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To better describe and understand the time dynamics in functional data analysis, it is often desirable to recover the partial derivatives of the random surface. A novel approach is proposed based on marginal functional principal component analysis to derive the representation for partial derivatives. To obtain the Karhunen-Loeve expansion of the partial derivatives, an adaptive estimation is explored. Asymptotic results of the proposed estimates are established. Simulation studies show that the proposed methods perform well in finite samples. Application to the human mortality data reveals informative time dynamics in mortality rates.

Sea surface waves significantly affect the wind energy input to the Ekman layer in the upper ocean. In the study, we first incorporated the wave-induced Coriolis-Stokes forcing, the reduction of wind stress caused by wave generation, and wave dissipation into the classical Ekman model to investigate the kinetic energy balance in the wave-affected Ekman layer. Then, both the theoretical steady state solution for the idealized condition and the nonsteady state solution for the realistic ocean were derived. Total energy input to the wave-affected Ekman layer includes the wind stress energy input and the wave-induced energy input. Based on the WAVEWATCH III model, the wave spectrum was simulated to represent realistic random directional wave conditions. The wind stress energy input and the wave-induced energy input to the wave-affected Ekman layer in the Antarctic Circumpolar Current in the period from 1988 to 2010 were then calculated. The annual mean total energy input in the Antarctic Circumpolar Current region was 402.5 GW and the proportions of the wind stress energy input and the wave-induced energy input were, respectively, 85% and 15%. Particularly, total energy input in the Antarctic Circumpolar Current in the wave-affected Ekman layer model was 59.8% lower than that in the classical Ekman model. We conclude that surface waves play a significant role in the wind energy input to the Ekman layer.

In this paper, we analyze the connectivity in the underwater optical wireless networks in which similar nodes with a certain range and coverage angle, and random surface distribution are used. In our analysis, we first classify the nodes into two categories of nodes located in the inner area and nodes located in the border strip by defining the width of the border strip as the node range. Then, we conduct their connectivity analyses separately. Finally, by combining the mentioned analyses, we obtain closed form formulas to calculate the probability of connectivity (from orders 1 and 2). Moreover, by numerical evaluation, we will compare the results of the analyses with the results of computer simulation.

Nano-structured materials have become prominent in diversified fields of engineering and materials science. However, high cost and complicated techniques for synthesis of nanomaterials restrict their development. The use of different molecular dynamic simulation techniques simplified the validation of possible nanostructures and evaluation of their mechanical, physical, and chemical properties. In addition, the surface modification of nanomaterials to overcome the drawback of existing defects or improvement in interfacial properties has been a key issue for using such nanostructures in structural composites or thin films. Simulation techniques have also been found very useful to conduct random surface modification possibilities of nano-structured 2D materials without the need of time-consuming and sophisticated experiment setups which restrict the researchers for repetitive experimentations. This chapter entails typical simulation techniques which can be used for assessing different carbonous and non-carbonous nanomaterials. It will also enable to understand the various possibilities for surface modification and evaluation of properties of the characteristic nanomaterials.

Adding textures to surfaces is known to improve the external appearance of injection moulded components. However, when high surface quality is required, normally a paint coating is applied on top of the moulded textured surface. In this work, an alternative to painting for obtaining high quality surfaces is proposed, following an environmental-friendly process and having low production cost. Three different surface textures obtained by injection moulding have been characterized and compared with a painted one. Alternative topographical parameters such as the absolute functional height (AFH), the functional height distribution (FHD), texture slope (TS) or texture aperture angle (TAA) besides to the traditional roughness parameters such as the arithmetical mean height (Sa) and the root mean square height (Sq) have been utilized to characterize the random surface textures. The relationships between these parameters and the surface quality appearance represented by gloss and reflectivity contrast have been established using a new total appearance measurement (TAM) apparatus. It was found that by applying secondary operation on the textured mould cavity, such as adding micro roughness features or coatings, equal apparent quality to the ones obtained by painting can be reached.

