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AbstractThe packed beds with small tube–to-particle diameter (D/d) ratios are widely utilized in various industrial applications such as strong absorption, exothermic catalytic converters, and nuclear reactor coolers. However, due to the significant pore structure change, uneven flow and heat transfer become apparent. This study employs the DEM-CFD method to construct spherical disordered packed beds with 2 < D/d < 4. Packed beds’ flow and heat transfer characteristics with different D/d ratios are analyzed comprehensively from both local and global perspectives. The results indicate that pore structure and temperature influence the flow field distribution in the packed bed. The peak temperature can be reduced, and the heat transfer effect can be improved by decreasing the D/d ratio or increasing the inlet velocity. Simultaneously, there is a decrease in the average velocity peak value and its fluctuation. Specifically, when D/d ratio is from 3.96 to 2.97, there is a 9% decrease in peak temperature and an approximately 11% decrease in maximum velocity. These findings contribute to deepening our understanding of the packed bed’s flow phenomena and enhancing design optimization for small D/d < ratio packed beds in industrial settings. [ABSTRACT FROM AUTHOR]

In this study, we consider a class of multiple-drawing opposite-reinforcing urns with time-dependent replacement rules. The class has the symmetric property of a Friedman-type urn. We divide the class into a small-increment regime and a large-increment regime. For small-increment schemes, we prove almost-sure convergence and a central limit theorem for the proportion of white balls by stochastic approximation. For large-increment schemes, by assuming the affinity condition, we show almost-sure convergence of the proportion of white balls by martingale theory and present a way to identify the limit distribution of the proportion of white balls. [ABSTRACT FROM AUTHOR]

We study a system of M particles with jump dynamics on a network of N sites. The particles can exist in two states, active or inactive. Only the former can jump. The state of each particle depends on its position. A given particle is inactive when it is at a given site, and active when it moves to a change site. Indeed, each sleeping particle activates at a rate λ > 0 , leaves its initial site, and moves for an exponential random time of parameter μ > 0 before uniformly landing at a site and immediately returning to sleep. The behavior of each particle is independent of that of the others. These dynamics conserve the total number of particles; there is no limit on the number of particles at a given site. This system can be represented by a continuous-time Pólya urn with M balls where the colors are the sites, with an additional color to account for particles on the move at a given time t. First, using this Pólya interpretation for fixed M and N, we obtain the average number of particles at each site over time and, therefore, those on the move due to mass conservation. Secondly, we consider a large system in which the number of particles M and the number of sites N grow at the same rate, so that the M / N ratio tends to a scaling constant α > 0 . Using the moment-generating function technique added to some probabilistic arguments, we obtain the long-term distribution of the number of particles at each site. [ABSTRACT FROM AUTHOR]

There has been no consensus on post‐earthquake operating plan for high‐speed railway trains. In this paper, two three‐dimensional coupling model of track‐bridge system without and with trains for high‐speed railways were developed, and their performance were verified based on shaking table tests. The equivalent method of design seismic track irregularity for random structures was discussed, and the amplitude response spectra of design seismic track irregularity for all levels of seismic intensity were proposed. In addition, the rationality of design seismic track irregularity was evaluated based on engineering case analysis, providing a theoretical foundation of formulating post‐earthquake contingency plans for high‐speed railways. The results show that when span number increases, the design seismic track irregularity amplitude increases and then tends to be stable; when the span number reaches 9, the train dynamic response gradually becomes stable; the random structures with arbitrary span numbers are equivalent to a specific 9‐span structure when constructing design seismic track irregularity. When the seismic intensity is low, there is no significant difference in shape and amplitude between the measured pre‐earthquake and post‐earthquake track alignment irregularities, and the train can normally run with no significant deceleration required. The train dynamic response under the design post‐earthquake track irregularity is greater than that under the measured post‐earthquake track irregularity, indicating that the design seismic track irregularity has a reasonable safety margin and a good feasibility in engineering practice. [ABSTRACT FROM AUTHOR]

