Spectral Decay Rate Research Articles

Impact of Local and Nonlocal Vibronic Coupling on the Absorption and Emission Spectra of J- and H-Dimers.

The impact of exciton-vibrational (EV) coupling involving low-energy ("slow") intermolecular vibrations and higher-energy ("fast") intramolecular vibrations on the absorption and emission spectra of H- and J-dimers is studied theoretically for a pair of chromophores with excitonic coupling dominated by transition dipole-dipole coupling, JC. Exact quantum-mechanical solutions based on a Frenkel-Holstein-Peierls Hamiltonian reveal a fascinating interplay between the two coupling sources in determining the spectral line widths, Stoke shifts and radiative decay rates. It is shown that the ratio rules derived from the vibronic progression of the fast mode in molecular dimers remain valid under the influence of slow-mode EV coupling under most conditions. However, a highly unusual aggregate behavior occurs when the product of local and nonlocal couplings, |gLgNL|, exceeds 2ℏωs|JC|, where ℏωs is the energy of the slow mode. In this regime and when gL and gNL are in-phase, an H-dimer (JC > 0) becomes strongly emissive and can even be super-radiant, while a J-dimer (JC < 0) with out-of-phase gL and gNL values becomes subradiant. Such behaviors are in marked contrast to the predictions of Kasha theory and demonstrate the richness of the photophysical behavior resulting from EV coupling involving inter- and intramolecular vibrations.

Attentive Pooling-Based Weighted Sum of Spectral Decay Rates for Blind Estimation of Reverberation Time

Recently, deep learning-based methods for blind reverberation time estimation have been proposed, and outperform those based on conventional signal processing. The signal processing approaches extract the reverberant environmental features of sound by statistical analysis, while deep learning approaches train a network to capture the relationship between acoustic features and the reverberation time. In this letter, we propose a method for blind reverberation time estimation that explicitly reflects physical properties of reverberation by combining the deep learning approach, attentive pooling, and statistical characteristics of reverberant speech obtained using a signal processing method, i.e., spectral decay rates (SDRs). The results obtained with the proposed blind reverberation time estimation method are superior to the previously published state-of-the-art results for the EVAL dataset of the ACE Challenge. This work can be considered a good example of the collaboration between signal processing expertise and deep learning approach.

Determination of the Fractal Dimension of the Fracture Network System Using Image Processing Technique

Fractal dimension (FD) is a critical parameter in the characterization of a rock fracture network system. This parameter represents the distribution pattern of fractures in rock media. Moreover, it can be used for the modeling of fracture networks when the spatial distribution of fractures is described by the distribution of power law. The main objective of this research is to propose an automatic method to determine the rock mass FD in MATLAB using digital image processing techniques. This method not only accelerates analysis and reduces human error, but also eliminates the access limitation to a rock face. In the proposed method, the intensity of image brightness is corrected using the histogram equalization process and applying smoothing filters to the image followed by revealing the edges using the Canny edge detection algorithm. In the next step, FD is calculated in the program using the box-counting method, which is applied randomly to the pixels detected as fractures. This algorithm was implemented in different geological images to calculate their FDs. The FD of the images was determined using a simple Canny edge detection algorithm, a manual calculation method, and an indirect approach based on spectral decay rate. The results showed that the proposed method is a reliable and fast approach for calculating FD in fractured geological media.

Shear wave attenuation estimated from the spectral decay rate in the vicinity of the Petropavlovsk station, Kamchatka

The parameters of S-wave attenuation (the total effect of absorption and scattering) near the Petropavlovsk (PET) station in Kamchatka were estimated by means of the spectral method through an original procedure. The spectral method typically analyzes the changes with distance of the shape of spectra of the acceleration records assuming that the acceleration spectrum at the earthquake source is flat. In reality, this assumption is violated: the source acceleration spectra often have a high-frequency cutoff (the source-controlled fmax) which limits the spectral working bandwidth. Ignoring this phenomenon not only leads to a broad scatter of the individual estimates but also causes systematic errors in the form of overestimation of losses. In the approach applied in the present study, we primarily estimated the frequency of the mentioned high-frequency cutoff and then constructed the loss estimates only within the frequency range where the source spectrum is approximately flat. The shape of the source spectrum was preliminarily assessed by the approximate loss compensation technique. For this purpose, we used the tentative attenuation estimates which are close to the final ones. The difference in the logarithms of the spectral amplitudes at the edges of the working bandwidth is the input for calculating the attenuation. We used the digital accelerograms from the PET station, with 80 samples per second digitization rate, and based on them, we calculated the averaged spectrum of the S-waves as the root mean square along two horizontal components. Our analysis incorporates 384 spectra from the local earthquakes with M = 4–6.5 at the hypocentral distances ranging from 80 to 220 km. By applying the nonlinear least-square method, we found the following parameters of the loss model: the Q-factor Q0 = 156 ± 33 at frequency f = 1 Hz for the distance interval r = 0–100 km; the exponent in the power-law relationship describing the growth of the Q-factor with frequency, γ = 0.56 ± 0.08; and the loss parameter beneath the station κ0 = 0.03 ± 0.005 s. The actual accuracy of the estimates can probably be somewhat lower than the cited formal accuracy. It is also established (with a confidence level of 10%) that the losses decrease with distance.

