Principal Mode Analysis Research Articles

Method for Solving the Microwave Heating Temperature Distribution of the TE10 Mode

Microwave heating is a process in which the electric, magnetic, and temperature fields are coupled with each other and are characterised by strong non-linearity, high time variability, and infinite dimensionality. This paper proposes a method for predicting the microwave heating temperature distribution of the TE10 mode, because the traditional numerical calculation method is not conducive to designing microwave controllers. First, the spatial distribution of the main electromagnetic mode TE10 waves in a rectangular waveguide was analysed using the principal mode analysis method. An expression for the transient dissipated power and a heat balance equation with infinite-dimensional characteristics were constructed. Then, the microwave heating model was decomposed into electromagnetic and temperature field submodels. A time discretization approach was used to approximate the transient constant dielectric constant. The heating medium was meshed to solve the electric field strength and transient dissipated power in discrete domains, and the temperature distribution was obtained by substituting this value into the finite-dimensional temperature field submodel. Finally, the validity of the proposed numerical model was verified by comparing the results with the numerical results obtained with the conventional finite element method. The methodology presented in this paper provides a solid basis for designing microwave heating controllers.

Deciphering Exhaled Aerosol Fingerprints for Early Diagnosis and Personalized Therapeutics of Obstructive Respiratory Diseases in Small Airways

Respiratory diseases often show no apparent symptoms at their early stages and are usually diagnosed when permanent damages have been made to the lungs. A major site of lung pathogenesis is the small airways, which make it highly challenging to detect using current techniques due to the diseases’ location (inaccessibility to biopsy) and size (below normal CT/MRI resolution). In this review, we present a new method for lung disease detection and treatment in small airways based on exhaled aerosols, whose patterns are uniquely related to the health of the lungs. Proof-of-concept studies are first presented in idealized lung geometries. We subsequently describe the recent developments in feature extraction and classification of the exhaled aerosol images to establish the relationship between the images and the underlying airway remodeling. Different feature extraction algorithms (aerosol density, fractal dimension, principal mode analysis, and dynamic mode decomposition) and machine learning approaches (support vector machine, random forest, and convolutional neural network) are elaborated upon. Finally, future studies and frequent questions related to clinical applications of the proposed aerosol breath testing are discussed from the authors’ perspective. The proposed breath testing has clinical advantages over conventional approaches, such as easy-to-perform, non-invasive, providing real-time feedback, and is promising in detecting symptomless lung diseases at early stages.

New Modes and Mechanisms of Long‐Term Ionospheric TEC Variations From Global Ionosphere Maps

AbstractThe ionosphere is very active and complex due to photo‐ionization from the solar activity, while traditional empirical models can only give a rough description of its actual variations. Nowadays, global ionosphere maps (GIMs) derived from denser Global Navigation Satellite Systems (GNSS) world‐tracking data provide an excellent total electron content (TEC) data set for global ionospheric research and modeling. In this paper, long‐tern variations of 16‐year (2003–2018) TEC time series from GIMs are investigated by using the principal mode analysis (PCA) technique. We analyze the resulting modes in the time‐spectral domain and parameterize the main contributions in terms of solar and magnetospheric forcing, local solar time (LST), and annual variations. The results show that the TEC variability is strongly dependent on the geographical location of the Earth's magnetic field, and the Earth's diurnal rotation modulates its spatial patterns of variability. The latitudinal asymmetry in the global distribution of TEC variations is due to the effects caused by the irregular shape of the Earth's magnetic field along with its diurnal rotation. The analyses of residuals show that periodicities are correlated to the solar wind speed and magnetospheric forcing, especially those located near the southern dip pole at the night side. Furthermore, we found a TEC anomaly at about 15° from the South magnetic dip at the night side, more prominent around 52°S 155°E.

