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In this book, stagnation flows on a catalytic porous plate is modeled one-dimensionally coupled with multi-step surface reaction mechanisms and molecular transport (diffusion and conduction) in the flow field and in the porous catalyst. Internal and external mass transfer limitations as well as possible reaction routes in the catalyst are investigated for CO oxidation, WGS reaction, partial and steam reforming of methane over Rh/Al?O?.
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Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.
cross diffusion --- Turing patterns --- non-constant positive solution --- animal movement --- correlated random walk --- movement ecology --- population dynamics --- taxis --- telegrapher’s equation --- invasive species --- linear determinacy --- population growth --- mutation --- spreading speeds --- travelling waves --- optimal control --- partial differential equation --- invasive species in a river --- continuum models --- partial differential equations --- individual based models --- plant populations --- phenotypic plasticity --- vegetation pattern formation --- desertification --- homoclinic snaking --- front instabilities --- Evolutionary dynamics --- G-function --- Quorum Sensing --- Public Goods --- semi-linear parabolic system of equations --- generalist predator --- pattern formation --- Turing instability --- Turing-Hopf bifurcation --- bistability --- regime shift --- carrying capacity --- spatial heterogeneity --- Pearl-Verhulst logistic model --- reaction-diffusion model --- energy constraints --- total realized asymptotic population abundance --- chemostat model --- social dynamics --- wave of protests --- long transients --- ghost attractor --- prey–predator --- diffusion --- nonlocal interaction --- spatiotemporal pattern --- Allen–Cahn model --- Cahn–Hilliard model --- spatial patterns --- spatial fluctuation --- dynamic behaviors --- reaction-diffusion --- spatial ecology --- stage structure --- dispersal
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“Symmetry Breaking in Cells and Tissues” presents a collection of seventeen reviews, opinions and original research papers contributed by theoreticians, physicists and mathematicians, as well as experimental biologists, united by a common interest in biological pattern formation and morphogenesis. The contributors discuss diverse manifestations of symmetry breaking in biology and showcase recent developments in experimental and theoretical approaches to biological morphogenesis and pattern formation on multiple scales.
actin waves --- curved proteins --- dynamic instability --- podosomes --- diffusion --- cell polarity --- Cdc42 --- stress --- cellular memory --- phase separation --- prions --- apoptotic extrusion --- oncogenic extrusion --- contractility --- actomyosin --- bottom-up synthetic biology --- motor proteins --- pattern formation --- self-organization --- cell motility --- signal transduction --- actin dynamics --- intracellular waves --- polarization --- direction sensing --- symmetry-breaking --- biphasic responses --- reaction-diffusion --- membrane and cortical tension --- cell fusion --- cortexillin --- cytokinesis --- Dictyostelium --- myosin --- symmetry breaking --- cytoplasmic flow --- phase-space analysis --- nonlinear waves --- actin polymerization --- bifurcation theory --- mass conservation --- spatial localization --- activator–inhibitor models --- developmental transitions --- cell polarization --- mathematical model --- fission yeast --- reaction–diffusion model --- small GTPases --- Cdc42 oscillations --- pseudopod --- Ras activation --- cytoskeleton --- chemotaxis --- neutrophils --- natural variation --- modelling --- activator-substrate mechanism --- mass-conserved models --- intracellular polarization --- partial differential equations --- sensitivity analysis --- GTPase activating protein (GAP) --- fission yeast Schizosaccharomyces pombe --- CRY2-CIBN --- optogenetics --- clustering --- positive feedback --- network evolution --- Saccharomyces cerevisiae --- polarity --- modularity --- neutrality --- n/a
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Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding.
fractional diffusion --- continuous time random walks --- reaction–diffusion equations --- reaction kinetics --- multidimensional scaling --- fractals --- fractional calculus --- financial indices --- entropy --- Dow Jones --- complex systems --- Skellam process --- subordination --- Lévy measure --- Poisson process of order k --- running average --- complexity --- chaos --- logistic differential equation --- liouville-caputo fractional derivative --- local discontinuous Galerkin methods --- stability estimate --- Mittag-Leffler functions --- Wright functions --- fractional relaxation --- diffusion-wave equation --- Laplace and Fourier transform --- fractional Poisson process complex systems --- distributed-order operators --- viscoelasticity --- transport processes --- control theory --- fractional order PID control --- PMSM --- frequency-domain control design --- optimal tuning --- Gaussian watermarks --- statistical assessment --- false positive rate --- semi-fragile watermarking system --- fractional dynamics --- fractional-order thinking --- heavytailedness --- big data --- machine learning --- variability --- diversity --- telegrapher’s equations --- fractional telegrapher’s equation --- continuous time random walk --- transport problems --- fractional conservations laws --- variable fractional model --- turbulent flows --- fractional PINN --- physics-informed learning --- n/a --- reaction-diffusion equations --- Lévy measure --- telegrapher's equations --- fractional telegrapher's equation
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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.