Rupture characteristics of major and great (Mw ≥ 7.0) megathrust earthquakes from 1990 to 2015: 2. Depth dependence

AbstractDepth‐varying characteristics of high‐frequency seismic radiation for megathrust earthquakes have been inferred from several recent giant earthquakes and large tsunami earthquakes. To quantify any depth dependence more extensively, we analyzed 114 Mw ≥ 7.0 thrust‐faulting earthquakes with centroid depths from 5 to 55 km on circum‐Pacific megathrusts using teleseismic body wave finite‐fault inversions and source spectrum determinations. Large tsunami earthquakes and some other shallow events at depths less than about 18 km have unusually long source durations, and low values of static stress drop (ΔσE), Vr3ΔσE, and apparent stress, with relatively depleted high‐frequency radiation. Deeper events have no clear global trend with source depth for moment‐normalized centroid time or total duration, static stress drop, moment‐scaled radiated energy, apparent stress, or radiation efficiency. Regional behavior among the 17 sampled subduction zones generally conforms to the global composite. The source spectra have high‐frequency logarithmic spectral decay slopes averaging ~ −1.6. There is relative enrichment in high‐frequency spectral levels with increasing source depth manifested in reduced high‐frequency spectral decay slope. The ratio of high‐frequency (0.3–1 Hz) radiated energy to total energy increases correspondingly. These observations suggest that overall dynamic rupture processes are relatively insensitive to source depth, but varying scale lengths of megathrust heterogeneity may contribute to modest enrichment of high‐frequency seismic radiation for events deeper on the megathrust. A weak correlation of higher estimated average megathrust temperature at 30 km depth with higher spectral decay rate indicates that the depth‐varying pattern may in part result from frictional properties being influenced by temperature variations or by systematic reduction of average attenuation with increasing depth along the megathrust.

Energy Transfer in Silicon Nanocrystal Solids Made from All-Inorganic Colloidal Silicon Nanocrystals.

Energy transfer between silicon (Si) nanocrystals (NCs) in Si-NC solids was demonstrated by photoluminescence (PL) spectroscopy. Clear differences of PL spectra and the decay rates between solutions and solids of Si-NCs were observed. The change in the PL properties caused by the formation of solids could be explained by the energy transfer from small to large NCs in the size distribution. In order to obtain further evidence of NC-to-NC energy transfer, the size distribution was intentionally modified by mixing solutions of NCs with different size distributions. NC solids made from the mixed solutions exhibited significantly different PL spectral shape and decay rates from those made from unmixed solutions, providing clear evidence of NC-to-NC energy transfer in Si-NC solids.

Lateral heterogeneity scales in regional and global upper mantle shear velocity models

We analyse the lateral heterogeneity scales of recent upper mantle tomographic shear velocity (Vs) global and regional models. Our goal is to constrain the spherical harmonics power spectrum over the largest possible range of scales to get an estimate of the strength and statistical distribution of both long and small-scale structure. We use a spherical multitaper method to obtain high quality power spectral estimates from the regional models. After deconvolution of the employed taper functions, we combine global and regional spectral estimates from scales of 20 000 to around 200 km (degree 100). In contrast to previous studies that focus on linear power spectral densities, we interpret the logarithmic power per harmonic degree l as heterogeneity strength at a particular depth and horizontal scale. Throughout the mantle, we observe in recent global models, that their low degree spectrum is anisotropic with respect to Earth's rotation axis. We then constrain the uppermost mantle spectrum from global and regional models. Their power spectra transfer smoothly into each other in overlapping spectral bands, and model correlation is in general best in the uppermost 250 km (i.e. the ‘heterosphere’). In Europe, we see good correlation from the largest scales down to features of about 500 km. Detailed analysis and interpretation of spectral shape in this depth range shows that the heterosphere has several characteristic length scales and varying spectral decay rates. We interpret these as expressions of different physical processes. At larger depths, the correlation between different models drops, and the power spectrum exhibits strong small scale structure whose location and strength is not as well resolved at present. The spectrum also has bands with elevated power that likely correspond to length scales that are enhanced due to the inversion process.

