Showing papers on "Normal mode published in 2005"

Normal mode analysis : theory and applications to biological and chemical systems

Abstract: Normal mode theory and harmonic potential approximations Konrad Hinsen All-atom normal mode calculations of large molecular systems using iterative methods Liliane Mouawad and David Perahia The Gaussian network model: Theory and applications A.J. Radar, Chakra Chennubhotla, Lee-Wei Yang, Ivet Bahar Normal mode analysis of macromolecules: from enzyme activity site to molecular machines Guohui Li, Adam Van Wynsbergh, Omar N.A. Demerdash, Qiang Cui Functional information from slow mode shapes Yves-Henri Sanejouand Unveiling molecular mechanisms of biological functions in large macromolecular assemblies using elastic network normal mode analysis Florence Tama, Charles L. Brooks III Applications of normal mode analysis in structural refinement of supramolecular complexes Jianpeng Ma Normal mode analysis in studying protein motions with x-ray crystallography George N. Phillips, Jr. Optimizing the parameters of the Gaussian network model for ATP-binding proteins Taner Z. Sen, Robert L. Jernigan Effects of sequence, cyclization, and superhelical stress on the internet motions of DNA Atsushi Matsumoto, Wilma K. Olson Symmetry in normal mode analysis of icosahedral viruses Herman W.T. van Vlijmen Extension of the normal mode concept: Principal component analysis, jumping-among-minima model, and their applications to experimental data analysis Akio Kitao Imaginary-frequency, unstable instantaneous normal modes, the potential energy landscape, and diffusion in liquids T.Keyes Driven molecular dynamics for normal modes of biomolecules without the Hessian, and beyond Martina Kaledin, Alexey L. Kaledin, Alex Brown, and Joel Bowman Probing vibrational energy relaxation in proteins using normal modes Hiroshi Fujisaki, Lintao Bu, and John E. Straub Anharmonic decay of vibrational state in proteins Xin Yu, David M. Leitner Collective coordinate approaches to extended conformational sampling Michael Nilges, Rogher Abseher Using collective coordinates to guide conformational sampling in atomic simulations Haiyan Liu, Zhiyong Zhang, Jianbin He, Yunyu Shi

Geometric origin of excess low-frequency vibrational modes in weakly connected amorphous solids

Abstract: Glasses have an excess number of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature necessarily occurs in solids with low coordination. In particular, we analyze the density D(ω) of normal-mode frequencies ω and the nature of the low-frequency normal modes of a recently simulated system (O'Hern C., Silbert L. E., Liu A. J. and Nagel S. R., Phys. Rev. E, 68 (2003) 011306) comprised of weakly compressed spheres at zero temperature. We account for the observed a) convergence of D(ω) toward a non-zero constant as the frequency goes to zero, b) appearance of a low-frequency cutoff ω*, and c) power law increase of ω* with compression. We introduce a length scale l* which characterizes the vibrational modes that appear at ω*.

Continuum model for the vibration of multilayered graphene sheets

Abstract: The vibration analysis of multilayered graphene sheets (MLGSs) using a continuum model is reported in this paper. An explicit formula is derived to predict the van der Waals (vdW) interaction between any two sheets of a MLGS. Based on the derived formula, a continuum-plate model is developed for the vibration of MLGSs. Our investigation indicates that the lowest natural frequency (classical natural frequency) of a MLGS for a given combination of $m$ and $n$ is independent of the vdW interaction, but that all of the other higher natural frequencies (resonant frequencies) are significantly dependent on this interaction. The mode shapes that are associated with the natural frequencies are investigated for double-layered and ten-layered graphene sheets. We find that the vibration modes that are associated with the classical natural frequency of all the sheets are in the same direction and have the same amplitude, whereas the vibration modes of the sheets that are associated with the resonant frequencies are different due to the influence of the vdW interaction. Thus various resonance modes can be obtained by varying the number of layers of a MLGS.

Hydrodynamics of oscillating atomic force microscopy cantilevers in viscous fluids

Abstract: We present a study of thermal noise of commercially available atomic force microscopy (AFM) cantilevers in air and in water. The purpose of this work is to investigate the oscillation behavior of a clamped AFM microlever in liquids. Up to eight vibration modes are recorded. The experimental results are compared to theoretical predictions from the hydrodynamic functions corresponding to rigid transverse oscillations of an infinitely long rectangular beam. Except for the low-frequency modes, the known hydrodynamic functions cannot describe the amount of dissipated energy due to the liquid motion induced by the cantilever oscillation. The observed variation of the damping coefficient is smaller than the one predicted. The difference at higher modes between the mentioned theoretical description and experimental results is discussed with the help of numerical solutions of the three-dimensional Navier–Stokes equation.

