arXiv subjects

Boris Levant

Publications and source records attributed to Boris Levant.

7 recordsLinked to original sources

arXiv2022

Automatic defect segmentation by unsupervised anomaly learning

This paper addresses the problem of defect segmentation in semiconductor manufacturing. The input of our segmentation is a scanning-electron-microscopy (SEM) image of the candidate defect region. We train a U-net shape network to segment defects using a dataset of clean background images. The samples of the training phase are produced automatically such that no manual labeling is required. To enrich the dataset of clean background samples, we apply defect implant augmentation. To that end, we apply a copy-and-paste of a random image patch in the clean specimen. To improve the robustness of the unlabeled data scenario, we train the features of the network with unsupervised learning methods and loss functions. Our experiments show that we succeed to segment real defects with high quality, even though our dataset contains no defect examples. Our approach performs accurately also on the problem of supervised and labeled defect segmentation.

cs.CV↗

arXiv2009

On the Statistical Properties of the 3D Incompressible Navier-Stokes-Voigt Model

The Navier-Stokes-Voigt (NSV) model of viscoelastic incompressible fluid has been recently proposed as a regularization of the 3D Navier-Stokes equations for the purpose of direct numerical simulations. In this work we investigate its statistical properties by employing phenomenological heuristic arguments, in combination with Sabra shell model simulations of the analogue of the NSV model. For large values of the regularizing parameter, compared to the Kolmogorov length scale, simulations exhibit multiscaling inertial range, and the dissipation range displaying low intermittency. These facts provide evidence that the NSV regularization may reduce the stiffness of direct numerical simulations of turbulent flows, with a small impact on the energy containing scales.

physics.flu-dyn↗

arXiv2007

Gevrey regularity of the global attractor of the 3D Navier-Stokes-Voight equations

Recently, the Navier-Stokes-Voight (NSV) model of viscoelastic incompressible fluid has been proposed as a regularization of the 3D Navier-Stokes equations for the purpose of direct numerical simulations. In this work we prove that the global attractor of the $D NSV equations, driven by an analytic forcing, consists of analytic functions. A consequence of this result is that the spectrum of the solutions of the 3D NSV system, lying on the global attractor, have exponentially decaying tail, despite the fact that the equations behave like a damped hyperbolic system, rather than the parabolic one. This result provides an additional evidence that the 3D NSV with the small regularization parameter enjoys similar statistical properties as the 3D Navier-Stokes equations. Finally, we calculate a lower bound for the exponential decaying scale -- the scale at which the spectrum of the solution start to decay exponentially, and establish a similar bound for the steady state solutions of the 3D NSV and 3D Navier-Stokes equations. Our estimate coincides with similar available lower bound for the smallest dissipation length scale of solutions of the 3D Navier-Stokes equations.

math.AP↗

arXiv2006

Statistical Properties of Nonlinear Shell Models of Turbulence from Linear Advection Models: Rigorous Results

In a recent paper it was proposed that for some nonlinear shell models of turbulence one can construct a linear advection model for an auxiliary field such that the scaling exponents of all the structure functions of the linear and nonlinear fields coincide. The argument depended on an assumption of continuity of the solutions as a function of a parameter. The aim of this paper is to provide a rigorous proof for the validity of the assumption. In addition we clarify here when the swap of a nonlinear model by a linear one will not work.

nlin.CD↗

arXiv2006

Sharp Lower Bounds for the Dimension of the Global Attractor of the Sabra Shell Model of Turbulence

In this work we derive a lower bounds for the Hausdorff and fractal dimensions of the global attractor of the Sabra shell model of turbulence in different regimes of parameters. We show that for a particular choice of the forcing and for sufficiently small viscosity term $ν$, the Sabra shell model has a global attractor of large Hausdorff and fractal dimensions proportional to $\log_λν^{-1}$ for all values of the governing parameter $ε$, except for $ε=1$. The obtained lower bounds are sharp, matching the upper bounds for the dimension of the global attractor obtained in our previous work. Moreover, we show different scenarios of the transition to chaos for different parameters regime and for specific forcing. In the ``three-dimensional'' regime of parameters this scenario changes when the parameter $ε$ becomes sufficiently close to 0 or to 1. We also show that in the ``two-dimensional'' regime of parameters for a certain non-zero forcing term the long-time dynamics of the model becomes trivial for any value of the viscosity.

physics.flu-dyn↗

arXiv2006

A Note on the Regularity of Inviscid Shell Model of Turbulence

In this paper we continue the analytical study of the sabra shell model of energy turbulent cascade initiated in \cite{CLT05}. We prove the global existence of weak solutions of the inviscid sabra shell model, and show that these solutions are unique for some short interval of time. In addition, we prove that the solutions conserve the energy, provided that the components of the solution satisfy $|{u_n}| \le C k_n^{-1/3} (\sqrt{n} \log(n+1))^{-1}$, for some positive absolute constant $C$, which is the analogue of the Onsager's conjecture for the Euler's equations. Moreover, we give a Beal-Kato-Majda type criterion for the blow-up of solutions of the inviscid sabra shell model and show the global regularity of the solutions in the ``two-dimensional'' parameters regime.

physics.flu-dyn↗

arXiv2006

Analytic Study of Shell Models of Turbulence

In this paper we study analytically the viscous `sabra' shell model of energy turbulent cascade. We prove the global regularity of solutions and show that the shell model has finitely many asymptotic degrees of freedom, specifically: a finite dimensional global attractor and globally invariant inertial manifolds. Moreover, we establish the existence of exponentially decaying energy dissipation range for the sufficiently smooth forcing.

physics.flu-dyn↗