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Applied Analysis of Ordinary Differential Equations

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ISBN: 9783039217267 9783039217274 Year: Pages: 62 DOI: 10.3390/books978-3-03921-727-4 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:16
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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.

Kinetic Theory and Swarming Tools to Modeling Complex Systems—Symmetry problems in the Science of Living Systems

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ISBN: 9783039288793 / 9783039288809 Year: Pages: 118 DOI: 10.3390/books978-3-03928-880-9 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- Economics
Added to DOAB on : 2020-06-09 16:38:57
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This MPDI book comprises a number of selected contributions to a Special Issue devoted to the modeling and simulation of living systems based on developments in kinetic mathematical tools. The focus is on a fascinating research field which cannot be tackled by the approach of the so-called hard sciences—specifically mathematics—without the invention of new methods in view of a new mathematical theory. The contents proposed by eight contributions witness the growing interest of scientists this field. The first contribution is an editorial paper which presents the motivations for studying the mathematics and physics of living systems within the framework an interdisciplinary approach, where mathematics and physics interact with specific fields of the class of systems object of modeling and simulations. The different contributions refer to economy, collective learning, cell motion, vehicular traffic, crowd dynamics, and social swarms. The key problem towards modeling consists in capturing the complexity features of living systems. All articles refer to large systems of interaction living entities and follow, towards modeling, a common rationale which consists firstly in representing the system by a probability distribution over the microscopic state of the said entities, secondly, in deriving a general mathematical structure deemed to provide the conceptual basis for the derivation of models and, finally, in implementing the said structure by models of interactions at the microscopic scale. Therefore, the modeling approach transfers the dynamics at the low scale to collective behaviors. Interactions are modeled by theoretical tools of stochastic game theory. Overall, the interested reader will find, in the contents, a forward look comprising various research perspectives and issues, followed by hints on to tackle these.

Advances in Cholesteric Liquid Crystals

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ISBN: 9783039282289 9783039282296 Year: Pages: 122 DOI: 10.3390/books978-3-03928-229-6 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Chemistry (General) --- Science (General)
Added to DOAB on : 2020-04-07 23:07:08
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With their helical structure, cholesteric liquid crystals figure prominently in liquid crystal science. The selective reflection of light is their flagship property, and they offer a myriad of applications as advanced optical materials with multiscale properties. The cholesteric structure is also a ubiquitous design in the animal and plant kingdoms. This book contains eight contributions on fundamental investigations about defects, textures and structures of cholesteric materials, and experimental studies aimed at applications such as temperature sensors, head-up displays for improving automobile driving safety, or smart windows.

New Trends in Differential and Difference Equations and Applications

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ISBN: 9783039215386 9783039215393 Year: Pages: 198 DOI: 10.3390/books978-3-03921-539-3 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-12-09 11:49:15
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This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.

Keywords

Legendre wavelets --- collocation method --- three-step Taylor method --- asymptotic stability --- time-dependent partial differential equations --- non-instantaneous impulses --- Caputo fractional derivative --- differential equations --- state dependent delays --- lipschitz stability --- limit-periodic solutions --- difference equations --- exponential dichotomy --- strong nonlinearities --- effective existence criteria --- population dynamics --- discrete Lyapunov equation --- difference equations --- Hilbert space --- dichotomy --- exponential stability --- ?-Laplacian operator --- mean curvature operator --- heteroclinic solutions --- problems in the real line --- lower and upper solutions --- Nagumo condition on the real line --- fixed point theory --- coupled nonlinear systems --- functional boundary conditions --- Schauder’s fixed point theory --- Arzèla Ascoli theorem --- lower and upper solutions --- first order periodic systems --- SIRS epidemic model --- mathematical modelling --- Navier–Stokes equations --- global solutions --- regular solutions --- a priori estimates --- weak solutions --- kinetic energy --- dissipation --- Bäcklund transformation --- Clairin’s method --- generalized Liouville equation --- Miura transformation --- Korteweg-de Vries equation --- second-order differential/difference/q-difference equation of hypergeometric type --- non-uniform lattices --- divided-difference equations --- polynomial solution --- integro-differentials --- Sumudu decomposition method --- dynamical system

Responsive Architecture

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ISBN: 9783039216987 9783039216994 Year: Pages: 204 DOI: 10.3390/books978-3-03921-699-4 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Arts in general --- Architecture
Added to DOAB on : 2019-12-09 11:49:16
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This book is a collection of articles that have been published in the Special Issue “Responsive Architecture” of the MDPI journal Buildings. The eleven articles within cover various areas of sensitive architecture, including the design of packaging structures reacting to supporting components; structural efficiency of bent columns in indigenous houses; roof forms responsive to buildings depending on their resiliently transformed steel shell parts; creative design of building free shapes covered with transformed shells; artistic structural concepts of the architect and civil engineer; digitally designed airport terminal using wind analysis; rationalized shaping of sensitive curvilinear steel construction; interactive stories of responsive architecture; transformed shell roof constructions as the main determinant in the creative shaping of buildings without shapes that are sensitive to man-made and natural environments; thermally sensitive performances of a special shielding envelope on balconies; quantification of generality and adaptability of building layout using the SAGA method; and influence of initial conditions on the simulation of the transient temperature field inside a wall.

