arXiv subjects

Victor P. Ruban

Publications and source records attributed to Victor P. Ruban.

At least 37 records · Page 2Linked to original sources

arXiv2021

Instabilities of a Filled Vortex in a Two-Component Bose-Einstein Condensate

A two-component Bose-Einstein condensate of cold atoms with a strong intercomponent repulsion leading to the spatial separation of the components has been numerically studied. Configurations with a multiple quantized vortex in one component, where the vortex core is filled with the other component, are considered. The effective radius of the core can exceed the width of the transition layer between components, and then an analogy with a filled cylindrical vortex in the classical hydrodynamics of two immiscible ideal fluids appears. This analogy allows one to analyze the longitudinal "sausage" instability and the transverse instability of the filled vortex in the condensate caused by the "tangential discontinuity," as well as the stable regime in the parametric gap between them. The presence of long-lived coherent structures formed in some cases at the nonlinear stages of both instabilities is numerically discovered.

cond-mat.quant-gas↗

arXiv2020

Discrete Vortex Filaments on Arrays of Coupled Oscillators in the Nonlinear Resonant Mode

Numerical simulation has indicated that vortex structures can exist for a long time in the form of quantized filaments on arrays of coupled weakly dissipative nonlinear oscillators in a finite three-dimensional domain under a resonant external force applied at the boundary of the domain. Ranges of the parameters of the system and an external signal favorable for the formation of modulationally stable quasi-uniform energy background, which is a decisive factor for the occurrence of this phenomenon, have been qualitatively revealed.

nlin.PS↗

arXiv2020

Discrete Vortices in Systems of Coupled Nonlinear Oscillators: Numerical Results for an Electric Model

Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by relatively weak capacitances has been considered as a possible physical implementation of such objects. Numerical experiments have shown that a time-monochromatic external force applied to several oscillators leads to the formation of long-lived and nontrivially interacting vortices in the system against a quasistationary background in a wide range of parameters. The dynamics of vortices depends on the method of "coupling" of the opposite sides of a rectangular array by links, which determines the topology of the resulting manifold (torus, Klein bottle, projective plane, Möbius strip, ring, or disk).

nlin.PS↗

arXiv2020

Waves over Curved Bottom: The Method of Composite Conformal Mapping

A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of motion in terms of the so-called conformal variables are used. In addition to the previously known applications for shear flows with constant (including zero) vorticity, here a generalization is made to the case of potential flows in uniformly rotating coordinate systems, where centrifugal and Coriolis forces are added to the gravity force. A brief review is given of previous results obtained by this method in a number of physically interesting problems such as modeling of tsunami waves caused by the movement of nonuniform bottom, the dynamics of Bragg (gap) solitons over a spatially periodic bottom profile, the Fermi-Pasta-Ulam (FPU) recurrence phenomenon for waves in a finite pool, the formation of anomalous waves in an opposing nonuniform current, and the propagation of a solitary wave in a shear current and its runup on a depth difference. In addition, a number of new numerical results are presented concerning the nonlinear dynamics of a free boundary in closed rotating containers partially filled with a fluid -- centrifuges of complex shape. In this case, the equations of motion differ in some essential details from those of $x$-periodic systems.

physics.flu-dyn↗

arXiv2020

Discrete vortices on spatially nonuniform two-dimensional electric networks

Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly dissipative defocusing discrete nonlinear Schrödinger equation with translationally non-invariant linear dispersive coefficients. Behavior of quantized discrete vortices in such systems is shown to depend strongly on the spatial profile of the inter-node coupling as well as on the ratio between time-increasing healing length and lattice spacing. In particular, vortex clusters can be stably trapped for a some initial period of time by a circular barrier in the coupling profile, but then, due to gradual dissipative broadening of vortex cores, they lose stability and suddenly start to move.

nlin.PS↗

arXiv2019

Vortex knots on three-dimensional lattices of nonlinear oscillators coupled by space-varying links

