AN EXTENDED GREEN-SASAO HIERARCHY OF CANONICAL TERNARY GALOIS FORMS AND UNIVERSAL LOGIC MODULES

A new extended Green-Sasao hierarchy of families and forms with a new sub-family for many-valued Reed-Muller logic is introduced. Recently, two families of binary canonical Reed-Muller forms, called Inclusive Forms (IFs) and Generalized Inclusive Forms (GIFs) have been proposed, where the second family was the first to include all minimum Exclusive Sum-Of-Products (ESOPs). In this paper, we propose, analogously to the binary case, two general families of canonical ternary Reed-Muller forms, called Ternary Inclusive Forms (TIFs) and their generalization of Ternary Generalized Inclusive Forms (TGIFs), where the second family includes minimum Galois Field Sum-Of-Products (GFSOPs) over ternary Galois field GF(3). One of the basic motivations in this work is the application of these TIFs and TGIFs to find the minimum GFSOP for many-valued input-output functions within logic synthesis, where a GFSOP minimizer based on IF polarity can be used to minimize the many-valued GFSOP expression for any given function. The realization of the presented S/D trees using Universal Logic Modules (ULMs) is also introduced, whereULMs are complete systems that can implement all possible logic functions utilizing the corresponding S/D expansions of many-valuedShannon and Davio spectral transforms.   

Doctor of Philosophy

dissertationThe synthesis, characterization, and nonclassical optical properties of photonic crystals (PCs) created from naturally occurring biological templates was studied. Biotemplated PCs were created from several different natural structures using sol-gel chemistry methods. PCs were characterized using a combination of reflection spectroscopy, SEM image analysis, three-dimensional structure modeling, photonic band structure calculations, and density of optical states calculations. The effect our PCs had on the density of optical states (DOS) was probed using time correlated single photon counting spectroscopy. By carefully controlling the sol-gel chemistry used in the templating process, it is possible to synthesize hollow silica inverse, solid silica inverse, hollow titania inverse, solid titania inverse, and solid titania replicate structures. The inverse-type structures have the advantage of being accessible through a single templating step, while the titania replica is capable of a predicted full photonic band gap. Each structure was investigated using methods mentioned above. The reliability of reflectance spectroscopy was investigated. It was found that in certain cases, a continuum of structural parameters yield reflections that match photonic band structure calculations. Methods to improve this situation are discussed. When applied to titania inverse opals, it was found that the refractive index could be determined to ±0.05 and the volume fraction to ±0.5%. Accurately determining the refractive index of inverse opals is useful in estimating the refractive index of other PCs made from the same sol-gel. Calculation of the DOS using a combination of MIT's photonic bands package and house-written software was applied to biotemplated photonic crystals. It was found that even partial band gap photonic crystals can greatly modify the DOS. Finally, the rate of spontaneous emission of quantum dots embedded in photonic crystals was measured to indirectly probe the DOS. Three different models were used to extract the lifetime from radiative decay curves. It was found that a log-normal distribution of lifetimes was the most meaningful model. The radiative lifetime of quantum dots embedded in titania photonic crystals replicated from Lamprocyphus augustus was modified by up to a factor of ten, an amount unprecedented in the photonic crystal literature

New Data Structures and Algorithms for Logic Synthesis and Verification

The strong interaction between Electronic Design Automation (EDA) tools and Complementary Metal-Oxide Semiconductor (CMOS) technology contributed substantially to the advancement of modern digital electronics. The continuous downscaling of CMOS Field Effect Transistor (FET) dimensions enabled the semiconductor industry to fabricate digital systems with higher circuit density at reduced costs. To keep pace with technology, EDA tools are challenged to handle both digital designs with growing functionality and device models of increasing complexity. Nevertheless, whereas the downscaling of CMOS technology is requiring more complex physical design models, the logic abstraction of a transistor as a switch has not changed even with the introduction of 3D FinFET technology. As a consequence, modern EDA tools are fine tuned for CMOS technology and the underlying design methodologies are based on CMOS logic primitives, i.e., negative unate logic functions. While it is clear that CMOS logic primitives will be the ultimate building blocks for digital systems in the next ten years, no evidence is provided that CMOS logic primitives are also the optimal basis for EDA software. In EDA, the efficiency of methods and tools is measured by different metrics such as (i) the result quality, for example the performance of a digital circuit, (ii) the runtime and (iii) the memory footprint on the host computer. With the aim to optimize these metrics, the accordance to a specific logic model is no longer important. Indeed, the key to the success of an EDA technique is the expressive power of the logic primitives handling and solving the problem, which determines the capability to reach better metrics. In this thesis, we investigate new logic primitives for electronic design automation tools. We improve the efficiency of logic representation, manipulation and optimization tasks by taking advantage of majority and biconditional logic primitives. We develop synthesis tools exploiting the majority and biconditional expressiveness. Our tools show strong results as compared to state-of-the-art academic and commercial synthesis tools. Indeed, we produce the best results for several public benchmarks. On top of the enhanced synthesis power, our methods are the natural and native logic abstraction for circuit design in emerging nanotechnologies, where majority and biconditional logic are the primitive gates for physical implementation. We accelerate formal methods by (i) studying properties of logic circuits and (ii) developing new frameworks for logic reasoning engines. We prove non-trivial dualities for the property checking problem in logic circuits. Our findings enable sensible speed-ups in solving circuit satisfiability. We develop an alternative Boolean satisfiability framework based on majority functions. We prove that the general problem is still intractable but we show practical restrictions that can be solved efficiently. Finally, we focus on reversible logic where we propose a new equivalence checking approach. We exploit the invertibility of computation and the functionality of reversible gates in the formulation of the problem. This enables one order of magnitude speed up, as compared to the state-of-the-art solution. We argue that new approaches to solve EDA problems are necessary, as we have reached a point of technology where keeping pace with design goals is tougher than ever

