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Three-Dimensional Molecular Electronics and Integrated Circuits for Signal and Information Processing Platforms
Published in Sergey Edward Lyshevski, Nano and Molecular Electronics Handbook, 2018
The fundamental and technological limits are also imposed on molecular electronics and MPPs. Those limits are defined by the device physics, circuit, system, CAD, and synthesis constraints. Some of these limitations are reported in this chapter. However, there is no end to the progress, and one will evolve beyond molecular electronics and processing. What lies beyond these innovations and frontiers? The hypothetical answer is provided next. In 1993, the Dutch theoretical physicist G. Hooft proposed the Holographic Principle, postulating that the information contained in some region of space can be represented as a hologram that gives the bounded region of space, at most, one degree of freedom per the Planck unit of area (λp = 1.616 × 10−35 m). In this chapter, we will utilize the so-called standard model (particles are considered to be points moving through space and coherently represented by mass, electric charge, interaction, spin, etc.). The standard model is consistent within quantum mechanics and the special theory of relativity. Other concepts have also been developed, some even utilizing string theory, with its various aspects like string vibration, distinct forces, multidimensionality, etc. It is difficult to theorize which far-reaching paradigms will emerge. Therefore, we will focus here on sound and practical paradigms.
Nano- and Microscale Systems, Devices, and Structures
Published in Sergey Edward Lyshevski, Nano- and Micro-Electromechanical Systems, 2018
In 1993 the Dutch theoretical physicist G. Hooft proposed the holographic principle, which postulates that the information contained in some region of space can be represented as a hologram that gives the bounded region of space that contains at most one degree of freedom per Planck unit of area (λp = 1.616 × 10−35 m).
Electronics and Emerging Paradigms
Published in Sergey Edward Lyshevski, Molecular Electronics, Circuits, and Processing Platforms, 2018
The fundamental and technological limits are also imposed on molecular electronics and MPPs. Those limits are defined by the device physics, circuit, system, CAD, and synthesis constraints. Some of these limitations will be examined in Section 2.1. However, there is no end to progress, and new paradigms beyond molecular electronics and processing will be discovered. What lies beyond even molecular innovations and frontiers? The hypothetical answer is provided. In 1993, theoretical physicist G. Hooft proposed the holographic principle, which postulates that the information contained in some region of space can be represented as a hologram, which gives the bounded region of space that contains at most one degree of freedom per the Planck area, which is Għ/c3 = 2.612 × 10−70 m2, where G is the Newtonian constant of gravitation, G = 6.673 × 10−11 m3/kg sec2. A Planck area is the area enclosed by a square that has the side length equal to the Planck length λp, where λp is defined as the length scale on which the quantized nature of gravity should become evident, that is, λp=Gh/c3=4.05096×10−35m. Using the modified Planck constant, we obtain λp=Gћ/c3=4.05096×10−35m. The Planck time is the Planck length divided by the speed of light, e.g., tp = λp/c = 5.3906 × 10−44 sec. For microscopic systems, we utilize the so-called standard model (particles are considered to be points moving through space and coherently represented by mass, electric charge, interaction, spin, etc.). The standard model is consistent within quantum mechanics and relativity theory (the special theory of relativity was originated by Einstein in 1905). Other concepts have been developed, including the string theory. In general, one may envision to utilize string vibration, distinct forces, multidimensionality, and so forth.
The holographic principle for the differential game of active target defence
Published in International Journal of Control, 2022
Kamal Mammadov, Cheng-Chew Lim, Peng Shi
Target Symmetry and Defender Symmetry can be used to uniquely determine the state-feedback Nash equilibrium for all as follows. We already know what the optimal strategies are for the special case , this was easily derived using Theorem 2.2. The central hypothesis of the Holographic Principle is that there exists a mapping between any state to another state satisfying , such that , and . Note that obviously the value at is not the same as the value at , but the optimal strategies are the same between these two states, thus can be used to deduce the SFNE. To that end, we define the following rays.