We consider discrete random fractal surfaces with negative Hurst exponent $H, Comment: 35 pages. Replacement takes into account the comments of the two SciPost referees, which can be found at https://scipost.org/submissions/2005.11830v1/#report_1

We study the nominal (ensemble averaged) contact pressure $p(x)$ acting on a cylinder squeezed in contact with an elastic half-space with random surface roughness. The contact pressure is Hertzian-like for $\alpha < 0.01$ and Gaussian-like for $\alpha > 10$, where the dimensionless parameter $\alpha = h_{\rm rms}/\delta$ is the ratio between the root-mean-square roughness amplitude and the penetration for the smooth surfaces case (Hertz contact)., Comment: 6 pages, 5 figures. arXiv admin note: text overlap with arXiv:2007.13576

The various emerging technologies surrounding the use of generative machine learning allow for the automation of procedures which would normally take a large amount of human development time. This can be applied to the domain of simulations in low altitude flight imaging simulations. Low altitude imaging consists of images taken at an altitude of less than 500 feet above the surface in this context. Simulating the acquisition of such images using commercial game engines such as Unity or Unreal Engine 4 is possible. However one defect in the images thus taken is the repetition of material images on the terrain itself. This lowers the fidelity of the simulation since materials that represent certain characteristics of the ground are based on a single or small group of source images. In the past few years a set of generative neural network architectures known as generative adversarial networks (GANs) have seen much development. We propose a method using GANs in order to generate variations of similar terrain with a high degree of randomness in order to replace tiling caused by using similar images. We have been sucessful in developing textures for a variety of terrain types including sand and grass by utilizing the evaluation functions and blending algorithms we have constructed. Using these images as terrain textures will allow for a higher fidelity simulation and will provide a more accurate test bed for computer vision algorithms operating in the domain of low altitude flight.

Based on Kirchhoff approximation theory, the speckle phase near random surfaces with different roughness is numerically simulated. As expected, the properties of the speckle phase near the random surfaces are different from that in far field. In addition, as scattering distances and roughness increase, the average fluctuations of the speckle phase become larger. Unusually, the speckle phase is somewhat similar to the corresponding surface topography. We have performed experiments to verify the theoretical simulation results. Studies in this paper contribute to understanding the evolution of speckle phase near a random surface and provide a possible way to identify a random surface structure based on its speckle phase.

An accurate and efficient simulation model is developed for the scattering from a 3-D ship on a 2-D sea-like surface. The ship on the sea-like surface is modeled as a ship on a random surface with the impedance boundary condition. A full-wave simulation method is developed to simulate this model by using the self-dual integral equation and the parallel multilevel fast multipole algorithm. The simulation model is compared with the model of a ship on a flat surface and on a perfectly electrically conducting random surface, respectively. The application ranges of these models are concluded. Furthermore, the characteristics of the ship on a sea-like surface are studied by using the developed simulation model.

In this paper, we review the development of Gaussian free fields in recent years, including equivalent definitions, elegent properties, as well as delicate structures. We also introduce the Liouville quantum gravity (random surface) based on Gaussian free fields, including Liouville measure and Liouville Brownian motion.

We introduce and study a new random surface, which we call the hyperbolic Brownian plane and which is the near-critical scaling limit of the hyperbolic triangulations constructed by Curien (Probab Theory Relat Fields 165(3):509–540, 2016). The law of the hyperbolic Brownian plane is obtained after biasing the law of the Brownian plane of Curien and Le Gall (J Theoret Probab 27(4):1249–1291, 2014) by an explicit martingale depending on its perimeter and volume processes studied by Curien and Le Gall (Probab Theory Relat Fields 166(1):187–231, 2016). Although the hyperbolic Brownian plane has the same local properties as those of the Brownian plane, its large scale structure is much different since we prove e.g. that is has exponential volume growth.

Surface roughness is an important physical feature of nanometer-scale electromechanical (NEM) devices but typically is not considered in their numerical analysis. In this paper, computer simulations of a single-pole double-throw NEM switch with surface roughness are presented. Roughness is shown to modify the eigenfrequencies of the system, and also to make it possible for the switch to not close successfully. The importance of avoiding a free-standing cantilever is demonstrated.

In this note we show that the expected value of the separating systole of a random surface of genus $g$ with respect to Weil-Petersson volume behaves like $2\log g $ as the genus goes to infinity. This is in strong contrast to the behavior of the expected value of the systole which, by results of Mirzakhani and Petri, is independent of genus., Comment: 9 pages. Journal of the Institute of Mathematics of Jussieu, to appear

The Association of Official Analytical Chemists (AOAC) and the Canadian Health Protection Branch (CHPB) methods for detection of Salmonella spp. were compared for recovery of Salmonella javiana from experimentally contaminated mozzarella cheese. Ten trials were conducted with two levels of random surface contamination of cheese. Five samples per level of contamination were randomly chosen and analyzed by each method. The results showed that there was no significant difference between the two methods (P < 0.05). When S. javiana was directly added to shredded cheese and analyzed immediately, the recovery was identical with both methods; 7 of 10 samples were positive by each method. However, when the directly contaminated cheese was stored for 7 days and analyzed by both methods, the results differed. The AOAC method showed only 3 positive samples, whereas the CHPB yielded 6, compared to 7 positive samples before storage by both methods. During preenrichment the pH decreased to a greater extent with the AOAC method (7.4 to 4.4) than with the CHPB method (7.6 to 5.7) in 24 h; this pH decrease resulted in I log higher number of S. javiana counts in the latter (10 6 CFU/ml and 10 7 ml).

