Initial/boundary-value problems of tumor growth within a host tissue

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly degenerate parabolic equations, which include phenomenological terms related to specific cell functions. The paper discusses general modeling guidelines for such terms, as well as for initial and boundary conditions, aiming at both biological consistency and mathematical robustness of the resulting problems. Particularly, it addresses some qualitative properties such as a priori nonnegativity, boundedness, and uniqueness of the solutions. Existence of the solutions is studied in the one-dimensional time-independent case.Comment: 30 pages, 5 figure

Severe plastic deformation for producing superfunctional ultrafine-grained and heterostructured materials: An interdisciplinary review

Ultrafine-grained and heterostructured materials are currently of high interest due to their superior mechanical and functional properties. Severe plastic deformation (SPD) is one of the most effective methods to produce such materials with unique microstructure-property relationships. In this review paper, after summarizing the recent progress in developing various SPD methods for processing bulk, surface and powder of materials, the main structural and microstructural features of SPD-processed materials are explained including lattice defects, grain boundaries and phase transformations. The properties and potential applications of SPD-processed materials are then reviewed in detail including tensile properties, creep, superplasticity, hydrogen embrittlement resistance, electrical conductivity, magnetic properties, optical properties, solar energy harvesting, photocatalysis, electrocatalysis, hydrolysis, hydrogen storage, hydrogen production, CO2 conversion, corrosion resistance and biocompatibility. It is shown that achieving such properties is not limited to pure metals and conventional metallic alloys, and a wide range of materials are currently processed by SPD, including high-entropy alloys, glasses, semiconductors, ceramics and polymers. It is particularly emphasized that SPD has moved from a simple metal processing tool to a powerful means for the discovery and synthesis of new superfunctional metallic and nonmetallic materials. The article ends by declaring that the borders of SPD have been extended from materials science and it has become an interdisciplinary tool to address scientific questions such as the mechanisms of geological and astronomical phenomena and the origin of life

Characteristics of estimating the amplitude of ultrawideband quasi-radio signal

The synthesis and analysis of the maximum likelihood algorithm for estimating the amplitude of ultrawideband quasi-radio signal with unknown amplitude and phase have been performed. The duration of the specified signal can amount to several periods or a fraction of the period of harmonic oscillation. The characteristics of the classical maximum likelihood estimate of the amplitude of a narrow-band radio signal were found while receiving an ultrawideband quasi-radio signal. The conditions of applicability of the model of narrow-band radio signal were defined for solving the problem of amplitude estimation with the specified accuracy

Effectiveness of ultra-wideband range and velocity estimation in presence of narrowband interference

Characteristics of two estimate algorithms are found. Influence of narrow–band Gaussian interference on accuracy of estimates are investigated

Efficiency of ultra-wideband quasi-radio signal’s frequency estimation

Synthesis and analysis of maximum likelihood algorithm for estimating the frequency of ultrawideband quasiradiosignal have been realized. Which duration is equal to several periods or several parts of harmonic oscillation period. Dispersions estimates have been found

Phase estimation characteristics of ultra-wideband quasi-radio signal

Synthesis and analysis of the maximum likelihood algorithm for estimating the phase of ultra-wideband quasi-radio signal with unknown amplitude and phase are performed. Duration of the specified signal may amount to several periods or a fraction of the period of harmonic oscillation. Characteristics of the classical maximum likelihood phase estimate of a narrow-band radio signal are found when receiving an ultra-wideband quasi-radio signal. Applicability conditions of narrow-band radio signal model are defined for solving the problem of phase estimation with the specified accuracy

Impact of narrowband interference on the threshold characteristics of range and velocity estimates during the probing with a sequence of ultrawideband pulses

Threshold characteristics of two algorithms for the range and velocity estimation under exposure to the Gaussian narrowband interference have been found