In this paper, we consider a two-dimension symmetric random walk with reset. We give, in the first part, some results about the distribution of every component. In the second part, we give some results about the final altitude Z n . Finally, we analyse the statistical properties of N n X , the number of resets (the number of returns to state 1 after n steps) of the first component of the random walk. As a principal tool in these studies, we use the probability generating function. [ABSTRACT FROM AUTHOR]

We study a system of M particles with jump dynamics on a network of N sites. The particles can exist in two states, active or inactive. Only the former can jump. The state of each particle depends on its position. A given particle is inactive when it is at a given site, and active when it moves to a change site. Indeed, each sleeping particle activates at a rate λ>0, leaves its initial site, and moves for an exponential random time of parameter μ>0 before uniformly landing at a site and immediately returning to sleep. The behavior of each particle is independent of that of the others. These dynamics conserve the total number of particles; there is no limit on the number of particles at a given site. This system can be represented by a continuous-time Pólya urn with M balls where the colors are the sites, with an additional color to account for particles on the move at a given time t. First, using this Pólya interpretation for fixed M and N, we obtain the average number of particles at each site over time and, therefore, those on the move due to mass conservation. Secondly, we consider a large system in which the number of particles M and the number of sites N grow at the same rate, so that the M/N ratio tends to a scaling constant α>0. Using the moment-generating function technique added to some probabilistic arguments, we obtain the long-term distribution of the number of particles at each site.

In this paper, we consider a two-dimension symmetric random walk with reset. We give, in the first part, some results about the distribution of every component. In the second part, we give some results about the final altitude Zn. Finally, we analyse the statistical properties of NnX, the number of resets (the number of returns to state 1 after n steps) of the first component of the random walk. As a principal tool in these studies, we use the probability generating function.

In this study, we present a nanosized biosensor based on the photobiological properties of one-dimensional (1D) topological photonic crystals (PCs). A topological structure had been designed by combining two PC structures (PC 1 and PC 2) comprised of functional material layers, Si and SiO 2 . These two, PC 1 and PC 2, differ in terms of the thickness and arrangement of these dielectric materials. We carried out a comparison between two distinct topological PCs: one using random PCs, and the other featuring a mirror heterostructure. Tuberculosis may be diagnosed by inserting a sensor layer into 1D topological PCs. The sensing process is based on the refractive indexes of the analytes in the sensor layer. When the 1D-topological heterostructure-based PC and its mirror-image structures are stacked together, the sensor becomes more efficient for analyte detection than the conventional PCs. The random-based topological PC outperformed the heterostructure-based topological PC in analyte sensing. Photonic media witness notable blue shifts due to the analytes' variations in refractive index. The numerical results of the sensor are computed using the transfer matrix approach. Effective results are achieved by optimizing the thicknesses of the sensor layer and dielectric layers; number of periods and incident angle. In normal incident light, the developed sensor shows a high sensitivity of 1500 nm RIU -1 with a very low limit of detection in the order of 2.2 × 10 -06 RIU and a high-quality factor of 30 659.54., (© 2024 IOP Publishing Ltd.)

A mathematical model of diffusion of admixtures in a porous body with randomly distributed spherical pores of different radii is proposed. The skeleton of the body is modeled by closely packed spheres of different radii admitting the possibility of introduction of several effective diameters. We deduce a differential equation of mass transfer for the entire body with regard for the jump discontinuities of the unknown function and its derivative at the random interfaces. A new integrodifferential equation equivalent to the obtained initial-boundary-value problem is constructed and its solution is found in the form of a Neumann series. We perform the quantitative analysis of the process of mass transfer of admixtures in a porous layer under the condition of a uniform distribution of the phases. It is shown that the larger the volume fraction of porous inclusions in the body, the lower the means concentration of migrating substances. [ABSTRACT FROM AUTHOR]