Quantized vortices in a complex wave field described by a defocusing nonlinear Schrödinger equation with a space-varying dispersion coefficient are studied theoretically and compared to vortices in the Gross-Pitaevskii model with external potential. A discrete variant of the equation is used to demonstrate numerically that vortex knots in three-dimensional arrays of oscillators coupled by specially tuned weak links can exist for as long times as many tens of typical vortex turnover periods.

nlin.PS↗

arXiv2019

Optimal dynamics of a spherical squirmer in Eulerian description

The problem of optimization of a cycle of tangential deformations of the surface of a spherical object (microsquirmer) self-propelling in a viscous fluid at low Reynolds numbers is represented in a noncanonical Hamiltonian form. The evolution system of equations for the coefficients of expansion of the surface velocity in the associated Legendre polynomials $P^1_n(\cosθ)$ is obtained. The system is quadratically nonlinear, but it is integrable in the three-mode approximation. This allows a theoretical interpretation of numerical results previously obtained for this problem.

physics.flu-dyn↗

arXiv2019

Quasi-stable quantum vortex knots and links in anisotropic harmonically trapped Bose-Einstein condensates

Long-time existence of topologically nontrivial configurations of quantum vortices in the form of torus knots and links in trapped Bose-Einstein condensates is demonstrated numerically within the three-dimensional Gross-Pitaevskii equation with external anisotropic parabolic potential. We find out parametric domains near the trap anisotropy -- axial over planar frequency trapping ratio $λ\approx 1.5-1.6$ where the lifetime of such quasi-stationary rotating vortex structures is many hundreds of typical rotation times. This suggests the potential experimental observability of the structures. We quantify the relevant lifetimes as a function of the model parameters (e.g. $λ$) and initial condition parameters of the knot profile.

physics.atom-ph↗

arXiv2018

Three-dimensional numerical simulation of long-lived quantum vortex knots and links in a trapped Bose-Einstein condensate

Dynamics of simplest vortex knots, unknots, and links of torus type inside an atomic Bose-Einstein condensate in anisotropic harmonic trap at zero temperature has been numerically simulated using three-dimensional Gross-Pitaevskii equation. The lifetime for such quasi-stationary rotating vortex structures has been found quite long in wide parametric domains of the system. This result is in qualitative agreement with a previous prediction based on a simplified one-dimensional model approximately describing dynamics of vortex filaments [V.P. Ruban, JETP 126, 397 (2018)].

cond-mat.quant-gas↗

arXiv2018

Quasi-stable configurations of torus vortex knots and links

The dynamics of torus vortex configurations $V_{n,p,q}$ in a superfluid liquid at zero temperature ($n$ is the number of quantum vortices, $p$ is the number of turns of each filament around the symmetry axis of the torus, and $q$ is the number of turns of the filament around its central circle; radii $R_0$ and $r_0$ of the torus at the initial instant are much larger than vortex core width $ξ$) has been simulated numerically based on a regularized Biot-Savart law. The lifetime of vortex systems till the instant of their substantial deformation has been calculated with a small step in parameter $B_0=r_0/R_0$ for various values of parameter $Λ=\log(R_0/ξ)$. It turns out that for certain values of $n$, $p$, and $q$, there exist quasi-stability regions in the plane of parameters $(B_0,Λ)$, in which the vortices remain almost invariable during dozens and even hundreds of characteristic times.

cond-mat.other↗

arXiv2018

Three-dimensional stability of leapfrogging quantum vortex rings

It is shown by numerical simulations within a regularized Biot-Savart law that dynamical systems of two or three leapfrogging coaxial quantum vortex rings having a core width $ξ$ and initially placed near a torus of radii $R_0$ and $r_0$, can be three-dimensionally (quasi-)stable in some regions of parameters $Λ=\ln(R_0/ξ)$ and $W=r_0/R_0$. At fixed $Λ$, stable bands on $W$ are intervals between non-overlapping main parametric resonances for different (integer) azimuthal wave numbers $m$. The stable intervals are most wide ($ΔW\sim$ 0.01--0.05) between $m$-pairs $(1,2)$ and $(2,3)$ at $Λ\approx$ 4--12 thus corresponding to micro/mesoscopic sizes of vortex rings in the case of superfluid $^4$He. With four and more rings, at least for $W>0.1$, resonances overlap for all $Λ$ and no stable domains exist.