Prospects for Declarative Mathematical Modeling of Complex Biological Systems

Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation program, in a general-purpose programming language. Examples of such computations on models include model analysis, relatively general-purpose model-reduction maps, and the initial phases of model implementation, all of which should preserve or approximate the mathematical semantics of a complex biological model. The potential advantages are particularly relevant in the case of developmental modeling, wherein complex spatial structures exhibit dynamics at molecular, cellular, and organogenic levels to relate genotype to multicellular phenotype. Multiscale modeling can benefit from both the expressive power of declarative modeling languages and the application of model reduction methods to link models across scale. Based on previous work, here we define declarative modeling of complex biological systems by defining the operator algebra semantics of an increasingly powerful series of declarative modeling languages including reaction-like dynamics of parameterized and extended objects; we define semantics-preserving implementation and semantics-approximating model reduction transformations; and we outline a "meta-hierarchy" for organizing declarative models and the mathematical methods that can fruitfully manipulate them

Cellular Automata

Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented

Computation with spin foam models of quantum gravity

The focus of this thesis is the study of spin foam models of quantum gravity on a computer. These models include the standard Barrett-Crane (BC) spin foam model, as well as the new Engle-Pereira-Rovelli (EPR) and Freidel-Krasnov (FK) models. New numerical algorithms are developed and implemented, based on the existing Christensen-Egan (CE) algorithm, to allow computations with the BC model in the presence of a cosmological constant (implemented through g-deformation) and to allow computations with the recently proposed EPR and FK models. For the first time, we show that the inclusion of a positive cosmological constant, a long standing open problem for spin foams, curiously changes the behavior of the BC model, rendering the expectation values of its observables discontinuous in the limit of zero cosmological constant. Also, unlike previous work, this investigation was carried out on large triangulations, which are closer to large semiclassical space-times. Efficient numerical algorithms are described and implemented, for the first time, allowing the evaluation of the EPR and FK spin foam vertex amplitudes. An initial application of these algorithms is the study of the effective single vertex large spin asymptotics of the new models. Their asymptotic behavior is found to be qualitatively similar to that of the BC model. The leading asymptotic behavior does not exhibit the oscillatory character expected by analogy with the Ponzano-Regge model. Two important tests of the spin foam semiclassical limit are wave packet propagation and evaluation of the graviton propagator matrix elements. These tests are generalized to encompass the three major spin foam models. The wave packet propagation test is carried out in greater generality than previously. The results indicate that conjectures about good semiclassical behavior of the new spin foam models may have been premature