Coronal loop oscillations Calculation of resonantly damped MHD quasi-mode kink oscillations of longitudinally stratified loops

Abstract: The observed coronal loop oscillations and their damping are often theoretically described by the use of a very simple coronal loop model, viz. a straight, longitudinally invariant, axi-symmetric, and pressureless flux tube with a different density inside and outside of the loop. In this paper we generalize the model by including longitudinal density stratification and we examine how the longitudinal density stratification alters the linear eigenmodes of the system, their oscillation frequencies, and the damping rates by resonant absorption.

Magnetic normal modes of nanoelements

Abstract: Micromagnetic calculations are used to determine the eigenfrequencies and precession patterns of some of the lowest-frequency magnetic normal modes of submicron patterned elements. Two examples are presented. For a Permalloy-like ellipse, 350nm×160nm×5nm thick in zero field, the lowest frequency normal mode at 4GHz corresponds to precession in the “ends” of the ellipse. Other resonant frequencies are compared with the frequencies of spinwaves with discrete wave vectors. For a normally magnetized 50nmdiameter×15nm thick cobalt disk, the calculated eigenfrequencies increase linearly with applied field, mimicking the behavior of the experimental critical current for spin transfer instabilities in an experimental realization of this disk.

Resonance analysis of multi-layered graphene sheets used as nanoscale resonators

Abstract: A stacked plate model for the vibration of multi-layered graphene sheets (MLGSs), in which the van der Waals (vdW) interaction between layers is described by an explicit formula, is presented. Explicit formulae are derived for predicting the natural frequencies of double- and triple-layered graphene sheets, and they clearly indicate the effect of vdW interaction on the natural frequencies. The natural frequencies are calculated for various numbers of layered graphene sheets, and the results show that the vdW interaction has no influence on the lowest natural frequency (classical frequency) of an MLGS but plays a significant role in all higher natural frequencies (resonant frequencies) for a given combination of m and n. The vibration modes that are associated with the classical frequencies for each sheet of an MLGS are identical. In contrast, the vibration modes that are associated with the resonant frequencies are non-identical and give various vibration patterns, which indicates that MLGSs are highly suited to use as high frequency resonators.

Frequency Analysis of the Tuned Mass Damper

Abstract: The damping properties of the viscous tuned mass damper are characterized by dynamic amplification analysis as well as identification of the locus of the complex natural frequencies. Optimal damping is identified by a combined analysis of the dynamic amplification of the motion of the structural mass as well as the relative motion of the damper mass. The resulting optimal damper parameter is about 15% higher than the classic value, and results in improved properties for the motion of the damper mass. The free vibration properties are characterized by analyzing the locus of the natural frequencies in the complex plane. It is demonstrated that for optimal frequency tuning the damping ratio of both vibration modes are equal and approximately half the damping ratio of the applied damper, when the damping is below a critical value corresponding to a bifurcation point. This limiting value corresponds to maximum modal damping and serves as an upper limit for damping to be applied in practice.

Principal modes in multimode waveguides

Abstract: We generalize the concept of principal states of polarization and prove the existence of principal modes in multimode waveguides. Principal modes do not suffer from modal dispersion to first order of frequency variation and form orthogonal bases at both the input and the output ends of the waveguide. We show that principal modes are generally different from eigenmodes, even in uniform waveguides, unlike the special case of a single-mode fiber with uniform birefringence. The difference is most pronounced when different eigenmodes possess similar group velocities and when their field patterns vary as a function of frequency. This work may provide a new basis for analysis and control of dispersion in multimode fiber systems.

Scaling factors for the prediction of vibrational spectra. II. The aniline molecule and several derivatives

Abstract: The structure of aniline was studied by semiempirical, ab initio, and density functional methods. Complete geometry optimization of the minimum energy structure and of the transition states for internal rotation and inversion of the amino group was carried out using several levels. The performance of the different methods in calculating and describing the vibrational frequencies of aniline was determined. The normal modes were characterized by the magnitudes and direction of the displacement vectors. Three procedures were used to obtain the scaled frequencies, two of them new, using specific scale factors and scaling equations from the benzene molecule. The errors obtained were compared with those calculated through other standard procedures. A reassignment of several bands was made. A comparison of the cost-effective method and procedure of scaling was carried out. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem 103: 394 - 421, 2005

Normal modes for predicting protein motions: A comprehensive database assessment and associated Web tool

Abstract: We carry out an extensive statistical study of the applicability of normal modes to the prediction of mobile regions in proteins. In particular, we assess the degree to which the observed motions found in a comprehensive data set of 377 nonredundant motions can be modeled by a single normal-mode vibration. We describe each motion in our data set by vectors connecting corresponding atoms in two crystallographically known conformations. We then measure the geometric overlap of these motion vectors with the displacement vectors of the lowest-frequency mode, for one of the conformations. Our study suggests that the lowest mode contains useful information about the parts of a protein that move most (i.e., have the largest amplitudes) and about the direction of this movement. Based on our findings, we developed a Web tool for motion prediction (available from http://molmovdb.org/nma) and apply it here to four representative motions—from bacteriorhodopsin, calmodulin, insulin, and T7 RNA polymerase.

