arXiv subjects

Alexander O. Korotkevich

Publications and source records attributed to Alexander O. Korotkevich.

16 recordsLinked to original sources

arXiv2026

Weakly nonlinear interaction of capillary waves in a finite system: leading interaction process and scales' range of direct energy cascade

During comprehensive study of weakly nonlinear interaction of surface capillary waves, processes of resonant and non-resonant interactions were considered both numerically and analytically: merging of two waves into one and waves on the ring (in Fourier space, isotropic spectrum) into larger diameter ring. It was shown numerically, that these resonant processes are the leading ones and other processes with respect to them are at least weaker if manifest themselves at all. It was confirmed, that resonant the processes are the major ones which contribute to the long time dynamics. In the case of isotropic turbulence of capillary waves the formation of wave turbulence's Zakharov-Filonenko spectrum is demonstrated. It was also shown, that this spectrum in finite systems has a finite range of scales. Due to finiteness of the numerical simulation or experimental area the discreteness of the wavenumbers grid arrest local in Fourier space resonant interaction when smaller scales are considered. Scaling of the range of realization of the Zakharov-Filonenko spectrum, depending on main parameters of the numerical or experimental setup (average steepness and characteristic size), is derived analytically and partially confirmed numerically.

physics.flu-dyn↗

arXiv2023

Optimizing the size of array for modern discrete Fourier transform libraries

The problem of optimization of the array size for modern discrete Fourier transform libraries is considered and reformulated as an integer linear programming problem. Acceleration of finding an optimal solution using standard freely available library with respect to brute force approach is demonstrated. Ad hoc recursive algorithm of finding the optimal solution is proposed, complexity scaling of the algorithm is estimated analytically. The problem can be used in a linear programming class as an example of purely integer programming problem (continuous linear programming solution has no sense), simple enough to be solved using even interpreting programming languages like Python or Matlab.

physics.comp-ph↗

arXiv2022

Inverse cascade of gravity waves in the presence of condensate: numerical simulation

During the set of direct numerical simulations of the forced isotropic turbulence of surface gravity waves in the framework of primordial dynamical equations, the universal inverse cascade spectrum was observed. The slope of the spectrum is the same (in the margin of error) for different levels of pumping and nonlinearity as well as dissipation present in the system. In all simulation runs formation of the inverse cascade spectrum was accompanied by appearance of strong long wave background (condensate). The observed slope of the spectrum $\sim k^{-3.07}$ is different from the constant wave action flux solution predicted by the Theory of Wave Turbulence $\sim k^{-23/6}$.

physics.flu-dyn↗

arXiv2022

Superharmonic Instability of Stokes Waves

A stability of nearly limiting Stokes waves to superharmonic perturbations is considered numerically. The new, previously inaccessible branches of superharmonic instability were investigated. Our numerical simulations suggest that eigenvalues of linearized dynamical equations, corresponding to the unstable modes, appear as a result of a collision of a pair of purely imaginary eigenvalues at the origin, and a subsequent appearance of a pair of purely real eigenvalues: a positive and a negative one that are symmetric with respect to zero. Complex conjugate pairs of purely imaginary eigenvalues correspond to stable modes, and as the steepness of the underlying Stokes wave grows, the pairs move toward the origin along the imaginary axis. Moreover, when studying the eigenvalues of linearized dynamical we find that as the steepness of the Stokes wave grows, the real eigenvalues follow a universal scaling law, that can be approximated by a power law. The asymptotic power law behaviour of this dependence for instability of Stokes waves close to the limiting one is proposed. Surface elevation profiles for several unstable eigenmodes are made available through http://stokeswave.org website.

physics.flu-dyn↗

arXiv2021

Comparison of Split-Step and Hamiltonian Integration Methods for Simulation of the Nonlinear Schrödinger Equation

We provide a systematic comparison of two numerical methods to solve the widely used nonlinear Schrödinger equation. The first one is the standard second order split-step (SS2) method based on operator splitting approach. The second one is the Hamiltonian integration method (HIM). It allows the exact conservation of the Hamiltonian at the cost of requiring the implicit time stepping. We found that numerical error for HIM method is systematically smaller than the SS2 solution for the same time step. At the same time, one can take orders of magnitude larger time steps in HIM compared with SS2 still ensuring numerical stability. In contrast, SS2 time step is limited by the numerical stability threshold.

