute the tidal response of a Kerr-like compact object in terms of its reflectivity, compactness, and spin, both in the static and the frequency-dependent case. Here we focus on the low-frequency regime, which can be solved fully analytically. We highlight some remarkable novel features, in particular, the following: (i) Even in the zero-frequency limit, the tidal Love numbers (TLNs) depend on the linear-in-frequency dependence of the object’s reflectivity in a nontrivial way. (ii) Intriguingly, although the static limit of the (phenomenologically more interesting) frequency-dependent TLNs is continuous, it differs from the strictly static TLNs for compact objects other than black holes. This shows that earlier findings regarding the static TLNs of ultracompact objects correspond to a measure-zero region in the parameter space, though the logarithmic behavior of the TLNs in the black hole limit is retained. (iii) In the nonrotating case, the TLNs in the zero-frequency limit (just like for a black hole), except when the reflectivity is R=1+O(Mω), in which case they vanish with a model-dependent scaling, which is generically logarithmic, in the black-hole limit. The TLNs initially grow with frequency, for any nonzero reflectivity, and then display oscillations and resonances tied up with the quasinormal modes of the object. (iv) For rotating compact objects, the TLNs decrease when the reflectivity decreases or the rotation parameter increases. Our results lay the theoretical groundwork to develop model-independent tests of the nature of compact objects using tidal effects in gravitational-wave signals. Published by the American Physical Society 2024

Isothermal magnetization and magnetoresistive variations in trilayer (La2/3Sr1/3MnO3/γ-Fe2O3/La2/3Sr1/3MnO3) hetero-structure

We report the magnetic field dependent magnetization and magnetoresistance (MR) properties of La2/3Sr1/3MnO3 (LSMO)/ γ -Fe2O3/LSMO trilayer heterostructure and single layer LSMO film grown on SiO2/Si (100) substrates utilizing Pulsed Laser Deposition technique. The metal- insulator-metal configuration is a magnetic tunnel junction topology, which is a parallel network of two metallic layers (LSMO) and one insulating layer ( γ -Fe2O3) in current-in-plane (CIP) geometry. The intrinsically inhomogeneous polycrystalline trilayer film shows much lower (almost half ) coercivity, compared to single layer LSMO film. The MR-H [MR = (ρ (H)-ρ (0))/ρ (0)] behavior of the films is studied under two regimes namely, Low Field Magnetoresistance (LFMR) and High Field Magnetoresistance (HFMR) at 5 K and 300 K in the field range of 0–7 T. Several equations were developed to simulate the experimental MR-H data of the studied samples. For both the films, in the LFMR region (0 T < H ≤ 1 T @ 5 K), the variation in MR exhibits a linear increase with H, followed by a logarithmic behavior in the HFMR region (1 T < H ≤ 7 T @ 5 K). For the trilayer film in CIP geometry, a negative MR of 16% is achieved at 5 K and 1 T field conditions, while LSMO single layer shows a negative MR of 13% at same temperature and field conditions. The MR obtained at high field (7 T) for both the films is quantitatively equal with a value of 38% @ 5 K and 15% @ 300 K. We obtained significantly better MR-H results for the trilayer in current-perpendicular-to-plane (CPP) configuration, where the two metallic layers and an insulating layer are in series. In the CPP configuration, MR is 21% @ 5 K and 1 T field, while it reached to 44% at 5 K and 7 T field. At room temperature, the trilayer heterostructure shows MR of 17% at 7 T field condition. At a higher field of 9 T, trilayer film in CPP mode exhibits MR value of 48% @ 5 K and 23% @ 300 K. Further, the anti-parallel and parallel magnetization states of the MIM device are well manifested in CIP and CPP geometries.