Normal-mode spectroscopy of a single-bound-atom-cavity system.

Abstract: The energy-level structure of a single atom strongly coupled to the mode of a high-finesse optical cavity is investigated. The atom is stored in an intracavity dipole trap and cavity cooling is used to compensate for inevitable heating. Two well-resolved normal modes are observed both in the cavity transmission and the trap lifetime. The experiment is in good agreement with a Monte Carlo simulation, demonstrating our ability to localize the atom to within $\ensuremath{\lambda}/10$ at a cavity antinode.

WEBnm@: a web application for normal mode analyses of proteins

Abstract: Normal mode analysis (NMA) has become the method of choice to investigate the slowest motions in macromolecular systems. NMA is especially useful for large biomolecular assemblies, such as transmembrane channels or virus capsids. NMA relies on the hypothesis that the vibrational normal modes having the lowest frequencies (also named soft modes) describe the largest movements in a protein and are the ones that are functionally relevant. We developed a web-based server to perform normal modes calculations and different types of analyses. Starting from a structure file provided by the user in the PDB format, the server calculates the normal modes and subsequently offers the user a series of automated calculations; normalized squared atomic displacements, vector field representation and animation of the first six vibrational modes. Each analysis is performed independently from the others and results can be visualized using only a web browser. No additional plug-in or software is required. For users who would like to analyze the results with their favorite software, raw results can also be downloaded. The application is available on http://www.bioinfo.no/tools/normalmodes . We present here the underlying theory, the application architecture and an illustration of its features using a large transmembrane protein as an example. We built an efficient and modular web application for normal mode analysis of proteins. Non specialists can easily and rapidly evaluate the degree of flexibility of multi-domain protein assemblies and characterize the large amplitude movements of their domains.

Temperature and pressure dependence of resonance in multi-layer microcantilevers

Abstract: The resonance frequency of the fundamental and four higher order modes of a silicon dioxide microcantilever is measured. The effect on these modes of depositing a 400 nm gold coating is investigated theoretically and experimentally. We derive an analytical solution to the eigenmodes of a multi-layered cantilever and verify its validity by comparison to finite-element analysis as well as the experimentally obtained results. The temperature and pressure dependence of the resonance frequencies is investigated experimentally and found to be in good agreement with theoretical models. An experimentally obtained value for the temperature dependence of Young's modulus of elasticity for thermally grown SiO2 is presented.

q-Breathers and the Fermi-Pasta-Ulam problem.

Abstract: The Fermi-Pasta-Ulam (FPU) paradox consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number $q$. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here $q$-breathers (QB). They are characterized by time periodicity, exponential localization in the $q$-space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.

Vortex-state oscillations in soft magnetic cylindrical dots

Abstract: We have studied magnetic vortex oscillations in soft submicron cylindrical dots with variable thickness and diameter by an analytical approach and micromagnetic simulations. We have considered two kinds of modes of the vortex magnetization oscillations: (1) low-frequency translation mode, corresponding to the movement of the vortex as a whole near its equilibrium position and (2) high-frequency vortex modes, which correspond to radially symmetric oscillations of the vortex magnetization, mainly outside the vortex core. The vortex translational eigenmode was calculated numerically in frequency and time domains for different dot aspect ratios. To describe the discrete set of vortex high-frequency modes we applied the linearized equation of motion of dynamic magnetization over the vortex ground state. We considered only radially symmetric magnetization oscillations modes. The eigenfrequencies of both kinds of the excitation modes are determined by magnetostatic interactions. They are proportional to the thickness/diameter ratio and lie in the GHz range for typical dot sizes.

