arXiv subjects

V. V. Lebedev

Publications and source records attributed to V. V. Lebedev.

At least 19 recordsLinked to original sources

arXiv2026

Pattern formation in nonlinear dynamics of nematic liquid crystals above the flexoelectric instability threshold

For many decades, researchers have been studying various types of electro-hydrodynamic instabilities in liquid crystals. A significant amount of experimental data has been collected, however, the theoretical interpretations of the results typically rely on linear analysis. In response to this limitation, we investigate the nonlinear stage of the flexoelectric instability in nematics, focusing on liquid crystals with a negative anisotropy in their dielectric permittivity and electrical conductivity. We base our analysis on a comprehensive set of nonlinear electro-hydrodynamic equations for these nematics influenced by an external alternating electric field. The equations predict an instability that is driven by the flexoelectric effect. In order to examine the peculiarities of this phenomenon, we use a model that was proposed in our previous publications, Refs. [1,2], which allows us to perform numerical simulation of nonlinear dynamics. We examine patterns that are formed above the instability threshold. Through numerical simulations, we have identified static and dynamic patterns that occur over a timescale that is much longer than the period of the external electric field. The static patterns are one-dimensional structures and dynamic patterns are standing or traveling one-dimensional waves. The type of the realized pattern depends on the material and experimentally controlled parameters. We found that the standing waves are stable with respect to small transverse perturbations, whereas the propagating waves are unstable. We present a Ginzburg-Landau-like phenomenology that applies near the instability threshold. This approach allows us to rationalize our numerical findings with a few parameters.

cond-mat.soft↗

arXiv2026

Correlations of the phase gradients of the light wave propagating in a turbulent medium in the regime of strong scintillations

We investigate analytically and numerically correlation functions of the phase of light waves that propagate through turbulent media. We examine the case of strong scintillations that occur at large values of the Rytov dispersion, $\sigma^2_R$. Then, it is possible to relate the pair correlation function of phase gradients to the known pair correlation function of the envelope dependent on the distance $r$ assuming Gaussianity of the envelope of the beam. Our direct numerical simulations show that the profile of the pair correlation function for phase gradients gradually approaches the theoretical expression as the value of $\sigma_R^2$ increases, if $r<r_0$ where $r_0$ is the Fried length. For larger $r$ the behavior of the computed correlation function is quite different because of destroying the Gaussianity.

physics.optics↗

arXiv2026

Correlations of the phase gradients of the light wave propagating in a turbulent medium in the regime of weak scintillations

We investigate numerically correlation functions of the phase of light waves that propagate through turbulent media. Special attention is paid to the off-diagonal component of the correlation function of the phase gradients which is insensitive to the outer scale of turbulence. The results of our simulations are in a good agreement with the analytical expressions obtained in Ref. \cite{KLS25}. Thus, we numerically confirm expectations based on uniformity of the perturbation theory for the logarithm of the envelope.

physics.optics↗

arXiv2026

Perturbation theory for phase correlations of a light wave propagating in a turbulent medium

We theoretically investigate the correlation functions of the phase of a light wave propagating through a turbulent medium. We use an equation for the logarithm of a wave packet envelope, which includes a second-order nonlinear term. Based on this equation, we develop a diagrammatic technique to calculate corrections to the correlation function obtained in the linear approximation. We calculate the first corrections determined by one-loop diagrams and find its asymptotic behaviors. Some non-perturbative conclusions are made using the symmetry properties of the equation. These results allow us to conclude that the applicability condition for the perturbation theory is the smallness of the Rytov dispersion, $\sigma_R^2$, and this condition holds uniformly over the distances between observation points.

physics.optics↗

arXiv2025

Geometric Intermittency in Turbulence

Equal-time scaling exponents in fully developed turbulence typically exhibit non anomalous scaling in the inverse cascade of two-dimensional (2D) turbulence and anomalous scaling in three dimensions. We demonstrate that multiscaling is not confined to longitudinal, scalar velocity increments, but also emerges in increments associated with the magnitude and orientation of the velocity vector. This decomposition uncovers a multiscaling in the 2D inverse cascade, which remains obscured when using conventional structure functions. Our results highlight a decoupling between velocity amplitude and flow geometry, offering new insight into the statistical structure of turbulent cascades as well as showing how different classes of multiscaling emerge.

