On solving discontinuous extremal problems

An approach to solving discontinuous problems of optimization and control is described. The approach is based on the concept of approximate gradient introduced in Ref. 1. Generalizations of the theorems of Kuhn-Tucker and Dubovitsky-Milyutin and the maximum principle of Pontryagin are proved. The mathematical constructions described allow one to solve a wide variety of applied problems of optimization and control within the class of nonsmooth (including discontinuous) functions. The paper continues the investigations of Refs. 1–2.     

Measurement of the Doppler Frequency Shift on Individual Rays Using a Chirp Ionosonde

We develop theoretically a method for determining the Doppler frequency shift on individual rays in ionospheric sounding. The method is based on using periodic chirp signals. The potential resolution and range of the measured Doppler-shifted frequencies are determined. Application of this method yields the relationship between the Doppler shift of the propagation-mode frequency and the velocity of a horizontal displacement of the hop tops along the Khabarovsk-Yoshkar-Ola radio path. Significant correlations between the mode order in the ionosphere and the Doppler shift, Doppler-spectrum width, and stationarity time of the propagation channel are found.     

The Features of Round-the-World Signal Propagation over the Paths of the Russian Chirp-Sounder Network during Low and Mild Solar Activity

We present the results of observations of round-the-world (RTW) signals by the Russian chirp-sounder network in 1997-1999. The frequency-time intervals of the RTW propagation with minimum attenuation are determined. Using numerical simulations of HF signals based on the waveguide and geometric-optical approaches, we perform the interpretation of the experimental data. It is shown that RTW-signal attenuation is mainly determined by the state of the low-latitude ionosphere in African and Asian-Pacific longitude regions. The possibilities of monitoring large-scale structures of the low-latitude ionosphere in regions poorly equipped with diagnostic tools using the RTW-signal characteristics of the Russian chirp-sounder network are discussed.     

Experimental study of different modes of block sliding along interface. Part 2. Field experiments and phenomenological model of the phenomenon

The paper reports the results of field experiments on studying different modes of gravitational sliding of a block on the natural fault surface. Various materials were used as interface filler to model the whole range of deformation events that can be arbitrarily divided into three groups: accelerated creep, slow slip, and dynamic slip. The experiments show that the type of modeled deformation events is defined by both structural parameters of contact between blocks and material composition of the contact filler.Foundations for a new geomechanical model of occurrence of different-type dynamic events were developed. The model is based on the idea that “contact spots” form subnormally to the crack edges during shear deformation; the “spots” are clusters of force mesostructures whose evolution governs the deformation mode. The spatial configuration of “contact spots” remains unchanged during the entire “loading-slip” cycle but changes after the dynamic event occurrence. The destroyed force mesostructures can be replaced by similar structures under intergranular interaction forces when the external influence is fully compensated. Unless “contact spots” are incompletely destroyed, the deformation process dynamics is defined by their rheology. The migration of “contact spots” during deformation of a crack filled with heterogeneous material causes changes in deformation parameters and transformation of the mode itself due to changing rheology of local contact areas between blocks.It is found by fractal analysis that in order for dynamic slip to occur, spatially structured “contact spots” characterized by low fractal dimension must be formed; slow slip events can exist only in a certain parametric domain called the “dome of slow events”. It is found that the probability of slow slip occurrence is higher on fault regions characterized by maximum fractal dimension values: fault tips, fault branching and fault intersection zones.     

Preliminary results of the ultralong-range sounding of ionospheric irregularities using the ducted mode

We present preliminary experimental results concerning transequatorial propagation (TEP) of HF waves upon chirp sounding over the 11950-km path alice Springs (Australia)-Yoshkar-Ola (Russia). The measurements were made in August, 1998. Two anomalous signals with delays of 3.0 and 4.5 ms with respect to the main mode were observed during night time (21:30–23:00 UT). The maximum observed frequencies (MOF) of these signals were 2–3 MHz greater than the main-mode MOF. Simulations allowed us to identify these signals as the ducted signals trapped in theFE interlayer duct due to radiowave refraction on a negative gradient of the electron density and that escaped from the duct due to the scattering by small-scale field-aligned irregularities of the subpolar ionosphere. We discuss radiophysical and geophysical aspects concerning localization of the irregularities responsible for scattering and perspectives of using the ducted mode for over-the-horizon diagnostics of the inhomogeneous structure of the ionosphere with a global network of chirp sounders and HF radars. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 12, pp. 1136–1142, December 1999.