Modelling the Relationship between Water Jetting Parameters and Material Failure in Heat Exchanger Tubes

The Zeeland-Flemish region has a robust process industry where heat exchangers (HEX) are essential for managing heat transfer. However, Fouling in HEX occurs when deposits of contaminants form on surfaces affecting heat transfer. HEX maintenance/cleaning can harm the material of construction (MoC). This study explores how altering Water Jetting (WJ) parameters affects MoC failure mechanisms. This knowledge can optimize processes to prevent unwanted MoC failure while achieving desired fouling control. In this study, a three-factorial experiment was designed to investigate how increased water pressure and flow rates impact the structural health of copper used in HEX tubes during WJ cleaning. Then, we compared these results with experiments using steel as the MoC. Statistical and mathematical analysis were employed to understand the effect of process parameters on damage mechanisms and identify the most influential parameter. For copper samples, we observed that higher water pressure consistently increased damage across all flow rates, following a linear trend of α_p =0.001(gm loss/gm sample. Kpsi). Flow rate's impact on damage exhibited logarithmic behavior, which can be split into two ranges. At low to medium flow levels, increased flow rates raised damage at a rate of α_f =0.007(gm loss/gm sample. gpm). However, at high flow rates, the increase in flow had no effect on the damage as it was attributed solely to pressure. Comparing steel and copper at high pressure levels, it was found that steel experienced a lower linear increase in damage, β_f =0.0036(gm loss/gm sample. gpm), compared to α_f for copper. These results offer insights for optimizing water jetting cleaning processes to minimize material damage during HEX maintenance, enhancing overall efficiency.

A Curvilinear Transfer Function for Wide Dynamic Range Compression with Expansion

Wide Dynamic Range Compression in hearing aids is becoming increasingly more complex as the number of channels and adjustable parameters grow. At the same time, there is growing demand for customization and user self-adjustment of hearing aids, necessitating a balance between complexity and user accessibility. Compression in hearing aids is governed by the input-output transfer function, which relates input magnitude to output magnitude, and is typically defined as a combination of linear piecewise segments resembling logarithmic behavior. This work presents an alternative to the conventional compression transfer function that consolidates multiple compression parameters and revisits expansion in hearing aids. The curvilinear transfer function is a continuous curve with logarithm-like behavior, governed by two parameters—gain and compression ratio. Experimental results show that curvilinear compression reduces the amplification of low-level noise, improves signal-to-noise ratio by up to 1.0 dB, improves sound quality as measured by the Hearing Aids Speech Quality Index by up to 6.7%, and provides comparable intelligibility as measured by the Hearing Aids Speech Perception Index, with simplified parameterization compared to conventional compression. The consolidated curvilinear transfer function is highly applicable to over-the-counter hearing aids and offers more capabilities for customization than current prominent over-the-counter and self-adjusted hearing aids.

Rethinking the Roughness Height: An Improved Description of Temperature Profiles over Short Vegetation

In this study, we present an extension to the Monin–Obukov similarity theory (MOST) for the roughness sublayer (RSL) over short vegetation. We test our theory using temperature measurements from fiber optic cables in an array-shaped set-up. This provides a high vertical measurement resolution that enables us to measure the sharp temperature gradients near the surface. It is well-known that MOST is invalid in the RSL as the flow is distorted by roughness elements. However, to derive the surface temperature, it is common practice to extrapolate the logarithmic profiles down to the surface through the RSL. Instead of logarithmic behaviour defined by MOST near the surface, our observations show near-linear temperature profiles. This log-to-linear transition is described over an aerodynamically smooth surface by the Van Driest equation in classical turbulence literature. Here we propose that the Van Driest equation can also be used to describe this transition over a rough surface, by replacing the viscous length scale with a surface length scale Ls\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_s$$\\end{document} that represents the size of the smallest eddies near the grass structures. We show that Ls\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_s$$\\end{document} scales with the geometry of the vegetation and that the model shows the potential to be scaled up to tall canopies. The adapted Van Driest model outperforms the roughness length concept in describing the temperature profiles near the surface and predicting the surface temperature.

Impact of dephasing probes on incommensurate lattices

We investigate open quantum dynamics for a one-dimensional incommensurate Aubry–André–Harper lattice chain, a part of which is initially filled with electrons and is further connected to dephasing probes at the filled lattice sites. This setup is akin to a step-initial configuration where the non-zero part of the step is subjected to dephasing. We investigate the quantum dynamics of local electron density, the scaling of the density front as a function of time both inside and outside of the initial step, and the growth of the total number of electrons outside the step. We analyze these quantities in all three regimes, namely, the de-localized, critical, and localized phases of the underlying lattice. Outside the initial step, we observe that the density front spreads according to the underlying nature of single-particle states of the lattice, for both the de-localized and critical phases. For the localized phase, the spread of the density front hints at a logarithmic behavior in time that has no parallel in the isolated case (i.e. in the absence of probes). Inside the initial step, due to the presence of the probes, the density front spreads in a diffusive manner for all the phases. This combination of rich and different dynamical behavior, outside and inside the initial step, results in the emergence of mixed dynamical phases. While the total occupation of electrons remains conserved, the value outside or inside the initial step turns out to have a rich dynamical behavior. Our work is widely adaptable and has interesting consequences when disordered/quasi-disordered systems are subjected to a thermodynamically large number of probes.