Keywords

bent piles --- structural systems --- vernacular houses --- Ammatoan houses --- building structure --- effectivity --- strength --- corrugated shell roof --- free-form building --- architectural form --- folded sheet --- thin-walled profile --- shape transformation --- steel construction --- building free-form structure --- corrugated shell roof --- architectural form --- thin-walled open profile --- shape transformation --- folded sheet --- steel construction --- performance-oriented design --- parametric architecture --- form-finding --- CFD --- wind analysis --- digital tools --- steel bar structures --- structural analysis --- parametric design --- algorithmic-aided shaping --- responsive architecture --- shadows --- Grasshopper --- Karamba 3D --- interactive architecture --- interaction narrative --- user experience --- situatedness --- agent-based theory --- building free form structure --- corrugated shell roof --- integrated architectural form --- thin-walled open profile --- shape transformation --- folded sheet --- adaptive envelope --- thermal performances --- spanish balcony --- simulation and computational design studies --- responsive architecture --- kinetic envelope --- adaptive design --- interactive architecture --- moveable facade components --- carrier component structures --- sensor interaction --- digital fabrication --- adaptability --- generality --- flexibility --- evaluation tool --- network analysis --- Space Syntax --- justified plan graphs --- spatial analysis --- architectural morphology --- space plan --- boundary conditions for simulation --- initial conditions --- thermal conditions --- heat flow --- numerical analysis --- experimental measurement --- outdoor test cells

Recent Advances in Mechanics of Non-Newtonian Fluids

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ISBN: 9783039283088 9783039283095 Year: Pages: 252 DOI: 10.3390/books978-3-03928-309-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2020-04-07 23:07:08
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Non-Newtonian (non-linear) fluids are common in nature, for example, in mud and honey, but also in many chemical, biological, food, pharmaceutical, and personal care processing industries. This Special Issue of Fluids is dedicated to the recent advances in the mathematical and physical modeling of non-linear fluids with industrial applications, especially those concerned with CFD studies. These fluids include traditional non-Newtonian fluid models, electro- or magneto-rheological fluids, granular materials, slurries, drilling fluids, polymers, blood and other biofluids, mixtures of fluids and particles, etc.

Keywords

inhomogeneous fluids --- non-newtonian fluids --- lubrication approximation (76A05, 76D08, 76A20) --- particle interaction --- viscoplastic fluid --- Bingham fluid --- computational fluid dynamics --- porous media --- convection --- Bingham fluid --- yield stress --- channel flow --- power-law fluid --- shear-dependent viscosity --- Reynolds equation --- lubrication approximation --- lid-driven cavity --- projection method --- shear-thinning --- aspect ratio --- Re numbers --- Brinkman equation --- viscosity ratio --- first- and second-order slip --- similarity transformation --- porous medium --- generalised simplified PTT --- Phan-Thien–Tanner (PTT) model --- Mittag–Leffler --- Couette flow --- Poiseuille–Couette flow --- non-isothermal flows --- creeping flows --- viscous fluid --- optimal control --- boundary control --- pressure boundary conditions --- weak solution --- existence theorem --- marginal function --- hemoglobin --- biological capacitor --- non-equilibrium thermodynamics --- hemoglobe capacitor --- thermodynamic capacitor --- smoothed particle hydrodynamics (SPH) --- meshless --- fluid-solid interaction (FSI) --- membrane --- rupture --- SPH-FEM --- stokesian dynamics --- dense suspension --- rheology --- bubble suspension --- suspension viscosity --- Gamma densitometer --- high viscosity oil --- slug translational velocity --- closure relationship --- wormlike micellar solutions (WMS) --- enhanced oil recovery (EOR) --- chemical EOR (cEOR) --- viscoelastic surfactants (VES) --- non-linear fluids --- variable viscosity --- natural convection --- convection-diffusion --- buoyancy force --- lubrication --- suspensions --- viscoplastic fluids --- cement --- biofluids --- oil recovery --- porous media

Integral Transforms and Operational Calculus

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ISBN: 9783039216185 9783039216192 Year: Pages: 510 DOI: 10.3390/books978-3-03921-619-2 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.