Thin films are basic components of many types of optoelectronic devices such as thin-film solar cells, planar light-emitting diodes, and photodetectors. The preparation of nanostructured films can optimize the photoelectric properties of the films, improving the performance of optoelectronic devices, and has, therefore, received intense research attention. Nanostructuring can change the interaction of the film with incident light to optimize the optical properties of thin films. Many physical and chemical methods have been developed to prepare nanostructured films and can now be successfully used for the realization of specific functions. Nanostructured films have been widely used for controlling the optical reflection, transmission and absorption of transparent films, semiconductor films and metal films. In this paper, the preparation methods of nanostructured films and the optimization of their optical properties are reviewed. [ABSTRACT FROM AUTHOR]

The pore-scale numerical simulation of fluid flow and heat transfer processes in the random structures are given. By comparing the simulation results with the corresponding experimental data, the validity of the structure model and the heat transfer model are verified. The macro analysis is given, it is found that the mean porosity, various flow scalars and heat transfer scalars in the packed structures are all periodically distributed, and the influence of inlet velocities, spheres size and other parameters on the turbulence and temperature field in porous media is described in detail. The large eddy simulation (LES) method is used to study the flow and temperature field under pore-scale in the local porous structure, the distribution characteristic of eddies in porous structure was obtained, and the change regulation of isothermal surface shape (fractal dimension of surface) with heating is also given. Unlabelled Image • A method is proposed to build real geometric structures of packed beds of pellets. • The LES method is used to simulate the heat transfer process on pore-scale. • Local transient interactions between eddies and isothermal surface are shown. • The fractal dimension of isothermal surface is calculated by box dimension method. • The fractal dimension of isothermal surface increases exponentially during heating. [ABSTRACT FROM AUTHOR]

• A high order moment based saddlepoint approximation method is developed. • Coupling of moment matching method and saddlepoint technique. • Fourth order moments-based approximate cumulant generating function is constructed. • Valid for reliability evaluation of uncertain structures follow any types of distribution. • Performance of the method demonstrated with some representative examples. Moment-based methods use only statistical moments of random variables for reliability analysis. The cumulative distribution function (CDF) or probability density function (PDF) of a performance function can be constructed from the perspective of the first few statistical moments, and the failure probability can be evaluated accordingly. However, existing moment-based methods may lead to large errors or instability. As such, the present paper focuses on the high order moment method for higher accuracy of reliability estimation by combining the common saddlepoint approximation technique, and an improved high order moment-based saddlepoint approximation (SPA) method for reliability analysis is presented. The approximated cumulant generating function (CGF) and the CDF of the performance function in terms of its first four statistical-moments are constructed. The developed method can be used for reliability evaluation of uncertain structures follow any types of distribution. Several numerical examples are given to demonstrate the efficacy and accuracy of the proposed method. Comparisons of the new method and several existing high order moment methods are also made on the reliability assessment. [ABSTRACT FROM AUTHOR]

The random structure model of porous media is constructed by the gravity packed method, which can give a random packed structure that is similar to the actual packed bed structure by simulating the free fall, collision and stacking process of pellets via the OpenFOAM. Different from the existing ordered structure model of porous media, the structure model adopted in this paper has strong randomness since it simulates the actual generation process of the porous media material. Meanwhile, the following batch modeling instructions are completed with the MATLAB, which can ensure that the random structure model of porous media has the advantages of high similarity with the actual porous structure and rapid modeling. [ABSTRACT FROM AUTHOR]

