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The pore space of a porous medium is typically considered to consist of a collection of curved capillaries with rough walls. A model describing roughness is established by applying fractal theory. As a result, a modified permeability model is derived theoretically, which is closely related to roughness. To validate this model, a new form of Kozeny–Carman (KC) equation is also developed for estimating permeability on a set of benchmark rock samples, and a good agreement was achieved in terms of small relative error between measured and predicted permeabilities. Therefore, we can conclude that pore roughness should not be ignored in predicting permeability. Although the improved KC equation can predict permeability effectively too, it is not practical as the KC constant is difficult to determine.

With the advent of the semiconductor age and later the age of nanotechnology, the thin film and coating field have established their importance and reasons for doing in-depth studies. Different sophisticated physical techniques, like chemical vapor deposition, sputtering, evaporation, molecular beam epitaxy, etc., and the conventional spin coating or dip coating, have been employed to get thin films of specific materials/compounds. Of all these, physical techniques are particularly preferred for their ability to develop good quality thin film with high uniformity. In the field of experimental material science, there are tremendous efforts in thin film development and the study of their different properties. The properties include topological, electrical, electronic, optical, or other. At the same time, though less explored, there are developments of theoretical understanding regarding the basic mechanism of thin film growth by specific growth mechanism. In doing this, the basic mechanism of thin film growth has been categorized into different broad classes with specific features. The main features include the time dependence of interface width and values of different scaling exponents. Apart from these, studies also addressed different morphological, optical, or electrical properties of the as-grown thin films of specific material. This paper gathers the existing literature that reports the simulation-based theoretical studies related to thin film growth by different algorithms like random deposition, ballistic deposition, random deposition with surface relaxation, or their different combinations. Not only that, but the paper also summarizes different reports related to the simulation-based prediction of the material properties. As the topic is relatively new, the collection of reports added in the last 20 years has been considered.

The paper has different sections. Section 1 gives basic introductory ideas related to thin film development and its properties. Sections 2 and 3, respectively, deal with the basics of different existing models and the basic steps involved in the simulation. Section 4 gathers the related results reported by various researchers, followed by a short discussion and final concluding remarks. Undoubtedly, this paper is the first review work in this field and thus will serve as an invaluable source of information for future workers.

In this investigation, Ti6Al4V was used as the base material for the shot peening process. Three major influencing parameters such as peening time, peening distance, and peening pressure were examined. The substrate was shot peened with stainless steel shot, with an average diameter of 0.6mm. The process parameters were optimized using the statistical tool Response Surface Methodology. A three-factor, five-level composite design matrix was employed to minimize the number of trial runs. The effect of shot peening parameters on hardness, surface roughness, and coefficient of friction was optimized. The adequacy of the model was checked using an analysis of variance. From the test results, it was observed that the peening performed with a shot peening time of 20s, a peening distance of 100mm, and a peening pressure of 3 bar resulted in a higher hardness of 433 VHN, a surface roughness of 5.8, and a coefficient of friction of 0.22. This may be attributed to the optimal residual compressive strength achieved through the shot peening process.

In this study, a procedure for constructing pavement roughness in a three-dimensional bridge subjected to a vehicle using Abaqus is proposed for numerical simulation of vehicle–bridge interaction problems. As the plug-in RufGen, a graphical user interface in Abaqus/CAE for surface interaction, creates a hexahedron with a rough surface and attaches it to the bridge deck, the resulting weight of a bridge model can be much larger than the original one. In the vehicle scanning method, it is essential to keep a finite element bridge model with an unchanged weight after imposing a rough surface on it in consideration of the roughness effect for bridge health monitoring. As such, the proposed procedure is aimed at resolving this issue, with the following two highlights: First, the Toeplitz matrix is introduced to generate a rough surface in three dimensions to ensure the randomness of roughness in the two perpendicular directions under a given roughness profile. Second, a shell-type rough pavement is established for directly using as the bridge pavement or attaching to the bridge deck, which minimizes weight increment in the bridge.

