Exponential Decay Coefficient Research Articles

Short wave attenuation by a kelp forest canopy

AbstractGiant kelp (Macrocystis pyrifera) forests are common along the California coast. Attached on the rocky bottom at depths of approximately 5–25 m, the kelp, when mature, spans the water column and develops dense, buoyant canopies that interact with waves and currents. We present two novel results based on observations of surface gravity waves in a kelp forest in Point Loma, California. First, we report short wave (1–3 s) attenuation in kelp, quantified by an exponential decay coefficient —comparable to the dampening effect of sea ice. Second, we identify seasonal and tidal changes in attenuation, peaking mid‐summer with maximum kelp cover, and during low tide when a greater proportion of the fronds are at the surface. Thus, the naturally occurring surface canopies of kelp forests can act as temporally varying, high‐frequency filters of wave energy.

Analysis of Dynamic Characteristics of Tristable Exponential Section of Piezoelectric Energy Harvester

Variable-cross-section beams have better mass and strength distribution compared with constant cross-section beams, which can optimize the harvesting power of piezoelectric vibration energy harvesters, which are widely used in self-supplied and low-power electronic devices, providing more convenience and innovation for the development of micromechanical intelligence and portable mobile devices. This paper proposes a piezoelectric energy harvester with a tristable-exponential-decay cross section, which optimizes the strain distribution of the cantilever beam through exponential decay changes to improve the harvesting efficiency of the harvester in low-frequency environments. First, the nonlinear magnetic force is obtained based on the magnetic dipole, and the dynamic model is established by using the Euler–Bernoulli beam theory and Lagrangian equation. The influence of the structural parameters of the harvester on the system dynamics and output characteristics is analyzed in the two dimensions of time and frequency, and the influence of the exponential decay coefficient on the system dynamic response and output power is deeply studied. The research shows that the exponential decay section can reduce the first natural frequency of the cantilever beam; by changing the amplitude, frequency, d and dg of the excitation acceleration, the switching of the monostable, tristable and bistable states of the system can be realized. With a decrease in the exponential decay coefficient, under a low-frequency excitation of 0–7 Hz, the output power of the cantilever beam per unit volume is significantly improved, and under a 4 Hz low-frequency excitation, the acquisition output power per unit volume of the cantilever beam is increased by 7 times, thus realizing low-frequency, high-efficiency energy harvesting.

Examination of the decomposition of willow (Salix sp.), poplar (Populus sp.), reed (Phragmites australis) and mixed leaf litter with litterbag technique

Leaf litter decomposition is one of the main ecological material cycle processes in waterfront areas. In this microcosm experiment, the rate of decomposition of the most frequently occurring dominant waterside plants were examined in the summer months of 2022 in a class “A” evaporation pan, using litterbag technique. The study provides information about the decomposition dynamics of willow (Salix sp.), poplar (Populus sp.), reed (Phragmites australis) and different leaf litter mixture combinations. Dry mass, exponential decay coefficient and the chemical parameters of the water (pH, conductivity, NH4+, PO43-, SO42-) were determined during the 84 days long experimental period. The weight loss curves showed negative exponential pattern in every case. On average, the different samples lost ~ 57% of their initial dry mass during the experimental period. The largest mass loss was measured in case of poplar (67.2%), while reed leaves had the smallest mass loss (47.25%). Based on the results, it cannot be proven, that mixed leaf litter accelerates the rate of decomposition.

The long-time behavior of solitary waves for the weakly damped KdV equation

In this paper, we first introduce the long-time behavior stability of solitary waves for the weakly damped Korteweg–de Vries equation. More concretely, solutions of the dissipative system with the initial values near a c_{0}-speed solitary wave, are approximated by a long curve on the family of solitary waves with the time-varying speed |c(t)-c_{0}| being small, in the long-time period (i.e., 0leqslant tleqslant O(frac{1}{epsilon ^{tau}})). Meanwhile, the approximation difference in a suitably weighted space H^{1}_{a}(mathbb{R}) is of the order of the damping coefficient and of some kind of exponential weight form. As a comparison, we also study the long-time behavior stability, i.e., for 0leqslant t<+infty , the solutions are approximated by a long curve on the family of solitary waves with the exponential decay speed c(t)= c_{0}e^{-beta t} (0<beta leqslant 1), when the initial values are near a c_{0}-speed solitary wave. However, here, the approximation difference merely defined in H^{1}(mathbb{R}) depends on the damping coefficient ϵ and the exponential decay coefficient β.