Computation with spin foam models of quantum gravity

The focus of this thesis is the study of spin foam models of quantum gravity on a computer. These models include the standard Barrett-Crane (BC) spin foam model, as well as the new Engle-Pereira-Rovelli (EPR) and Freidel-Krasnov (FK) models. New numerical algorithms are developed and implemented, based on the existing Christensen-Egan (CE) algorithm, to allow computations with the BC model in the presence of a cosmological constant (implemented through g-deformation) and to allow computations with the recently proposed EPR and FK models. For the first time, we show that the inclusion of a positive cosmological constant, a long standing open problem for spin foams, curiously changes the behavior of the BC model, rendering the expectation values of its observables discontinuous in the limit of zero cosmological constant. Also, unlike previous work, this investigation was carried out on large triangulations, which are closer to large semiclassical space-times. Efficient numerical algorithms are described and implemented, for the first time, allowing the evaluation of the EPR and FK spin foam vertex amplitudes. An initial application of these algorithms is the study of the effective single vertex large spin asymptotics of the new models. Their asymptotic behavior is found to be qualitatively similar to that of the BC model. The leading asymptotic behavior does not exhibit the oscillatory character expected by analogy with the Ponzano-Regge model. Two important tests of the spin foam semiclassical limit are wave packet propagation and evaluation of the graviton propagator matrix elements. These tests are generalized to encompass the three major spin foam models. The wave packet propagation test is carried out in greater generality than previously. The results indicate that conjectures about good semiclassical behavior of the new spin foam models may have been premature

Quantum formulation for nanoscale optical and material chirality: symmetry issues, space and time parity, and observables

To properly represent the interplay and coupling of optical and material chirality at the photon-molecule or photon-nanoparticle level invites a recognition of quantum facets in the fundamental aspects and mechanisms of light-matter interaction. It is therefore appropriate to cast theory in a general quantum form, one that is applicable to both linear and nonlinear optics as well as various forms of chiroptical interaction including chiral optomechanics. Such a framework, fully accounting for both radiation and matter in quantum terms, facilitates the scrutiny and identification of key issues concerning spatial and temporal parity, scale, dissipation and measurement. Furthermore it fully provides for describing the interactions of light beams with a vortex character, and it leads to the complete identification of symmetry conditions for materials to provide for chiral discrimination. Quantum considerations also lend a distinctive perspective to the very different senses in which other aspects of chirality are recognized in metamaterials. Duly attending to the symmetry principles governing allowed or disallowed forms of chiral discrimination supports an objective appraisal of the experimental possibilities and developing applications

