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The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology.

Differentiable dynamical systems. --- Chaotic behavior in systems. --- Stochastic systems. --- Systems, Stochastic --- Stochastic processes --- System analysis --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Affine transformation. --- Amplitude. --- Arbitrarily large. --- Attractor. --- Autocovariance. --- Big O notation. --- Central limit theorem. --- Change of variables. --- Chaos theory. --- Coefficient of variation. --- Compound Probability. --- Computational problem. --- Control theory. --- Convolution. --- Coriolis force. --- Correlation coefficient. --- Covariance function. --- Cross-covariance. --- Cumulative distribution function. --- Cutoff frequency. --- Deformation (mechanics). --- Derivative. --- Deterministic system. --- Diagram (category theory). --- Diffeomorphism. --- Differential equation. --- Dirac delta function. --- Discriminant. --- Dissipation. --- Dissipative system. --- Dynamical system. --- Eigenvalues and eigenvectors. --- Equations of motion. --- Even and odd functions. --- Excitation (magnetic). --- Exponential decay. --- Extreme value theory. --- Flow velocity. --- Fluid dynamics. --- Forcing (recursion theory). --- Fourier series. --- Fourier transform. --- Fractal dimension. --- Frequency domain. --- Gaussian noise. --- Gaussian process. --- Harmonic analysis. --- Harmonic function. --- Heteroclinic orbit. --- Homeomorphism. --- Homoclinic orbit. --- Hyperbolic point. --- Inference. --- Initial condition. --- Instability. --- Integrable system. --- Invariant manifold. --- Iteration. --- Joint probability distribution. --- LTI system theory. --- Limit cycle. --- Linear differential equation. --- Logistic map. --- Marginal distribution. --- Moduli (physics). --- Multiplicative noise. --- Noise (electronics). --- Nonlinear control. --- Nonlinear system. --- Ornstein–Uhlenbeck process. --- Oscillation. --- Parameter space. --- Parameter. --- Partial differential equation. --- Perturbation function. --- Phase plane. --- Phase space. --- Poisson distribution. --- Probability density function. --- Probability distribution. --- Probability theory. --- Probability. --- Production–possibility frontier. --- Relative velocity. --- Scale factor. --- Shear stress. --- Spectral density. --- Spectral gap. --- Standard deviation. --- Stochastic process. --- Stochastic resonance. --- Stochastic. --- Stream function. --- Surface stress. --- Symbolic dynamics. --- The Signal and the Noise. --- Topological conjugacy. --- Transfer function. --- Variance. --- Vorticity.

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This book contains the successful submissions to a Special Issue of Energies entitled “Engineering Fluid Dynamics 2019–2020”. The topic of engineering fluid dynamics includes both experimental and computational studies. Of special interest were submissions from the fields of mechanical, chemical, marine, safety, and energy engineering. We welcomed original research articles and review articles. After one-and-a-half years, 59 papers were submitted and 31 were accepted for publication. The average processing time was about 41 days. The authors had the following geographical distribution: China (15); Korea (7); Japan (3); Norway (2); Sweden (2); Vietnam (2); Australia (1); Denmark (1); Germany (1); Mexico (1); Poland (1); Saudi Arabia (1); USA (1); Serbia (1). Papers covered a wide range of topics including analysis of free-surface waves, bridge girders, gear boxes, hills, radiation heat transfer, spillways, turbulent flames, pipe flow, open channels, jets, combustion chambers, welding, sprinkler, slug flow, turbines, thermoelectric power generation, airfoils, bed formation, fires in tunnels, shell-and-tube heat exchangers, and pumps.