cond-mat.other↗

arXiv2018

Long-lived quantum vortex knots

Dynamics of simplest quantum vortex knots of torus type in a superfluid at zero temperature has been simulated within a regularized Biot-Savart law (the torus radii $R_0$ and $r_0$ for initial vortex configuration were large in comparison with a vortex core width $ξ$). Computations of evolution times of knots until their significant deformation were carried out with a small step on parameter $B_0=r_0/R_0$ for different values of parameter $Λ=\log(R_0/ξ)$. It has been found that at $Λ\gtrsim 3$, bands of quasi-stability appear in a region of $B_0\lesssim 0.2$, which correspond to long knot lifetimes and to very large traveling distances --- up to several hundreds of $R_0$. This result is new and quite unexpected, because previously it was believed that maximal lifetime of torus knots until reconnection does not exceed several typical periods. The opening of quasi-stable 'windows' at increasing $Λ$ is due to narrowing main parametric resonances of the dynamical system on parameter $B_0$.

cond-mat.other↗

arXiv2017

Stable and unstable vortex knots in a trapped Bose-Einstein condensate

The dynamics of a quantum vortex torus knot ${\cal T}_{P,Q}$ and similar knots in an atomic Bose-Einstein condensate at zero temperature in the Thomas-Fermi regime has been considered in the hydrodynamic approximation. The condensate has a spatially nonuniform equilibrium density profile $ρ(z,r)$ due to an external axisymmetric potential. It is assumed that $z_*=0$, $r_*=1$ is a maximum point for function $rρ(z,r)$, with $δ(rρ)\approx-(α-ε) z^2/2 -(α+ε) (δr)^2/2$ at small $z$ and $δr$. Configuration of knot in the cylindrical coordinates is specified by a complex $2πP$-periodic function $A(φ,t)=Z(φ,t)+i [R(φ,t)-1]$. In the case $|A|\ll 1$ the system is described by relatively simple approximate equations for re-scaled functions $W_n(φ)\propto A(2πn+φ)$, where $n=0,\dots,P-1$, and $iW_{n,t}=-(W_{n,φφ}+αW_n -εW_n^*)/2-\sum_{j\neq n}1/(W_n^*-W_j^*)$. At $ε=0$, numerical examples of stable solutions as $W_n=θ_n(φ-γt)\exp(-iωt)$ with non-trivial topology have been found for $P=3$. Besides that, dynamics of various non-stationary knots with $P=3$ was simulated, and in some cases a tendency towards a finite-time singularity has been detected. For $P=2$ at small $ε\neq 0$, rotating around $z$ axis configurations of the form $(W_0-W_1)\approx B_0\exp(iζ)+εC(B_0,α)\exp(-iζ) + εD(B_0,α)\exp(3iζ)$ have been investigated, where $B_0>0$ is an arbitrary constant, $ζ=k_0φ-Ω_0 t+ζ_0$, $k_0=Q/2$, $Ω_0=(k_0^2-α)/2-2/B_0^2$. In the parameter space $(α, B_0)$, wide stability regions for such solutions have been found. In unstable bands, a recurrence of the vortex knot to a weakly excited state has been noted to be possible.

