Recent developments in spintronics have drawn renewed attention to the spin dynamics of cubic ferromagnetic crystals EuO and EuS. These ferromagnets have the simplest possible magnetic structure, making them the most suitable systems for testing various theoretical models of magnetic materials. A commonly used Weiss meanfield approximation (MFA) provides only a qualitative description of the magnetization temperature dependence M(T ). We develop a consistent theory for M(T ) based on the perturbation diagrammatic technique for spin operators. Our theory is in excellent quantitative agreement with the experimental dependence of M(T ) for EuO and EuS throughout the entire temperature range from T = 0 to Curie temperature TC. In particular, our theoretical dependence M(T ) demonstrates a scaling behavior M(T ) proportional to (TC - T )beta & lowast; with the scaling index beta & lowast; approximate to 1/3 in a wide range of temperatures, in agreement with the experimentally observed apparent scaling in EuO and EuS. The scaling behavior with beta & lowast; approximate to 1/3 is manifested in the temperature range T <= TC where corrections to the magnetization due to its fluctuations 8M(T ) <= M(T ). To distinguish it from the narrow "critical" range T approximate to TC with 8M(T ) > M(T ), we term this T-range "precritical." The precritical corrections 8M(T ) are still large enough to affect the M(T ) behavior. The index beta & lowast; fundamentally differs from the "normal" scaling index beta MFA = 1/2 predicted by the MFA, which neglects the magnetization fluctuations. We refer to the apparent magnetization scaling with beta & lowast; approximate to 1/3, which emerges in our theory, as "precritical anomalous."

Molecular sorting in biological membranes is essential for proper cellular function. It also plays a crucial role in the budding of enveloped viruses from host cells. We recently proposed that this process is driven by phase separation, where the formation and growth of sorting domains depend primarily on direct intermolecular interactions. In addition to these, Casimir-like forces—arising from entropic effects in fluctuating membranes —may also play a significant role in the molecular distillation process. Here, using a combination of theoretical analysis and numerical simulations, we explore how Casimir-like forces between rigid membrane inclusions contribute to sorting, particularly in the biologically relevant regime where direct intermolecular interactions are weak. Our results show that these forces enhance molecular distillation by reducing the critical radius for the formation of new sorting domains and facilitating the capture of molecules within these domains. We identify the relative rigidity of the membrane and supermolecular domains as a key parameter controlling molecular sorting efficiency, offering new insights into the physical principles underlying molecular sorting in biological systems.

A numerical method for approximating the equations of dynamics of a polymer solution flow is proposed. The proposed technique is based on a hybrid approach. The hydrodynamic component of the flow is described by a system of Navier–Stokes equations and is numerically approximated using the linearized Godunov method. The polymer component of the flow is described by a system of equations for the polymer stretching vector 𝐑 and is numerically approximated by the Kurganov–Tadmor method. Using this scheme, stability of the polymer solution flow at low Reynolds numbers Re∼ 10 in a square cell under the action of an external periodic force is investigated. The instability of this type of flow characterized by a violation of its laminarity is studied by means of a numerical experiment. The spectral characteristics of the polymer solution at low Reynolds numbers are constructed.

The diffraction of a light wave by fluctuations in the refractive index in a turbulent medium leads to its distortions. Their analysis allows one to extract the main parameters of turbulence. In this paper, we propose a new method based on measurements of the correlation function of the gradients of the light wave phase, which allows us to independently find the Fried parameter r0 and, then, the outer scale of turbulence L0. The method has been successfully tested on measurement data obtained during the passage of laser radiation through a gaseous medium with artificially created turbulence.

The problem of two-dimensional flow of a viscous weakly compressible fluid in a square cell under excitation by a spatially periodic static external force (Kolmogorov flow) is considered. A new method for determining the flow structure is presented. It is based on the analysis of the vorticity field at different times. This method is used to classify types of flows the characteristics of which were obtained by numerical simulation. The main flow regimes are identified depending on the values of the friction coefficient against the bottom and the pumping force: laminar, chaotic and vortex regimes. Transitional types of flow are studied separately: the quasi-periodic regime, which arises through a sequence of bifurcations when the laminar and chaotic flow regimes change, and the alternation regime, which occurs during the transition from the chaotic to vortex flow. Phase diagrams are constructed in the space the amplitude of the external force–the friction coefficient against the bottom, which made it possible to classify the type of flow on the basis of the values of the friction coefficient against the bottom and the pumping force.

