Contributions Of Individual Modes Research Articles

Contribution of individual phonon to the band gap renormalization in semiconductors

Understanding the origin of temperature-dependent bandgap in semiconductors is essential for their applications in photovoltaics, optoelectronic and space applications. In this regard the electron–phonon coupling is known to play a crucial role in the temperature dependence of the bandgap of semiconductors. Several models have also been proposed in this regard which are also found experimentally compatible; however, these models need to account for more information about the contribution of individual modes in band gap renormalization. The present report is an analytical attempt to do so by utilizing the Bose–Einstein oscillator model, thereby discussing a method for finding the individual renormalization term contributed by respective phonon modes to the overall bandgap. This study contributes to the fundamental understanding of the temperature variation of optical properties of semiconductors that correlates with the role of electron–phonon interaction.

Understanding the Origin of the Particularly Small and Anisotropic Thermal Expansion of MOF‐74

AbstractMetal–organic frameworks often display large positive or negative thermal expansion coefficients. MOF‐74, a material envisioned for many applications, shows a different behavior. Temperature‐dependent X‐ray diffraction reveals particularly small negative (positive) thermal expansion coefficients perpendicular (parallel) to the hexagonally arranged pores. These trends are explained by combining density‐functional theory calculations with the Grüneisen theory of thermal expansion, which allows tracing back thermal expansion to contributions of individual phonons. On the macroscopic level, the small thermal expansion coefficients arise from compensation effects caused by the large coupling between perpendicular stress and strain and by the small magnitudes of the mean Grüneisen tensor elements, 〈γ〉. These provide information on how strains impact phonon frequencies. To understand the small value of 〈〉, the individual mode contributions are analyzed using the corresponding atomic motions. This reveals that only the lowest frequency modes up to ≈3 THz provide non‐negligible contributions, such that 〈〉 drops sharply at higher temperatures. These considerations reveal, how the details of the anharmonic properties of specific phonon bands determine the magnitude and sign of thermal expansion in a prototypical material like MOF‐74. Beyond that, the authors also discuss, how the choice of the theoretical methodology impacts the obtained results.

Principal component analysis of alpha-helix deformations in transmembrane proteins.

α-helices are deformable secondary structural components regularly observed in protein folds. The overall flexibility of an α-helix can be resolved into constituent physical deformations such as bending in two orthogonal planes and twisting along the principal axis. We used Principal Component Analysis to identify and quantify the contribution of each of these dominant deformation modes in transmembrane α-helices, extramembrane α-helices, and α-helices in soluble proteins. Using three α-helical samples from Protein Data Bank entries spanning these three cellular contexts, we determined that the relative contributions of these modes towards total deformation are independent of the α-helix's surroundings. This conclusion is supported by the observation that the identities of the top three deformation modes, the scaling behaviours of mode eigenvalues as a function of α-helix length, and the percentage contribution of individual modes on total variance were comparable across all three α-helical samples. These findings highlight that α-helical deformations are independent of cellular location and will prove to be valuable in furthering the development of flexible templates in de novo protein design.

Balancing fast flexible gyroscopic systems at low speed using parametric excitation

Abstract Presented is a method to identify the projection of imbalance forces on high speed related modes of vibration, using data measured rotating at low rotating speeds. The method employs two actuators and several sensors to generate information not available otherwise in rotating structures. The challenges this method aims to solve are: (i) Overcome the inability to detect the small response at low speed due to imbalance which is often below noise level; (ii) Isolate the contribution of individual modes although the measured response, far from critical speeds, combines the effect of many modes; (iii) Lack of suitable formulation for the dynamics of fast rotating structures exhibiting gyroscopic and imbalance forces, parametric excitation and nonlinear stiffness. To overcome these obstacles, a new formulation for parametrically excited gyroscopic systems is developed and an amplification scheme projecting the imbalance forces on any mode of vibration is developed. The paper outlines the mathematical background and verifies the results using finite element simulations incorporating parametric excitation and nonlinear feedback computed in real time by a digital processor and imposed by electromechanics actuators.

Interface conductance modal analysis of a crystalline Si-amorphous SiO2 interface

We studied the modal contributions to heat conduction across an interface between crystalline Si and amorphous SiO2, using the interface conductance modal analysis (ICMA) method. Our results show that >70% of the thermal interface conductance (TIC) arises from the extended modes. Using ICMA, we could also determine the contribution of interfacial modes to the TIC. Interestingly, we observed that although the number of these modes is <5% of all modes, interfacial modes contribute significantly to the TIC (>15%). Such an observation shows the non-negligible role of localized modes in facilitating heat conduction across systems with interfaces between dissimilar materials, specifically in a system that is straightforward to fabricate and study experimentally. Our observations suggest that neglecting the contribution of localized modes would be an oversimplification of the actual mechanisms at play. Determining the individual mode contributions is therefore of vital importance, since these values are directly utilized in predicting the temperature dependent TIC, which is important to silicon on insulator technologies with a myriad of applications within microelectronics and optoelectronics.