complexity --- cuckoo search --- magnetic resonance imaging --- fractional calculus --- musical signal --- pinning synchronization --- Fourier transform --- optimal randomness --- fractional-order system --- Mittag-Leffler function --- meaning --- parameter --- diffusion-wave equation --- anomalous diffusion --- Laplace transform --- time-varying delays --- mass absorption --- swarm-based search --- fractional --- adaptive control --- time series --- Hurst exponent --- fractional derivative --- control --- PID --- global optimization --- reaction–diffusion terms --- audio signal processing --- Caputo derivative --- harmonic impact --- fractional complex networks --- heavy-tailed distribution --- impulses --- long memory --- linear prediction
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Mathematical modelling in biomedicine is a rapidly developing scientific discipline at the intersection of medicine, biology, mathematics, physics, and computer science. Its progress is stimulated by fundamental scientific questions and by the applications to public health. This book represents a collection of papers devoted to mathematical modelling of various physiological problems in normal and pathological conditions. It covers a broad range of topics including cardiovascular system and diseases, heart and brain modelling, tumor growth, viral infections, and immune response. Computational models of blood circulation are used to study the influence of heart arrhythmias on coronary blood flow and on operating modes for left-ventricle-assisted devices. Wave propagation in the cardiac tissue is investigated in order to show the influence of tissue heterogeneity and fibrosis. The models of tumor growth are used to determine optimal protocols of antiangiogenic and radiotherapy. The models of viral hepatitis kinetics are considered for the parameter identification, and the evolution of viral quasi-species is investigated. The book presents the state-of-the-art in mathematical modelling in biomedicine and opens new perspectives in this passionate field of research.
virus density distribution --- genotype --- virus infection --- immune response --- resistance to treatment --- nonlocal interaction --- quasi-species diversification --- mathematical oncology --- spatially distributed modeling --- reaction-diffusion-convection equations --- computer experiment --- spiral wave --- heterogeneity --- heart modeling --- myocardium --- left ventricle --- neural field model --- integro-differential equation --- waves --- brain stimulation --- mathematical modeling --- cardiac mechanics --- multiscale simulation --- cardiomyopathies --- left ventricle remodeling --- spatially-distributed modeling --- gradient descent --- 1D haemodynamics --- systole variations --- coronary circulation --- cardiac pacing --- tachycardia --- bradycardia --- interventricular asynchrony --- long QT syndrome --- premature ventricular contraction --- rotary blood pump --- lumped heart model --- cardiac fibrosis --- excitable media --- wave break --- elongated obstacle --- lymph flow --- mathematical modelling --- lymphatic vessels --- lymph nodes --- parameter estimation --- constrained optimization --- derivative free optimization --- multiscale models --- differential equations --- viral hepatitis
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This Special Issue presents selected papers from the 8th
stretchable electronic device --- Cu-Ni alloy --- n/a --- bioremediation --- flexible electronic device --- microfluidic device --- tactile sensor --- self-organization --- stretchability --- origami --- flexible device --- pH indicator --- additive manufacturing --- fatigue --- Nafion --- Game of Life --- MEMS --- micropatterns --- stretchable elastomer --- microcantilever --- wearable --- polydimethylsiloxane --- reaction-diffusion system --- capacitive force sensor --- slipping detection --- microfabrication --- alginate hydrogel --- microfluidics --- shape from silhouette --- artificial cochlea --- micro/nano technology --- ion concentration polarization --- thermoelectric generator --- ultraviolet treatment --- micro-stereolithography --- proximity sensor --- blink --- 3D shape reconstruction --- reductive sintering --- cellular automata --- crack configuration --- Young model --- transparent object --- femtosecond laser --- piezoelectric material --- Turing pattern model --- microtubes --- thermoelectric film --- luciferin–luciferase assay --- fluorescein isothiocyanate (FITC) --- printing --- triple-coaxial flow --- photopolymer --- metal conductive track --- ion depletion zone --- sensors --- microbes --- direct writing --- outer hair cell --- dye-sensitized photovoltaic cells --- microfiber spinning --- ATP --- 3D printing --- parasitic capacitance --- luciferin-luciferase assay
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This open access book deals with a rich variety of taxis-type cross-diffusive equations. Particularly, it intends to show the key role played by quasi-energy inequality in the derivation of some necessary a priori estimates. This book addresses applied mathematics and all researchers interested in mathematical development of reaction-diffusion theory and its application and can be a basis for a graduate course in applied mathematics.