Nonlocal Massive Gravity from Einstein Gravity.

We present a top-down construction of a three-dimensional nonlocal theory of massive gravity. This "nonlocal massive gravity" (NLMG) is obtained as the gravitational theory induced by Einstein gravity on a brane inserted in anti-de Sitter space modified by an overall minus sign. The theory involves an infinite series of increasingly complicated higher-derivative corrections to the Einstein-Hilbert action, with the quadratic term coinciding with new massive gravity. We obtain an analytic formula for the quadratic action of NLMG and show that its linearized spectrum consists of an infinite tower of positive-energy massive spin-2 modes. We compute the Newtonian potential and show that the introduction of the infinite series of terms makes it behave as ∼1/r at short distances, as opposed to the logarithmic behavior encountered when the series is truncated at any finite order. We use this and input from brane-world holography to argue that the theory may contain asymptotically flat black hole solutions.

Turbulent Channel Flow: Direct Numerical Simulation-Data-Driven Modeling

Turbulent Channel Flow: Direct Numerical Simulation-Data-Driven Modeling

Robust relation of streamwise velocity autocorrelation in atmospheric surface layers based on an autoregressive moving average model

We construct an autoregressive moving average (ARMA) model consisting of the history and random effects for the streamwise velocity fluctuation in boundary-layer turbulence. The distance to the wall and the boundary-layer thickness determine the time step and the order of the ARMA model, respectively. Based on the autocorrelation's analytical expression of the ARMA model, we obtain a global analytical expression for the second-order structure function, which asymptotically captures the inertial, dynamic and large-scale ranges. Specifically, the exponential autocorrelation of the ARMA model arises from the autoregressive coefficients and is modified to logarithmic behaviour by the moving-average coefficients. The asymptotic expressions enable us to determine model coefficients by existing parameters, such as the Kolmogorov and the Townsend–Perry constants. A consequent double-log expression for the characteristic length scale is derived and is justified by direct numerical simulation data with $Re_\tau \approx 5200$ and field-measured neutral atmospheric surface layer data with $Re_\tau \sim O(10^6)$ from the Qingtu Lake Observation Array site. This relation is robust because it applies to $Re_\tau$ from $O(10^4)$ to $O(10^6)$ , and even when the statistics of natural ASL deviate from those of canonical boundary-layer turbulence, e.g. in the case of imbalance in energy production and dissipation, and when the Townsend–Perry constant deviates from traditional values.

Performance evaluation of logarithmic spiral search and selective mechanism based arithmetic optimizer for parameter extraction of different photovoltaic cell models.

The imperative shift towards renewable energy sources, driven by environmental concerns and climate change, has cast a spotlight on solar energy as a clean, abundant, and cost-effective solution. To harness its potential, accurate modeling of photovoltaic (PV) systems is crucial. However, this relies on estimating elusive parameters concealed within PV models. This study addresses these challenges through innovative parameter estimation by introducing the logarithmic spiral search and selective mechanism-based arithmetic optimization algorithm (Ls-AOA). Ls-AOA is an improved version of the arithmetic optimization algorithm (AOA). It combines logarithmic search behavior and a selective mechanism to improve exploration capabilities. This makes it easier to obtain accurate parameter extraction. The RTC France solar cell is employed as a benchmark case study in order to ensure consistency and impartiality. A standardized experimental framework integrates Ls-AOA into the parameter tuning process for three PV models: single-diode, double-diode, and three-diode models. The choice of RTC France solar cell underscores its significance in the field, providing a robust evaluation platform for Ls-AOA. Statistical and convergence analyses enable rigorous assessment. Ls-AOA consistently attains low RMSE values, indicating accurate current-voltage characteristic estimation. Smooth convergence behavior reinforces its efficacy. Comparing Ls-AOA to other methods strengthens its superiority in optimizing solar PV model parameters, showing that it has the potential to improve the use of solar energy.