A Study on Emissions of Small Diesel Engines

Taking a small diesel engine as the prototype, emission researches for its structural features and different uses are carried out. Obvious differences of emissions for the same diesel engine using different test cycles are shown. By analyzing the test result, it has been found that the weighting factor of each mode is only part of the factors for the large differences of the emission values. The contributions of individual modes are used to analyze the mechanism of changing emissions of the diesel engine and it is found that reducing NOX of the full load for the mobile non-road diesel engine is the key to reach emission standard; for the fixed diesel engine, CO emission must be controlled at the same time. It has been found that it is necessary to take different combustion optimization parameters or measures to reduce the emission of the diesel engine according to the different uses of small diesel engine engines.

Transforming and separating rotating disk vibrations using a sensor array

This paper presents a method to separate the complex vibration pattern of a rotating disk into simpler entities. The decomposition transforms data measured by an array of sensors into time domain signals representing the contribution of individual modes of vibration. Having performed the decomposition with respect to wavelength, speed and direction of travel, the obtained measurements can be projected onto a rotating body experiencing variable rotational speed relative to the sensors. Unlike previous works, the vibrations here are decomposed into time domain signals that provide better insight into stress levels and fatigue than frequency domain based decompositions. Furthermore, the proposed method works under non-stationary conditions, e.g. under rapid angular acceleration and during transient motions. By exploiting the spatial deployment of sensors, the proposed transformation can produce information about the deformations in the body-fixed or material coordinates which is essential for stress analysis. The main feature of the method is the ability to separate modes of vibration that normally overlap in the frequency domain, to enable better insight into the sources of vibration. The method is demonstrated by analytical, numerical and experimental examples.

Excited state distortions in a charge transfer state of a donor–acceptor [2]rotaxane

The charge transfer excited state of a mechanically interlocked [2]rotaxane (R(4+)) with a donor 1,5-dioxynaphthalene (DNP) unit in the rod and the acceptor cyclobis(paraquat-p-phenylene) (CBPQT(4+)) ring component, along with the analogous non-interlocked [2]pseudorotaxane (P(4+)), is studied by resonance Raman spectroscopy and electronic absorption spectroscopy. Resonance Raman excitation profiles are obtained, calculated quantitatively using time-dependent theoretical methods, and interpreted with the assistance of DFT calculations. The active vibrational modes are consistent with an electron transfer from the HOMO centered on the DNP unit to the LUMO on the CBPQT(4+) ring. Displacement vectors of highly distorted modes agree with the bonding changes predicted from the MO nodal pattern. Subtle changes in the frequency of some modes in the free components compared with those in R(4+) are observed. The largest distortions are found for modes involving ring breathing in the DNP unit of the rod and the paraquat units of the CBPQT(4+) ring. The individual mode contributions to the vibrational reorganization energy, as well as the total vibrational reorganization energy, are calculated. Very similar values of λ(v) for R(4+) and P(4+) are calculated (∼2910 cm(-1)), indicating that the mechanical stoppers in the interlocked system do not significantly affect the excited state properties of R(4+) compared with P(4+).

China’s container-related dynamics, 1990–2005

This study seeks to gauge how far China’s container-related dynamics between 1990 and 2005 fit into the wider perspective about transport and development within developing countries. In particular, attention is focussed on the role of specific modes to determine the extent of the penetration of containers within China. Before addressing these key issues extant models relating to an understanding of port and transport evolution in less-developed countries are recalled, synthesized and used as a base upon which an appropriate review of China’s case can be conducted. Applying them to China’s northern, central and southern port ranges not only helps assess the efficacy of these models but also highlights the contribution of individual modes.

New Design Approach for Computing Peak Dynamic Response of Turbo Generator Pedestals Using Modal Synthesis

Turbo generator pedestals are one of the critical structures in any power plant complex. Stringent vibration requirements particularly at the bearing locations have been stipulated for proper functioning of turbo generator installations. Normally the dynamic analysis is carried out using a deterministic approach with constant material properties. The effect of variability of modulus of elasticity of concrete, and operating speed of the turbo generator can lead to increased amplitudes of vibration. The designer always looks for conservative estimates of the expected responses and is interested in keeping them within allowable limits. This paper provides a methodology for computing peak dynamic response at bearing locations once the results of the dynamic analysis with a given input stiffness is available. The approach is essentially based on modal synthesis of responses, namely contribution of individual modes to amplitude of vibration at a particular location. The frequency range of interest is divided into three regions, namely, nonresonant region where undertuned conditions exist, nonresonant region where overtuned conditions exist, and the resonant region. Simple analytical formulation has been developed to compute the peak dynamic response and is illustrated with an example. The suggested method can be programmed for effective use through spread sheet and MS EXCEL software.