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.

We examine fluctuations of vorticity excited by an external random force in two-dimensional fluid in the presence of a strong external shear flow. The problem is motivated by the analysis of big coherent vortices appearing as a consequence of the inverse energy cascade in a finite box at large Reynolds numbers. We develop the perturbation theory for calculating nonlinear corrections to correlation functions of the flow fluctuations assuming that the external force is short correlated in time. We analyze corrections to the pair correlation function of vorticity and some moments. The analysis enables one to establish validity of the perturbation theory for laboratory experiments and numerical simulations.

We examine statistics of fluctuations of the light beam intensity at its propagating in a turbulent atmosphere. We are interested in the probability of relatively large values of the beam intensity. The model of a phase screen is considered. We find the tail of the probability density function characterized by the stretched exponent with power 7/12. Conditions of realizing the tail are established. The general picture is discussed.

A two-dimensional flow of a viscous fluid in a cell of finite size is studied numerically. The flow arises as a result of an inverse cascade supported by a constant pumping. Several distinct states are observed. One of them is dominated by a large eddy with a well-defined average velocity profile. In the second state, strong chaotic large-scale fluctuations predominate. A laminar flow is observed in the third state. The nature of the resulting state depends on the fluid kinematic viscosity coefficient, the magnitude of the external pumping force wave vector, and the value of the bottom friction factor. When the values of the kinematic viscosity and wave vector are fixed, a small value of the bottom friction factor leads to the appearance of the first state. As the coefficient of the bottom friction factor increases, there occurs a transition from a flow with one large vortex to a laminar flow through a series of states with several unstable vortices, which we call chaotic motion. The paper presents the results of numerical simulation of a weakly compressible viscous fluid flow in a closed cell with no-slip boundary conditions on the walls. Pumping is carried out by a static force periodic in space in two directions. The simulation is carried out for various values of the bottom friction factor.

We investigate fluctuations of vorticity inside a coherent vortex generated by the inverse energy cascade in two-dimensional turbulence. Temporal and spatial correlations can be characterized by the pair correlation function. The interaction of fluctuations leads to a nonzero third moment of vorticity. We analyze the pair correlation function and the third moment using a model in which the pumping is short-correlated in time and derive explicit expressions for the Gaussian spatial correlation function for the pumping force.

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.

We examine statistics of fluctuations of the laser beam intensity at its propagating in turbulent atmosphere. We are interested in relatively large propagating distances and the remote tail of the probability density function. The tail is determined by the stretched exponent, we find its index.

We examine analytically and numerically the state of a two-dimensional fluid in a finite box appearing as a result of the inverse cascade supported by a permanent pumping. We argue that there are two different states. One of the states is dominated by big coherent vortices with a well-defined mean profile. The other state is dominated by strong chaotic large-scale fluctuations. The character of the realized state depends on the ratio νkf2/α where ν is the kinematic viscosity coefficient, kf is the characteristic wave vector of the pumping force and α the bottom friction coefficient. If the ratio νkf2/α is large then one expects to observe the first state, whereas in the opposite state the second (chaotic) state is expected. To check the prediction we performed the direct numerical simulations of hydrodynamics of a weakly compressible two-dimensional fluid with no-slip boundary conditions. The pumping force is static and contains some spacial harmonics. The simulations are performed for different values of pumping and of the ratio νkf2/α. We introduce the criterion based on presence/absence of long time correlations to distinguish two above states. The numerical results confirm the analytical predictions.

Численное моделирование течения Колмогорова в вязких средах под действием периодической в пространстве статической силы

We introduce a simple physical picture to explain the process of molecular sorting, whereby specific proteins are concentrated and distilled into submicrometric lipid vesicles in eukaryotic cells. To this purpose, we formulate a model based on the coupling of spontaneous molecular aggregation with vesicle nucleation. Its implications are studied by means of a phenomenological theory describing the diffusion of molecules toward multiple sorting centers that grow due to molecule absorption and are extracted when they reach a sufficiently large size. The predictions of the theory are compared with numerical simulations of a lattice-gas realization of the model and with experimental observations. The efficiency of the distillation process is found to be optimal for intermediate aggregation rates, where the density of sorted molecules is minimal and the process obeys simple scaling laws. Quantitative measures of endocytic sorting performed in primary endothelial cells are compatible with the hypothesis that these optimal conditions are realized in living cells.