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The gas foil bearing (GFB) technology is a key factor for the transition to oil-free rotating machinery. Among numerous advantages, GFBs offer the unique ability to be lubricated with working fluids such as refrigerants. However, the computational analysis of refrigerant-lubricated GFB–rotor systems represents an interdisciplinary problem of enormous complexity. This work pushes forward existing limits of feasibility and establishes a new strategy that enables stability and bifurcation analyses.

Mechanical engineering & materials --- Bifurkationsanalyse --- Fluidschmierung --- Rotordynamik --- Thermodynamik --- Tribologie --- Bifurcation Analysis --- Fluid Film Lubrication --- Rotor Dynamics --- Thermodynamics --- Tribology

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In recent research on natural processes, mathematical modeling has become a very useful tool. It is often the case that, in fields such as economics and biology, a temporal lag between cause and effect must often be taken into consideration. In modeling, a natural and practical implementation of this phenomenon is through the use of distributed delays. This is because they illustrate the situation where temporal lags arise in certain ranges of values for certain related probability distributions, taking into account the variables’ entire history of behavior. Another mathematical tool that allows for the memory and inherited properties of systems to be encompassed in a model is the replacement of integer-order derivatives with fractional derivatives. To address realistic conditions, stochastic perturbation framed by a stochastic differential delay system can be used to explain the ambiguity about the context in which the system operates. The present book comprises all the 16 articles accepted and published in the Special Issue “Advances in Differential Dynamical Systems with Applications to Economics and Biology” of the MDPI journal Mathematics, with focuses on the dynamical analysis of mathematical models, arising from economy and biology, and innovative developments in mathematical techniques for their applications. We expect that the international scientific community will find this collection of research papers influential and that they will spur additional investigations on diverse applications with respect to dynamical systems in all scientific areas.

Research & information: general --- Mathematics & science --- dynamical systems --- time delay --- stability --- bifurcation analysis in economic and biological systems --- chaotic behaviors --- fractional order systems --- numerical methods --- economic modeling --- infection modeling --- epidemic spreading --- blood flow models --- optimal control --- reaction&ndash --- diffusion systems

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Modern biology is rapidly becoming a study of large sets of data. Understanding these data sets is a major challenge for most life sciences, including the medical, environmental, and bioprocess fields. Computational biology approaches are essential for leveraging this ongoing revolution in omics data. A primary goal of this Special Issue, entitled “Methods in Computational Biology”, is the communication of computational biology methods, which can extract biological design principles from complex data sets, described in enough detail to permit the reproduction of the results. This issue integrates interdisciplinary researchers such as biologists, computer scientists, engineers, and mathematicians to advance biological systems analysis. The Special Issue contains the following sections:•Reviews of Computational Methods•Computational Analysis of Biological Dynamics: From Molecular to Cellular to Tissue/Consortia Levels•The Interface of Biotic and Abiotic Processes•Processing of Large Data Sets for Enhanced Analysis•Parameter Optimization and Measurement

n/a --- inosine --- immune checkpoint inhibitor --- geometric singular perturbation theory --- simulation --- BioModels Database --- ADAR --- calcium current --- bifurcation analysis --- bacterial biofilms --- nonlinear dynamics --- explanatory model --- turning point bifurcation --- oscillator --- workflow --- bioreactor integrated modeling --- modeling methods --- elementary flux modes visualization --- multiscale systems biology --- evolutionary algorithm --- metabolic model --- differential evolution --- reduced-order model --- computational model --- gut microbiota dysbiosis --- canard-induced EADs --- computational biology --- metabolic modelling --- methods --- SREBP-2 --- mechanistic model --- systems modeling --- biological networks --- macromolecular composition --- provenance --- flux balance analysis --- immunotherapy --- compartmental modeling --- immuno-oncology --- metabolic network visualization --- mechanism --- bistable switch --- Clostridium difficile infection --- bioreactor operation optimization --- microRNA targeting --- CFD simulation --- biomass reaction --- RNA editing --- ordinary differential equation --- metabolic modeling --- mass-action networks --- hybrid model --- multiple time scales --- quantitative systems pharmacology (QSP) --- mathematical modeling --- microRNA --- cancer --- parameter optimization --- Hopf bifurcation --- breast