Ｔｈｒｅｅ ｄｉｍｅｎｓｉｏｎａｌ ｒａｎｄｏｍ ｇｅｏｍｅｔｒｉｃ ｓｔｒｕｃｔｕｒｅ ｏｆ ｐｅｌｌｅｔｓ ｐａｃｋｅｄ ｂｅｄ ｗａｓ ｍｏｄｅｌｅｄ ｕｓｉｎｇ ｔｈｅ ｄｉｓｃｒｅｔｅ ｅｌｅｍｅｎｔ ｓｏｆｔｗａｒｅ ＬＩＧＧＧＨＴＳ. Ｌａｒｇｅ ｅｄｄｙ ｓｉｍｕｌａｔｉｏｎ ｍｅｔｈｏｄꎬ ｔｗｏ-ｔｅｍｐｅｒａｔｕｒｅ ｍｏｄｅｌ ａｎｄ ＥＢＵ-Ａｒｒｈｅｎｉｕｓ ｃｏｍｂｕｓｔｉｏｎ ｍｏｄｅｌ ｗｅｒｅ ｅｍｐｌｏｙｅｄ ｔｏ ｓｉｍｕｌａｔｅ ｔｈｅ ｐｒｅｍｉｘｅｄ ｃｏｍｂｕｓｔｉｏｎ ｐｒｏｃｅｓｓ ｏｆ ｍｅｔｈａｎｅ-ａｉｒ ｉｎ ｔｈｅ ｒａｎｄｏｍｌｙ ｐａｃｋｅｄ ｂｅｄ. Ｔｈｅ ｃａｌｃｕｌａｔｅｄ ｒｅｓｕｌｔｓ ａｒｅ ｃｏｍｐａｒｅｄ ｗｉｔｈ ｅｘｐｅｒｉｍｅｎｔ ｄａｔａ ｔｏ ｖｅｒｉｆｙ ｅｆｆｅｃｔｉｖｅｎｅｓｓ ｏｆ ｔｈｅ ｍｏｄｅｌ. Ｔｈｅ ｓｔｒｕｃｔｕｒｅ ａｎｄ ｔｈｅ ｓｈａｐｅ ｏｆ ｔｈｅ ｆｌａｍｅ ａｎｄ ｔｈｅ ｔｅｍｐｅｒａｔｕｒｅ ｄｉｓｔｒｉｂｕｔｉｏｎ ｉｎ ｔｈｅ ｐａｃｋｅｄ ｂｅｄ ｗｅｒｅ ａｎａｌｙｚｅｄ. Ｔｈｅ ｓｉｍｕｌａｔｉｏｎ ｒｅｓｕｌｔｓ ｓｈｏｗ ｔｈａｔ ｔｈｅ ｔｅｍｐｅｒａｔｕｒｅ ｏｆ ｓｏｌｉｄ ｉｓ ｈｉｇｈｅｒ ｔｈａｎ ｔｈａｔ ｏｆ ｇａｓ ｏｎ ｔｈｅ ｓａｍｅ ｈｅｉｇｈｔ ｏｆ ｔｈｅ ｐａｃｋｅｄ ｂｅｄ ｄｕｒｉｎｇ ｔｈｅ ｌａｔｅ ｓｔａｇｅ ｏｆ ｃｏｍｂｕｓｔｉｏｎꎬ ｗｈｉｃｈ ｒｅｆｌｅｃｔｓ ａ ｇｏｏｄ ｔｈｅｒｍａｌ ｓｔｏｒａｇｅ ｃａｐａｃｉｔｙ ｏｆ ｔｈｅ ｐｏｒｏｕｓ ｍｅｄｉｕｍ. Ｔｈｅ ｈｅｉｇｈｔ ｄｉｆｆｅｒｅｎｃｅ ｏｆ ｔｈｅ ｆａｍｅ ｓｕｒｆａｃｅ ｂｅｔｗｅｅｎ ｔｈｅ ｔｕｂｅ ｗａｌｌ ａｎｄ ｔｈｅ ｃｅｎｔｅｒ ｉｎ ｔｈｅ ｐａｃｋｅｄ ｂｅｄ ｉｓ ｍｕｃｈ ｓｍａｌｌｅｒ ｔｈａｎ ｔｈａｔ ｉｎ ｔｕｂｅ ｗｉｔｈｏｕｔ ｐｏｒｏｕｓ ｍｅｄｉａꎬ ｗｈｉｃｈ ｓｕｇｇｅｓｔｓ ｔｈａｔ ｔｈｅ ｆｌａｍｅ ｉｓ ｄｉｖｉｄｅｄ ｂｙ ｔｈｅ ｐａｃｋｅｄ ｂｅｄ ａｎｄ ｔｈｅｎ ｔｈｅ ｕｎｉｆｏｒｍｉｔｙ ａｎｄ ｓｔａｂｉｌｉｔｙ ｏｆ ｔｈｅ ｃｏｍｂｕｓｔｉｏｎ ｗｉｔｈｉｎ ａ ｐｏｒｏｕｓ ｍｅｄｉｕｍ ａｒｅ ｉｍｐｒｏｖｅｄ. [ABSTRACT FROM AUTHOR]