Electronic Conductance of Nano Composite Polymer Single Walled Nanotube with Spin Spray Variant

We have studied electronic conductance of nano composite polymer single walled nanotube with spin spray variant by using layer by layer technique. The study showed that there existed a critical number of polyelectrolyte bilayer below which the electronic conductance of the material was negligible. The sheet conductance increased above the critical value. This indicated that the material conductivity was controlled by the formation of a percolating network of highly conducting nanotubes in an insulating polymetric matrix. We have presented the dependence of junction resistance on the layer separation leaded to the logarithmic behavior. The quasi two dimensional model treated the nanotube as infinitely conducting rods with resistive junctions. A junction was formed when projections of two nanotubes on the plane of the material intersect. The junction resistance increased with inter layer separation. The results found were compared with previous results and were found in good agreement

Aging of Plasma-Activated Polyethylene and Hydrophobic Recovery of Polyethylene Polymers.

Available literature on the aging of plasma-activated polyethylene due to hydrophobic recovery has been reviewed and critically assessed. A common method for the evaluation of hydrophobic recovery is the determination of the static water contact angle, while the surface free energy does not reveal significant correlations. Surface-sensitive methods for the characterization of chemical composition and structure have limited applicability in studying the aging phenomenon. Aging is driven by thermodynamics, so it is observed even upon storage in a vacuum, and hydrophobic recovery increases with increasing temperature. Storage of plasma-activated polyethylene in the air at ambient conditions follows almost logarithmic behavior during the period studied by most authors; i.e., up to one month. The influence of the storage medium is somehow controversial because some authors reported aging suppression by storing in polar liquids, but others reported the loss of hydrophilicity even after a brief immersion into distilled water. Methods for suppressing aging by hydrophobic recovery include plasma treatment at elevated temperature followed by brief treatment at room temperature and application of energetic ions and photons in the vacuum ultraviolet range. Storing at low temperatures is a trivial alternative, but not very practical. The aging of plasma-activated polyethylene suppresses the adhesion of many coatings, but the correlation between the surface free energy and the adhesion force has yet to be addressed adequately.

Graphite- and Graphene-Based Polymer Nanocomposites for Flexible Sensors and Actuators in Health Care and Soft Robotics Applications

Flexible sensors and actuators have broad applications in the fields of wearable electronics for health, sports, functional textiles, robotics and cobot applications. Graphene-or graphite-based polymer nanocomposites are promising materials for the development of soft sensors and actuators. This study investigates strain sensing properties of silicon rubber with various graphene filler concentrations (8wt%-12wt%). Current-voltage characteristics have been measured under various strains. We obtain that the sensor’s electrical resistance, for a given voltage, can be approximated by a linear fit of the logarithmic resistance as function of the extension ratio of the sensor. The obtained mechanically induced logarithmic resistor behavior of the polymer nanocomposite is highly promising for the development of electronic sensing and control. Furthermore, thin film graphite layers were investigated on highly stretchable silicone membranes.

Reynolds number dependence of turbulent kinetic energy and energy balance of 3-component turbulence intensity in a pipe flow

Measurement data sets are presented for the turbulence intensity profile of three velocity components ( $u$ , $v$ and $w$ ) and turbulent kinetic energy (TKE, $k$ ) over a wide range of Reynolds numbers from $Re_\tau =990$ to 20 750 in a pipe flow. The turbulence intensity profiles of the $u$ - and $w$ -component show logarithmic behaviour, and that of the $v$ -component shows a constant region at high Reynolds numbers, $Re_\tau &gt;10\,000$ . Furthermore, a logarithmic region is also observed in the TKE profile at $y/R=0.055\unicode{x2013}0.25$ . The Reynolds number dependences of peak values of $u$ -, $w$ -component and TKE fit to both a logarithmic law (Marusic et al., Phys. Rev. Fluids, vol. 2, 2017, 100502) and an asymptotic law (Chen and Sreenivasan, J. Fluid Mech., vol. 908, 2020, R3), within the uncertainty of measurement. The Reynolds number dependence of the bulk TKE $k^+_{bulk}$ , which is the total amount of TKE in the cross-sectional area of the pipe also fits to both laws. When the asymptotic law is applied to the $k^+_{bulk}$ , it asymptotically increases to the finite value $k^+_{bulk}=11$ as the Reynolds number increases. The contribution ratio $\langle u'^2\rangle /k$ reaches a plateau, and the value tends to be constant within $100&lt; y^+&lt;1000$ at $Re_\tau &gt;10\ 000$ . Therefore, the local balance of each velocity component also indicates asymptotic behaviour. The contribution ratios are balanced in this region at high Reynolds numbers as $\langle u'^2\rangle /k\simeq 1.25$ , $\langle w'^2\rangle /k\simeq 0.5$ and $\langle v'^2\rangle /k \simeq 0.25$ .