Spatiotemporal Characterization of Extracellular Matrix Microstructures in Engineered Tissue: A Whole-Field Spectroscopic Imaging Approach

Quality and functionality of engineered tissues are closely related to the microstructures and integrity of their extracellular matrix (ECM). However, currently available methods for characterizing ECM structures are often labor-intensive, destructive, and limited to a small fraction of the total area. These methods are also inappropriate for assessing temporal variations in ECM structures. In this study, to overcome these limitations and challenges, we propose an elastic light scattering approach to spatiotemporally assess ECM microstructures in a relatively large area in a nondestructive manner. To demonstrate its feasibility, we analyze spectroscopic imaging data obtained from acellular collagen scaffolds and dermal equivalents as model ECM structures. For spatial characterization, acellular scaffolds are examined after a freeze/thaw process mimicking a cryopreservation procedure to quantify freezing-induced structural changes in the collagen matrix. We further analyze spatial and temporal changes in ECM structures during cell-driven compaction in dermal equivalents. The results show that spectral dependence of light elastically backscattered from engineered tissue is sensitively associated with alterations in ECM microstructures. In particular, a spectral decay rate over the wavelength can serve as an indicator for the pore size changes in ECM structures, which are at nanometer scale. A decrease in the spectral decay rate suggests enlarged pore sizes of ECM structures. The combination of this approach with a whole-field imaging platform further allows visualization of spatial heterogeneity of EMC microstructures in engineered tissues. This demonstrates the feasibility of the proposed method that nano- and micrometer scale alteration of the ECM structure can be detected and visualized at a whole-field level. Thus, we envision that this spectroscopic imaging approach could potentially serve as an effective characterization tool to nondestructively, accurately, and rapidly quantify ECM microstructures in engineered tissue in a large area.

Earthquake spectra and near‐source attenuation in the Cascadia subduction zone

Models of seismic source displacement spectra are flat from zero to some corner frequency, fc, regardless of source type. At higher frequencies spectral models decay as f−1 for slow events and as f−2 for fast earthquakes. We show that at least in Cascadia, wave propagation effects likely control spectral decay rates above ∼2 Hz. We use seismograms from multiple small‐aperture arrays to estimate the spectral decay rates of near‐source spectra of 37 small ‘events’ and find strong correlation between source location and decay rate. The decay rates (1) vary overall by an amount in excess of that inferred to distinguish slow sources from fast earthquakes, (2) are indistinguishable for sources separated by a few tens of km or less, and (3) separate into two populations that correlate with propagation through and outside a low‐velocity zone imaged tomographically. We find that some events repeat, as is characteristic of low‐frequency earthquakes (LFEs), but have spectra similar to those of non‐repeating earthquakes. We also find no correlation between spectral decay rates and rates of ambient tremor activity. These results suggest that earthquakes near the plate boundary, at least in Cascadia, do not distinctly separate into ‘slow’ and ‘fast’ classes, and correctly accounting for propagation effects is necessary to characterize sources.

Spectral and spatial transfer and diffusion of excitons in multiple quantum dot structures

A formalism is developed for resonant and nonresonant spectral and spatial energy transfer of excitons in disordered semiconductor multiple-quantum-dot structures. Dipole-dipole and photon-exchange energy-transfer mechanisms are considered. For nonresonant transfer, we study two-site transfer rates in a disordered system as a function of the energy mismatch, the temperature, and the distance. The total time-dependent decay rate of the initial spectral intensity excited at a given energy in the inhomogeneous spectral profile is calculated. For resonant transfer, two-site transfer rates are studied as a function of the distance. The diffusion constant is calculated exactly in a regular quantum dot lattice in order to assess the upper limit of the diffusion constant of a disordered system. We find that the total time-dependent spectral decay rate and the diffusion constant are dominated by the weak long-range photon-exchange interaction mechanism over the standard short-range F\"orster (dipole-dipole) mechanism in a uniform macroscopic multi-quantum-dot system due to the long mean-free path of the photons.