Finite-temperature infrared spectroscopy of polycyclic aromatic hydrocarbon molecules. II. Principal mode analysis and self-consistent phonons

Following previous work [F. Calvo et al. J. Chem. Phys. 132, 124308 (2010)], infrared spectra of several polycyclic aromatic hydrocarbon molecules are simulated with classical and quantum molecular dynamics trajectories. The interactions are modeled using a tight-binding potential energy surface and quantum delocalization is accounted for using the partially adiabatic centroid and ring-polymer molecular dynamics frameworks, both built upon the path-integral representation. The spectra obtained directly by Fourier transformation of the dipole moment autocorrelation function are here compared with several quasiharmonic approximations that provide additional information about the vibrational modes. A principal mode analysis (PMA) is carried out from the covariance matrix of atomic displacements in classical and quantum trajectories. The method systematically overestimates the line shifts due to anharmonicities, except in the power spectra of atomic displacements, and is not robust in predicting IR intensities for such large molecules. Alternatively, effective normal modes have also been determined by adapting the self-consistent phonon (SCP) theory of condensed matter physics to the present tight-binding model, in both classical and quantum mechanical descriptions. The SCP approximation turns out as semiquantitative in estimating the redshift of tight stretching modes, and performs better for classical systems. More problematic, it predicts that many low- or medium-frequency modes should be blueshifted, in contradiction with the molecular dynamics results. The sets of anharmonic normal modes extracted from the PMA and SCP approaches reveal important mixings within the tightest C-H and C-C stretching modes, which are also manifested on the corresponding power spectra.

Extracting effective normal modes from equilibrium dynamics at finite temperature

A general method for obtaining effective normal modes of a molecular system from molecular dynamics simulations is presented. The method is based on a localization criterion for the Fourier transformed velocity time-correlation functions of the effective modes. For a given choice of the localization function used, the method becomes equivalent to the principal mode analysis (PMA) based on covariance matrix diagonalization. On the other hand, a proper choice of the localization function leads to a novel method with a strong analogy with the usual normal mode analysis of equilibrium structures, where the Hessian system at the minimum energy structure is replaced by the thermal averaged Hessian, although the Hessian itself is never actually calculated. This method does not introduce any extra numerical cost during the simulation and bears the same simplicity as PMA itself. It can thus be readily applied to ab initio molecular dynamics simulations. Three such examples are provided here. First we recover effective normal modes of an isolated formaldehyde molecule computed at 20 K in very good agreement with the results of a normal mode analysis performed at its equilibrium structure. We then illustrate the applicability of the method for liquid phase studies. The effective normal modes of a water molecule in liquid water and of a uracil molecule in aqueous solution can be extracted from ab initio molecular dynamics simulations of these two systems at 300 K.

Ultrafast vibrational energy transfer from O–H stretching modes of liquid water

Vibrational energy transfer from the O–H stretching modes in liquid water is studied by using QM/MM simulations and principal mode analysis (PMA). Two energy relaxation time scales of 0.6–0.7 and 0.3 ps are obtained by decorrelating the vibrational energy into principal modes. The longer time is interpreted as a vibrational energy relaxation (VER) process from the solute to bath, while the shorter time scale is attributed to an intramolecular vibrational energy redistribution (IVR) between the two O–H stretching modes.

Vibrational spectra from atomic fluctuations in dynamics simulations. I. Theory, limitations, and a sample application

Hybrid molecular dynamics (MD) simulations, which combine density functional theory (DFT) descriptions of a molecule with a molecular mechanics (MM) modeling of its solvent environment, have opened the way towards accurate computations of solvation effects in the vibrational spectra of molecules. Recently, Wheeler et al. [ChemPhysChem 4, 382 (2002)] have suggested to compute these spectra from DFT/MM-MD trajectories by diagonalizing the covariance matrix of atomic fluctuations. This so-called principal mode analysis (PMA) allegedly can replace the well-established approaches, which are based on Fourier transform methods or on conventional normal mode analyses. By scrutinizing and revising the PMA approach we identify five conditions, which must be guaranteed if PMA is supposed to render exact vibrational frequencies. Besides specific choices of (a) coordinates and (b) coordinate systems, these conditions cover (c) a harmonic intramolecular potential, (d) a complete thermal equilibrium within the molecule, and (e) a molecular Hamiltonian independent of time. However, the PMA conditions [(c)-(d)] and [(c)-(e)] are generally violated in gas phase DFT-MD and liquid phase DFT/MM-MD trajectories, respectively. Based on a series of simple analytical model calculations and on the analysis of MD trajectories calculated for the formaldehyde molecule in the gas phase (DFT) and in liquid water (DFT/MM) we show that in both phases the violation of condition (d) can cause huge errors in PMA frequency computations, whereas the inevitable violations of conditions (c) and (e), the latter being generic to the liquid phase, imply systematic and sizable underestimates of the vibrational frequencies by PMA. We demonstrate that the huge errors, which are caused by an incomplete thermal equilibrium violating (d), can be avoided if one introduces mode-specific temperatures T(j) and calculates the frequencies from a "generalized virial" (GV) expression instead from PMA. Concerning ways to additionally remove the remaining errors, which GV still shares with PMA, we refer to Paper II of this work [M. Schmitz and P. Tavan, J. Chem. Phys. 121, 12247 (2004)].