Entanglement entropy in conformal quantum mechanics

We consider sets of states in conformal quantum mechanics associated to generators of time evolution whose orbits cover different regions of the time domain. States labelled by a continuous global time variable define the two-point correlation functions of the theory seen as a one-dimensional conformal field theory. Such states exhibit the structure of a thermofield double built on bipartite eigenstates of generators of non-global time evolution. In terms of the correspondence between radial conformal symmetries in Minkowski space-time and time evolution in conformal quantum mechanics proposed in [1, 2] these generators coincide with conformal Killing vectors tangent to worldlines of Milne and diamond observers at constant radius. The temperature of the thermofield double states in conformal quantum mechanics reproduces the temperatures perceived by such diamond and Milne observers. We calculate the entanglement entropy associated to the thermofield double states and obtain a UV divergent logarithmic behaviour analogous to known results in two-dimensional conformal field theory in which the entangling boundary is point-like.

Gravimetric and electrochemical investigation of the impact of various factors on XC48 carbon steel corrosion in different environments

ur main motivation in this study was to review the effects of acid concentration and solution temperature on the corrosion behavior of XC48 carbon steel in acidic and saline environments. We conducted both gravimetric and electrochemical analyses to evaluate the extent of corrosion. The gravimetric study revealed interesting findings regarding the influence of acid concentration on the corrosion rate. Initially, as the acid concentration increased, the corrosion rate showed an upward trend, reaching a peak at approximately 6M (44.1%) of sulfuric acid. However, at higher concentrations, such as 10.3M (65.15%) the corrosion rate decreased to a lower value at different immersion times. A similar trend was observed with phosphoric acid, where the maximum corrosion rate occurred at around 10M (66.6%), but decreased at 14.5M (84.68%) over different immersion times. Notably, in the case of hydrochloric acid, the corrosion rate exhibited a logarithmic behavior at higher concentrations (6M, 7M, 10M), which can be attributed to the formation of passive layers. The decrease in corrosion rate at higher concentrations indicates the protective effect of these passive layers. During the electrochemical analysis, we investigated the effect of temperature and NaCl concentration on the corrosion rate. Our results indicated that the corrosion rate increased with an elevation in temperature and NaCl concentration. The maximum corrosion rate was observed within the range of 3 to 4% of NaCl. Overall, this study provides valuable insights into the corrosion behavior of XC48 carbon steel in acidic and saline environments. The gravimetric analysis highlighted the influence of acid concentration on corrosion rate, including the formation of passive layers at high concentrations. The electrochemical study demonstrated the impact of temperature and NaCl concentration on corrosion rate, with higher values observed at elevated temperatures and increased NaCl concentrations. These findings contribute to a better understanding of the corrosion mechanisms and can aid in the development of effective corrosion prevention strategies for carbon steel in similar environments

Slightly broken higher-spin current in bosonic and fermionic QED in the large-$N$ limit

We study the slightly broken higher-spin currents in various CFTs with U(1) gauge field, including the tricritical QED, scalar QED, fermionic QED and QED-Gross-Neveu-Yukawa theory. We calculate their anomalous dimension by making use of the classical non-conservation equation and the equations of motion. We find a logarithmic asymptotic behaviour (\gamma_s\sim 16/(N\pi^2)γs∼16/(Nπ2) log s ) of the anomalous dimension at large spin ss, which is different from other interacting CFTs without gauge fields and may indicate certain unique features of gauge theories. We also study slightly broken higher-spin currents of the SU(N)_11 WZW model at d=2+\epsilond=2+ϵ dimensions by formulating them as the QED theory, and we again find its anomalous dimension has a logarithmic asymptotic behaviour with respect to spin. This result resolves the mystery regarding the mechanism of breaking higher spin currents of Virasoro symmetry at d=2+\epsilond=2+ϵ dimensions, and may be applicable to other interesting problems such as the 2+\epsilon2+ϵ expansion of Ising CFT.