Optimal stabilizing controllers for linear discrete‐time stochastic systems

AbstractThe following summarizes the corrections on the online version of the paper, which will be incorporated in the print publication. Section 3. Spectral radius, decay rate and optimal controllers. Theorem 1: The statement ‘For system (1), ρ(MA,C)⩽β∈(0, 1) holds if and only if system (1) has decay rate β−1’ should read as ‘For system (1), if ρ(MA,C)&lt;β∈(0, 1) holds, then system (1) has decay rate β−1. Moreover, if β−1 is a decay rate, then ρ(MA,C)&lt;β∈(0, 1)’. Section 3. Proof necessity. Line 20: Delete ‘(necessity)’; line 21: ‘ρ(MA,C)⩽β∈(0, 1)’ should read as ‘ρ(MA,C)&lt;β∈(0, 1)’; line 22: ‘small arbitrarily ε0&gt;0’ should read as ‘sufficiently small ε0&lt;0’. Sixth page. Line 5: ‘the necessity’ should read as ‘the first part of Theorem 1’; line 7: ‘Sufficiency: Notice’ should read as ‘For the second part, notice’; line 8: ‘decay rate β’ should read as ‘decay rate β−1’; line 11: ‘To prove sufficiency we only need’ should read as ‘We only need’. Seventh page. Corollary 3: The statement ‘For system (5), ρ(M)⩽β∈(0, 1) holds if and only if system …’ should read as ‘For system (5), if ρ(M)&lt;β∈(0, 1) holds, then system …’ Seventh page. Line 14, and eighth page, line 20: ‘decay rate β−1∈(0, 1)’ should read as ‘decay rate β−1’. Seventh page. Line 17, and eighth page, line 23, ‘⩽’ should be ‘&lt;’.

Prototype measurements of pressure fluctuations in The Dalles Dam stilling basin

At The Dalles Dam on the Columbia River, fish are believed to sustain injury from exposure to turbulence and from collisions with baffle blocks and end sills in the stilling basin at high spillway discharges. Because taking velocity measurements would be exceedingly difficult in this environment, a system of pressure transducers was installed to record high-frequency pressure data for a range of spillway discharges. The sensors were mounted below two of the spillbays on the tops, faces, and sides of baffle blocks; in the gaps between baffle blocks; and on the top and face of the end sill. Statistical analyses on results from three sensors below one of the two spillways showed that mean pressure increased during head-on flow, decreased in flow separation zones, and was proportional to water depth. Power spectra indicate increased low-frequency spectral power with increased discharge, typical spectral decay rates, and the existence of spectral peaks of possible hydraulic origin. The high-frequency pressure data collected at full scale in extremely turbulent environments will contribute to efforts to improve fish passage and to develop and validate three-dimensional computational fluid dynamics models.

Heat Fluxes and Airflow Patterns Through Roof Windows in a Naturally Ventilated Enclosure

Experiments were carried out to study the airflow and heat transfer through continuous vertical roof openings of a naturally ventilated greenhouse. The major goals of this work were to investigate the effect of ambient wind speed and direction with respect to the greenhouse on the mean and turbulent characteristics of the air velocity and heat transfer through openings with and without insect-proof screens. Air velocity and temperature were measured simultaneously at two edges of the opening using one-dimensional sonic anemometers and miniature thermocouples. It is shown that when the wind is not perpendicular to the plane of the openings there are outflow and inflow, at the windward and leeward edges of the openings respectively. A wind blowing from the back of the openings and nearly perpendicular to them reduced the mean air velocity at the two edges but did not change the turbulent velocity much. Over a considerable part of the day the mean and turbulent air velocities scale with the ambient wind; the total heat flux (mean plus turbulent) scales with the product of the ambient wind and temperature while the turbulent heat flux does not. The integral length scale of the inflow was approximately equal to the height of the opening and was larger than that of the outflow. Installing screens on the openings generated smaller scales and increased the spectral decay rate in comparison with openings without screens. A quadrant analysis enabled the determination of the events that significantly contribute to the turbulent heat flux. It is shown that at the outflow the turbulent heat flux is mainly due to eddies of cool air entering from the surrounding to the greenhouse while at the inflow it is due to both warm and cool eddies leaving and entering the greenhouse respectively.

High-resolution exponential analysis via regularized numerical inversion of Laplace transforms

The paper describes a new, robust method for the exponential analysis problem solving. In discrete case the regularizing operators of the inverse Laplace transformation are used for transformation of experimental data into a form that is more suitable for determination of decay rates and amplitudes. In the case of a continuous distribution a spectral function is obtained by regularized inverse Laplace transformation of the transient. The proposed method has advantages over known methods and is tolerant to the baseline offset. The results of numerical testing show that the proposed method can be used in high-resolution analysis for determination of spectral functions, decay rates and amplitudes from experimentally measured transients.