physics.flu-dyn↗

arXiv2024

Dynamic flexoelectric instabilities in nematic liquid crystals

Electro-hydrodynamic phenomena in liquid crystals constitute an old but still very active research area. The reason is that these phenomena play the key role in various applications of liquid crystals and due to the general interest of physical community to out-of-equilibrium systems. Nematic liquid crystals (NLCs) are ideally representative for such investigations. Our article aims to study theoretically the linear NLCs dynamics. We include into consideration orientation elastic energy, hydrodynamic motion, external alternating electric field, electric conductivity and flexoelectric polarization. We analyze the linear stability of the NLC film, determining dynamics of perturbations with respect to the homogeneous initial state of the NLC. For the purpose we compute eigen-values of the evolution matrix for a period of the external alternating electric field. These eigen-values determine the amplification factors for the modes during the period. The instability occurs when the principal eigen-value of the evolution matrix becomes unity by its absolute value. The condition determines the threshold (critical field) for the instability of the uniform state. It turns out that one might expect various types of the instability, only partially known and investigated in the literature. Particularly, we find that the flexoelectric instability may lead to two-dimensionally space modulated patterns exhibiting time oscillations. This type of the structures was somehow overlooked in the previous works.

cond-mat.soft↗

arXiv2024

Pair correlation function of vorticity in a coherent vortex

We study the correlations of vorticity fluctuations inside a coherent vortex resulting from the inverse energy cascade in two-dimensional turbulence. The presence of a coherent flow, which is a differential rotation, suppresses small-scale fluctuations of the flow, which are created by an external force, and lead to the fact that these fluctuations can be considered as non-interacting and, therefore, examined in a linear approximation. We calculate the pair correlation function of vorticity and demonstrate that it has a power-law behavior both in space and in time. The obtained results allow us to start a systematic study of the effects associated with the nonlinear interaction of fluctuations, which play an essential role on the periphery of a coherent vortex. Our results are also applicable to the statistics of a passive scalar in a strong shear flow.

physics.flu-dyn↗

arXiv2024

Correlations in a weakly interacting two-dimensional random flow

We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow fluctuations found in the linear approximation. We calculate the correction to the pair correlation function and the triple correlation function. It enables us to establish the criterion of validity of the perturbation theory for different ratios of viscosity and bottom friction. We find that the corrections to the second moment are anomalously weak in the cases of small bottom friction and small viscosity and relate the weakness to the energy and enstrophy balances. We demonstrate that at small bottom friction the triple correlation function is characterized by universal scaling behavior in some region of lengths. The developed perturbation method was verified and confirmed by direct numerical simulations.

physics.flu-dyn↗

arXiv2022

Nonlinear electro-hydrodynamics of liquid crystals

We present nonlinear dynamic equations for nematic and smectic $A$ liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is expressed as a sum of external electric field and the fields originating from feedback of liquid crystal order parameter, and a field, created by charged impurities. The system tends to decrease the total electric field, because it lowers the energy density. This basically nonlinear problem is not a pure academic interest. In the realm of liquid crystals and their applications, utilized nowadays modern experimental techniques have progressed to the point where even small deviations from the linear behavior can be observed and measured with a high accuracy. Hydrodynamics is the macroscopic description of condensed matter systems in the low frequency, long wavelength limit. Nonlinear hydrodynamic equations are well established to describe simple fluids. Similar approaches (with degrees of freedom related to the broken orientational or translational symmetry included) have been used also for liquid crystals. However to study behavior of strongly perturbed well above the thresholds of various electro-hydrodynamic instabilities of liquid crystals the nonlinear equations should include soft electromagnetic degrees of freedom as well. The self-consistent derivation of the complete set of the nonlinear electro-hydrodynamic equations for liquid crystals became an actual task. The aim of our work is to present these equations, which is a mandatory step to handle any nonlinear phenomenon in liquid crystals.

cond-mat.soft↗

arXiv2022

Long-range interactions between membrane inclusions: Electric field induced giant amplification of the pairwise potential

The aim of this work is to revisit the phenomenological theory of the interaction between membrane inclusions, mediated by the membrane fluctuations. We consider the case where the inclusions are separated by distances larger than their characteristic size. Within our macroscopic approach a physical nature of such inclusions is not essential, however we have always in mind two prototypes of such inclusions: proteins and RNA macromolecules. Because the interaction is driven by the membrane fluctuations, and the coupling between inclusions and the membrane, it is possible to change the interaction potential by external actions affecting these factors. As an example of such external action we consider an electric field. Under external electric field (both dc or ac), we propose a new coupling mechanism between inclusions possessing dipole moments (as it is the case for most protein macromolecules) and the membrane. We found, quite unexpected and presumably for the first time, that the new coupling mechanism yields to giant enhancement of the pairwise potential of the inclusions. This result opens up a way to handle purposefully the interaction energy, and as well to test of the theory set forth in our article.

cond-mat.soft↗

arXiv2021

Broadband chip-based source of a quantum noise with electrically-controllable beam splitter

For the first time, the theory and practical realization of a broadband quantum noise generator based on original integrated optical beam splitter in the form of a Mach-Zehnder interferometer is demonstrated. The beam splitter with a double output, made on a lithium niobate substrate, provided accurate electro-optical balancing of the homodyne quantum noise detection circuit. According to our knowledge, the experimentally obtained excess of quantum noise over classical noise by 12 dB in the frequency band over 4 GHz, which is the best parameters of quantum noise generators known from the literature.

