Superposition Theory Research Articles

Photonic Crystal Ring Resonators: Characteristics and Applications

We review the characteristics and applications of photonic crystal ring resonators (PCRRs), which can potentially provide a good alternative to the traditional micro ring resonators, as one of the key contributors to the emerging low-power nanophotonic technology. Applying numerical analysis together with the theory of mode superposition, the properties of PCRRs have been comprehensively investigated. We will report PCRR key characteristics, including diameter (D)-dependent loss, quality factor (Q), and free spectral range (FSR). No size-dependent loss was found in PCRRs, unlike the approximately 1/D dependent loss in micro-strip resonators, making PCRRs a promising candidate for ultra-compact ring resonators.

On stress analysis for a penny-shaped crack interacting with inclusions and voids

An analytical approach to calculate the stress of an arbitrary located penny-shaped crack interacting with inclusions and voids is presented. First, the interaction between a penny-shaped crack and two spherical inclusions is analyzed by considering the three-dimensional problem of an infinite solid, composed of an elastic matrix, a penny-shaped crack and two spherical inclusions, under tension. Based on Eshelby’s equivalent inclusion method, superposition theory of elasticity and an approximation according to the Saint–Venant principle, the interaction between the crack and the inclusions is systematically analyzed. The stress intensity factor for the crack is evaluated to investigate the effect of the existence of inclusions and the crack–inclusions interaction on the crack propagation. To validate the current framework, the present predictions are compared with a noninteracting solution, an interacting solution for one spherical inclusion, and other theoretical approximations. Finally, the proposed analytical approach is extended to study the interaction of a crack with two voids and the interaction of a crack with an inclusion and a void.

Simulation of hydrogen trapping at defects in Pd

Abstract The interaction of hydrogen with defects in palladium was studied using qualitative electronic structure calculations in the framework of the Atom Superposition and Electron Delocalization Molecular Orbital (ASED-MO) theory. Interatomic distances, energies and electronic structure for hydrogen at a dislocation and at a vacancy were determined and compared with that for an octahedral site in the Pd fcc lattice. We found that a repulsive H–H interaction is developed if these atoms occupy interstitial sites in a regular lattice. However, when the H atoms are close to a dislocation, the accumulation becomes possible. It was found that the dislocation allows hydrogen association at interatomic distances close to molecular hydrogen. The Density of States (DOS) and Crystal Orbital Overlap Population (COOP) curves were used to shed more light on the interstitial-Pd-defect interactions. Hydrogen produce changes in the local and global electronic structure of the host metal and induce changes in the cohesive forces between atoms in the host matrix. In all cases, it was found that strong bonds between Pd and H atoms are formed while metal–metal bonds are weakened. The metal–hydrogen bonds were characterized by charge transfer from metal atoms to hydrogen.

High-order modes suppression in large-mode-area fiber amplifiers and lasers by controlling the mode power allocations

The modal weight factors and their changing properties in large-mode-area fibers are investigated when the optical beam propagates from one fiber into another one with a different cross-sectional structure. Based on a weighted mode power superposition theory, a novel scheme of inserting a filter fiber to change the power allocation among the co-existing modes in active fibers is proposed. In order to verify the effectiveness of this method in practical implementations, the mode power propagation of a fiber laser and a fiber amplifier with an inserted filter fiber are calculated, respectively. Compared with the cases without a filter fiber, the numerical results show an obvious suppression effect of high-order modes.

DDS Driven PLL 구조 주파수 합성기의 위상 잡음 분석

In this paper, we have proposed a phase noise model of fast frequency hopping synthesizer with DDS Driven PLL architecture. To accurately model the phase noise contribution of noise sources in frequency hopping synthesizer, they were investigated using model of digital divider for PLL, DAC for DDS and Leeson`s model for reference oscillator and VCO. Especially it was proposed that the noise component of low pass filter was considered together with the phase noise of VCO. Under assuming linear operation of a phase locked loop, the phase noise transfer functions from noise sources to the output of synthesizer was analyzed by superposition theory. The proposed phase noise prediction model was evaluated and its results were compared with measured data.