History of engineering & technology --- CFD --- gap resonance --- hydrodynamic forces --- free surface waves --- URANS --- twin-box deck --- aerodynamics --- vortex shedding --- splash lubrication --- dynamic motion --- gearbox --- churning power losses --- non-inertial coordinate system --- ground roughness --- hill shape --- hill slope --- large-eddy simulations --- turbulent flow fields --- turbulent structure --- computational fluid dynamics (CFD) --- large eddy simulations (LES) --- 3D hill --- canopy --- flow fields --- radiation --- blocked-off-region procedure --- heat recuperation --- anisotropic scattering --- mie particles --- numerical simulation --- horizontal face angle --- energy dissipation rates --- stepped spillway --- ultra-low specific speed magnetic drive pump --- orthogonal test --- splitter blades --- optimized design --- pressure fluctuation --- radial force --- dilution --- turbulent flame --- premixed --- OH --- CH2O --- planar laser-induced fluorescence --- self-excited oscillation jet --- organ–Helmholtz nozzle --- pulse waterjet --- pressure pulsation amplitude --- WMLES --- VLSMs --- LSMs --- turbulent boundary flow --- roughness --- surrogate model --- deep neural network --- multiphase flow --- horizontal pipe --- liquid holdup --- pressure gradient --- coherent structures --- turbulent boundary layer --- stability --- pre-multiplied wind velocity spectrum --- spatial correlation coefficient field --- tunnel fires --- jet fan speed --- heat release rate --- aspect ratio --- smoke movement --- visibility --- smoke layer thickness --- smoke stratification --- orifice shape --- vertical jet --- velocity ratio --- numerical investigation --- hydraulic characteristics --- impinging water jet --- impinging height --- numerical calculation --- swirler --- optimized --- genetic algorithms --- recirculation --- combustion --- experimental validation --- welding spatter --- distribution --- shield arc metal welding --- particle heat transfer --- fire risk --- sprinkler --- fire dynamics simulator (FDS) --- fire suppression --- extinguishing coefficient --- smoke logging --- smoke spread --- pipe insulation --- fire growth rate index --- scale factor --- volume fraction --- ignition heat source --- maximum heat release rate --- time to reach maximum HRR (heat release rate) --- control --- cylinder --- energy efficiency --- clamping --- pneumatics --- unsteady RANS simulation --- two-phase flow --- riser-induced slug flow --- LedaFlow --- VOF-model --- evacuation --- interaction between smoke and evacuees --- inner smoke force --- modified BR-smoke model --- twin H-rotor vertical-axis turbines --- wake --- instability --- wavelet transform --- computational fluid dynamics (CFD), multiphysics --- heat transfer --- thermoelectricity --- automotive --- traditional market --- fire spread rate --- radiant heat flux --- separation distance --- rotor stator interaction --- boundary layer --- secondary vortex --- unsteady flow --- submerged jet --- climate change --- renewable energy --- wind power --- accelerators --- turbines --- power extraction --- Betz --- freestream theory --- hybrid simulation method --- multi-fluid model --- discrete element method, sedimentation, bed formation --- PIV --- shell-and-tube --- shell side --- tube bundle --- heat exchanger --- baffle --- maldistribution

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• Reference Manager
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This book contains the successful submissions to a Special Issue of Energies entitled “Engineering Fluid Dynamics 2019–2020”. The topic of engineering fluid dynamics includes both experimental and computational studies. Of special interest were submissions from the fields of mechanical, chemical, marine, safety, and energy engineering. We welcomed original research articles and review articles. After one-and-a-half years, 59 papers were submitted and 31 were accepted for publication. The average processing time was about 41 days. The authors had the following geographical distribution: China (15); Korea (7); Japan (3); Norway (2); Sweden (2); Vietnam (2); Australia (1); Denmark (1); Germany (1); Mexico (1); Poland (1); Saudi Arabia (1); USA (1); Serbia (1). Papers covered a wide range of topics including analysis of free-surface waves, bridge girders, gear boxes, hills, radiation heat transfer, spillways, turbulent flames, pipe flow, open channels, jets, combustion chambers, welding, sprinkler, slug flow, turbines, thermoelectric power generation, airfoils, bed formation, fires in tunnels, shell-and-tube heat exchangers, and pumps.

CFD --- gap resonance --- hydrodynamic forces --- free surface waves --- URANS --- twin-box deck --- aerodynamics --- vortex shedding --- splash lubrication --- dynamic motion --- gearbox --- churning power losses --- non-inertial coordinate system --- ground roughness --- hill shape --- hill slope --- large-eddy simulations --- turbulent flow fields --- turbulent structure --- computational fluid dynamics (CFD) --- large eddy simulations (LES) --- 3D hill --- canopy --- flow fields --- radiation --- blocked-off-region procedure --- heat recuperation --- anisotropic scattering --- mie particles --- numerical simulation --- horizontal face angle --- energy dissipation rates --- stepped spillway --- ultra-low specific speed magnetic drive pump --- orthogonal test --- splitter blades --- optimized design --- pressure fluctuation --- radial force --- dilution --- turbulent flame --- premixed --- OH --- CH2O --- planar laser-induced fluorescence --- self-excited oscillation jet --- organ–Helmholtz nozzle --- pulse waterjet --- pressure pulsation amplitude --- WMLES --- VLSMs --- LSMs --- turbulent boundary flow --- roughness --- surrogate model --- deep neural network --- multiphase flow --- horizontal pipe --- liquid holdup --- pressure gradient --- coherent structures --- turbulent boundary layer --- stability --- pre-multiplied wind velocity spectrum --- spatial correlation coefficient field --- tunnel fires --- jet fan speed --- heat release rate --- aspect ratio --- smoke movement --- visibility --- smoke layer thickness --- smoke stratification --- orifice shape --- vertical jet --- velocity ratio --- numerical investigation --- hydraulic characteristics --- impinging water jet --- impinging height --- numerical calculation --- swirler --- optimized --- genetic algorithms --- recirculation --- combustion --- experimental validation --- welding spatter --- distribution --- shield arc metal welding --- particle heat transfer --- fire risk --- sprinkler --- fire dynamics simulator (FDS) --- fire suppression --- extinguishing coefficient --- smoke logging --- smoke spread --- pipe insulation --- fire growth rate index --- scale factor --- volume fraction --- ignition heat source --- maximum heat release rate --- time to reach maximum HRR (heat release rate) --- control --- cylinder --- energy efficiency --- clamping --- pneumatics --- unsteady RANS simulation --- two-phase flow --- riser-induced slug flow --- LedaFlow --- VOF-model --- evacuation --- interaction between smoke and evacuees --- inner smoke force --- modified BR-smoke model --- twin H-rotor vertical-axis turbines --- wake --- instability --- wavelet transform --- computational fluid dynamics (CFD), multiphysics --- heat transfer --- thermoelectricity --- automotive --- traditional market --- fire spread rate --- radiant heat flux --- separation distance --- rotor stator interaction --- boundary layer --- secondary vortex --- unsteady flow --- submerged jet --- climate change --- renewable energy --- wind power --- accelerators --- turbines --- power extraction --- Betz --- freestream theory --- hybrid simulation method --- multi-fluid model --- discrete element method, sedimentation, bed formation --- PIV --- shell-and-tube --- shell side --- tube bundle --- heat exchanger --- baffle --- maldistribution