Multiparameter two‐dimensional inversion of scattered teleseismic body waves 1. Theory for oblique incidence

This is the first paper in a three‐part series that examines formal inversion of the teleseismic P wave coda for discontinuous variations in elastic properties beneath dense, three‐component, seismic arrays. In this paper, we develop the theoretical framework for a migration method that draws upon the tenets of inverse scattering theory and is amenable to practical implementation. The forward problem is formulated for two‐dimensional (2‐D) heterogeneity in observance of formal sampling requirements and currently accessible instrumentation. A ray theoretic Green's function, corresponding to a line source with axial component of forcing, is employed within the 2‐D Born approximation to accommodate planar, incident wave fields at arbitrary back azimuths. Both the forward scattered response generated by the upgoing incident wave field and the backscattered response created by its reflection at the free surface are included within the formulation. In accordance with the high‐frequency and single‐scattering approximations employed in the forward problem the inverse problem is cast as a generalized Radon transform. The resulting back projection operator is well suited to the teleseismic context in several respects. It is tolerant of irregularities in array geometry and source distribution and allows a full complement of global seismicity to be utilized through its accommodation of oblique incidence. By permitting both independent and simultaneous treatment of different scattering modes (reflections, transmissions, conversions) the inversion formula facilitates a direct appraisal of individual mode contributions to the recovery of structure. In particular, it becomes evident that incorporation of backscattered modes leads to (1) a better localization of structure than possible using forward scattered energy and (2) the imposition of complementary constraints on elastic properties.

SYSTEM IDENTIFICATION AND MODEL REDUCTION FOR A SINGLE-LINK FLEXIBLE MANIPULATOR

A new model reduction and updating technique is proposed and applied in modelling of a single-link flexible manipulator. The Observability Range Space Extraction algorithm is used to generate an initial overparameterized state-space model. The identified model is transformed into modal realization. The modal responses of individual modes are evaluated. A new measure is proposed to quantify the contribution of individual modes to the total responses. Using the proposed measure, a reduced order model is obtained by retaining the most significant modes. To improve model accuracy, either the reduced input or output matrix can be recalculated by a proposed method. Several critical issues related to the experimental identification are addressed. Experimental identification results are presented to illustrate the proposed technique.

Modal decomposition of operational response measurements in a multi-source environment.

An approach is developed combining experimental modal analysis with operational deflection measurements to determine the contributions of individual modes to the response of a structure subjected to multiple uncorrelated sources. Singular value decomposition is applied to measured cross spectral functions to decompose the response measurements into contributions associated with each significant source. A modal decomposition is then performed on fully coherent deflection patterns associated with each source. The modal participation due to each source in the total response is determined. Damping and natural frequency estimates from the modal analysis are used to determine the generalized force inputs to each mode from each source. Finally, by constraining possible degrees of freedom, estimates of the excitation force vectors associated with each source are made. To demonstrate the approach, standard experimental modal analysis techniques are applied to frequency response functions generated via a numerical model. The results are then combined with numerical simulations of both single and multi-source response measurements to obtain the modal participation spectra. These results are further reduced to determine the generalized forces and physical force vectors associated with each source.

Modal Truncation for Flexible Spacecraft

A hierarchy of dynamical models is identified for large nonspinning flexible spacecraft. At each level, techniques are explained for reducing the order of the model before proceeding to the next level. These techniques have in common the presupposition that the model has at each stage been expressed in terms of its natural modes, some of which can, if necessary, be deleted based on the evaluation of one or more of the quantitative criteria proposed. These criteria are based on insights from several different perspectives, including inertial completeness, frequency relationships, controllability and observability considerations, and the contributions of individual modes to a mission-dependent cost functional (modal cost analysis). With the aid of these criteria, many of the engineering judgments related to model order reduction can be made on a rigorous quantitative basis.

Modal Analysis of Random Structural Systems

This paper presents a method for computing the statistical variance of a structural system's eigenvalues and eigenvectors by component mode synthesis. The method relies on a modal summation to obtain engenvector derivatives where the contributions of individual modes are shown to diminish in importance as their natural frequencies become further separated from that of the eigenvector being differentiated. The convergence of mean eigenvalues and eigenvectors and their standard deviations is evaluated as the number of component modes used in the syntheses is increased. It is found that convergence proceeds in that order, with the standard deviations of eigenvectors requiring the largest number of modes for convergence. Numerical investigations show that the standard deviations of eigenvectors tend to converge for the first several modes when only a small fraction of the total number of component modes are taken into account. The dependence of convergence on the distribution of randomness and its spatial correlation is considered.

Theoretical Investigation of a Double Family of Normal Modes in an Underwater Acoustic Surface Duct

This article investigates an underwater surface duct model that requires two distinct families of normal modes for the representation of the acoustic field in the image-interference region. Each family contains an infinite number of modes. In the image-interference region, the propagation losses of mode and ray theory give almost identical results, with the mode approach being limited at short ranges by the large number of modes required and by the necessity for extreme computational accuracy in determining the contributions of individual modes. By means of phase velocity, the first and second family of modes are associated with ray groups that, respectively, do or do not reflect from the ocean surface. A new method of identifying mode number by phase changes in the mode depth function is presented. The fallacy of the incoherent addition of modes at close range is illustrated. Mathematical techniques for determining eigenvalues are discussed in detail. The analysis of a number of limiting cases leads to explicit approximations that provide guides to the general theory that can be expressed only in complicated forms.