quant-ph↗

arXiv2019

Landau theory for smectic-A -- hexatic-B coexistence in smectic films

We explain theoretically peculiarities of the smectic A -- hexatic B equilibrium phase coexistence in a finite temperature range recently observed experimentally in free standing smectic films [I.A.Zaluzhnyy et al., Physical Review E, volume 98, 052703 (2018)]. We quantitatively describe this unexpected phenomenon within Landau phase transitions theory assuming that the film state is close to a tricritical point. We found that the surface hexatic order leads to diminishing the phase coexistence range as the film thickness decreases shrinking it at some minimal film thickness, of the order of the hexatic correlation length. We established universal laws for the temperature width of the phase coexistence in terms of the reduced variables. Our theory is in agreement with the existing experimental data.

cond-mat.soft↗

arXiv2018

Uniformly convergent Fourier series and multiplication of functions

Let $U(\mathbb T)$ be the space of all continuous functions on the circle $\mathbb T$ whose Fourier series converges uniformly. Salem's well-known example shows that a product of two functions in $U(\mathbb T)$ does not always belongs to $U(\mathbb T)$ even if one of the factors belongs to the Wiener algebra $A(\mathbb T)$. In this paper we consider pointwise multipliers of the space $U(\mathbb T)$, i.e., the functions $m$ such that $mf\in U(\mathbb T)$ whenever $f\in U(\mathbb T)$. We present certain sufficient conditions for a function to be a multiplier and also obtain some results of Salem type.

math.CA↗

arXiv2017

Profile of a coherent vortex in two-dimensional turbulence at static pumping

We examine the velocity profile of coherent vortices appearing as a consequence of the inverse cascade of two-dimensional turbulence in a finite box in the case of static pumping. We demonstrate that in the passive regime the flat velocity profile is realized, as in the case of pumping short correlated in time. However, in the static case the energy flux to large scales is dependent on the system parameters. We demonstrate that it is proportional to $f^{4/3}$ where $f$ is the characteristic force exciting turbulence.

physics.flu-dyn↗

arXiv2016

Velocity statistics inside coherent vortices generated by the inverse cascade of $2d$ turbulence

We analyze velocity fluctuations inside coherent vortices generated as a result of the inverse cascade in the two-dimensional ($2d$) turbulence in a finite box. As we demonstrated in \cite{16KL}, the universal velocity profile, established in \cite{14LBFKL}, corresponds to the passive regime of flow fluctuations. The property enables one to calculate correlation functions of the velocity fluctuations in the universal region. We present results of the calculations that demonstrate a non-trivial scaling of the structure function. In addition the calculations reveal strong anisotropy of the structure function.

physics.flu-dyn↗

arXiv2016

Effect of thin film on the generation of vorticity by surface waves

Recently a theoretical scheme explaining the vorticity generation by surface waves in liquids was developed [S. Filatov et al., Phys. Rev. Lett. 116, 054501 (2016)]. Here we study how a thin (monomolecular) film presented at the surface of liquid affects the generated vorticity. We demonstrate that the vorticity becomes parametrically larger than for the case with a clean surface and now it depends on viscosity of the liquid. We also discuss the motion of particles passively advected by the generated surface flow. The results can be used in different applications: from the analysis of pollutants' diffusion on the ocean surface till the reconstruction of vorticity based on the particle image velocimetry (PIV) measurements.

physics.flu-dyn↗

arXiv2016

Why the smectic A -- hexatic phase transition does not follow its universality class?

We resolve the old riddle related to the critical behavior of the heat capacity near the smectic A -- hexatic second order phase transition. Experiment suggests a "large" positive specific heat critical exponent inconsistent with the universality class for this phase transition implying the very small negative exponent. We show that essential features of the heat capacity for the smectic A -- hexatic phase transition can be rationalized in the framework of a theoretical model treating jointly fluctuations of the hexatic orientational order and of the positional (translational) order parameters. Assuming that the positional (translational) correlation length is larger than the hexatic correlation length, we calculate a temperature dependence of the specific heat in the critical region near the smectic A -- hexatic phase transition. Our results are in a quantitative agreement with the calorimetric experimental data.

cond-mat.soft↗

arXiv2016

A short and simple proof of the Jurkat--Waterman theorem on conjugate functions

It is well--known that certain properties of continuous functions on the circle $\mathbb T$, related to the Fourier expansion, can be improved by a change of variable, i.e., by a homeomorphism of the circle onto itself. One of the results in this area is the Jurkat--Waterman theorem on conjugate functions, which improves the classical Bohr--Pál theorem. In the present work we provide a short and technically very simple proof of the Jurkat--Waterman theorem. Our approach yields a stronger result.

math.CA↗