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Nonlinear science is the science of, among other exotic phenomena, unexpected and unpredictable behavior, catastrophes, complex interactions, and significant perturbations. Ocean and atmosphere dynamics, weather, many bodies in interaction, ultra-high intensity excitations, life, formation of natural patterns, and coupled interactions between components or different scales are only a few examples of systems where nonlinear science is necessary. All outstanding, self-sustained, and stable structures in space and time exist and protrude out of a regular linear background of states mainly because they identify themselves from the rest by being highly localized in range, time, configuration, states, and phase spaces. Guessing how high up you drive toward the top of the mountain by compiling your speed, road slope, and trip duration is a linear model, but predicting the occurrence around a turn of a boulder fallen on the road is a nonlinear phenomenon. In an effort to grasp and understand nonlinear phenomena, scientists have developed several mathematical approaches including inverse scattering theory, Backlund and groups of transformations, bilinear method, and several other detailed technical procedures. In this Special Issue, we introduce a few very recent approaches together with their physical meaning and applications. We present here five important papers on waves, unsteady flows, phases separation, ocean dynamics, nonlinear optic, viral dynamics, and the self-appearance of patterns for spatially extended systems, which are problems that have aroused scientists’ interest for decades, yet still cannot be predicted and have their generating mechanism and stability open to debate. The aim of this Special Issue was to present these most debated and interesting topics from nonlinear science for which, despite the existence of highly developed mathematical tools of investigation, there are still fundamental open questions.
diffusion --- viral infection --- non-Newtonian fluid --- convergence --- Navier–Stokes–Voigt equations --- existence --- Lyapunov functional --- Faedo–Galerkin approximations --- probability distribution --- strong solutions --- stability --- multigrid method --- parabolic equations --- long-time behavior --- Fokker–Planck equation --- viscoelastic models --- Cauchy problem --- unconditionally gradient stable scheme --- uniqueness --- existence and uniqueness theorem --- continuum spectrum pulse equation --- Stokes operator --- Lagrangian scheme --- Cahn–Hilliard equation --- Feller equation
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This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the Martingale problem and therefore the existence of the associated Markov process. Charles Epstein and Rafe Mazzeo use an "integral kernel method" to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high co-dimensional strata of the boundary. Epstein and Mazzeo establish the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. They show that the semigroups defined by these operators have holomorphic extensions to the right half-plane. Epstein and Mazzeo also demonstrate precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.
Elliptic operators. --- Markov processes. --- Population biology --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Stochastic processes --- Differential operators, Elliptic --- Operators, Elliptic --- Partial differential operators --- Mathematical models. --- 1-dimensional integral. --- Euclidean model problem. --- Euclidean space. --- Hlder space. --- Hopf boundary point. --- Kimura diffusion equation. --- Kimura diffusion operator. --- Laplace transform. --- Schauder estimate. --- WrightІisher geometry. --- adjoint operator. --- backward Kolmogorov equation. --- boundary behavior. --- degenerate elliptic operator. --- doubling. --- elliptic Kimura operator. --- elliptic equation. --- forward Kolmogorov equation. --- function space. --- general model problem. --- generalized Kimura diffusion. --- heat equation. --- heat kernel. --- higher dimensional corner. --- higher regularity. --- holomorphic semi-group. --- homogeneous Cauchy problem. --- hybrid space. --- hypersurface boundary. --- induction hypothesis. --- induction. --- inhomogeneous problem. --- irregular solution. --- long time asymptotics. --- long-time behavior. --- manifold with corners. --- martingale problem. --- mathematical finance. --- model problem. --- normal form. --- normal vector. --- null-space. --- off-diagonal behavior. --- open orthant. --- parabolic equation. --- perturbation theory. --- polyhedron. --- population genetics. --- probability theory. --- regularity. --- resolvent operator. --- semi-group. --- solution operator. --- uniqueness.
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This book, entitled “Elemental Concentration and Pollution in Soil, Water, and Sediment”, presents an updated overview of the main trace elements in living organisms. This collection brings researchers from different fields together, including those from biogeochemistry and ecotoxicology in various environmental media, in order to provide a more comprehensive understanding of the environmental fate of trace elements in their biogeochemical cycles for different ecosystems.