cond-mat.quant-gas↗

arXiv2017

Non-stationary vortex ring in a Bose-Einstein condensate with Gaussian density

The local induction equation, approximately describing dynamics of a quantized vortex filament in a trapped Bose-Einstein condensate in the Thomas-Fermi regime on a spatially nonuniform density background $ρ({\bf r})$ and taking dimensionless form ${\mathbf R}_t=\varkappa {\mathbf b}+[\nabla\lnρ({\mathbf R})\times {\boldsymbol τ}]$ (where $\varkappa$ is a local curvature of the filament, ${\mathbf b}$ is the unit binormal vector, and ${\boldsymbol τ}$ is the unit tangent vector), is shown to admit a finite-dimensional reduction if the density profile is an isotropic Gaussian, $ρ\propto\exp(-|{\bf r}|^2/2)$. The reduction corresponds to a geometrically perfect vortex ring centered at position ${\bf A}(t)$, with orientation and size both determined by a vector ${\bf B}(t)$. Parameters ${\bf A}$ and ${\bf B}$ exhibit the same dynamics as velocity and position of a Newtonian particle do in 3D: $\dot {\bf A}={\bf B}/|{\bf B}|^2-{\bf B}$, and $\dot {\bf B}={\bf A}$.

cond-mat.quant-gas↗

arXiv2017

Parametric instability of oscillations of a vortex ring in a $z$-periodic Bose-Einstein condensate and the recurrence to starting state

The dynamics of deformations of a quantum vortex ring in a Bose-Einstein condensate with periodic equilibrium density $ρ(z)= 1-ε\cos z$ has been considered within the local induction approximation. Parametric instabilities of the normal modes with azimuthal numbers $\pm m$ have been revealed at the energy integral $E$ near values $E_m^{(p)}=2m\sqrt{m^2-1}/p$, where $p$ is the resonance order. Numerical simulations have shown that already at $ε\sim 0.03$ a rapid growth of unstable modes with $m=2$, $p=1$ to magnitudes of order of unity is typical, which is then followed, after a few large oscillations, by fast return to a weakly excited state. Such behavior corresponds to an integrable Hamiltonian of the form $H\propto σ(E_2^{(1)}-E)(|b_+|^2 + |b_-|^2) -ε(b_+ b_- + b_+^* b_-^*) +u(|b_+|^4 +|b_-|^4) + w |b_+|^2|b_-|^2$ for two complex envelopes $b_\pm(t)$. The results have been compared to parametric instabilities of vortex ring in condensate with density $ρ(z,r)=1-r^2-αz^2$, which take place at $α\approx 8/5$ and at $α\approx 16/7$.

cond-mat.quant-gas↗

arXiv2006

"Breathing" rogue wave observed in numerical experiment

Numerical simulations of the recently derived fully nonlinear equations of motion for weakly three-dimensional water waves [V.P. Ruban, Phys. Rev. E {\bf 71}, 055303(R) (2005)] with quasi-random initial conditions are reported, which show the spontaneous formation of a single extreme wave on the deep water. This rogue wave behaves in an oscillating manner and exists for a relatively long time (many wave periods) without significant change of its maximal amplitude.

physics.flu-dyn↗

arXiv2005

Numerical modeling of quasiplanar giant water waves

In this work we present a further analytical development and a numerical implementation of the recently suggested theoretical model for highly nonlinear potential long-crested water waves, where weak three-dimensional effects are included as small corrections to exact two-dimensional equations written in the conformal variables [V.P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Numerical experiments based on this theory describe the spontaneous formation of a single weakly three-dimensional large-amplitude wave (alternatively called freak, killer, rogue or giant wave) on the deep water.

physics.flu-dyn↗

arXiv2005

Quasi-planar steep water waves

A new description for highly nonlinear potential water waves is suggested, where weak 3D effects are included as small corrections to exact 2D equations written in conformal variables. Contrary to the traditional approach, a small parameter in this theory is not the surface slope, but it is the ratio of a typical wave length to a large transversal scale along the second horizontal coordinate. A first-order correction for the Hamiltonian functional is calculated, and the corresponding equations of motion are derived for steep water waves over an arbitrary inhomogeneous quasi-1D bottom profile.

physics.flu-dyn↗