arXiv subjects

Konstantin Ilin

Publications and source records attributed to Konstantin Ilin.

27 records · Page 2Linked to original sources

arXiv2017

Shallow-water models for a vibrating fluid

We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency) free-surface waves. The first set of equations is obtained without assuming that the waves are long. These equations are as difficult to solve as the exact equations for irrotational water waves in a non-vibrating fluid. The other two models describe long waves. These models are obtained under two different assumptions about the amplitude of the vibration. Surprisingly, the governing equations have exactly the same form in both cases (up to interpretation of some constants). These equations reduce to the standard dispersionless shallow-water equations if the vibration is absent, and the vibration manifests itself via an additional term which makes the equations dispersive and, for small-amplitude waves, is similar to the term that would appear if surface tension were taken into account. We show that our dispersive shallow water equations have both solitary and periodic travelling waves solutions and discuss an analogy between these solutions and travelling capillary-gravity waves in a non-vibrating fluid.

physics.flu-dyn↗

arXiv2016

Inviscid instability of an incompressible flow between rotating porous cylinders to three-dimensional perturbations

We study the stability of two-dimensional inviscid flows in an annulus between two porous cylinders with respect to three-dimensional perturbations. The basic flow is irrotational, and both radial and azimuthal components of the velocity are non-zero. The direction of the radial flow can be from the inner cylinder to the outer one (the diverging flow) or from the outer cylinder to the inner one (the converging flow). It had been shown earlier in Ref. \cite{IM2013a} that, independent of the direction of the radial flow, the basic flow can be unstable to small two-dimensional perturbations. In the present paper, we prove first that purely radial flow is stable and that flows with both radial and azimuthal components are always stable to axisymmetric perturbations. Then we show that both the diverging and converging flows are unstable with respect to non-axisymmetric three-dimensional perturbations provided that the ratio of the azimuthal component of the velocity to the radial one is sufficiently large. Neutral curves in the space of parameters of the problem are computed and it is demonstrated that for any ratio of the radii of the cylinders, the most unstable modes (corresponding to the smallest ratio of the azimuthal velocity to the radial one) are the two-dimensional ones. We also consider the corresponding viscous stability problem and construct an asymptotic expansion of its solutions for large radial Reynolds numbers. We compute the first-order viscous correction to inviscid eigenvalues and show that the asymptotic results give a good approximation to the viscous eigenvalues even for moderate values of radial Reynolds number, which indicates that the instability may be observed in real flows.

physics.flu-dyn↗

arXiv2015

Superconducting single photon detectors integrated with diamond nanophotonic circuits

Photonic quantum technologies promise to repeat the success of integrated nanophotonic circuits in non-classical applications. Using linear optical elements, quantum optical computations can be performed with integrated optical circuits and thus allow for overcoming existing limitations in terms of scalability. Besides passive optical devices for realizing photonic quantum gates, active elements such as single photon sources and single photon detectors are essential ingredients for future optical quantum circuits. Material systems which allow for the monolithic integration of all components are particularly attractive, including III-V semiconductors, silicon and also diamond. Here we demonstrate nanophotonic integrated circuits made from high quality polycrystalline diamond thin films in combination with on-chip single photon detectors. Using superconducting nanowires coupled evanescently to travelling waves we achieve high detection efficiencies up to 66 % combined with low dark count rates and timing resolution of 190 ps. Our devices are fully scalable and hold promise for functional diamond photonic quantum devices.

physics.optics↗

arXiv2013

Instability of a viscous flow between rotating porous cylinders with radial flow

The stability of a two-dimensional viscous flow between two rotating porous cylinders is studied. The basic steady flow is the most general rotationally-invariant solution of the Navier-Stokes equations in which the velocity has both radial and azimuthal components, and the azimuthal velocity profile depends on the Reynolds number. It is shown that for a wide range of the parameters of the problem, the basic flow is unstable to small two-dimensional perturbations. Neutral curves in the space of parameters of the problem are computed. Calculations show that the stability properties of this flow are determined by the azimuthal velocity at the inner cylinder when the direction of the radial flow is from the inner cylinder to the outer one and by the azimuthal velocity at the outer cylinder when the direction of the radial flow is reversed. This work is a continuation of our previous study of an inviscid instability in flows between rotating porous cylinders (see \cite{IM2013}).

physics.flu-dyn↗

arXiv2013

An asymptotic model in acoustics: acoustic drift equations

A rigorous asymptotic procedure with the Mach number as a small parameter is used to derive the equations of mean flows which coexist and are affected by the background acoustic waves in the limit of very high Reynolds number.

physics.flu-dyn↗

arXiv2012

Instability of diverging and converging flows in an annulus

The stability of two-dimensional diverging and converging flows in an annulus between two permeable cylinders is examined. The basic flow is irrotational and has both the radial and azimuthal components. It is shown that for a wide range of the parameters of the problem, the basic flow is unstable to small two-dimensional perturbations. The instability is inviscid and oscillatory and persists if the viscosity of the fluid is taken into consideration.

physics.flu-dyn↗

arXiv2011

Steady streaming in a channel with permeable walls

We study steady streaming in a channel between two parallel permeable walls induced by oscillating (in time) blowing/suction at the walls. We obtain an asymptotic expansion of the solution of the Navier-Stokes equations in the limit when the amplitude of the normal displacements of fluid particles near the walls is much smaller that both the width of the channel and the thickness of the Stokes layer. It is demonstrated that the magnitude of the steady streaming is much bigger than the corresponding quantity in the case of the steady streaming produced by vibrations of impermeable boundaries.

physics.flu-dyn↗

arXiv2011

Steady streaming between two vibrating planes at high Reynolds numbers

We consider incompressible flows between two transversely vibrating solid walls and construct an asymptotic expansion of solutions of the Navier-Stokes equations in the limit when both the amplitude of vibrations and the thickness of the Stokes layer are small and have the same order of magnitude. Our asymptotic expansion is valid up to the flow boundary. In particular, we derive equations and boundary conditions, for the averaged flow. In the leading order, the averaged flow is described by the stationary Navier-Stokes equations with an additional term which contains the leading-order Stokes drift velocity. In a slightly different context (for a flow induced by an oscillating conservative body force), the same equations had been derived earlier by Riley (2001). The general theory is applied to two particular examples of steady streaming induced by transverse vibrations of the walls in the form of standing and travelling plane waves. In particular, in the case of waves travelling in the same direction, the induced flow is plane-parallel and the Lagrangian velocity profile can be computed analytically. This example may be viewed as an extension of the theory of peristaltic pumping to the case of high Reynolds numbers.

physics.flu-dyn↗

arXiv2004

Probability of the resistive state formation caused by absorption of a single-photon in current-carrying superconducting nano-strips

We have studied supercurrent-assisted formation of the resistive state in nano-structured Nb and NbN superconducting films after absorption of a single photon. In amorphous narrow NbN strips the probability of the resistive state formation has a pronounced spectral cut-off. The corresponding threshold photon energy decreases with the bias current. Analysis of the experimental data in the framework of the generalized hot-spot model suggests that the quantum yield for near-infrared photons increases faster than the photon nergy. Relaxation of the resistive state depends on the photon energy making the phenomenon feasible for the development of energy resolving single-photon detectors.

cond-mat.supr-con↗