Generation of the 40-Hz auditory steady-state response (ASSR) explained using convolution

Objective In this study, the superposition theory of the 40-Hz auditory steady-state response (ASSR) generation is investigated using auditory brainstem response (ABR) and middle latency responses (MLRs) obtained with 40 Hz jittered sequences with the continuous loop averaging deconvolution (CLAD) algorithm. Methods Click sequences at around 40 Hz with high (maximum length sequence), medium and low jitters were presented to normal hearing awake adult subjects monaurally. Overlapping MLR responses were deconvolved using the frequency domain CLAD method. In addition, conventional auditory MLRs at 4.88 Hz and ASSRs at 39.1 Hz were obtained in all subjects. Synthetic ASSRs were constructed using different rate and jitter MLRs as base recordings. Contributions of the primary components were investigated by wave elimination using phasors. Results Findings indicate that the generation of the 40-Hz ASSRs can be explained successfully by the superposition of the ABR and MLR waves generated at that stimulation rate. N a–P a and N b–P b components of the MLR contribute about equally (45% each), while the wave V of the ABR contributes a lesser amount (10%). Conclusions Forty-Hertz ASSRs are composite responses generated by the superposition of the major waves of the ABR and the MLR. Dramatic amplitude increase of the ASSR at 40 Hz is primarily due to the superposition of the resonating P b component to the P a wave. Significance Several unexplained properties of the 40-Hz ASSR can be explained by the stimulus and brain state dependent characteristics of the slow ABR, the P a and the P b components of the MLR.

The construction of a model of the growth of a defect for finite strains: Non-local criteria

A version of a model of the growth of a defect (an inclusion or cracks of non-zero opening) is presented. When constructing the model, the axiomatic of the mechanics of a deformable solid is used, as well as the idea of a zone of pre-existing imperfection as part of the body, in which, due to the action of external loads, applied to the body, a change in the properties of the material occurs. The apparatus of the theory of multiple superposition of large deformations and certain strength criteria are used.

Phase Noise Model of Single Loop Frequency Synthesizer

The phase noise spectrum of a single loop frequency synthesizer for S-band, which can be utilized in broadcasting terminals, was predicted based on the analyses for phase noise contributions of noise sources. The proposed phase noise model in this paper more accurately predicts the phase noise spectrum of a frequency synthesizer. To accurately model the phase noise contributions of noise sources in the frequency synthesizer, the phase noise sources were analyzed via modeling of the frequency divider and phase noise components using Leeson model for the reference signal source and VCO. The phase noise transfer functions to VCO from noise sources were analyzed by superposition theory and linear operation of the phase-locked loop. The frequency synthesizers were fabricated and the phase noise prediction model was evaluated by measured data and prediction data.

Effects of fibers on the dynamic properties of asphalt mixtures

The dynamic characteristics of fiber-modified asphalt mixture were investigated. Cellulose fiber, polyester fiber and mineral fiber were used as additives for asphalt mixture, and the dosage was 0.3%, 0.3%, 0.4%, respectively. Dynamic modulus test using SuperPave simple performance tester (SPT) was conducted to study the dynamic modulus (E*) and phase angle (δ) for the control asphalt mixture and fiber-modified ones at various temperatures and frequencies. Experimental results show that all fiber-modified asphalt mixtures have higher dynamic modulus compared with control mixture. The dynamic modulus master curves of each type of asphalt mixtures are determined based on nonlinear least square regression in accordance with the timetemperature superposition theory at a control temperature (21.1°C). The fatigue parameter E*×sinδ and rutting parameter E*/sinδ of asphalt mixture are adopted to study the fatigue and rutting-resistance properties, and experimental results indicate that such properties can be improved by fiber additives.

Design of practical deflection field in nanometer-scale focused ion beam system

Two pre-lens deflectors were optimized to reduce the deflection chromatic aberration in a focused ion optical column. Correction principles of the dynamic focus lens and stigmator were researched in detail. The deflection field curvature, astigmatism and distortion can be eliminated by superposing suitable signals on the objective lens and deflectors, which effectively reduces the complexity of the ion optical column. The optical properties of the two deflectors with dynamic correction were simulated and their power supply circuit was built based on superposition theory of electric signals. When the beam current is 1 nA, the pre-lens deflectors can obtain nanometer-scale focused ion beam at the corner of 0.2×0.2 mm 2.

Effect of temperature and concentration on rheological behavior of xanthan-carob mixed gels

The gelation and melting behavior of 1∶1, 1∶3 xanthan-carob mixed gels were evaluated at isothermal and non-isothermal states, as a function of total polymer concentrations of 0.1, 0.5 and 1%. A thermal hysteresis was observed between gelation and melting. The higher the polymer concentration, the higher the melting temperature. The gelation points were determined by three criteria. Depending on the criterion used the gelation temperature was different (52 to 70°C). Pseudoequilibrium modulus and elastic active network chain (EANC) concentration were calculated from the plateau modulus in the frequency spectrum. Temperature dependence of the monomeric friction coefficient was estimated from the relaxation time and EANC. Time-temperature superposition theory was not applicable due to dramatic phase transitions occurring during the gelation of X/C mixture.