Keywords

highly oscillatory --- convolution quadrature rule --- volterra integral equation --- Bessel kernel --- convergence --- higher order Schwarzian derivatives --- Janowski star-like function --- Janowski convex function --- bound on derivatives --- tangent numbers --- tangent polynomials --- Carlitz-type q-tangent numbers --- Carlitz-type q-tangent polynomials --- (p,q)-analogue of tangent numbers and polynomials --- (p,q)-analogue of tangent zeta function --- symmetric identities --- zeros --- Lommel functions --- univalent functions --- starlike functions --- convex functions --- inclusion relationships --- analytic function --- Hankel determinant --- exponential function --- upper bound --- nonlinear boundary value problems --- fractional-order differential equations --- Riemann-Stieltjes functional integral --- Liouville-Caputo fractional derivative --- infinite-point boundary conditions --- advanced and deviated arguments --- existence of at least one solution --- Fredholm integral equation --- Schauder fixed point theorem --- Hölder condition --- generalized Kuramoto–Sivashinsky equation --- modified Kudryashov method --- exact solutions --- Maple graphs --- analytic function --- Hadamard product (convolution) --- partial sum --- Srivastava–Tomovski generalization of Mittag–Leffler function --- subordination --- differential equation --- differential inclusion --- Liouville–Caputo-type fractional derivative --- fractional integral --- existence --- fixed point --- Bernoulli spiral --- Grandi curves --- Chebyshev polynomials --- pseudo-Chebyshev polynomials --- orthogonality property --- symmetric --- encryption --- password --- hash --- cryptography --- PBKDF --- q–Bleimann–Butzer–Hahn operators --- (p,q)-integers --- (p,q)-Bernstein operators --- (p,q)-Bleimann–Butzer–Hahn operators --- modulus of continuity --- rate of approximation --- K-functional --- Hurwitz-Lerch zeta function --- generalized functions --- analytic number theory --- ?-generalized Hurwitz-Lerch zeta functions --- derivative properties --- series representation --- basic hypergeometric functions --- generating functions --- q-polynomials --- analytic functions --- Mittag–Leffler functions --- starlike functions --- convex functions --- Hardy space --- vibrating string equation --- initial conditions --- spectral decomposition --- regular solution --- the uniqueness of the solution --- the existence of a solution --- analytic --- ?-convex function --- starlike function --- strongly-starlike function --- subordination --- q -Sheffer–Appell polynomials --- generating relations --- determinant definition --- recurrence relation --- q -Hermite–Bernoulli polynomials --- q -Hermite–Euler polynomials --- q -Hermite–Genocchi polynomials --- Volterra integral equations --- highly oscillatory Bessel kernel --- Hermite interpolation --- direct Hermite collocation method --- piecewise Hermite collocation method --- differential operator --- q-hypergeometric functions --- meromorphic function --- Mittag–Leffler function --- Hadamard product --- differential subordination --- starlike functions --- Bell numbers --- radius estimate --- (p, q)-integers --- Dunkl analogue --- generating functions --- generalization of exponential function --- Szász operator --- modulus of continuity --- function spaces and their duals --- distributions --- tempered distributions --- Schwartz testing function space --- generalized functions --- distribution space --- wavelet transform of generalized functions --- Fourier transform --- analytic function --- subordination --- Dziok–Srivastava operator --- nonlinear boundary value problem --- nonlocal --- multi-point --- multi-strip --- existence --- Ulam stability --- functions of bounded boundary and bounded radius rotations --- subordination --- functions with positive real part --- uniformly starlike and convex functions --- analytic functions --- univalent functions --- starlike and q-starlike functions --- q-derivative (or q-difference) operator --- sufficient conditions --- distortion theorems --- Janowski functions --- analytic number theory --- ?-generalized Hurwitz–Lerch zeta functions --- derivative properties --- recurrence relations --- integral representations --- Mellin transform --- natural transform --- Adomian decomposition method --- Caputo fractional derivative --- generalized mittag-leffler function --- analytic functions --- Hadamard product --- starlike functions --- q-derivative (or q-difference) operator --- Hankel determinant --- q-starlike functions --- fuzzy volterra integro-differential equations --- fuzzy general linear method --- fuzzy differential equations --- generalized Hukuhara differentiability --- spectrum symmetry --- DCT --- MFCC --- audio features --- anuran calls --- analytic functions --- convex functions --- starlike functions --- strongly convex functions --- strongly starlike functions --- uniformly convex functions --- Struve functions --- truncated-exponential polynomials --- monomiality principle --- generating functions --- Apostol-type polynomials and Apostol-type numbers --- Bernoulli, Euler and Genocchi polynomials --- Bernoulli, Euler, and Genocchi numbers --- operational methods --- summation formulas --- symmetric identities --- Euler numbers and polynomials --- q-Euler numbers and polynomials --- Hurwitz-Euler eta function --- multiple Hurwitz-Euler eta function --- higher order q-Euler numbers and polynomials --- (p, q)-Euler numbers and polynomials of higher order --- symmetric identities --- symmetry of the zero

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