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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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This master thesis concerns the implementation of a novel, computationally efficient bifurcation numerical analysis interface in the Julia compiled programming language. The interface involves the use of the well-known bisection or Newton-Raphson methods in order to locate bifurcations in the neuron models, as well as the use of numerical approximation methods of Jacobian matrices through forward numerical differentiation of the system's equations. The interface that is built aims at the identification of the bifurcations in neuron models in order to determine their excitability type. A recent paper-motivated canonical model is chosen as an example to which the interface can be applied as a proof of concept. This numerical analysis of the example model outputs results that highlight the importance of dynamical analysis of neuron models, i.e. analysis over a range of time-scale parameters, versus the more common static analysis of models through the visual inspection of their phase plane representation. Normal form identification based on visual inspection only is at considerable risk that the original system is identified to may not be the correct one. The results obtained through the use of this interface on a two-dimensional therefore motivate the need for extensive numerical analysis of original high-dimensional neuron models for various values of time-scale separation in order to reliably identify the bifurcation normal form that they can be reduced to.
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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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One might say that ordinary differential equations (notably, in Isaac Newton’s analysis of the motion of celestial bodies) had a central role in the development of modern applied mathematics. This book is devoted to research articles which build upon this spirit: combining analysis with the applications of ordinary differential equations (ODEs). ODEs arise across a spectrum of applications in physics, engineering, geophysics, biology, chemistry, economics, etc., because the rules governing the time-variation of relevant fields is often naturally expressed in terms of relationships between rates of change. ODEs also emerge in stochastic models—for example, when considering the evolution of a probability density function—and in large networks of interconnected agents. The increasing ease of numerically simulating large systems of ODEs has resulted in a plethora of publications in this area; nevertheless, the difficulty of parametrizing models means that the computational results by themselves are sometimes questionable. Therefore, analysis cannot be ignored. This book comprises articles that possess both interesting applications and the mathematical analysis driven by such applications.
heteroclinic tangle --- n/a --- coupled system --- integral boundary conditions --- EADs --- transport --- bifurcation analysis --- SIR epidemic model --- ion current interactions --- green’s function --- surface of section --- endemic equilibrium --- age structure --- MATCONT --- Ulam’s stability --- nonlinear dynamics --- stability --- basic reproduction number --- green's function --- Ulam's stability
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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
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