비공유 화학적 도핑을 이용한 단일층 그래핀 소자의 전자특성 최적화

학위논문(박사) -- 서울대학교대학원 : 자연과학대학 화학부, 2022. 8. 홍병희.2004년 그래핀은 테이프를 이용한 (고배향 열분해성) 흑연(highly oriented pyrolytic graphite; HOPG)으로부터의 박리를 통해 최초 발견되었다. 이후 수많은 연구들에 의해 그래핀이 우수한 열적, 기계적, 전기적, 광학적 특성을 지녔음이 알려졌다. 2009년에 이르러 화학기상증착(chemical vapor deposition; CVD) 방식을 이용한 다결정 그래핀의 대면적 합성이 실험적으로 가능해졌고, 이로써 그래핀이 다양한 분야에 응용될 수 있는 발판이 마련되었다. 특히 그래핀의 응용분야 중 전기전자특성을 이용한 분야가 각광을 받고 있다. 그래핀은 높은 전자이동도, 전기전도도 및 열전도도를 지닌 재료이며, 밀접결합(tight-binding; TB) 근사 모형을 이용하여 계산한, 결함이 없는 단결정 단층 그래핀의 밴드갭(band gap)은 0임이 밝혀졌다. 재료의 전자특성 조절은 전자소자로의 응용에 필수적 공정이고, 도핑은 전자특성 조절에 주로 쓰이는 방법 중 하나이다. 그래핀에 도핑 처리를 함으로써 밴드갭, 전기전도도 및 일함수와 같은 전기전자특성을 조절할 수 있다. 그래핀에 대한 도핑 방법으로는 원자 치환, 전계 인가, 분자나 금속 나노입자 등의 물리적 흡착 등이 있다. 이 중 물리적 흡착 방식은 결함 없이 간단하고 우수한 도핑 효과를 얻을 수 있어 그래핀 도핑 방법으로 널리 사용되고 있다. 본 논문에서는 화학기상증착 방식으로 합성한 그래핀의 전자특성 최적화 방법 및 전자소자로의 응용에 관한 연구를 다루었다. 그래핀의 전자특성 최적화 방식으로 물리적 흡착을 통한 비공유 화학적 도핑을 택하였으며, 도핑된 그래핀의 전자소자로의 응용 가능성에 대하여 확인하였다. 제1장에서는 그래핀의 물리적 특성 중 전기전자특성에 초점을 맞춰 설명하였다. 또한, 연구에 사용한 도핑 방법과 도핑된 그래핀의 전하 이동현상에 관하여 소개하였다. 제2장에서는 그래핀의 합성, 전사 및 도핑 방법에 관하여 서술하였다. 연구에 사용된 그래핀은 화학기상증착 방식으로 합성되었으며, 합성된 그래핀은 구리 식각 및 전사 공정을 통해 소자 연구를 위한 시편으로 제작되었다. 그래핀은 자기조립단층(self-assembled monolayer; SAM)을 형성하는 분자 외 다양한 나노물질을 이용한 물리적 흡착 방식에 의해 화학적 도핑된다. 라만 분광분석을 통해 합성 및 도핑 직후의 그래핀 시편의 품질을 평가하였고, 3 전극 시스템을 이용한 전계효과 트랜지스터를 제작하여 그래핀의 전자특성을 분석하였다. 제3장에서는 화학기상증착 방식으로 합성한 그래핀에 다양한 나노물질을 차례로 제공함으로써 화학적 도핑 효과의 변화를 나타낸 전자소자 연구를 기술하였다. 그래핀 표면에 금 나노입자를 물리적 흡착 방식으로 도핑하여 비공유 기능화하고, 이를 이용한 그래핀을 전계효과 트랜지스터 소자로 제작하였다. 제작된 소자에 존재하는 금 나노입자에 4-머캅토벤조산(4-mercaptobenzoic acid; 4-MBA) 분자를 흡착시킴으로써 자기조립단층을 형성케 한다. 이때 수은 이온을 주입하면 자기조립단층을 형성한 4-MBA 분자의 카복시기(carboxyl group)가 리간드로 작용하여 수은 이온을 포획하면서 킬레이트(chelate) 복합체를 구성한다. 각 단계의 그래핀 전계효과 트랜지스터 소자의 전자특성 분석을 통해, 각 나노물질 요소에 의해 그래핀 표면의 도핑 효과가 미세 조정됨을 알 수 있다. 본 연구를 통해 그래핀 전계효과 트랜지스터의 화학적 기능화에 대한 가능성을 확인하였다. 제4장에서는 화학기상증착 방식으로 합성한 그래핀에 n-알킬아민(n-alkylamine; H2NCn) 분자를 도입함으로써, n형 도핑된 그래핀을 이용한 열전소자 성능의 향상에 관하여 기술하였다. n-알킬아민 분자는 그래핀 표면에서 자기조립단층을 형성하고 비공유 기능화를 통해 전자를 그래핀에 제공한다. 탄소사슬 길이가 각기 다른 n-알킬아민 분자를 이용하여 도핑한 그래핀을 3 전극 시스템을 통해 분석함으로써, 서로 다른 길이의 분자를 통해 그래핀 시편의 전하운반자 농도의 조절이 가능함을 확인하였다. n-알킬아민 분자의 자기조립단층이 형성된 각 그래핀 시편 위로 산화갈륨(Ga2O3) 박막층 및 갈륨-인듐 공융합금(eutectic Ga-In alloy; EGaIn) 벌크층을 차례로 적층하여 열전소자를 제작하였다. n-알킬아민 분자의 비공유 접합에 의해 유도 갭 상태(induced-gap state)가 그래핀 열전소자(SLG//H2NCn//Ga2O3/EGaIn)에 도입되었다. 금 박막층과 n-알케인싸이올레이트(n-alkanethiolates; SCn) 분자의 접합으로 구성된 종래의 열전소자(Au/SCn//Ga2O3/EGaIn)와의 비교를 통해, 상기한 방식으로 제작된 그래핀 열전소자가 우수한 열전특성을 지니고 있음을 증명하였다.Since its first discovery as a flake-form from mechanical exfoliation of highly-oriented pyrolytic graphite (HOPG) using tape in 2004, numerous studies have shown that graphene has outstanding and extraordinary thermal, mechanical, electrical, electronic and optical properties. In 2009, large-area synthesis of polycrystalline graphene using a chemical vapor deposition (CVD) method became experimentally possible, thereby establishing a foothold for the graphene to be applied to various fields. In particular, the field of application using electrical and electronic characteristics of graphene is in the spotlight. Graphene is a remarkable material with high electron mobility, electrical conductivity and thermal conductivity. Furthermore, the pristine single-layer graphene (SLG) has zero gap, a theoretical value calculated by a tight-binding (TB) approximation model. Engineering the electronic properties of materials is an essential process for application to electronic devices, and doping is one of the methods mainly used to control electronic properties. By doping graphene, electrical and electronic characteristics such as band gap, electrical conductivity, and work function (WF) can be modified and controlled. Doping methods for graphene include atomic substitution, applying electric field, physisorption (physical adsorption) of molecules and metal nanoparticles, etc. Among those methods, the physisorption is widely used as a graphene doping method because it can obtain a simple and superior doping effect without crystallographic defects. This paper describes researches on optimization methods of the electronic properties of graphene synthesized by CVD method and its applications of electronic devices. Noncovalent chemical doping by the physisorption was selected as the optimization method of the electronic properties of graphene, and the possibility of application of the doped graphene to an electronic device was verified. Chapter 1 delineates the physical properties