Engineering topics
Publications and source records attributed to Zak, Michail A..
Report presents theoretical study of dynamics of neural network organizing own response in both phase space and in position space. Postulates several mathematical models of dynamics including spatial derivatives representing local interconnections among neurons. Shows how neural responses propagate via these interconnections and how spatial pattern of neural responses formed in homogeneous biological neural network.
Paper discusses approach to mathematical modeling of artificial neural networks exhibiting complicated behaviors reminiscent of creativity and intelligence of biological neural networks. Neural network treated as non-Lipschitzian dynamical system - as described in "Non-Lipschitzian Dynamics For Modeling Neural Networks" (NPO-17814). System serves as tool for modeling of temporal-pattern memories and recognition of complicated spatial patterns.
Neural networks made to "learn" faster. Report presents theoretical study of terminal attractors in neural networks. Includes systematic analysis of applications to activation dynamics of neural networks.
Report presents analysis of turbulence in simple shear flow. In mathematical model used in study, turbulence considered to arise from growth of small fluctuations in initially unstable plane Poiseuille flow. Invoking principle of stabilization, fluctuations in velocity, therefore, Reynolds stresses, considered to grow until new stable state approached. Principle enables one to find Reynolds stresses and mean velocity of turbulent flow arising from initial plane Poiseulle flow.
Report discusses propagation of vibrations in structure in response to impulsive and/or concentrated loads. Effects of pulsed loads treated by analyzing propagation of characteristic vibrational waves explicitly through each member of structure. This wave-front analysis used in combination with usual finite-element modal analysis to obtain more accurate representation of overall vibrational behavior.
Criteria of stability different in different sets of coordinates. Report discusses dependence of criteria of hydrodynamic instability upon frame of reference used to analyze motion of fluid.
Report discusses global instability in orbital motion of two-link planar mechanism. Principal objective, contributes to understanding of chaotic motions in robot manipulators and other deterministic mechanical systems. Discussion begins with brief review of previous studies of chaotic motion and introduces notion of orbital instability in nonlinear systems. Introduces geometric approach useful in representation of orbital instability.