Engineering Papers⌕ Search

Engineering topics

Zak, Michail

Publications and source records attributed to Zak, Michail.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

High precision computing with charge domain devices and a pseudo-spectral method therefor

The present invention enhances the bit resolution of a CCD/CID MVM processor by storing each bit of each matrix element as a separate CCD charge packet. The bits of each input vector are separately multiplied by each bit of each matrix element in massive parallelism and the resulting products are combined appropriately to synthesize the correct product. In another aspect of the invention, such arrays are employed in a pseudo-spectral method of the invention, in which partial differential equations are solved by expressing each derivative analytically as matrices, and the state function is updated at each computation cycle by multiplying it by the matrices. The matrices are treated as synaptic arrays of a neural network and the state function vector elements are treated as neurons. In a further aspect of the invention, moving target detection is performed by driving the soliton equation with a vector of detector outputs. The neural architecture consists of two synaptic arrays corresponding to the two differential terms of the soliton-equation and an adder connected to the output thereof and to the output of the detector array to drive the soliton equation.

Barhen, Jacob↗
NASA NTRS1997

Quantum Neural Nets

The capacity of classical neurocomputers is limited by the number of classical degrees of freedom which is roughly proportional to the size of the computer. By Contrast, a Hypothetical quantum neurocomputer can implement an exponentially large number of the degrees of freedom within the same size. In this paper an attempt is made to reconcile linear reversible structure of quantum evolution with nonlinear irreversible dynamics for neural nets.

Quantum Neural nets↗
NASA NTRS1997

Incompatible Stochastic Processes and Complex Probabilities

The definition of conditional probabilities is based upon the existence of a joint probability. However, a reconstruction of the joint probability from given conditional probabilities imposes certain constraints upon the latter, so that if several conditional probabilities are chosen arbitrarily, the corresponding joint probability may not exist.

Probabilities Mathematics↗
NASA NTRS1997

Non-Lipschitz Approach to Quantum Mechnics

An attempt to reconcile quantum mechanics with Newton's laws represented by the non-Lipschitz formalism has been made. As a Proof-of-concept, a line of equally spaced atoms was studied. It appeared that enforcement of atom incompressibility required relaxation of the lipschitz condition at the points of contact.

Quantum Mechanics↗
NASA NTRS1996

Non-Newtonian Effects In Viscous Flows

Report presents theoretical study addressing persistent problem of explaining random aspects of flows of real fluids in terms of classical governing equations.

Zak, Michail↗
NASA NTRS1996

Non-newtonian Effects in Viscous Flows

Revision of the mathematical formalism of fluid dynamics suggests that some physical inconsistencies (infinite time of approaching equilibrium and fully deterministic solutions to the Navier-Stokes equations) can be removed by relaxing the Lipschitz conditions, i.e., the boundedness of the derivatives, in the constitutive equations. Physically such a modification can be interpreted as an incorporation of an infinitesimal static friction in the constitutive law. A modified version of the Navier-Stokes equations is introduced, discussed, and illustrated by examples. It is demonstrated that all the new effects in the modified model emerge within vanishingly small neighborhoods of equilibrium states which are the only domains where the governing equations are different from classical.

Zak, Michail↗
NASA NTRS1996

Probability Simulations by Non-Lipschitz Chaos

It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-Lipschitz dynamics, without utilization of any man-made devices. Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.

classical dynamics classical probabilities probabi↗
NASA NTRS1996

Introduction to Quantum Intelligence

An impact of ideas associated with the concept of a hypothetical quantum computer upon classical computing is analyzed. Two fundamental properties of quantum computing: direct simulations of probabilities, and influence between different branches of probabilistic scenarios, as well as their classical versions, are discussed.