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book contains the successful submissions to a Special Issue of Energies entitled “Engineering Fluid Dynamics 2019–2020”. The topic of engineering fluid dynamics includes both experimental and computational studies. Of special interest were submissions from the fields of mechanical, chemical, marine, safety, and energy engineering. We welcomed original research articles and review articles. After one-and-a-half years, 59 papers were submitted and 31 were accepted for publication. The average processing time was about 41 days. The authors had the following geographical distribution: China (15); Korea (7); Japan (3); Norway (2); Sweden (2); Vietnam (2); Australia (1); Denmark (1); Germany (1); Mexico (1); Poland (1); Saudi Arabia (1); USA (1); Serbia (1). Papers covered a wide range of topics including analysis of free-surface waves, bridge girders, gear boxes, hills, radiation heat transfer, spillways, turbulent flames, pipe flow, open channels, jets, combustion chambers, welding, sprinkler, slug flow, turbines, thermoelectric power generation, airfoils, bed formation, fires in tunnels, shell-and-tube heat exchangers, and pumps.

History of engineering & technology --- CFD --- gap resonance --- hydrodynamic forces --- free surface waves --- URANS --- twin-box deck --- aerodynamics --- vortex shedding --- splash lubrication --- dynamic motion --- gearbox --- churning power losses --- non-inertial coordinate system --- ground roughness --- hill shape --- hill slope --- large-eddy simulations --- turbulent flow fields --- turbulent structure --- computational fluid dynamics (CFD) --- large eddy simulations (LES) --- 3D hill --- canopy --- flow fields --- radiation --- blocked-off-region procedure --- heat recuperation --- anisotropic scattering --- mie particles --- numerical simulation --- horizontal face angle --- energy dissipation rates --- stepped spillway --- ultra-low specific speed magnetic drive pump --- orthogonal test --- splitter blades --- optimized design --- pressure fluctuation --- radial force --- dilution --- turbulent flame --- premixed --- OH --- CH2O --- planar laser-induced fluorescence --- self-excited oscillation jet --- organ–Helmholtz nozzle --- pulse waterjet --- pressure pulsation amplitude --- WMLES --- VLSMs --- LSMs --- turbulent boundary flow --- roughness --- surrogate model --- deep neural network --- multiphase flow --- horizontal pipe --- liquid holdup --- pressure gradient --- coherent structures --- turbulent boundary layer --- stability --- pre-multiplied wind velocity spectrum --- spatial correlation coefficient field --- tunnel fires --- jet fan speed --- heat release rate --- aspect ratio --- smoke movement --- visibility --- smoke layer thickness --- smoke stratification --- orifice shape --- vertical jet --- velocity ratio --- numerical investigation --- hydraulic characteristics --- impinging water jet --- impinging height --- numerical calculation --- swirler --- optimized --- genetic algorithms --- recirculation --- combustion --- experimental validation --- welding spatter --- distribution --- shield arc metal welding --- particle heat transfer --- fire risk --- sprinkler --- fire dynamics simulator (FDS) --- fire suppression --- extinguishing coefficient --- smoke logging --- smoke spread --- pipe insulation --- fire growth rate index --- scale factor --- volume fraction --- ignition heat source --- maximum heat release rate --- time to reach maximum HRR (heat release rate) --- control --- cylinder --- energy efficiency --- clamping --- pneumatics --- unsteady RANS simulation --- two-phase flow --- riser-induced slug flow --- LedaFlow --- VOF-model --- evacuation --- interaction between smoke and evacuees --- inner smoke force --- modified BR-smoke model --- twin H-rotor vertical-axis turbines --- wake --- instability --- wavelet transform --- computational fluid dynamics (CFD), multiphysics --- heat transfer --- thermoelectricity --- automotive --- traditional market --- fire spread rate --- radiant heat flux --- separation distance --- rotor stator interaction --- boundary layer --- secondary vortex --- unsteady flow --- submerged jet --- climate change --- renewable energy --- wind power --- accelerators --- turbines --- power extraction --- Betz --- freestream theory --- hybrid simulation method --- multi-fluid model --- discrete element method, sedimentation, bed formation --- PIV --- shell-and-tube --- shell side --- tube bundle --- heat exchanger --- baffle --- maldistribution