On the influence of viscosity on the characteristic time of the instability of a charged drop

A nonlinear integral equation describing the evolution of spheroidal deformation of a drop that is unstable with respect to its intrinsic charge is derived and solved for arbitrary values of viscosity. It was shown that, due to an essentially nonlinear character of the phenomenon, the characteristic time of instability develop-ment equals the time of tenfold increase in the amplitude of an initial, physically infinitesimal spheroidal deformation of an unstable drop. The dependence of the instability characteristic time on the drop viscosity is described by an increasing linear function.     

Inconsistency in the application of the adiabatic theorem

The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic if the change in eigenstate is significant, regardless of how closely the evolution satisfies the requirements of the adiabatic theorem. We also introduce an example of a two-level system with an exactly solvable evolution to demonstrate the inapplicability of the adiabatic approximation for a particular slowly varying Hamiltonian.     

Dependence of the temperature behaviour of the sputtering ratio on the channelled fraction of the ion beam

A method of calculation is presented for the yield of an electron excitation process by a channelled particle in a single encounter with an atomic row or plane in a crystal. It is shown that, if ψ is the initial angle between the ion trajectory and the row or plane, the number of inner-shell electrons excited is an increasing function of ψ whereas the number of outer electrons excited may decrease with increasing ψ.     

Determination of the glueball mass with allowance for the relativistic character of interaction

Nonperturbative corrections to an interaction Hamiltonian that are associated with relativistic motion and a large coupling constant are determined on the basis of an investigation of the asymptotic behavior of the polarization loop for charged scalar particles in an external gauge field. The mass spectrum of a bound state is determined analytically. The mechanism responsible for the emergence of the constituent mass of particles that form a bound state is explained. It is shown that the contribution of the vector potential and the contribution of the potential associated with a nonperturbative character of interaction cancel each other and that the slope of the Regge trajectory is determined in terms of the string tension.     

Control over the instability wave in terms of the two-dimensional model of a nozzle edge

The problem of generation of an instability wave leaving the edge of a half-plane that separates an immobile medium from a moving medium is considered. It is assumed that the instability wave is initiated by an acoustic wave arriving from the moving medium. The possibility of suppressing the instability wave by another acoustic wave incident from the nonflowing medium is considered. It is shown that the suppression is always possible by adjusting the amplitude and phase of the control perturbation to the parameters of the instability wave.     

On the Spread of Drug-Resistant Diseases

We introduce an interacting particle system to model the emergence of drug-resistant diseases, one of the most serious health problems in modern society. We are interested in diseases for which a natural strain may mutate into a drug-resistant strain. This happens, for instance, when antibiotics are misused. The main result of our analysis is that with an efficient drug against the natural strain, if there is even a small chance that the natural strain mutates into the drug-resistant one, then there will eventually be an outbreak of the drug-resistant strain throughout the population. In that case the natural strain disappears and is replaced by the drug-resistant strain. The disturbing part of this is that an efficient treatment of the natural strain gives an edge to the drug-resistant strain.     

On the influence of the argon flow rate on the parameters of a negative corona

The pulsed-periodic regime of a negative corona in an argon flow is studied experimentally. It is found that an increase in the gas flow rate makes a negative corona current pulse longer and changes its shape.     

Determination of the Space-Charge Field Amplitude by the Phase Modulation Method

Results of experimental and theoretical investigations into the conversion of the phase modulation of light into its intensity modulation in photorefractive crystals are presented. Based on the vector diffraction theory, an analytical expression describing a phase demodulation in crystals in an external electric field applied in an arbitrary direction is derived. The phase demodulation is used to determine the space-charge field amplitude in cubic crystals. It is demonstrated that the space-charge magnitude measured in GaP and Bi₁₂TiO₂₀ crystals is less than that predicted by the Kukhtarev single-level model.     

大气湍流对遥感系统分辨力的影响

以平面波为例,分别针对较弱和较强的湍流模型,通过计算到达角起伏讨论了高空光学遥感系统由大气湍流引起的地面图像分辨力问题。结果表明,对于给定的遥感系统口径和高度,较强湍流引起的图像分辨力的1cm左右;而较强湍流引起的图像分辨力则可达10cm量级。对于自身的地面分辨力具有m的量级的传统光学遥感系统,上述影响并不明显。对于现代高辨力光学遥感系统,这种影响便不容忽略,特别是对较强的湍流,往往需要用自适应光学等方法加以补偿。     

On the covariance of the Fokker-Planck equation

We study the covariance of the Fokker-Planck equation under general gross variables transformations by means of Riemann differential geometry using an affine connection Γ^?_μν unsymmetric in their lower indices and without assuming that the covariant derivative of the diffusion tensor D^μν_;? be zero. We come to the conclusion that to achieve our aim we only need the value of the contraction Γ^?_?ν, all other components of the affine connection remaining completely arbitrary. We argue, therefore, that the most economic way of presenting the covariance of the Fokker-Planck equation is by means of exterior differential calculus. As an application we study physical systems under detailed balance showing that for them the irreversible part of the contravariant drift vector, that is then uniquely determined, is related only to a symmetric tensor while its reversible component is exclusively related to an antisymmetric tensor. A criticism of a compact Fokker-Planck equation is also included.     