Direct synthesis of Al-HKUST-1 was successfully carried out using the solvothermal method. The Al2O3 added into the reaction mixture was varied at 10, 20, 40, and 80% with respect to the weight of HKUST-1. The diffractogram patterns of the synthesized HKUST-1 and Al-HKUST-1 displayed characteristic peaks at 2 θ of 6.5, 9.3, 11.4 and 13.3°, where all of these matched with that of the HKUST-1 standard. The FTIR spectra of the synthesized materials demonstrated an adsorption band at the same wavenumber as the reported HKUST-1. The surface morphology of the synthesized HKUST-1 had an octahedral form, whereas the synthesized Al-HKUST-1 had a random surface morphology. The N 2 adsorption–desorption isotherms showed that the specific surface areas of Al(10)-HKUST-1 and Al(40)-HKUST-1 were 512.6 dan 380.9 m2/g respectively, all of which were smaller than HKUST-1, which was 784.1 m2/g. The measurement results of the adsorption capacity of Al-HKUST-1 against congo red dye (CR) in water showed that Al(20)-HKUST-1 had the highest adsorption capacity of 315.15 mg/g, and followed the pseudo-second order kinetic and Langmuir isothermal adsorption.

This work is devoted to the elaboration of the new methodology for the wear parts contact estimation using 3D surface roughness parameters defined in the standard ISO 25178-2:2012 for friction and wear rate determination. In our research the random surface model was used, where the height of surface asperities h (x,y) has a normal probability distribution. As a result of research the equations for estimation of the elastic contact area and friction coefficient were derived. The existence of the correlation between friction coefficient and 3D surface roughness parameters was proven as well. The results of this work could have wide practical application, for example in design, for the texture specification on drawings, calculation of load, etc.

This paper presents a unified method for characterizing the hydrodynamic, mixed and boundary lubrication regimes in cold strip rolling. The analysis involves random surface asperities, multi-scale plastic deformation of both the asperities and workpiece, and a statistical modeling of an equivalent interface between the lubricated surfaces in contact sliding. This new method enables us to understand the effect of asperity plastic deformation on the interface lubrication and on the surface topography evolution of a strip surface during rolling. It is expected that the method is also applicable to other contact sliding processes involving complex lubrication and plastic asperity deformation.

Motzkin and Fredkin spin chains exhibit the extraordinary amount of entanglement scaling as a square-root of the volume, which is beyond logarithmic scaling in the ordinary critical systems. Intensive study of such spin systems is urged to reveal novel features of quantum entanglement. As a study of the systems from a different viewpoint, we introduce large-N matrix models with so-called ABAB interactions, in which correlation functions reproduce the entanglement scaling in tree and planar Feynman diagrams. Including loop diagrams naturally defines an extension of the Motzkin and Fredkin spin chains. Contribution from the whole loop effects at large N gives the growth of the power of 3/2 (with logarithmic correction), further beyond the square-root scaling. The loop contribution provides fluctuating two-dimensional bulk geometry, and the enhancement of the entanglement is understood as an effect of quantum gravity., 29 pages, 6 figures, submitted to Special Issue "Selected Papers: 10th Mathematical Physics Meeting" in Symmetry; (v2) typos corrected; (v3) reference added, version close to the publication

A turbulent jet breakup model is derived using concepts from probability theory. Velocity fluctuations at the free surface are hypothesized to be the cause of turbulent jet breakup. We formalize this idea by treating the fluctuations as random variables, subject to damping from the free surface. In contrast to previous theories, we use a conditional ensemble average to determine quantities of interest because not all fluctuations produce droplets. An energy balance and a closure model are used to determine the Sauter mean diameter. Similar approaches are used to determine the breakup onset location, breakup length, and spray angle. A criteria for the transition to the turbulent atomization regime is derived under the hypothesis that the cause is a change in the minimum velocity from the Hinze scale to the Kolmogorov scale. To validate the model, we compiled data from previous experimental studies using long pipe nozzles. The little data for rough pipes was used to include turbulence intensity in our study.