The permeability of fractured rock mass is directly related to engineering safety and resource exploitation efficiency. However, due to the fracture network’s complexity and the fracture surface’s irregularity, accurate prediction of the permeability of fractured rock mass has always been a difficult problem in the field of geotechnical engineering. Complex network theory provides a powerful tool for studying the spatial distribution and connection characteristics of fracture networks, while fractal theory can effectively describe the roughness and self-similarity of fracture surfaces. Based on the above two theories, this paper analyzes the permeability of fractured rock mass. The permeability model of the rough fractured rock is derived by considering the roughness of the fracture. It has been discovered that the permeability of fractured rock is influenced by structural parameters, including the self-similarity index, roughness and porosity. Specifically, permeability is directly proportional to the surface density of the fractures but inversely proportional to the roughness of the fracture surfaces. The model is compared with the existing numerical simulation results to verify its correctness and effectiveness.

Joint ground states of two directed polymers in a random medium are investigated. Using exact min-cost flow optimization, the true two-line ground-state is compared with the single line ground state plus its first excited state with "worst-possible" initial conditions, where the two lines start next to each other. It is found that these two-line configurations are (for almost all disorder configurations) distinct implying that the true two-line ground-state is nonseparable, which means that the two-line ground state cannot be obtained by adding a second line to the first line in the one-line ground state without deforming the first line. The effective interaction energy between the two lines scales with the system size with the scaling exponents 0.39 ± 0.03 and 0.21 ± 0.02 in 2D and 3D, respectively.

In the presence of buoyancy, multiple diffusion coefficients, and porous media, the dispersion of solutes can be remarkably complex. The lattice-Boltzmann (LB) method is ideal for modeling dispersion in flow through complex geometries; yet, LB models of solute fingers or slugs can suffer from peculiar numerical conditions (e.g., denormal generation) that degrade computational performance by factors of 6 or more. Simple code optimizations recover performance and yield simulation rates up to ~3 million site updates per second on inexpensive, single-CPU systems. Two examples illustrate limits of the methods: (1) Dispersion of solute in a thin duct is often approximated with dispersion between infinite parallel plates. However, Doshi, Daiya and Gill (DDG) showed that for a smooth-walled duct, this approximation is in error by a factor of ~8. But in the presence of wall roughness (found in all real fractures), the DDG phenomenon can be diminished. (2) Double-diffusive convection drives "salt-fingering", a process for mixing of fresh-cold and warm-salty waters in many coastal regions. Fingering experiments are typically performed in Hele-Shaw cells, and can be modeled with the 2D (pseudo-3D) LB method with velocity-proportional drag forces. However, the 2D models cannot capture Taylor–Aris dispersion from the cell walls. We compare 2D and true 3D fingering models against observations from laboratory experiments.

The random deposition model must be enhanced to reflect the variety of surface roughness due to some material characteristics of the film growing by vacuum deposition or sputtering. The essence of the computer simulation in this case is to account for possible surface migration of atoms just after the deposition, in connection with the binding energy between atoms (as the mechanism provoking the diffusion) and/or diffusion energy barrier. The interplay of these two factors leads to different morphologies of the growing surfaces, from flat and smooth ones to rough and spiky ones. In this paper, we extended our earlier calculation by applying an extra diffusion barrier at the edges of terrace-like structures, known as the Ehrlich–Schwoebel barrier. It is experimentally observed that atoms avoid descending when the terrace edge is approached, and these barriers mimic this tendency. Results of our Monte Carlo computer simulations are discussed in terms of surface roughness, and compared with other model calculations and some experiments from literature. The power law of the surface roughness σ against film thickness t was confirmed. The nonzero minimum value of the growth exponent β near 0.2 was obtained which is due to the limited range of the surface diffusion and the Ehrlich–Schwoebel barrier. Observations for different diffusion ranges are also discussed. The results are also confirimed with some deterministic growth models.

