Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media. Two main types of particle deposition,namely, cake filtration at the inlet and deep bed filtratio...
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Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media. Two main types of particle deposition,namely, cake filtration at the inlet and deep bed filtration throughout the entire porous medium, are studied by different models. A unified approach for the transport and deposition of particles based on the deep bed filtration model is proposed. A variable suspension flow rate, proportional to the number of free pores at the inlet of the porous medium, is considered. To model cake filtration, this flow rate is introduced into the mass balance equation of deep bed filtration. For the cake filtration without deposit erosion,the suspension flow rate decreases to zero, and the suspension does not penetrate deep into the porous medium. In the case of the cake filtration with erosion, the suspension flow rate is nonzero, and the deposit is distributed throughout the entire porous medium. An exact solution is obtained for a constant filtration function. The method of characteristics is used to construct the asymptotics of the concentration front of suspended and retained particles for a filtration function in a general form. Explicit formulae are obtained for a linear filtration function. The properties of these solutions are studied in detail.
We demonstrate a toroidal classification for quantum spin systems, revealing an intrinsic geometric duality within this structure. Through our classification and duality, we reveal that various bipartite quantum featu...
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We demonstrate a toroidal classification for quantum spin systems, revealing an intrinsic geometric duality within this structure. Through our classification and duality, we reveal that various bipartite quantum features in magnon systems can manifest equivalently in both bipartite ferromagnetic and antiferromagnetic materials, based upon the availability of relevant Hamiltonian parameters. Additionally, the results highlight the antiferromagnetic regime as an ultrafast dual counterpart to the ferromagnetic regime, both exhibiting identical capabilities for quantum spintronics and technological applications. Concrete illustrations are provided, demonstrating how splitting and squeezing types of two-mode magnon quantum correlations can be realized across ferro- and antiferromagnetic regimes.
In this work, a novel methodological approach to multi-attribute decision-making problems is developed and the notion of Heptapartitioned Neutrosophic Set Distance Measures (HNSDM) is introduced. By averaging the Pent...
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Foundation models(FMs) [1] have revolutionized software development and become the core components of large software systems. This paradigm shift, however, demands fundamental re-imagining of software engineering theo...
Foundation models(FMs) [1] have revolutionized software development and become the core components of large software systems. This paradigm shift, however, demands fundamental re-imagining of software engineering theories and methodologies [2]. Instead of replacing existing software modules implemented by symbolic logic, incorporating FMs' capabilities to build software systems requires entirely new modules that leverage the unique capabilities of ***, while FMs excel at handling uncertainty, recognizing patterns, and processing unstructured data, we need new engineering theories that support the paradigm shift from explicitly programming and maintaining user-defined symbolic logic to creating rich, expressive requirements that FMs can accurately perceive and implement.
In the context of the digital age, online public opinion has rapidly emerged as a key manifestation of social sentiment. The spread of campus public opinion is primarily through the internet, characterized by high att...
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In order to overcome the challenges caused by flash memories and also to protect against errors related to reading information stored in DNA molecules in the shotgun sequencing method, the rank modulation method has b...
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Graph theory plays a significant role in the applications of chemistry,pharmacy,communication,maps,and aeronautical *** molecules of chemical compounds are modelled as a graph to study the properties of the *** geomet...
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Graph theory plays a significant role in the applications of chemistry,pharmacy,communication,maps,and aeronautical *** molecules of chemical compounds are modelled as a graph to study the properties of the *** geometric structure of the compound relates to a few physical properties such as boiling point,enthalpy,π-electron energy,andmolecular *** article aims to determine the practical application of graph theory by solving one of the interdisciplinary problems describing the structures of benzenoid hydrocarbons and *** topological index is an invariant of a molecular graph associated with the chemical structure,which shows the correlation of chemical structures using many physical,chemical properties and biological *** study aims to introduce some novel degree-based entropy descriptors such as ENTSO,ENTGH,ENTHG,ENTSS,ENTNSO,ENTNReZ1,ENTNReZ2 and ENTNSS using the respective topological ***,the above-mentioned entropy measures and physico-chemical properties of benzenoid hydrocarbons are fitted using linear regression models and calculated for graphenylene structure.
For the subject of arbitrary image style transfer, there have been some proposed architectures that directly compute the transformation matrix of the whitening and coloring transformation (WCT) to obtain more satisfac...
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The class of maximal-length cellular automata (CAs) has gained significant attention over the last few years due to the fact that it can generate cycles with the longest possible lengths. For every l of the form l = 2...
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The paper generalizes the direct method of moving planes to the Logarithmic Laplacian ***,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at ***,the radial symmetry of th...
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The paper generalizes the direct method of moving planes to the Logarithmic Laplacian ***,some key ingredients of the method are discussed,for example,Narrow region principle and Decay at ***,the radial symmetry of the solution of the Logarithmic Laplacian system is obtained.
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