Diffusion-Driven Frictional Aging in Silicon Carbide

Friction is the force resisting relative motion of objects. The force depends on material properties, loading conditions and external factors such as temperature and humidity, but also contact aging has been identified as a primary factor. Several aging mechanisms have been proposed, including increased “contact quantity” due to plastic or elastic creep and enhanced “contact quality” due to formation of strong interfacial bonds. However, comparatively less attention has been given to other mechanisms that enhance the “contact quantity”. In this study, we explore the influence of crystal faceting on the augmentation of “contact quantity” in cubic silicon carbide, driven by the minimization of surface free energy. Our observations reveal that the temporal evolution of the frictional aging effect follows a logarithmic pattern, akin to several other aging mechanisms. However, this particular mechanism is driven by internal capillary forces instead of the normal force typically associated with friction. Due to this fundamental distinction, existing frictional aging models fail to comprehensively explain the observed behavior. In light of these findings, we derive a model for the evolution of contact area caused by diffusion-driven frictional aging, drawing upon principles from statistical mechanics. Upon application of a normal force, the friction force is increased due to plastic creep. This investigation presents an alternative explanation for the logarithmic aging behavior observed and offers the potential to contribute to the development of more accurate friction models.Graphical

Fermion Disorder Operator at Gross-Neveu and Deconfined Quantum Criticalities.

The fermion disorder operator has been shown to reveal the entanglement information in 1D Luttinger liquids and 2D free and interacting Fermi and non-Fermi liquids emerging at quantum critical points (QCPs) [W. Jiang etal., arXiv:2209.07103]. Here we study, by means of large-scale quantum MonteCarlo simulation, the scaling behavior of the disorder operator in correlated Dirac systems. We first demonstrate the logarithmic scaling behavior of the disorder operator at the Gross-Neveu (GN) chiral Ising and Heisenberg QCPs, where consistent conformal field theory (CFT) content of the GN-QCP in its coefficient is found. Then we study a 2D monopole-free deconfined quantum critical point (DQCP) realized between a quantum-spin Hall insulator and a superconductor. Our data point to negative values of the logarithmic coefficients such that the DQCP does not correspond to a unitary CFT. Density matrix renormalization group calculations of the disorder operator on a 1D DQCP model also detect emergent continuous symmetries.

Secondary motions and wall-attached structures in a turbulent flow over a random rough surface

Large-eddy simulations (LESs) are performed to explore the effects of roughness on the secondary motions (SMs) and wall-attached structures in a turbulent open-channel flow over a random rough surface at a friction Reynolds number of Reτ≈1000. Turbulent flow over two groups of rough walls – a homogeneous random arrangement and a clustered arrangement – is considered, and the results are compared with the turbulence over a smooth wall. The results show that the two roughness arrangements exhibit minor differences in the variation of mean streamwise velocity. The rough surfaces of a clustered arrangement can generate large-scale SMs, resulting in spanwise-alternating high-momentum pathways (HMPs) and low-momentum pathways (LMPs) in the time-averaged velocity. Because of SMs, the streamwise turbulence intensity is enhanced in the outer region and a larger-scale spectral peak occurs in the turbulence energy spectra. On the other hand, the outer-layer similarity is still satisfied for the homogeneous random arrangement. The wall-attached structures of streamwise velocity fluctuations in the presence of roughness are extracted through a three-dimensional clustering identification approach. The wall-attached structures retain their geometric self-similarity for both rough surfaces, whereas the length and width of these structures decreases and increases, respectively. The population density scales inversely with the height, reflecting the hierarchical nature of the structures. In addition, when the streamwise velocity fluctuations within the wall-attached structures are conditionally averaged, the profile exhibits logarithmic behavior in the logarithmic region for the homogeneous random arrangement; in the case of the clustered arrangement, the reconstructed profile is affected by the SMs. A new identification approach is applied to decompose the secondary flow structures into wall-detached structures, and the logarithmic behavior of the streamwise turbulence intensity is reconstructed on the basis of the new wall-attached structures. The present results provide evidence of the presence of the wall-attached structures in instantaneous flow fields of rough-wall turbulence, for both homogeneous and heterogeneous roughness arrangements.