Simulation of negative permittivity and negative permeability by means of evanescent waveguide Modes-theory and experiment

Abstract: In this paper, the theoretical foundations of the equivalence between waveguide propagation below cutoff and artificial plasmas are carefully analyzed through the derivation of the propagation constants of normal modes in waveguides filled with anisotropic plasmas. The equivalence between waveguide and dielectric plasma proposed by Marquees et al., which is valid for evanescent TE modes, has a dual counterpart for magnetic plasmas and evanescent TM modes. This new equivalence states that a negative magnetic permeability medium can be simulated by means of TM modes below their cutoff frequencies. The need of an anisotropic filling of the waveguide for the equivalence between plasmas and evanescent modes is also highlighted. To exemplify the applicability of this new equivalence, a structure that implements a double-negative medium has been proposed. Full-wave simulations of the proposed structure and measurements from an experimental setup are presented, both of which corroborate the new equivalence's validity.

Wave attractors and the asymptotic dissipation rate of tidal disturbances

Abstract: Linear waves in bounded inviscid fluids do not generally form normal modes with regular eigenfunctions. Examples are provided by inertial waves in a rotating fluid contained in a spherical annulus, and internal gravity waves in a stratified fluid contained in a tank with a non-rectangular cross-section. For wave frequencies in the ranges of interest, the inviscid linearized equations are spatially hyperbolic and their characteristic rays are typically focused onto wave attractors. When these systems experience periodic forcing, for example of tidal origin, the response of the fluid can become localized in the neighbourhood of a wave attractor. In this paper, I define a prototypical problem of this form and construct analytically the long-term response to a periodic body force in the asymptotic limit of small viscosity. The vorticity of the fluid is localized in a detached shear layer close to the wave attractor in such a way that the total rate of dissipation of energy is asymptotically independent of the viscosity. I further demonstrate that the same asymptotic dissipation rate is obtained if a non-viscous damping force is substituted for the Navier–Stokes viscosity. I discuss the application of these results to the problem of tidal forcing in giant planets and stars, where the excitation and dissipation of inertial waves may make a dominant, or at least important, contribution to the orbital and spin evolution.

Analytical approach to dielectric optical bent slab waveguides

Abstract: A rigorous classical analytic frequency domain model of con?ned optical wave propagation along 2D bent slab waveguides and curved dielectric interfaces is investigated, based on a piecewise ansatz for bend mode profiles in terms of Bessel and Hankel functions This approach provides a clear picture of the behaviour of bend modes, concerning their decay for large radial arguments or effects of varying bend radius Fast and accurate routines are required to evaluate Bessel functions with large complex orders and large arguments Our implementation enabled detailed studies of bent waveguide properties, including higher order bend modes and whispering gallery modes, their interference patterns, and issues related to bend mode normalization and orthogonality properties

Large-Scale Modes in a Rotating Atmosphere with Radiative–Convective Instability and WISHE

Abstract: A highly simplified parameterization of diabatic processes is applied to linearized equations on a equatorial beta plane. The diabatic processes include moist convection, cloud–radiation interactions (CRI), and wind-induced surface heat exchange (WISHE). The precipitation rate is assumed to increase linearly as the vertically averaged saturation deficit decreases. The modeled modes are Matsuno’s normal modes, that is, Kelvin waves, mixed Rossby–gravity waves, Rossby waves, and inertio–gravity waves, and an additional mode called here a slow moisture mode. All of the Matsuno modes are damped and remain stable even when CRI and WISHE are turned on. Their phase speeds do not vary much from Matsuno’s adiabatic values except for very long wavelength Kelvin and Rossby modes, for which the phase speeds are reduced compared to the adiabatic values. The slow moisture modes are stationary and unstable under CRI, while WISHE causes them to propagate. Under CRI and WISHE together the slow moisture modes are ...

Coupled Dynamic Analysis and Equivalent Static Wind Loads on Buildings with Three-Dimensional Modes

Abstract: Buildings with either complex geometric shapes or structural systems with noncoincident centers of mass and resistance, or both, may undergo three-dimensional ~3D! coupled motions when exposed to spatiotemporally varying dynamic wind loads. To capture the dynamic load effects, this paper presents a framework for the analysis of 3D coupled dynamic response of buildings and modeling of the equivalent static wind loads ~ESWLs!. This framework takes into account the correlation among wind loads in principle directions and the intermodal coupling of modal response components. The wind loading input for this scheme may be derived either from multiple point synchronous scanning of pressures on building models or through high-frequency force balance ~HFFB! measurements. The ESWL for a given peak response is expressed as a linear combination of the background and resonant loads, which respectively reflect the fluctuating wind load characteristics and inertial loads in fundamental modes of vibration. The nuances of utilizing HFFB measurements for buildings with 3D coupled mode shapes are elucidated with a focus on the evaluation of the generalized forces including mode shape corrections, the background and resonant responses, and the associated ESWLs. Utilizing a representative tall building with 3D mode shapes and closely spaced frequencies, the framework for the analysis of coupled dynamic load effects and modeling of 3D ESWLs is demonstrated.