Bridging the Gap Between FEA Field Solution and the Magnetic Component Model

The use of finite element analysis (FEA) solvers in order to explore the field distribution is a common practice for designing custom made magnetic components. However, the use of the field distribution information for the generation of a model valid to be simulated in a circuit simulator is not evident. There are several issues that need to be addressed in order to obtain a model based on the field solution. This paper presents the steps that should be taken to generate a FEA based magnetic component model. In addition, the paper describes the appropriate path (analytical or FEA based) that should be followed depending on the model needs. The presented procedure applies superposition theory to obtain a model valid for any arbitrary electrical waveform. This model is not restricted to sinusoidal regime

Unified mechanical approach to piezoelectric bender modeling

A new analytical modeling approach for piezoelectric bending elements is described. The approach is based on the beam theory under quasi-static equilibrium condition. It uses the theory of superposition of piezoelectric action in the bender and external moments and forces acting on the bender. Due to the differential approach, this model is applicable to any geometrical design for which the beam theory holds. The distinction between the piezoelectric action and the external loads makes the model applicable for any boundary conditions. The bottom-up approach from the electrically induced strain in the piezoelectric part enables the determination of stresses and strains at every point in the bender. The effects on internal strain distribution by the different kinds of actuation where demonstrated in an experiment. The resulting model from this approach will be well suited to design and optimize piezoelectric bending actuators for any purpose. The implied calculation of the strain and stress in the modeling allows the dimensioning of actuators that are equipped with strain gauges as well as the calculation of the electrical properties for capacitive transducers.

Domain reorientation of piezoelectric bending actuators

Several types of bending actuators were studied in the present paper to investigate the effect of actuator configuration on domain reorientation. The configurations studied include series bimorph, parallel bimorph, monomorph, unimorph and piezo tube actuator. It was found that due to electric field redistribution, one-loop polarization-shaped displacement hysteresis curve was formed in the antiparallel-poled series bimorph and piezo tube; while in monomorph actuator, the two-looped displacement curve was observed. In the case where the electric field without redistribution is exactly applied on the individual ceramic plate, such as in the case of parallel bimorph and unimorph, the shape of the displacement curve depends on the structure of the actuator. The parallel bimorph gives a three-looped displacement hysteresis curve; while the unimorph gives a butterfly-shaped curve. The superposition theory was proposed to explain the formation of the different displacement hysteresis curves.

Mechanism of Water Attacking on Brooker’s Merocyanine Dye and Its Effect on the Molecular and Electronic Structures: Theoretical Study

Abstract Semiempirical molecular orbital calculations have been performed to study the mechanism by which water molecules attack the highly negative oxycyclic oxygen atom of Brooker’s merocyanine 1-methyl-4-(4′-oxidostyryl)pyridinium betaine, M, to form mono-, di-, and tri-hydrated merocyanine complexes. In the case of mono- and di-hydrated complexes, one or two water molecules attack the oxygen atom, respectively, but in the case of the tri-hydrated complex, only two water molecules attack the oxygen atom of M with sp2 hybridization, while the third one forms a H-bond with either one of the oxygen atoms of the coordinated water molecules. The effect of H-bond formation on the molecular and electronic structures of merocyanine is investigated using the atom superposition and electron delocalization molecular orbital (ASED-MO) theory. The calculations show that the hydrated complexes are shifted towards the benzenoid valence structures in the ground state, but shifted towards quinonoid ones upon excitation. On the basis of the calculated charge distribution over the whole skeleton of the complexes, it is found that the dipole moments of the complexes are slightly affected by H-bond formation in the ground state, but strongly decrease upon excitation. The formation of hydrated merocyanine complexes are highly exothermic, downhill reactions, which is explained with respect to the stabilization of the HOMO and oxygen lone-pair levels. We believe that the attacking by water with acidic character on the basic site oxygen atom of merocyanine is a kind of acid–base interaction.

A technique for studying interacting cracks of complex geometry in 2D

A method for studying brittle fracture in an infinite plate containing interacting cracks of complex shape under general loading conditions is developed and studied for accuracy and potential applications. This technique is based on superposition and dislocation theory and can be used to determine the full stress and displacement fields in a cracked body. In addition, stress intensity factors at both crack tips and wedges, created by crack kinking and branching, are calculated so that crack growth and initiation can be analyzed at these locations of possible crack propagation. Such information can then be used to study damage accumulation in structures containing a large number of interacting cracks.

