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Numerical Modeling of COVID-19 Neurological Effects ODE/PDE Analysis in R

Numerical Modeling of COVID-19 Neurological Effects ODE/PDE Analysis in R

Covid-19 is primarily a respiratory disease which results in impaired oxygenation of blood. The O2-deficient blood then moves through the body and for the study in this book the focus is on the blood flowing to the brain. The dynamics of blood flow along the brain capillaries and tissue is modeled as systems of ordinary and partial differential equations (ODE/PDEs). The ODE/PDE methodology is presented through a series of examples 1. A basic one PDE model for O2 concentration in the brain capillary blood. 2. A two PDE model for O2 concentration in the brain capillary blood and in the brain tissue with O2 transport across the blood brain barrier (BBB). 3. The two model extended to three PDEs to include the brain functional neuron cell density. Cognitive impairment could result from reduced neuron cell density in time and space (in the brain) that follows from lowered O2 concentration (hypoxia). The computer-based implementation of the example models is presented through routines coded (programmed) in R a quality open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized e. g. no theorems and proofs. Rather the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The PDE analysis is based on the method of lines (MOL) an established general algorithm for PDEs implemented with finite differences. The routines are available from a download link so that the example models can be executed without having to first study numerical methods and computer coding. The routines can then be applied to variations and extensions of the blood/brain hypoxia models such as changes in the ODE/PDE parameters (constants) and form of the model equations. | Numerical Modeling of COVID-19 Neurological Effects ODE/PDE Analysis in R

GBP 82.99
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Spectroscopic Techniques and Hindered Molecular Motion

Spectroscopic Techniques and Hindered Molecular Motion

Spectroscopic Techniques and Hindered Molecular Motion presents a united theoretical approach to studying classical local thermal motion of small molecules and molecular fragments in crystals by spectroscopic techniques. Mono- and polycrystalline case studies demonstrate performance validity. The book focuses on small molecules and molecular fragments such as N2 HCl CO2 CH4 H2O NH4 BeF4 NH3 CH2 CH3 C6H6 SF6 and other symmetrical atomic formations which exhibit local hindered motion in molecular condensed media: molecular and ionic crystals molecular liquids liquid crystals polymeric solids and biological objects. It reviews the state of studying the hindered molecular motion (HMM) phenomenon and the experimental works on the basis of the latest theoretical research. Case StudiesPhysical models of hindered molecular motionGeneral solution of the stochastic problem for the hindered molecular motion in crystalsFormulae of the angular autocorrelation function symmetrized on the crystallographic point symmetry groups Formulae of the spectral line shapes concerning the dielectric infrared Raman nuclear magnetic relaxation and neutron scattering spectroscopy in the presence of the hindered molecular motionExperimental probation of the theoretical outcomesProton relaxation in three-atomic molecular fragments undergoing axial symmetry hindered motion Structural distortion in the ordered phase of crystalline ammonium chlorideOrganic compounds polymers pharmaceutical products and biological systems consist of the molecular fragments which possess rotational or conformational degrees of freedom or an atomic exchange within the fragme

GBP 59.99
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