We present a physical model to describe the equilibrium probability distribution function (PDF) of velocity differences across an inertial-range distance in 3D isotropic turbulence. The form of the non-Gaussian PDF ag...
We present a physical model to describe the equilibrium probability distribution function (PDF) of velocity differences across an inertial-range distance in 3D isotropic turbulence. The form of the non-Gaussian PDF agrees well with data from direct numerical simulations. It is shown that these PDF’s obey a self-similar property, and the resulting inertial-range exponents of high-order velocity structure functions are in agreement with both experimental and numerical data. The model suggests a physical explanation for the phenomenon of intermittency and the nature of multifractality in fully developed turbulence, namely, local self-distortion of turbulent structures.
Direct numerical simulations with up to 40962 resolution are performed to address the question of universality of statistical properties of the enstrophy cascade in homogeneous two-dimensional turbulence driven by lar...
Direct numerical simulations with up to 40962 resolution are performed to address the question of universality of statistical properties of the enstrophy cascade in homogeneous two-dimensional turbulence driven by large-scale Gaussian white-in-time noise. Data with different Reynolds numbers are compared with each other. The energy spectrum is found to be very close to 1/k3. It is shown that the primary contribution to the enstrophy transfer function comes from wave-number triads with one small leg and two long ones, corresponding to wave numbers in the inertial range.
We propose two algorithms for the solution of the optimal control of ergodic McKean-Vlasov dynamics. Both algorithms are based on approximations of the theoretical solutions by neural networks, the latter being charac...
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Direct numerical simulations with up to 10242 resolution are performed to study statistical properties of the inverse energy cascade in stationary homogeneous two-dimensional turbulence driven by small-scale Gaussian ...
Direct numerical simulations with up to 10242 resolution are performed to study statistical properties of the inverse energy cascade in stationary homogeneous two-dimensional turbulence driven by small-scale Gaussian white-in-time noise. The energy spectra for the inverse energy cascade deviate strongly from the expected k−5/3 law and are close (somewhat flatter) to k−3. The reason for the deviation is traced to the emergence of strong vortices distributed over all scales. Statistical properties of the vortices are explored.
The boundary element (BE) technique is used to analyze the effect of defect structures upon desorption processes on two-dimensional chemically active surfaces. The standard BE algorithm for diffusion is modified to in...
The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss...
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The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective Maxwell equations for the macroscopic electric and magnetic fields are derived s...
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The behavior of interacting electrons in a perfect crystal under macroscopic external electric and magnetic fields is studied. Effective Maxwell equations for the macroscopic electric and magnetic fields are derived starting from time-dependent density functional theory. Effective permittivity and permeability coefficients are obtained.
The classic Hegselmann-Krause (HK) model for opinion dynamics consists of a set of agents on the real line, each one instructed to move, at every time step, to the mass center of the agents within a fixed distance R. ...
3D structure recovery from a collection of 2D images requires the estimation of the camera locations and orientations, i.e. the camera motion. For large, irregular collections of images, existing methods for the locat...
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A controlled quantum system possesses a search landscape defined by the observable value as a functional of the control field. Within the search landscape, there exist level sets of controls giving the same observable...
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