Approximate analytical solutions for the overall adsorption functions based on the Fowler-Guggenheim local isotherm with a patchwise topology of adsorption centres location and four different adsorption heat distribution functions have been obtained. The Gaussian, constant, linear (as a particular case of power distribution), and exponential distribution functions have been applied. Overall adsorption functions have been analytically obtained, studied and commented. The Gaussian-related adsorption function reproduces the classic computational result nearly perfectly.
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http://dx.doi.org/10.1016/j.heliyon.2020.e05738 | DOI Listing |
J Chem Phys
January 2025
Joint Institute for High Temperatures, Russian Academy of Sciences, Izhorskaya 13, Building 2, Moscow 125412, Russia.
This paper deals with the trapping of a particle diffusing in a cylindrical cavity by two circular absorbing spots of arbitrary radii located in the centers of the cavity bases. The focus is on the mean particle lifetime, which is its mean first-passage time to one of the spots. When the spots are small and their radii are well below the cavity radius, this time can be analyzed using the narrow escape (NE) theory, which describes it as a function of the spot radii and the only parameter of the cavity, its volume, independent of the cavity shape and the particle initial position.
View Article and Find Full Text PDFFront Epidemiol
December 2024
Biostatistics and Medical Biometry, Medical School OWL, Bielefeld University, Bielefeld, Germany.
During the SARS-CoV-2 pandemic, the effective reproduction number (R-eff) has frequently been used to describe the course of the pandemic. Analytical properties of R-eff are rarely studied. We analytically examine how and under which conditions the conventional susceptible-infected-removed (SIR) model (without infection age) serves as an approximation to the infection-age-structured SIR model.
View Article and Find Full Text PDFMath Biosci
December 2024
Department of Biology, Duke University, Durham, NC, USA.
Synchronized behavior among individuals, broadly defined, is a ubiquitous feature of populations. Understanding mechanisms of (de)synchronization demands meaningful, interpretable, computable quantifications of synchrony, relevant to measurements that can be made of complex, dynamic populations. Despite the importance to analyzing and modeling populations, existing notions of synchrony often lack rigorous definitions, may be specialized to a particular experimental system and/or measurement, or may have undesirable properties that limit their utility.
View Article and Find Full Text PDFISA Trans
December 2024
ATS Lab, Air Force Engineering University, 710038 Xi'an, China.
The prediction of the remaining useful life (RUL) holds significant importance within the field of prognostics and health management (PHM), which may provide lifetime information about the system. The foundation for effectively estimating RUL is constructing an applicable degradation model for the system. However, the majority of existing degradation models only consider the issue of age dependence and disregard state dependence.
View Article and Find Full Text PDFJASA Express Lett
December 2024
Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78766-9767, USA.
Analytical solutions for acoustic vortex beams radiated by sources with uniform circular amplitude distributions are derived in the paraxial approximation. Evaluation of the Fresnel diffraction integral in the far field of an unfocused source and in the focal plane of a focused source leads to solutions in terms of an infinite series of Bessel functions for orbital numbers ℓ>-2. These solutions are reduced to closed forms for 0≤ℓ≤4, which correspond to orbital numbers commonly used in experiments.
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