physics.comp-ph↗

arXiv2020

A new set of efficient SMP-parallel 2D Fourier subroutines

Extensive set of tests on different platforms indicated that there is a performance drop of current standard de facto software library for the Discrete Fourier Transform (DFT) in case of large 2D array sizes (larger than 16384x16384). Parallel performance for Symmetric Multi Processor (SMP) systems was seriously affected. The remedy for this problem was proposed and implemented as a software library for 2D out of place complex to complex DFTs. Proposed library was thoroughly tested on different available architectures and hardware configurations and demonstrated significant (38-94%) performance boost on vast majority of them. The new library together with the testing suite and results of all tests is published as a project on GitHub.com platform under free software license (GNU GPL v3). Comprehensive description of programming interface as well as provided testing programs is given.

physics.comp-ph↗

arXiv2016

Operator Splitting Method for Simulation of Dynamic Flows in Natural Gas Pipeline Networks

We develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme is unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.

physics.comp-ph↗

arXiv2015

On the comparison of energy sources: feasibility of radio frequency and ambient light harvesting

With growing interest in multi source energy harvesting including integrated microchips we propose a comparison of radio frequency (RF) and solar energy sources in a typical city. Harvesting devices for RF and solar energy will be competing for space of a compact micro or nano device as well as for orientation with respect to the energy source. This is why it is important to investigate importance of every source of energy and make a decision whether it will be worthwhile to include such harvesters. We considered theoretically possible irradiance by RF signal in different situations, typical for the modern urban environment and compared it with ambient solar energy sources available through the night, including moon light. Our estimations show that solar light energy dominates by far margin practically all the time, even during the night, if there is a full moon in the absence of clouds. At the same time, in the closed compartments or at the new moon RF harvesting can be beneficial as a source of "free" energy.

physics.ins-det↗

arXiv2013

Beyond the random phase approximation: Stimulated Brillouin backscatter for finite laser coherence times

We develop a statistical theory of stimulated Brillouin backscatter (BSBS) of a spatially and temporally partially incoherent laser beam for laser fusion relevant plasma. We find a new collective regime of BSBS (CBSBS) with intensity threshold controlled by diffraction, an insensitive function of the laser coherence time, $T_c$, once light travel time during $T_c$ exceeds a laser speckle length. The BSBS spatial gain rate is approximately the sum of that due to CBSBS, and a part which is independent of diffraction and varies linearly with $T_c$. We find that the bandwidth of KrF-laser-based fusion systems would be large enough to allow additional suppression of BSBS.

physics.plasm-ph↗

arXiv2013

Optical Pulse Dynamics in Active Metamaterials with Positive and Negative Refractive Index

We study numerically the propagation of two-color light pulses through a metamaterial doped with active atoms such that the carrier frequencies of the pulses are in resonance with two atomic transitions in the $Λ$ configuration and that one color propagates in the regime of positive refraction and the other in the regime of negative refraction. In such a metamaterial, one resonant color of light propagates with positive and the other with negative group velocity. We investigate nonlinear interaction of these forward- and backward-propagating waves, and find self-trapped waves, counter-propagating radiation waves, and hot spots of medium excitation.

physics.optics↗

arXiv2012

Direct numerical experiment on measuring of dispersion relation for gravity waves in the presence of condensate

During previous numerical experiments on isotropic turbulence of surface gravity waves we observed formation of the long wave background (condensate). It was shown (Korotkevich, Phys. Rev. Lett. vol. 101 (7), 074504 (2008)), that presence of the condensate changes a spectrum of direct cascade, corresponding to the flux of energy to the small scales from pumping region (large scales). Recent experiments show that the inverse cascade spectrum is also affected by the condensate. In this case mechanism proposed as a cause for the change of direct cascade spectrum cannot work. But inverse cascade is directly influenced by the linear dispersion relation for waves, as a result direct measurement of the dispersion relation in the presence of condensate is necessary. We performed the measurement of this dispersion relation from the direct numerical experiment. The results demonstrate that in the region of inverse cascade influence of the condensate cannot be neglected.