Perceptual analysis of synthesized struck bars

This study is part of a project seeking to understand musical timbre and perceptual phenomena of the sound environment. It concerns the sensitivity of listeners to sounds emitted by simple vibrating structures, such as xylophone bars. Previous studies of timbre have characterized this attribute in terms of a small number of perceptual dimensions of an analytic nature (attack time, spectral centroid, spectral flux). Other studies have suggested a return to the physical characteristics of the sound sources themselves in order to understand their influence on timbre perception. Sounds were synthesized with a computer model of the vibrating bar developed at ENST that allows precise control of physical parameters. Listeners made dissimilarity judgments on all pairs of different sounds. Multidimensional scaling analyses of these data yield a perceptual space with dimensions that correspond strongly to the varied physical parameters (material density and the first term of internal damping) as well as to salient auditory dimensions (pitch for the former and a combination of spectral centroid and decay rate for the latter). These results argue in favor of a privileged processing of source characteristics by the auditory system.

A Study of Backscattering From Multiscale Rough Surface

Most of the rough surfaces are generally multiscale in nature as observed by radar even at narrow-band. In this paper, we apply the modulation concept to study the characteristics of backscattering from such a multiscale surface, using the IEM scattering model. The modulated surface is special kind of multiscale surface in that a random surface is superimposed upon a periodic type surface. The modulation is rationed from the fact the measured correlation function usually exhibits zero-crossing which equally states the fact that the maxima of surface spectra is shifted toward the higher wavenumber. The amount of the frequency shift depends on the modulation wavenumber. It changes the spectral decay rates behind the peak valued. The normal incidence angle can be significantly shifted as well. It is also found the maximum modulation wavenumber is related by the inverse of base-band correlation length. In all cases studied, it was found that the modulation effects significantly changes the backscattering behavior, both its angular trend and level, and is polarization dependent. It is inferred from this study that the actual surface correlation length is very difficult to measure and may not be defined by a single parameter. In fact, radar can only observe effective correlation length under an operation frequency, which in turns depends on modulation wavenumber. In particular, in terms of retrieval, the correlation length measured by the radar and that by field measured may have quite different meanings.

Interaction of turbulent plasma flow with a hypersonic shock wave

A transient increase is observed in both the spectral energy decay rate and the degree of chaotic complexity at the interface of a shock wave and a turbulent ionized gas. Even though the gas is apparently brought to rest by the shock wave, no evidence is found either of prompt relaminarization or of any systematic influence of end-wall material thermal conductivities on the turbulence parameters.

A molecular approach to 4′,6-diamidine-2-phenylindole (DAPI) photophysical behaviour at different pH values

The photophysical mechanisms which determine the spectral properties and decay rates of 4′,6-diamidine-2-phenylindole (DAPI) in solution and in association with nucleic acids have not yet been fully elucidated. We have performed steady-state and time-resolved fluorescence experiments on DAPI in a wide pH range to investigate the hypothesis that different ground-state conformations are responsible for the photophysical properties of the probe. Several excited-state mechanisms are investigated and it is concluded that among the proposed models, the hypothesis of ground-state heterogeneity with rapid interconversion among conformations is the only one consistent with the experiments in the entire pH range investigated.

Q P andQ S in Beijing and Jianchuan, Yunnan areas

Events from the December 1982 Huairou County, Beijing, and the July 1982 Jianchuan, Yunnan earthquake series were recorded at one station in Beijing City and at four stations in Eryuan area, Yunnan, respectively. Dividing the spectra (for P and S waves) from the smaller events in the series by spectra (for corresponding P and S waves) from the larger events in cach region, we have determined the high frequency source spectral decay rate to be ω−1in both cases. Through trial and error method, we are able to determine the appropriate constantQP andQS that corrects the individual spectra to the proper high frequency decay rate. It is found that aQP of 800 and aQS of 550 can adequately compensate for the attenuation of the waves in Beijing area. For Jianchuan, Yunnan area the corresponding values are 900 and 400.

Failure of self-similarity for large (Mω&amp;gt; 814) earthquakes

AbstractWe compare teleseismic P-wave records for earthquakes in the magnitude range from 6.0 to 9.5 with synthetics for a self-similar, ω2 source model and conclude that the energy radiated by very large earthquakes (Mw &amp;gt; 814) is not self-similar to that radiated from smaller earthquakes (Mw &amp;lt; 814). Furthermore, in the period band from 2 sec to several tens of seconds, we conclude that large subduction earthquakes have an average spectral decay rate of ω-1.5. This spectral decay rate is consistent with a previously noted tendency of the ω2 model to overestimate Ms for large earthquakes.