classical probabilities probabilities Turing machi↗
NASA NTRS1996

Dynamical Simulation of Probabilities

It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-Lipschitz dynamics, without utilization of any man-made devices(such as random number generators). Self-orgainizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed. Special attention was focused upon coupled stochastic processes, defined in terms of conditional probabilities, for which joint probability does not exist. Simulations of quantum probabilities are also discussed.

number generators quantum probabilities↗
NASA NTRS1995

Terminal Dynamics Approach to Discrete Event Systems

This paper presents and discusses a mathematical formalism for simulation of discrete event dynamic (DED)-a special type of 'man-made' systems to serve specific purposes of information processing. The main objective of this work is to demonstrate that the mathematical formalism for DED can be based upon a terminal model of Newtonian dynamics which allows one to relax Lipschitz conditions at some discrete points.!.

discrete event systems↗
NASA NTRS1994

Physical Models of Cognition

This paper presents and discusses physical models for simulating some aspects of neural intelligence, and, in particular, the process of cognition. The main departure from the classical approach here is in utilization of a terminal version of classical dynamics introduced by the author earlier. Based upon violations of the Lipschitz condition at equilibrium points, terminal dynamics attains two new fundamental properties: it is spontaneous and nondeterministic. Special attention is focused on terminal neurodynamics as a particular architecture of terminal dynamics which is suitable for modeling of information flows. Terminal neurodynamics possesses a well-organized probabilistic structure which can be analytically predicted, prescribed, and controlled, and therefore which presents a powerful tool for modeling real-life uncertainties. Two basic phenomena associated with random behavior of neurodynamic solutions are exploited. The first one is a stochastic attractor ; a stable stationary stochastic process to which random solutions of a closed system converge. As a model of the cognition process, a stochastic attractor can be viewed as a universal tool for generalization and formation of classes of patterns. The concept of stochastic attractor is applied to model a collective brain paradigm explaining coordination between simple units of intelligence which perform a collective task without direct exchange of information. The second fundamental phenomenon discussed is terminal chaos which occurs in open systems. Applications of terminal chaos to information fusion as well as to explanation and modeling of coordination among neurons in biological systems are discussed. It should be emphasized that all the models of terminal neurodynamics are implementable in analog devices, which means that all the cognition processes discussed in the paper are reducible to the laws of Newtonian mechanics.

Zak, Michail↗
NASA NTRS1994

Terminal Model Of Newtonian Dynamics

Paper presents study of theory of Newtonian dynamics of terminal attractors and repellers, focusing on issues of reversibility vs. irreversibility and deterministic evolution vs. probabilistic or chaotic evolution of dynamic systems. Theory developed called "terminal dynamics" emphasizes difference between it and classical Newtonian dynamics. Also holds promise for explaining irreversibility, unpredictability, probabilistic behavior, and chaos in turbulent flows, in thermodynamic phenomena, and in other dynamic phenomena and systems.

Zak, Michail↗
NASA NTRS1994

Postinstability Models in Dynamics

This paper is devoted to the concept of instability in dynamical systems with the main emphasis on orbital, Hadamard, and Reynolds instabilities. It demonstrates that the requirement about differentiability in dynamics in some cases is not consistent with the physical nature of motions, and may lead to unrealistic solutions. Special attention is paid to the fact that instability is not an invariant of motion: it depends upon frames of reference, the metric of configuration space, and classes of functions selected for mathematical models of physical phenomena. This leads to the possibility of elimination of certain types of instabilities (in particular, those which lead to chaos and turbulence) by enlarging the class of functions using the Reynolds-type transformation in combination with the stabilization principle: the additional terms (the so-called Reynolds stresses) are found from the conditions that they suppress the original instability. Based upon these ideas, a new approach to chaos and turbulence as well as a new mathematical formalism for nonlinear dynamics are discussed.

Zak, Michail↗
NASA NTRS1994

Posinstability Models in Dynamics

This paper is devoted to the concept of instability in dynamical systems with the main emphasis ofn Orbital, Hadamard's, and Reynold's instabilities.

instability↗