physics.ao-ph↗

arXiv2011

Proof of concept implementation of the massively parallel algorithm for simulation of dispersion-managed WDM optical fiber systems

We perform a proof-of-concept implementation of the massively parallel algorithm (P.M. Lushnikov, Opt. Lett., v. 27, 939 (2002)) for simulation of dispersion-managed wavelength-division-multiplexed optical fiber systems. Linear scalability of the algorithm with the number of computer cores is demonstrated. Exact result on the accuracy of the implemented algorithm is found analytically and confirmed numerically as well as it is compared with to accuracy of the standard split-step algorithm.

physics.comp-ph↗

arXiv2011

Collective stimulated Brillouin scatter

We develop a statistical theory of stimulated Brillouin backscatter (BSBS) of a spatially and temporally partially incoherent laser beam for laser fusion relevant plasma. We find a new collective regime of BSBS which has a much larger threshold than the classical threshold of a coherent beam in long-scale-length laser fusion plasma. We identify two contributions to BSBS convective instability increment. The first is collective with intensity threshold independent of the laser correlation time and controlled by diffraction. The second is independent of diffraction, it grows with increase of the correlation time and does not have an intensity threshold. The instability threshold is inside the typical parameter region of National Ignition Facility (NIF). We also find that the bandwidth of KrF-laser-based fusion systems would be large enough to allow additional suppression of BSBS.

physics.plasm-ph↗

arXiv2010

On the Doppler distortion of the sea-wave spectra

Discussions on a form of a frequency spectrum of wind-driven sea waves just above the spectral maximum have continued for the last three decades. In 1958 Phillips made a conjecture that wave breaking is the main mechanism responsible for the spectrum formation (Phillips, 1958). That leads to the spectrum decay $\sim ω^{-5}$, where $ω$ is the frequency of waves. There is a contradiction between the numerous experimental data and this spectrum. Experiments frequently show decay $\simω^{-4}$ (Toba, 1973),(Donelan et al, 1985), and (Hwang et al, 1999). There are several ways of the explanation of this phenomenon. One of them (proposed by Banner (Banner, 1990)) takes into account the Doppler effect due to surface circular currents generated by underlying waves in the Phillips model. In this article the influence of the Doppler effect on an arbitrary averaged spectrum is considered using both analytic and numerical approaches. Although we mostly concentrated on the very important case of Phillips model the developed technique and general formula can be used for the analysis of other spectra. For the particular case of Phillips spectra we got analytic asymptotics in the vicinity of spectral maximum and for high frequencies. Results were obtained for two most important angular dependences of the spectra: isotropic and strongly anisotropic. Together with the analytic investigation we performed numerical calculations in a wide range of frequencies. Both high and low frequency asymptotics are in very good agreement with the numerical results. It was shown that at least at low frequencies correction to the spectrum due to the Doppler shift is negligible. At high frequencies there is an asymptotic with tail $\sim ω^{-3}$.

physics.geo-ph↗

arXiv2008

Simultaneous numerical simulation of direct and inverse cascades in wave turbulence

Results of direct numerical simulation of isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations are presented. For the first time simultaneous formation of both direct and inverse cascades was observed in the framework of primordial dynamical equations. At the same time, strong long waves background was developed. It was shown, that obtained Kolmogorov spectra are very sensitive to the presence of this condensate. Such situation has to be typical for experimental wave tanks, flumes, and small lakes.

physics.flu-dyn↗

arXiv2007

In a book "Tsunami and Nonlinear Waves": Numerical Verification of the Hasselmann equation

The purpose of this article is numerical verification of the thory of weak turbulence. We performed numerical simulation of an ensemble of nonlinearly interacting free gravity waves (swell) by two different methods: solution of primordial dynamical equations describing potential flow of the ideal fluid with a free surface and, solution of the kinetic Hasselmann equation, describing the wave ensemble in the framework of the theory of weak turbulence. Comparison of the results demonstrates pretty good applicability of the weak turbulent approach.

physics.ao-ph↗