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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 timevariation 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.
coupled system  green’s function  integral boundary conditions  Ulam’s stability  nonlinear dynamics  bifurcation analysis  ion current interactions  EADs  MATCONT  SIR epidemic model  age structure  endemic equilibrium  stability  basic reproduction number  surface of section  transport  heteroclinic tangle  n/a
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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 socalled 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.
crowd dynamics  scaling  kinetic models  safety  learning dynamics  kinetic theory  complex systems  multiscale modeling  cell movement  haptotaxis  kinetic theory  opinion dynamics  symmetric interactions  kinetic equations  integrodifferential equations  conformist society  individualistic society  Efficient frontier  kinetic theory  CVaR  vehicular traffic  short and longrange interactions  kinetic theory  Crowd dynamics  kinetic models  stress conditions  boundary conditions  safety  kinetic theory  living systems  social dynamics  active particles  learning  social dynamics  pattern formation
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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, headup displays for improving automobile driving safety, or smart windows.
chirality  cholesterics  nanorods  Onsager theory  polydispersity  liquidcrystalline dispersions of DNA  cholesteric and hexagonal packing of DNA  theoretically calculated and experimental circular dichroism spectra  textures of the DNA liquidcrystalline phases  “reentrant” cholesteric phase of DNA  anthracyclines drugs  chelate complexes  nanobridges  “rigid” particles of DNA  dielectric heating  cholesteric liquid crystals  uniform lying helix  cholesteric liquid crystal  twolength scale surface wrinkling  capillary shape equation  anisotropic surface energy  liquid crystal  cholesteric  nematic  conical boundary conditions  orientational structure  director configuration  topological defect  cholesteric liquid crystals  polymer  radical polymerization  cationic polymerization  electrooptical property  microstructure  geometry phase  cholesteric liquid crystal  headup display  liquid crystal  cholesteric liquid crystals  optical fiber  sidepolished fiber  sensor
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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 reallife 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.
Legendre wavelets  collocation method  threestep Taylor method  asymptotic stability  timedependent partial differential equations  noninstantaneous impulses  Caputo fractional derivative  differential equations  state dependent delays  lipschitz stability  limitperiodic 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  Kortewegde Vries equation  secondorder differential/difference/qdifference equation of hypergeometric type  nonuniform lattices  divideddifference equations  polynomial solution  integrodifferentials  Sumudu decomposition method  dynamical system
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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 manmade 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.
bent piles  structural systems  vernacular houses  Ammatoan houses  building structure  effectivity  strength  corrugated shell roof  freeform building  architectural form  folded sheet  thinwalled profile  shape transformation  steel construction  building freeform structure  corrugated shell roof  architectural form  thinwalled open profile  shape transformation  folded sheet  steel construction  performanceoriented design  parametric architecture  formfinding  CFD  wind analysis  digital tools  steel bar structures  structural analysis  parametric design  algorithmicaided shaping  responsive architecture  shadows  Grasshopper  Karamba 3D  interactive architecture  interaction narrative  user experience  situatedness  agentbased theory  building free form structure  corrugated shell roof  integrated architectural form  thinwalled 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
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NonNewtonian (nonlinear) 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 nonlinear fluids with industrial applications, especially those concerned with CFD studies. These fluids include traditional nonNewtonian fluid models, electro or magnetorheological fluids, granular materials, slurries, drilling fluids, polymers, blood and other biofluids, mixtures of fluids and particles, etc.
inhomogeneous fluids  nonnewtonian fluids  lubrication approximation (76A05, 76D08, 76A20)  particle interaction  viscoplastic fluid  Bingham fluid  computational fluid dynamics  porous media  convection  Bingham fluid  yield stress  channel flow  powerlaw fluid  sheardependent viscosity  Reynolds equation  lubrication approximation  liddriven cavity  projection method  shearthinning  aspect ratio  Re numbers  Brinkman equation  viscosity ratio  first and secondorder slip  similarity transformation  porous medium  generalised simplified PTT  PhanThien–Tanner (PTT) model  Mittag–Leffler  Couette flow  Poiseuille–Couette flow  nonisothermal flows  creeping flows  viscous fluid  optimal control  boundary control  pressure boundary conditions  weak solution  existence theorem  marginal function  hemoglobin  biological capacitor  nonequilibrium thermodynamics  hemoglobe capacitor  thermodynamic capacitor  smoothed particle hydrodynamics (SPH)  meshless  fluidsolid interaction (FSI)  membrane  rupture  SPHFEM  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)  nonlinear fluids  variable viscosity  natural convection  convectiondiffusion  buoyancy force  lubrication  suspensions  viscoplastic fluids  cement  biofluids  oil recovery  porous media
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.
highly oscillatory  convolution quadrature rule  volterra integral equation  Bessel kernel  convergence  higher order Schwarzian derivatives  Janowski starlike function  Janowski convex function  bound on derivatives  tangent numbers  tangent polynomials  Carlitztype qtangent numbers  Carlitztype qtangent 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  fractionalorder differential equations  RiemannStieltjes functional integral  LiouvilleCaputo fractional derivative  infinitepoint 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–Caputotype fractional derivative  fractional integral  existence  fixed point  Bernoulli spiral  Grandi curves  Chebyshev polynomials  pseudoChebyshev 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  Kfunctional  HurwitzLerch zeta function  generalized functions  analytic number theory  ?generalized HurwitzLerch zeta functions  derivative properties  series representation  basic hypergeometric functions  generating functions  qpolynomials  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  stronglystarlike 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  qhypergeometric 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  multipoint  multistrip  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 qstarlike functions  qderivative (or qdifference) 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 mittagleffler function  analytic functions  Hadamard product  starlike functions  qderivative (or qdifference) operator  Hankel determinant  qstarlike functions  fuzzy volterra integrodifferential 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  truncatedexponential polynomials  monomiality principle  generating functions  Apostoltype polynomials and Apostoltype numbers  Bernoulli, Euler and Genocchi polynomials  Bernoulli, Euler, and Genocchi numbers  operational methods  summation formulas  symmetric identities  Euler numbers and polynomials  qEuler numbers and polynomials  HurwitzEuler eta function  multiple HurwitzEuler eta function  higher order qEuler numbers and polynomials  (p, q)Euler numbers and polynomials of higher order  symmetric identities  symmetry of the zero
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