Research & information: general --- Chemistry --- marine sediments --- trace metals --- speciation --- contamination --- San Simon Bay --- soil remediation --- toxicity bioassays --- humic substances --- calcium carbonate --- iron oxides --- polyphenolic compounds --- heavy metals --- soil --- enrichment factor --- geoaccumulation index --- contamination factor --- pollution indices --- soil contamination --- geogenic and anthropogenic origin --- iron ore deposits --- tailing dumps --- seepage water --- water balance of the enterprise --- metals --- p-arsanilic acid --- adsorption --- natural fluorine-enriched soil --- natural sources --- chemical extraction resistance --- low washing efficiency --- lacustrine sediments --- geochemical mapping --- spatial distribution --- contamination assessment --- environmental risk assessments --- sediment quality guidelines --- pollution --- bottom sediments --- river --- acid mine drainage --- abandoned coal mine --- potentially toxic elements --- pollution level --- potential ecological risk --- sewage sludge --- calcareous soil --- extraction DTPA --- crop --- transfer --- long time --- engineered nanoparticles --- organic matter --- phosphorus --- nutrients --- volcanic soil --- agricultural land contamination --- sediment --- irrigation canal --- heavy metal --- copper --- cadmium --- Daphnia pulex --- ecotoxicology --- LC50 --- ecological risk assessment --- karst areas --- soil properties --- urban ecology --- trace metal pollution --- soil organisms --- diversity --- Western Siberia --- snow pollution --- trace metals and metalloids --- atmospheric depositions --- solubility --- sediments --- bioindicators --- geochemical background --- risk assessment code --- sequential extraction --- groundwater --- precipitation --- caustic calcined magnesia (CCM) --- permeable reactive barrier (PRB) --- natural water --- water quality --- Arctic region --- elemental composition --- springs --- QR code --- modern sedimentation processes --- mineralogy --- geochemistry --- authigenic minerals --- hydrogen sulfide contamination --- arid climate --- Caspian Sea --- marine sediments --- trace metals --- speciation --- contamination --- San Simon Bay --- soil remediation --- toxicity bioassays --- humic substances --- calcium carbonate --- iron oxides --- polyphenolic compounds --- heavy metals --- soil --- enrichment factor --- geoaccumulation index --- contamination factor --- pollution indices --- soil contamination --- geogenic and anthropogenic origin --- iron ore deposits --- tailing dumps --- seepage water --- water balance of the enterprise --- metals --- p-arsanilic acid --- adsorption --- natural fluorine-enriched soil --- natural sources --- chemical extraction resistance --- low washing efficiency --- lacustrine sediments --- geochemical mapping --- spatial distribution --- contamination assessment --- environmental risk assessments --- sediment quality guidelines --- pollution --- bottom sediments --- river --- acid mine drainage --- abandoned coal mine --- potentially toxic elements --- pollution level --- potential ecological risk --- sewage sludge --- calcareous soil --- extraction DTPA --- crop --- transfer --- long time --- engineered nanoparticles --- organic matter --- phosphorus --- nutrients --- volcanic soil --- agricultural land contamination --- sediment --- irrigation canal --- heavy metal --- copper --- cadmium --- Daphnia pulex --- ecotoxicology --- LC50 --- ecological risk assessment --- karst areas --- soil properties --- urban ecology --- trace metal pollution --- soil organisms --- diversity --- Western Siberia --- snow pollution --- trace metals and metalloids --- atmospheric depositions --- solubility --- sediments --- bioindicators --- geochemical background --- risk assessment code --- sequential extraction --- groundwater --- precipitation --- caustic calcined magnesia (CCM) --- permeable reactive barrier (PRB) --- natural water --- water quality --- Arctic region --- elemental composition --- springs --- QR code --- modern sedimentation processes --- mineralogy --- geochemistry --- authigenic minerals --- hydrogen sulfide contamination --- arid climate --- Caspian Sea
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This book, entitled “Elemental Concentration and Pollution in Soil, Water, and Sediment”, presents an updated overview of the main trace elements in living organisms. This collection brings researchers from different fields together, including those from biogeochemistry and ecotoxicology in various environmental media, in order to provide a more comprehensive understanding of the environmental fate of trace elements in their biogeochemical cycles for different ecosystems.