Improvement of the quality factor has now been an active area of research due to the growing interest of researchers in the field of the photonic crystal-based ring resonator and its applications in photonic devices. The introduction of randomness into the photonic crystal structures has proved to be an effective way to enhance the quality factor. A theoretical model of photonic crystal structure with a size disorder of the rod radius is investigated. The radius of the inner rods of the ring is modulated with the Gaussian random distribution function. The effect of a change in the disorder parameter (standard deviation) on the quality factor of the photonic crystal structure and the effects on the quality factors for variation of the refractive index of the structure and the analyte sample are evaluated. [ABSTRACT FROM AUTHOR]

• This paper proposes a method for calculating design seismic-induced irregularity for random high-speed railway structures under arbitrarily seismic intensity and structural damping ratio, providing a basis for the determination of post-earthquake driving speed. The determination of post-earthquake driving speed is one of the key issues for railway operation in seismic areas. Currently, research on design seismic irregularity is based on specific damping ratios, but the damping ratios of high-speed railway bridges are not constant. In this paper, the effects of damping ratios on seismic-induced irregularity and design seismic-induced irregularity were compared. The amplitude response spectrum of design seismic-induced irregularity considering the impact of damping ratios was established. The structural random adjustment coefficient of amplitude response spectrum was determined. The research results show that, when the characteristic period remained unchanged, the position of amplitude response spectrum rises with the increase of seismic intensity. When the seismic intensity remained unchanged, the position of amplitude response spectrum rises with the increase of characteristic period. High-speed trains should be appropriately decelerated when traveling from a hard site to a soft site with the same seismic intensity or traveling from a near field site to a far field site. With the increase in seismic intensity, the structural random adjustment coefficient drops obviously. As the characteristic period increases, the structural random adjustment coefficients show no noticeable change. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) is a production process for the fabrication of three-dimensional items characterized by complex geometries. Several technologies employ a localized melting of metal dust through the application of focused energy sources, such as lasers or electron beams, on a powder bed. Despite the high potential of AM, numerous burdens afflict this production technology; for example, the few materials available, thermal stress due to the focused thermal source, low surface finishing, anisotropic properties, and the high cost of raw materials and the manufacturing process. In this paper, the combination by AM of meltable resins with metal casting for an indirect additive manufacturing (I-AM) is proposed. The process is applied to the production of open cells metal foams, similar in shape to the products available in commerce. However, their cellular structure features were designed and optimized by graphical editor Grasshopper®. The metal foams produced by AM were cast with a lost wax process and compared with commercial metal foams by means of compression tests.

Discrete element software LIGGGHTS is introduced to reproduce the forming process of sphere packed bed by gravity， and a 3D random geometric model similar to the actual accumulation structure is presented. Two ordered models， the in-line packed model and the staggered packed model， are also established to contrast with the random packed model. CFD software of Fluent 14.0 is employed to study the turbulence flows in the packed bed. The effectiveness of the random model is validated by analysis of the macroscopic pressure drop and the resistance coefficient， and the velocity field and the turbulence parameters of the three structures are predicted and discussed. Simulation results show that the macroscopic resistance coefficient and the macroscopic pressure drop of the random packed bed model are consistent with the classical formula of Ergun， with maximum relative error less than 6%. Compared with the orderly packed bed， the random packed model is characterized with more homogeneous velocity field， larger tail vortex size， stronger disturbance and extremely larger turbulence dissipation. [ABSTRACT FROM AUTHOR]