In this paper we present a generalization of a simple solid-on-solid epitaxial model of thin film growth, when surface morphology anisotropy is provoked by anisotropy in the model control parameters of binding energy and/or diffusion barrier. The anisotropy is discussed in terms of the height–height correlation function. It was experimentally confirmed that the difference in diffusion barriers yields anisotropy in morphology of the surface. We obtained antisymmetric correlations in the two in-plane directions for antisymmetric binding.

Dispersion forces start to play an important role when the bodies are separated by the distances smaller than 100 nm. Such small gaps characterize modern nano- or microelectromechanical systems. Although the forces were reliably measured and compared to the theory in the range of 30–100 nm, severe problems appear at distances shorter than 30nm due to jump-to-contact instability. In this paper we propose a new measurement method, which does not suffer the short-distance instability. The method is based on the shape of an adhered cantilever that is sensitive to the forces acting near the adhered end. Two values are measured simultaneously: the dispersion pressure at minimal separation (close to contact) and the adhesion energy. Roughness of interacting surfaces plays a crucial role. We discuss possible realization of this experiment and propose the choice of optimal parameters.

The Casimir forces induced by fluctuations of electromagnetic field have been measured with a high precision at distances above $60$ nm. Although at shorter separations the magnitude of the force increases, it is more complicated to measure the forces at distances below $50$ nm. We review the problems that appear in this range of distances and their possible solutions. The first problem is related to the pull-in instability that occurs when two surfaces get too close to each other. As a particular manifestation of this problem, the spontaneous formation of the capillary bridges at distances $\sim 10$ nm is discussed. As an alternative, we discuss the method of adhered cantilever, which does not suffer from the pull-in instability. The second problem is related to the roughness of interacting surfaces that gives a significant deviation of the force from the expected scaling with the distance. We explain how the deviation can be related to the contribution of high asperities to the force. Characterization of the deposited rough films is also covered with a special emphasis on the excessive number of high asperities for the films deposited under nonequilibrium conditions. The third problem is related to the poor precision in the determination of the absolute distance between the bodies that results in a large total error in the force. We discuss the methods to determine the distance upon contact and cover a proposition to improve this precision in the method of adhered cantilever.

Top and bottom NiO-pinning spin valves, e.g. Ta/NiO/Co/Cu/Co/Ta and Ta/Co/Cu/Co/NiO/Ta multilayers, were investigated extensively. At the same thickness of the Cu layer, the GMR ratio for the bottom one is about 30% larger than that for the top one, which is unambiguously due to the roughness effect at the NiO/Co interface. The roughness of NiO/Co interface of the top NiO-pinning spin valve is much larger than that of the bottom one, which may be due to the deposition sequence. On the other hand, although the preferred orientation of the top NiO-pinning spin valve is more prominent than that of the bottom one, it seems not favorable to the specular reflection effect.

The steady velocities and volume flow rates (up to the second order) of an Eyring-fluids along the cross-section of an (approximated) wavy-rough nanotube are obtained analytically by using the verified fluid model and boundary perturbation method. Our results show that the wavy-roughness could tune the flow rate especially for larger forcing due to the larger surface-to-volume ratio and slip-velocity effect. The effects of wave number and slip length are also addressed.

Certain high-speed trains often suffer from the erosion of wind-drift sand during the serving period. The present paper simulated this sand-blasting process with consideration of sand-blasting pressure, angle, distance and sand particle size representing different natural conditions. Results show that the grit size has the greatest influence on roughness and residual stress of the 7N01 aluminum alloy based on the orthogonal test. The samples after low intensity sand-blasting (LISB) were characterized by micro-hardness, surface morphology and fatigue test. Results show that the surface of the blasted sample was severely impinged in form of extruded ridges crater-like morphology, representing different roughness values. The LISB causes a similar spoon shape residual stress distribution along the depth direction and it also increases the hardness of the surface zone. Finally, the residual compressive stress plays an important role in the improvement of the fatigue life, and the increase of roughness can seriously shorten the fatigue life.