The kinetics of the anomalous state formation and the growth of helium crystals at high supersaturation

The kinetics of the formation of an anomalous state of a helium crystal with a fast-growing surface are investigated. It is demonstrated experimentally that it is external supersaturation that is the determining factor of formation of an anomalous state. The dependence of the time of formation of anomalous state on temperature and initial supersaturation is measured. The problem of crystal growth with the excitation of the first-sound wave in the container is solved. This solution is used to determine the dependence of the kinetic coefficient of growth of anomalous facets on temperature and initial supersaturation. It is demonstrated that the kinetic coefficient of facet growth decreases on approaching the boundaries of the region of the existence of an anomalous state. The kinetic coefficient of growth of atomically rough surfaces in an anomalous state is determined by the damping of pressure oscillation. It is found that the value of the latter coefficient is three-four times that of the respective value for the facets but is considerably, by an order of magnitude, less than the value of the coefficient of growth of such surfaces in the normal state. Phenomena are treated which accompany the spiral growth of facets, namely, the excitation of oscillations of a screw dislocation during spiral rotation and the emergence of vortex rings in superfluid helium. The effect of these phenomena on the kinetics of facet growth and on the formation of an anomalous state is discussed.     

The influence of metastable atoms and the effect of the nonlocal character of the electron distribution on the characteristics of the positive column in an argon discharge

Commercial CFDRC software () is used to self-consistently simulate the plasma of the positive column (PC) of a dc discharge in argon. The software allows simulations in an arbitrary 3D geometry by using Poisson’s equation for the electric potential and fluid equations for the heavy components and by solving a nonlocal kinetic equation for electrons. It is shown that, in calculating the electron distribution function, the local approximation is almost always inapplicable under real conditions of a diffuse PC usually met in practice (pR<(5–10) cm Torr). The influence of metastable atoms, which can substantially affect the parameters of the PC plasma, is considered. It is shown that superelasic collisions play an important role in enriching the fast component of the electron distribution function and that the Penning ionization can result in an ascending volt-ampere characteristic of the positive column.     

On the calculation of the Debye-Waller factor of alloys

Relations are derived and discussed for the temperature dependence of the diffraction of X-rays on alloys. It is shown that in a certain approximation one can separate the influence of the inter-atomic force constants from that of the masses of the alloy atoms. A reciprocal matrix is found for the linear chain and the equation for the diffraction of X-rays on an alloy is transformed in a certain approximation to an equation for diffraction on a perfect chain.     

On the effect of spin on the gravitational field

Using a solution of Trautman's recently formulated Einstein-Cartan equations, it is shown that if an isolated body is embedded in an expanding universe consisting of a dust of spinning particles, then the local gravitational field of the body is influenced by spin, even when the cosmological constant is neglected.     

Influence of the optical axis distribution in the anisotropic layer surrounding a spherical particle on the scattering of light

The problem of light scattering from an anisotropic layer with a spherically symmetric distribution of the optical axis is solved exactly. The dependence of the scattering efficiency on the particle size, the anisotropy parameter, and the layer thickness is studied numerically for various anisotropy types. It is shown that the scattering cross section is strongly affected by the type of anisotropy and that the presence of disclinations increases the scattering efficiency. As an additional effect specific to anisotropic scatterers, it is found that, in the case of configurations with broken central symmetry, the scattering amplitudes contain a phase shift that scales logarithmically with the thickness of the anisotropic layer.     

Imaging the cone state of the spin reorientation transition

The magnetization behavior and the domain pattern in remanence are studied in Co/Pt multilayers. The reorientation of magnetization from perpendicular to in plane is found to happen via the state of canted magnetization. In the transition from an easy axis to an easy plane a stable domain pattern in the in-plane magnetization components is found for Co/Pt multilayers. The analysis of the domain pattern reveals that the magnetization canting is such that all in-plane orientations of magnetization are equally occupied. The found structure is appointed to the cone state.     

On the fixed points and invariants of Dykhne transformations and the stability of the solutions of the problem of the effective conductivity of randomly inhomogeneous two-phase media

The fixed points and invariants of Dykhne transformations are determined. It is established that they correspond to the exact solutions and duality relations for the effective characteristics of an inhomogeneous medium. The stability of the exact solutions for the effective conductivity, which are fixed points of the Dykhne transformations, is studied by bifurcation-theory methods, and a classification of these fixed points by stability type is given. It is shown that the effective conductivity tensor of a two-phase medium in magnetic and ac electric fields for certain parameters of the medium can be an unstable point of the “saddle” type.     

On the verification of the applicability of the orthotropic plate wave theory to paper

In the literature one basic work can be found that describes an attempt to verify the applicability of the orthotropic plate wave theory to paper. In the present study we have repeated the key experiment and also modified the original experimental set-up to be able to make new complementary measurements. The performed verification attempt is based on a key experiment in which an ultrasonic resonance method is used. When it is applied to paper, a second resonance can be observed in addition to the one that originates from the asymmetric A0 mode. The result of the verification experiment is conclusive only if the source of this second resonance is the symmetric S0 mode. Our results show that the second resonance is not generated by the S0 mode. Instead, they indicate that the source is a longitudinal wave propagating in the thickness direction of the paper. We therefore conclude that the applicability of the orthotropic plate wave theory to paper cannot be verified by performing the key experiment that is described in the literature.     

On the realization of the Hunt-Ott strange nonchaotic attractor in a physical system

The object of investigation is a system consisting of two coupled nonautonomous van der Pol oscillators the characteristics frequencies of which differ by a factor of 2. The system is subjected to an external action in the form of slow periodic modulation of an oscillation-controlling parameter and also to an additional action at a frequency that is in an irrational relation with the modulation frequency. It is shown that the variation of the oscillation phase over a modulation period can be approximated by a 2D map on a torus that has a robust (structurally stable) Hunt-Ott strange nonchaotic attractor. Calculations of the quantitative characteristics of the attractor corresponding to the initial set of nonautonomous coupled oscillators (such as phase sensitivity exponent, structures and scaling of rational approximations, as well as Lyapunov exponents and their parameter dependence) confirm the presence of the Hunt-Ott strange nonchaotic attractor.