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A topical research activity in statistical physics concerns the study of complex and disordered systems. Generally, these systems are characterized by an elevated level of interconnection and interaction between the parts so that they give rise to a rich structure in the phase space that selforganizes under the control of internal nonlinear dynamics. These emergent collective dynamics confer new behaviours to the whole system that are no longer the direct consequence of the properties of the single parts, but rather characterize the whole system as a new entity with its own features, giving rise to the birth of new phenomenologies. As is highlighted in this collection of papers, the methodologies of statistical physics have become very promising in understanding these new phenomena. This volume groups together 12 research works showing the use of typical tools developed within the framework of statistical mechanics, in nonlinear kinetic and information geometry, to investigate emerging features in complex physical and physicallike systems.A topical research activity in statistical physics concerns the study of complex and disordered systems. Generally, these systems are characterized by an elevated level of interconnection and interaction between the parts so that they give rise to a rich structure in the phase space that selforganizes under the control of internal nonlinear dynamics. These emergent collective dynamics confer new behaviours to the whole system that are no longer the direct consequence of the properties of the single parts, but rather characterize the whole system as a new entity with its own features, giving rise to the birth of new phenomenologies. As is highlighted in this collection of papers, the methodologies of statistical physics have become very promising in understanding these new phenomena. This volume groups together 12 research works showing the use of typical tools developed within the framework of statistical mechanics, in nonlinear kinetic and information geometry, to investigate emerging features in complex physical and physicallike systems.
Generalized statistical mechanics  information theory  anomalous diffusion  stochastic processes  collective phenomena  disordered systems
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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 realworld 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.
anomalous diffusion  complexity  magnetic resonance imaging  fractional calculus  fractional complex networks  adaptive control  pinning synchronization  timevarying delays  impulses  reaction–diffusion terms  fractional calculus  mass absorption  diffusionwave equation  Caputo derivative  harmonic impact  Laplace transform  Fourier transform  MittagLeffler function  fractional calculus  fractionalorder system  long memory  time series  Hurst exponent  fractional  control  PID  parameter  meaning  audio signal processing  linear prediction  fractional derivative  musical signal  optimal randomness  swarmbased search  cuckoo search  heavytailed distribution  global optimization
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There is overwhelming evidence, from laboratory experiments, observations, and computational studies, that coherent structures can cause intermittent transport, dramatically enhancing transport. A proper description of this intermittent phenomenon, however, is extremely difficult, requiring a new nonperturbative theory, such as statistical description. Furthermore, multiscale interactions are responsible for inevitably complex dynamics in strongly nonequilibrium systems, a proper understanding of which remains a main challenge in classical physics. As a remarkable consequence of multiscale interaction, a quasiequilibrium state (the socalled selforganisation) can however be maintained. This special issue aims to present different theories of statistical mechanics to understand this challenging multiscale problem in turbulence. The 14 contributions to this Special issue focus on the various aspects of intermittency, coherent structures, selforganisation, bifurcation and nonlocality. Given the ubiquity of turbulence, the contributions cover a broad range of systems covering laboratory fluids (channel flow, the Von Kármán flow), plasmas (magnetic fusion), laser cavity, wind turbine, air flow around a highspeed train, solar wind and industrial application.
pipe flow boundary layer  turbulent transition  large eddy simulation  channel flow  kinetic theory  fluid dynamics  turbulence  selforganisation  shear flows  coherent structures  turbulence  stochastic processes  Langevin equation  FokkerPlanck equation  information length  trailingedge flap  control strategy  floating wind turbine  turbulence  free vortex wake  nonlocal theory  Lévy noise  Tsallis entropy  fractional Fokker–Plank equation  anomalous diffusion  hybrid (U)RANSLES  IDDES methodology  attached and separated flows  complex dynamics  microcavity laser  spatiotemporal chaos  turbulent boundary layer  low speed streaks  magnetic confinement fusion  turbulence  heat transport  Tjunction  denoise  coherent structure  continuous wavelet transform  solar wind  scaling properties  fractals  chaos  turbulence  intermittency  multifractal  thermodynamics  drop breakage  drop coalescence  local intermittency  turbulent flow  population balance equation  high efficiency impeller  Rushton turbine  energy cascade  bifurcations  Lyapunov theory  turbulence  statistical mechanics  intermittency  coherent structure  multiscale problem  selforganisation  bifurcation  nonlocality  scaling  multifractal
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The many technical and computational problems that appear to be constantly emerging in various branches of physics and engineering beg for a more detailed understanding of the fundamental mathematics that serves as the cornerstone of our way of understanding natural phenomena. The purpose of this Special Issue was to establish a brief collection of carefully selected articles authored by promising young scientists and the world's leading experts in pure and applied mathematics, highlighting the stateoftheart of the various research lines focusing on the study of analytical and numerical mathematical methods for pure and applied sciences.
ultraparabolic equation  ultradiffusion process  probabilistic representation  mathematical finance  linear elastostatics  layer potentials  fredholmian operators  fractional differential equations  fractional derivative  Abeltype integral  time delay  distributed lag  gamma distribution  macroeconomics  Keynesian model  integral transforms  Laplace integral transform  transmutation operator  generating operator  integral equations  differential equations  operational calculus of Mikusinski type  Mellin integral transform  fractional derivative  fractional integral  Mittag–Leffler function  Riemann–Liouville derivative  Caputo derivative  Grünwald–Letnikov derivative  spacetime fractional diffusion equation  fractional Laplacian  subordination principle  MittagLeffler function  Bessel function  exterior calculus  exterior algebra  electromagnetism  Maxwell equations  differential forms  tensor calculus  Fourier Theory  DFT in polar coordinates  polar coordinates  multidimensional DFT  discrete Hankel Transform  discrete Fourier Transform  Orthogonality  multispecies biofilm  biosorption  free boundary value problem  heavy metals toxicity  method of characteristics  relativistic diffusion equation  Caputo fractional derivatives of a function with respect to another function  BesselRiesz motion  Mittag–Leffler function  matrix function  Schur decomposition  Laplace transform  fractional calculus  central limit theorem  anomalous diffusion  stable distribution  fractional calculus  power law  n/a
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