Stability of a family of weighted finite-difference schemes

Existence and uniqueness theorems are proved for a weighted finite-difference scheme approximating the heat equation with a nonlocal boundary condition containing a parameter. Bounds are derived that guarantee stability of the solution in the initial values in the mean-square grid norm. Translated from Prikladnaya Matematika i Informatika, No. 29, 2008, pp. 64–87.     

N1‐(2,6‐Di­methyl­phenyl)‐N2‐hydroxy‐α‐oxo‐α‐phenyl­acet­amidine

The structure of the title compound, C₁₆H₁₆N₂O₂, consists of a dimeric arrangement around an inversion centre of acet­amidine mol­ecules linked via O—H⋯N hydrogen bonds. There are also H⋯π‐ring interactions. All these interactions result in the formation of infinite chains parallel to the (101) axis. The oxime group has an E conformation.     

Numerical calculation of the correlation moments of the sound field scattered by a rough surface

Numerically calculated two-dimensional correlation moments of the surface-scattered sound field are presented in the form of correlation surfaces and analyzed. The models of three-dimensional anisotropic and two-dimensional quasi-harmonic surface waves are considered. Data are presented on the angular dependence of the space-time correlation domains of the scattered sound field for receivers spaced across the propagation path in both horizontal and vertical directions, as well as on the shapes of the time-frequency and space-frequency correlation domains.     

A Nonlocal Finite-Difference Boundary-Value Problem

We investigate the stability of difference schemes for the equation of heat conduction with nonlocal boundary conditions. An example is given which in a certain sense imitates the problem with variable coefficients and has an exact solution in analytical form. It is shown that the difference operator has a simple spectrum and that multiple eigenvalues appear only in the case with constant coefficients. The simple spectrum ensures that the eigenvectors of the finite-difference problem form a basis. This enables us to apply to the nonlocal problem the theory of stability of symmetrizable difference schemes.     

Statistical modelling of the backscattered field in a one-dimensional non-stationary stochastic problem

Within the framework of an exact wave approach in the spatial-time domain, the one-dimensional stochastic problem of sound pulse scattering by a layered random medium is considered. On the basis of a unification of methods which has been developed by the authors, previously applied to the investigation of non-stationary deterministic wave problems and stochastic stationary wave problems, an analytical-numerical simulation of the behaviour of the backscattered field stochastic characteristics was carried out. Several forms of incident pulses and signals are analysed. We assume that random fluctuations of a medium are described by virtue of the Gaussian Markov process with an exponential correlation function. The most important parameters appearing in the problem are discussed; namely, the time scales of diffusion, pulse durations, the medium layer thickness or the largest observation time scale in comparison with the time scale of one correlation length for the case of a half-space. An exact pattern of the pulse backscattering processes is obtained. It is illustrated by the behaviour of the backscattered field statistical moments for all observation times which are of interest. It is shown that during the time interval when the main part of the pulse energy leaves the medium, the backscattered field is a substantially non-stationary process, having a non-zero mean value and an average intensity that decays according to a power law. There are various power indices for the different duration incident pulses, however, they are not the same as those of previous papers, which were obtained on the basis of an approximate and asymptotic analysis. We have also verified that the Gaussian law is valid for the probability density function of the backscattered field in the case of any incident pulse duration.     

234Th-based measurements of particle flux in surface water of the Bransfield Strait, western Antarctica

Measurements of particulate and dissolved ²³⁴Th were carried out in March 2002 in the Bransfield Strait located between the Antarctic Peninsula and the South Shetland Islands. The ²³⁴Th/²³⁸U disequilibrium found in the upper water column has allowed evaluation of downward particle fluxes across a frontal zone, which divides water masses coming from the Bellingshausen Sea and the Weddell Sea. The highest particle flux has been found in this mixing zone, where it was 3–5 times greater than in the adjacent waters. Total mass fluxes in the upper 150-m water column were estimated as about 2.2 g m^?2 day^?1 in the eastern part of the Strait and 3.1 g m^?2 day^?1 in the western area.     

Laser system for the detection of critical surface deformations

A laser system for the detection of deformations, based on the interruption of an optical signal at the curvature of the channel of laser radiation distribution due to the deformation of a controllable surface, is presented. Techniques and constructive solutions for executing devices to detect critical deformations of objects are proposed that enable us to recognize a pre-emergency situation with confidence and take prompt steps to eliminate the danger.     

Relationship between the Omniphobic Properties and the Swelling Degree of SLIPS Coatings Based on Polymer Gel Thin Films

Doklady Physical Chemistry - The study addresses the relationship between the omniphobic properties of coatings based on polymer matrices doped with liquid lubricants (Slippery Liquid-Infused...     

Proton radioactivity half-lives with nuclear asymmetry factor

The dependence of proton emission half-lives on the nuclear asymmetry parameter is investigated using the WKB method and two types of empirical formula.Using the single-folding formalism with asymmetry-depend-ent nuclear radius and surface diffuseness of nuclear matter,the nuclear potential and consequently the half-life are functions of the asymmetry factor.Despite small values of asymmetry in neutron-deficient proton emitters,notice-able changes in the half-lives are observed.The addition of an asymmetry parameter term to the two forms of empir-ical formulas leads to a reduction in the rms error for ground state and isomeric transitions.A noticeable reduction of about 43%is obtained for isomeric transitions in the second form of the empirical formula.Considering ground state transitions in two categories,odd-even and odd-odd emitters,and adopting deformation and asymmetry-dependent empirical formulas,the rms decreases remarkably.The low est values of rms errors,viz.0.1492,0.2312,and 0.1999,are obtained for the aforementioned empirical formulas for ground state transitions of odd-even and odd-odd emit-ters and for all isomeric transitions,respectively.