The life time and quality of thermal spray coatings are strongly influenced by the technological parameters of the coating process and characteristics of the coated surface. In this paper, 16Mn steel substrates of different surface roughness are coated by Cr₃C₂-NiCr using a plasma spray technique. The adhesion of the coating to the substrate has been studied in relation to the roughness of the substrate and the plasma current of the spraying process. The results showed that the adhesion of the Cr₃C₂-NiCr coating to 16Mn steel substrate is strongly influenced by the roughness and the current intensity. The range of substrate surface roughness and current intensity at which the Cr₃C₂-NiCr exhibited high adhesion to the steel substrate are discussed in this paper.

The topography of crystalline MgF₂ surfaces eroded by low energy Ar⁺ beam has been investigated by atomic force microscopy (AFM). Applying the optimal experimental parameters, regular nanoripples of 83 nm wavelength have been fabricated on the surface and the ripples direction is parallel to the ion beam. It is also found that both the surface roughness and the ripple direction are of obvious energy dependence, which we attribute to competing balance between kinetic roughening and ion-induced surface diffusion. We also explain why the roughness value of produced ripples reaches maximum at a rather medium energy point, instead of increasing with the ion energy.

The time evolution of the roughness is investigated for one-dimensional systems described by the Kargar–Parisi–Zhang equation. Scaling behavior of the roughness is studied, and the scaling function is obtained.

The effect of surface roughness, magnetic field, and couple stress on the performance of secant slider bearing is studied in this paper. The effectiveness of the bearing is assessed by using a couple stress liquid as the lubricant in the process. Because of microstructural impacts, couple stress fluids have distinctive rheological characteristics. These features have the potential to make a major impact on the bearing’s performance. The novel aspect of this study is that the roughness of the secant slider is taken into consideration. The modified Reynolds equation is derived using Christensen’s stochastic theory for roughness. Here, both transverse and longitudinal roughness patterns are considered. The analytical solutions are obtained for steady-state pressure, load-carrying capacity, film stiffness, and damping coefficient. The results are presented for various parameters through graphs and tables. The combined effect of the magnetic field and couple stress is significant on bearing characteristics. It is noticed that the bearing features increase with the longitudinal roughness parameter, and the reverse phenomenon is observed with the transverse roughness parameter. When a transverse roughness pattern is assumed on a secant slider bearing, characteristics like pressure, load, stiffness of the film, and damping coefficient increase significantly.

Considering the small range of values that the self-affine exponent can take (0 to 1), the accuracy and precision of its determination are very important when it is used as a characteristic related to the evolution of physical phenomena or to the morphological nature of objects. In this work, a careful statistical evaluation of four common self-affine determination methods, applied to synthetic small profiles (N = 512) is reported. Accuracy, precision, confidence in the linear interval selection and computation speed are the parameters used to evaluate box counting (BC), rescaled-range analysis (Zmax), covariance analysis (Zdev) and wavelet transform (Wt) methods applied to profiles synthesized using the Weierstrass-Mandelbrot function (WMf) and the middle point displacement (Mp) methods. The results show that the log-log plot from which the self-affine exponent is computed, does not have the linear form of the BC and Zmax methods; the Wt and Zstd are the most accurate while Wt has the lowest precision. In light of these results, it is recommended to use only the Zstd or Wt methods for sample sizes of more than 100 profiles.

The aim of our work is to elaborate a method to build parametric shapes (curves, surfaces, …) with a non uniform local aspect: every point is assigned a "geometric texture" that evolves continuously from a smooth aspect to a rough aspect.

We rely on previous work that enables us to represent both smooth and fractal free form curves to propose a formalism based on finite families of iterated function systems that generalizes this previous approach. The principle is to blend shapes with uniform aspects to define a shape with a variable aspect.