Absorption, fluorescence, and semiempirical ASED-MO studies on a typical Brooker's merocyanine dye

Solvatochromism and Solvatofluorchromism of Brooker's merocyanine 1-methyl-4- (4′-hydroxystyryl) pyridinium betaine, M, were studied in twelve polar protic and aprotic solvents. Moderate hypsochromic fluorescence energy shifts are 4.57 kcal mole −1 while strong hypsochromic absorption energy shifts are 16.63 kcal mole −1. Decreasing of the dipole moment of M upon excitation is the factor, which is responsible for the difference between the two energy shifts. The change of both energies rectilinearly with solvent acidity scale shows the importance of oxygen atom of M as a strong basic center. The application of the atom superposition and electron delocalization molecular orbital (ASED-MO) theory reproduces geometrical and electronic structures for M, which agree well with the experimental observations. The calculations suggest strongly that the dye has a benzenoid valence structure in the ground state and shifts towards a quinonoid one upon excitation with an observed decreasing of the dipole moment. The changing of the dipole moment is explained clearly depending upon the calculated charge distribution over the whole skeleton of the molecule. The formation of a H-bond between the water molecule and the highly negative oxycyclic oxygen atom of M has slightly effect on its dipole moment in the ground state. This leads to suggest that this kind of interaction could be represented as attacking of water with acidic character on the basic site of M. Also, the calculations predict that the formation of monohydrated complex is an exothermic, down hill reaction, which is confirmed from the stabilization of the frontier molecular orbitals, oxygen lone-pair and the HOMO levels.

UV–vis, IR and 1H NMR spectroscopic studies of some mono- and bis-azo-compounds based on 2,7-dihydroxynaphthalene and aniline derivatives

The absorption spectra of mono- and bis-azo-derivatives obtained by coupling the diazonium salts of aromatic amines and 2,7-dihydroxynaphthalene have been studied in six organic solvents. The different absorption bands have been assigned and the effect of solvents on the charge transfer band is also discussed. The diagnostic IR spectral bands and 1H NMR signals are assigned and discussed in relation to molecular structure. Also, semi-empirical molecular orbital calculations using the atom superposition and electron delocalization molecular orbital (ASED-MO) theory have been performed to investigate the molecular and electronic structures of these compounds. According to these calculations, an intramolecular hydrogen bonding is essential for stabilization of such molecules.

UV–vis, IR and 1H NMR spectroscopic studies of some Schiff bases derivatives of 4-aminoantipyrine

Five Schiff bases derived from 4-aminoantipyrine and benzaldehyde derivatives (I) are prepared and their UV–vis, IR, 1H NMR and fluorescence spectra are investigated and discussed. The electronic absorption spectra of the hydroxy 4-aminoantipyrine Schiff bases Ib and Ie as well as the fluorescence spectra of Ie are studied in the organic solvents of different polarity. The UV–vis absorption spectra of 4-aminoantipyrine Schiff bases Ib, Id and Ie are investigated in aqueous buffer solutions of varying pH and utilized for the determination of p K a and Δ G of the ionization process. The reactions of the hydroxy compounds Ib and Ie with Ni(II) and Cu(II) ions are also studied. The results of spectral studies are supported by some molecular orbital calculations using an atom superposition and electron delocalization molecular orbital theory for a compound Ib.

Validity and limitation of manual rotational test to detect impaired visual–vestibular interaction due to cerebellar disorders

The aim of this study was to investigate validity and limitation of the novel infrared system to record and analyze horizontal visual–vestibular interaction using whole-body rotation rapidly and conveniently in the routine vestibular clinic. We examined 11 patients with cerebellar dysequilibrium and 25 patients with peripheral dysequilibrium for vestibulo-ocular reflex in darkness (DVOR), visually-enhanced vestibulo-ocular reflex (VEVOR), and fixation suppression of vestibulo-ocular reflex (FSVOR), and compared the results with those of examination for head-fixed smooth pursuit and fixation suppression during caloric stimulation. The manual rotation stimuli were 0.5–0.75 Hz in frequecny and 60–90°/s in maximal angular velocity. Gain of vestibulo-ocular reflex in darkness was not significantly correlated with maximal slow phase velocity (MSPV) of caloric-induced nystagmus at that stimulus condition either in patients with peripheral dysequilibrium or in those with cerebellar dysequilibrium. An index for fixation suppression of vestibulo-ocular reflex during rotation stimulus was significantly lower in patients with cerebellar dysequilibrium than in normal control subjects and those with peripheral dysequilbrium. On the other hand, there was no significant difference among the two disease groups and the normal control group in gain of visually-enhanced vestibulo-ocular reflex. In about a half of patients with cerebellar dysequilibrium, measured smooth pursuit gain was lower than estimated smooth pursuit gain calculated based on a simple superposition theory of vestibulo-ocular reflex and smooth pursuit. Testing fixation suppression using the present system is an unusually convenient tool for detection of cerebellar dysequilibrium.