Optimal spectrum estimation in statistical mechanics.

Better than a Fourier transform? More accurate and more flexible, principal component analysis is introduced as an alternative to Fourier transforming correlation functions to calculate condensed-phase spectra (see picture). Analytical proof and numerical tests illustrate the potential of principal mode analysis for calculating optimal vibrational spectra from quantum-mechanical/molecular-mechanical trajectories. In principal, the method is also appropriate for calculating other spectra and for analyzing Monte Carlo simulations or experimental data.

Correlated neuronal activity can represent multiple binding solutions

The correlated activity of neurons is being regarded as candidate mechanism for binding the responses of different feature selective cells. Binding, however, is rarely unique, especially at levels beyond feature detection. In this article the dynamical properties of a network of coupled oscillators as a model for a mental representation of visual stimuli are investigated. Oscillator networks have been analyzed previously, but here a new coupling scheme and a biologically more relevant transfer function are used. A principal mode analysis of the activity shows that the network sensibly handles ambiguous segmentations of a visual stimulus.

Variations in fault slip and strain accumulation at Parkfield, California: Initial results using two‐color geodimeter measurements, 1984–1988

Repeated length measurements of several geodetic baselines near Parkfield, California, have revealed significant variations in the local rates of shallow fault slip and strain. This network of baselines, surveyed several times each week, straddles the San Andreas fault in the transition zone between the creeping section to the northwest and the locked section to the southeast. The length measurements, characterized by a precision approaching 0.1 ppm, reveal large fluctuations in the rates of baseline extension. Principal mode analysis of the length change data indicates that the two largest components of the signal are (1) secular extensions and contractions consistent with surface slip on the main strand of the San Andreas fault, and (2) a large seasonal oscillation with no obvious spatial coherence. On most of these baselines, the second component appears to be in phase with seasonal rainfall. When data from the baselines with the largest amplitude of the seasonal signal are excluded, the remaining data can be modeled in terms of both spatial and temporal variations in surface slip, variations in the components of the changes in uniform strain, and the possible displacement of the central monument in this radial network. In parameterizing this model, the spatial variation of slip beneath the near surface is reflected by changes in shear strain. Although the computed secular shear is highly dependent upon the specified parameterization of surface slip, the data are consistent with the hypothesis that slip at intermediate depths lags behind the surface slip rate. However, the range in models that fit the data does not necessarily imply that there is a deficit in slip at depth relative to the surface. Comparison of the inferred values of surface slip from the model with the observed fault slip measured by very short baseline creep meters indicates close agreement in secular rates, but the short‐term variations observed with the creep meters are either highly attenuated or nonexistent in the modeled slip since the modeled slip is a spatial average which smooths out possible short‐wavelength variations in the surface slip for which the creep instruments are most sensitive. An interesting conclusion from the two‐color data is that surface slip on the San Andreas fault appears to be spread over a 2‐km‐wide zone on the south flank of Middle Mountain but is confined to a very narrow zone to the south as the fault passes through the center of the network. This conclusion is dependent upon the assumption that a few critical monuments are stable and track tectonic displacements in the long term. Finally, the largest observed strain change is an extensional strain coincident with the Kettleman Hills earthquake M5.5 in August 1985.