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In this paper we shall prove that any 2-transitive finitely homogeneous structure with a supersimple theory satisfying a generalized amalgamation property is a random structure. In particular, this adapts a result of Koponen for binary homogeneous structures to arbitrary ones without binary relations. Furthermore, we point out a relation between generalized amalgamation, triviality and quantifier elimination in simple theories. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) processes are used to fabricate three-dimensional complex geometries. There are several technologies that use laser or electron beam over metal powder beds. However, the direct AM processes have inconveniences such as specific set of materials, high thermal stress traced, high local energy absorbed, poor surface finish, anisotropic properties, high cost of material powder, and manufacturing with high-power beams. In this paper, an alternative process was developed. An indirect additive manufacturing (I-AM) combining a 3D print of castable resin and metal casting in order to obtain a cellular structure similar in shape to commercial metal foams but completely definable as design features was developed. Design of the cellular structure was made by the graphical algorithm editor Grasshopper®. Designed structures were realized by a lost-wax casting process and compared with commercial foam specimens by a system designed for this work. The designed metal foams showed a performance superior to that of commercial metal foam; in particular, the heat thermal coefficient of designed metal foams in the better case was 870 W/m2·K, almost doubled in comparison with the commercial foam tested in this work.

We study a class of balanced urn schemes on balls of two colors (say white and black). At each drawing, a sample of size m ≥ 1 is taken out from the urn, and ball addition rules are applied. We consider these multiple drawings under sampling with or without replacement. We further classify ball addition matrices according to the structure of the expected value into affine and nonaffine classes. We give a necessary and sufficient condition for a scheme to be in the affine subclass, for which we get explicit results for the expected value and second moment of the number of white balls after n steps and an asymptotic expansion of the variance. Moreover, we uncover a martingale structure. This unifies several earlier works focused on special cases of urn models with multiple drawings [5,6,17,19,20,22] as well as the special case of sample size m = 1 . The class is parametrized by Λ, specified by the ratio of the two eigenvalues of a “reduced” ball replacement matrix and the sample size. We categorize the class into small-index urns ( Λ < 1 2 ), critical-index urns ( Λ = 1 2 ), and large-index urns ( Λ > 1 2 ), and triangular urns. We obtain central limit theorems for small- and critical-index urns and prove almost-sure convergence for triangular and large-index urns. Moreover, we discuss the moment structure of large-index urns and triangular urns. [ABSTRACT FROM AUTHOR]

We demonstrate a broadband absorber using random structures on refractory plasmonic material. The random microstructure is fabricated by femtosecond laser on tungsten and characterized with surface roughness which described by root mean square (RMS) and correlation length. Results show that the absorption efficiency of random microstructure with RMS of 0.8 μm and correlation length of 0.55 μm is over 90 % in the wavelength range from 200 to 1100 nm. However, the sample with surface structure RMS of 0.08 μm has much lower absorption (less than 70 % for λ > 600 nm). Numerical simulations agree well with the experimental results and illustrate that the structure with 0.8-μm RMS and 0.55-μm correlation length has the cut-off wavelength of 2400 nm which prevents mid-infrared emission. The possibility of realizing broadband absorption by using random structures presents a flexible and efficient way for solar cell, thermophotovoltaics, and energy harvesting. [ABSTRACT FROM AUTHOR]

Suppose that ${\cal M}$ is countable, binary, primitive, homogeneous, and simple. We prove that the SU-rank of the complete theory of ${\cal M}$ is 1 and hence 1-based. It follows that ${\cal M}$ is a random structure. The conclusion that ${\cal M}$ is a random structure does not hold if the binarity condition is removed, as witnessed by the generic tetrahedron-free 3-hypergraph. However, to show that the generic tetrahedron-free 3-hypergraph is 1-based requires some work (it is known that it has the other properties) since this notion is defined in terms of imaginary elements. This is partly why we also characterize equivalence relations which are definable without parameters in the context of ω-categorical structures with degenerate algebraic closure. Another reason is that such characterizations may be useful in future research about simple (nonbinary) homogeneous structures. [ABSTRACT FROM PUBLISHER]