Boundary value problems. --- Chemotaxis --- Navier-Stokes equations. --- Mathematical models. --- Equations, Navier-Stokes --- Differential equations, Partial --- Fluid dynamics --- Viscous flow --- Chemiotaxis --- Chemotropism --- Biochemistry --- Growth --- Taxes (Biology) --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Problemes de contorn --- Quimiotaxi --- Models matemàtics --- Equacions de Navier-Stokes --- Navier-Stokes (Equacions) --- Dinàmica de fluids --- Equacions en derivades parcials --- Models (Matemàtica) --- Models experimentals --- Models teòrics --- Mètodes de simulació --- Anàlisi de sistemes --- Mètode de Montecarlo --- Modelització multiescala --- Models economètrics --- Models lineals (Estadística) --- Models multinivell (Estadística) --- Models no lineals (Estadística) --- Programació (Ordinadors) --- Simulació per ordinador --- Teoria de màquines --- Models biològics --- Bioquímica --- Creixement --- Problemes de valor límit --- Equacions diferencials --- Física matemàtica --- Funcions de variables complexes --- Dispersió (Matemàtica) --- Equacions de Von Kármán --- Problema de Dirichlet --- Problema de Neumann --- Problemes de Riemann-Hilbert --- Problemes de valor inicial --- Reaction-Diffusion --- Haptotaxis --- Navier-Stokes --- Cancer invasion --- Coral fertilization --- Sensity-suppressed motility --- Oncolytic virotherapy --- Foraging scrounging interplay
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The crystal chemistry of spin crossover (SCO) behavior in coordination compounds can potentially be in association with smart materials—promising materials for applications as components of memory devices, displays, sensors and mechanical devices and, especially, actuators, such as artificial muscles. This Special Issue is devoted to various aspects of SCO and related research, comprising 18 interesting original papers on valuable and important SCO topics. Significant and fundamental scientific attention has been focused on the SCO phenomena in a wide research range of fields of fundamental chemical and physical and related sciences, containing the interdisciplinary regions of chemical and physical sciences related to the SCO phenomena. Coordination materials with bistable systems between the LS and the HS states are usually triggered by external stimuli, such as temperature, light, pressure, guest molecule inclusion, soft X-ray, and nuclear decay. Since the first Hofmann-like spin crossover (SCO) behavior in {Fe(py)2[Ni(CN)4]}n (py = pyridine) was demonstrated, this crystal chemistry motif has been frequently used to design Fe(II) SCO materials to enable determination of the correlations between structural features and magnetic properties.
n/a --- hexadentate ligand --- X-ray diffraction --- structural disorder --- lattice energy --- 2-bis(4-pyridyl)ethane --- thermal hysteresis --- optical conductivity spectrum --- spin-state crossover --- solvate --- single crystal --- spin-crossover transition --- spin-crossover --- cobalt oxide --- amorphous --- metal dithiolene complexes --- qsal ligand --- impurity effect --- 3-triazole --- intermolecular interactions --- spin crossover --- hydrogen bonding --- 1 --- 2 --- optical microscopy --- supramolecular coordination polymer --- paramagnetic ligand --- magnetic susceptibility --- high spin --- [Fe(III)(3-OMesal2-trien)]+ --- aminoxyl --- cobalt(II) ion --- mosaicity --- Fe(III) coordination complexes --- nitroxides --- C–H···? interactions --- Fe(II) --- dithiooxalato ligand --- dinuclear triple helicate --- coordination polymers --- magnetization --- spiral structure --- magnetostructural correlations --- charge-transfer phase transition --- structure phase transition --- magnetic properties --- spin polaron --- substitution of 3d transition metal ion --- iron(II) complexes --- X-ray absorption spectroscopy --- coordination complexes --- crystal engineering --- fatigability --- soft X-ray induced excited spin state trapping --- spin transition --- dipyridyl-N-alkylamine ligands --- coordination polymer --- iron (II) --- iron mixed-valence complex --- chiral propeller structure --- spin cross-over (SCO) --- EPR spectroscopy --- Cu(II) complexes --- solvent effects --- ferromagnetism --- SQUID --- LIESST effect --- low spin (LS) --- 57Fe Mössbauer spectroscopy --- dielectric response --- iron(II) --- hetero metal complex --- atropisomerism --- switch --- Schiff base --- counter-anion --- DFT calculation --- Fe(III) complex --- Fe(II) complex --- high spin (HS) --- reaction diffusion --- thermochromism --- supramolecular isomerism --- phase transition --- magnetic transition --- mononuclear --- [Au(dmit)2]? --- UV-Vis spectroscopy --- phase transitions --- ?-? interactions --- [Au(dddt)2]? --- crystal structure --- linear pentadentate ligand --- ion-pair crystals --- C-H···? interactions --- 57Fe Mössbauer spectroscopy
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