of graphene, focusing on the electrical and electronic properties. In addition, the doping method used in the study and the charge transfer phenomenon of doped graphene were introduced. Chapter 2 gives a detailed description of the procedure such as the synthesis, transfer, and doping methods of graphene. Graphene used in these researches was synthesized by CVD method, and the synthesized graphene was manufactured as electronic device specimens through copper etching and transfer processes. Graphene is chemically doped by the physisorption method using various nanomaterials such as molecules forming self-assembled monolayers (SAM). Through Raman spectroscopy, the quality of graphene specimens immediately after synthesis and doping process was evaluated. Moreover, the electronic properties of graphene were analyzed by a 3-electrode system using field-effect transistor (FET) devices Chapter 3 depicts a study on electronic devices showing changes in chemical doping effects by sequentially providing various nanomaterials to graphene synthesized by CVD method. Gold nanoparticles were used as dopants on the surface of graphene by physisorption for a noncovalent functionalization, and the doped graphene was manufactured as FET devices. SAM is formed by adsorbing 4-mercaptobenzoic acid (4-MBA) molecules onto gold nanoparticles on the manufactured graphene device. And then, if mercury ions are injected, a carboxyl group of 4-MBA molecules constructing SAM acts as a ligand to capture mercury ions, thereby assembling a chelate complex. Through the analyses of the electronic properties of the graphene FET devices in each step, it can be seen that the doping effect of the graphene surface is finely adjusted by each nanomaterial element. Through this study, the possibility of chemical functionalization of graphene FET devices was exactly clarified. Chapter 4 describes the improvement in the performance of graphene thermoelectric devices using n-type doping by introducing n-alkylamine (H2NCn) molecules onto SLG film synthesized by CVD method. The n-alkylamine molecules form SAM on the surface of graphene and provide electrons to graphene through noncovalent functionalization. Graphene doped by n-alkylamine molecules with different lengths of carbon chain was manufactured as FET devices and analyzed by a 3-electrode system. Graphene FET devices were proved clearly that the concentration of charge carriers of graphene specimens could be regulated by chemical doping method using each molecule. Graphene thermoelectric devices was manufactured by sequentially stacking a gallium oxide (Ga2O3) thin film layer and a eutectic gallium-indium alloy (EGaIn) bulk layer onto the n-alkylamine SAM formed on each graphene specimen. An induced-gap state was introduced into the graphene layer in graphene thermoelectric devices (SLG//H2NCn//Ga2O3/EGaIn) by noncovalent junctions of n-alkylamine molecules. Through comparison with thermoelectric devices with a conventional structure (Au/SCn/Ga2O3/EGaIn) composed of the junction of gold thin film layer and n-alkanethiolates (SCn) molecules, it was shown that the graphene thermoelectric devices produced by the above method have improved and outstanding thermoelectric properties.Cover 1 Abstract 3 Table of Contents 6 List of Tables 8 List of Figures 9 Chapter 1. Introduction to Graphene 12 1. 1. Discovery and Advancement of Graphene 12 1. 2. Crystal Structure of Graphene 16 1. 3. Band Structure of Graphene 25 1. 4. Group Theory to Analyze Graphene 40 1. 5. Chemical Doping of Graphene 47 1. 6. Properties of Doped Graphene 50 Chapter 2. Experimental 54 2. 1. Graphene Synthesis by Chemical Vapor Deposition 54 2. 2. Pre-treatment Process for Graphene Transfer 65 2. 3. Graphene Transfer Process 66 2. 4. Graphene Doping by Physisorption 69 2. 5. Raman Spectroscopic Analyses for Graphene 70 2. 6. Electronic Analyses for Graphene Field-effect Transistor 80 Chapter 3. Gold Nanoparticle-Mediated Noncovalent Functionalization of Graphene for Field-Effect Transistors 94 3. 1. Abstract 94 3. 2. Introduction 95 3. 3. Experimental 96 3. 4. Results and Discussion 101 3. 5. Conclusion 123 Chapter 4. Enhanced Thermopower of Saturated Molecules by Noncovalent Anchor-Induced Electron Doping of Single-Layer Graphene 124 4. 1. Abstract 124 4. 2. Introduction 125 4. 3. Experimental 128 4. 4. Results and Discussion 138 4. 5. Conclusion 157 Bibliography 158 Abstract in Korean 178박