Research & information: general --- Chemistry --- marine sediments --- trace metals --- speciation --- contamination --- San Simon Bay --- soil remediation --- toxicity bioassays --- humic substances --- calcium carbonate --- iron oxides --- polyphenolic compounds --- heavy metals --- soil --- enrichment factor --- geoaccumulation index --- contamination factor --- pollution indices --- soil contamination --- geogenic and anthropogenic origin --- iron ore deposits --- tailing dumps --- seepage water --- water balance of the enterprise --- metals --- p-arsanilic acid --- adsorption --- natural fluorine-enriched soil --- natural sources --- chemical extraction resistance --- low washing efficiency --- lacustrine sediments --- geochemical mapping --- spatial distribution --- contamination assessment --- environmental risk assessments --- sediment quality guidelines --- pollution --- bottom sediments --- river --- acid mine drainage --- abandoned coal mine --- potentially toxic elements --- pollution level --- potential ecological risk --- sewage sludge --- calcareous soil --- extraction DTPA --- crop --- transfer --- long time --- engineered nanoparticles --- organic matter --- phosphorus --- nutrients --- volcanic soil --- agricultural land contamination --- sediment --- irrigation canal --- heavy metal --- copper --- cadmium --- Daphnia pulex --- ecotoxicology --- LC50 --- ecological risk assessment --- karst areas --- soil properties --- urban ecology --- trace metal pollution --- soil organisms --- diversity --- Western Siberia --- snow pollution --- trace metals and metalloids --- atmospheric depositions --- solubility --- sediments --- bioindicators --- geochemical background --- risk assessment code --- sequential extraction --- groundwater --- precipitation --- caustic calcined magnesia (CCM) --- permeable reactive barrier (PRB) --- natural water --- water quality --- Arctic region --- elemental composition --- springs --- QR code --- modern sedimentation processes --- mineralogy --- geochemistry --- authigenic minerals --- hydrogen sulfide contamination --- arid climate --- Caspian Sea --- n/a
Choose an application
This book, entitled “Elemental Concentration and Pollution in Soil, Water, and Sediment”, presents an updated overview of the main trace elements in living organisms. This collection brings researchers from different fields together, including those from biogeochemistry and ecotoxicology in various environmental media, in order to provide a more comprehensive understanding of the environmental fate of trace elements in their biogeochemical cycles for different ecosystems.
marine sediments --- trace metals --- speciation --- contamination --- San Simon Bay --- soil remediation --- toxicity bioassays --- humic substances --- calcium carbonate --- iron oxides --- polyphenolic compounds --- heavy metals --- soil --- enrichment factor --- geoaccumulation index --- contamination factor --- pollution indices --- soil contamination --- geogenic and anthropogenic origin --- iron ore deposits --- tailing dumps --- seepage water --- water balance of the enterprise --- metals --- p-arsanilic acid --- adsorption --- natural fluorine-enriched soil --- natural sources --- chemical extraction resistance --- low washing efficiency --- lacustrine sediments --- geochemical mapping --- spatial distribution --- contamination assessment --- environmental risk assessments --- sediment quality guidelines --- pollution --- bottom sediments --- river --- acid mine drainage --- abandoned coal mine --- potentially toxic elements --- pollution level --- potential ecological risk --- sewage sludge --- calcareous soil --- extraction DTPA --- crop --- transfer --- long time --- engineered nanoparticles --- organic matter --- phosphorus --- nutrients --- volcanic soil --- agricultural land contamination --- sediment --- irrigation canal --- heavy metal --- copper --- cadmium --- Daphnia pulex --- ecotoxicology --- LC50 --- ecological risk assessment --- karst areas --- soil properties --- urban ecology --- trace metal pollution --- soil organisms --- diversity --- Western Siberia --- snow pollution --- trace metals and metalloids --- atmospheric depositions --- solubility --- sediments --- bioindicators --- geochemical background --- risk assessment code --- sequential extraction --- groundwater --- precipitation --- caustic calcined magnesia (CCM) --- permeable reactive barrier (PRB) --- natural water --- water quality --- Arctic region --- elemental composition --- springs --- QR code --- modern sedimentation processes --- mineralogy --- geochemistry --- authigenic minerals --- hydrogen sulfide contamination --- arid climate --- Caspian Sea --- n/a
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