Dose response of coconut rhinoceros beetle (Coleoptera: Scarabaeidae) to 92 kV x‐ray irradiation

AbstractTo evaluate the potential suitability of x‐ray irradiation as a physical control method for invasive Coconut Rhinoceros Beetle (CRB) (Oryctes rhinoceros Linnaeus 1758; Coleoptera: Scarabaeidae), either through sterile insect technique (SIT) or through direct irradiation of naturally infested materials in the field, we recorded longevity of eggs, larval and adult life stages of CRB irradiated with different doses of x‐rays emitted from a tube energized at 92 kV. Eggs and larvae were highly susceptible to radiation at all tested doses (down to about 2–5 Gy), though adults required larger doses (at least 50 Gy) to render them incapable of reproducing. At exposures near 50 Gy sterilized adults nevertheless were observed to survive for more than a month, suggesting SIT may be a viable control approach for this beetle. Similarly, these results may facilitate the discovery of hidden breeding sites in the wild by tagging and releasing sterilized adults. While larvae were highly susceptible to x‐ray irradiation, irradiation would probably not be an effective tool for field control due to rapid attenuation of radiation energy (exponential decay coefficients ranging from about 0.3–0.6 cm−1) in the organic nesting materials we tested, and the tendency for CRB adults to burrow and oviposit deep in mulch (1 m or more).

Modelling long‐distance floating seed dispersal in salt marsh tidal channels

AbstractSeed dispersal is a primary factor influencing plant community development in salt‐marshes. However, studies on seed dispersal in marsh‐channel system are relatively scarce, and relevant mathematical modelling is particularly lacking. In this study, we developed a one‐dimensional advection–dispersion model to explore the patterns of long‐distance floating seed dispersal in tidal channels. Oscillatory tidal current velocity and water depth were assumed to represent the tidal effects. An exponential decay coefficient was introduced to account for the loss of floating seeds due to water‐logged deposition and retention by trapping agents along the channel banks. An analytical solution in integral form was derived using the method of Green's function. The developed model was applied to simulate floating Spartina densiflora seed dispersal in a real tidal channel. Seed floating duration and seed collection data reported in the literature were used for model calibration and validation. The leptokurtic seed dispersal kernel in the marsh‐channel system was quantified for the first time using the predicted spatio‐temporal distribution of deposited and retained seeds. The range of the long‐distance floating seed dispersal and its distribution concentration that have important implications for salt marsh protection and restoration activities were evaluated through statistical parameters such as the centroid displacement and the variance of the floating seed cloud and floating seed concentration contours. The developed model provides a useful tool for ecological management of tidal marshes, as data on the long‐distance floating seed dispersal are rarely available and hard to gather.

Investigation of Salix alba and Populus tremula leaf litter decomposition in the area of Lake Balaton and Kis-Balaton Wetland

Plant litter decomposition in inland waters contributes significantly to nutrient load, particularly in still waters, such as shallow lakes and wetlands. The decomposition rates of Salix alba and Populus tremula leaf litter was examined in Lake Balaton and Kis-Balaton Wetland, using litter bag technique. Leaf litter was incubated in small (ᴓ=3 mm) and large (ᴓ=900 μm) mesh size bags for the assessment of the relative contribution of macroinvertebrates to leaf litter decomposition. Dry mass, exponential decay coefficient and chemical parameters of water (pH, conductivity, NH4 +, NO3 -, SO4 2-, PO4 3-, Cl-) were determined. Leaf mass loss showed negative exponential pattern during the 168 days of the decomposition period. Leaf litter mass loss generally did not differ between the small and large mesh sizes, suggesting that macroinvertebrates generally have a negligible role in leaf decomposition in the winter period.

Vertical Profiles of Wave-Coherent Momentum Flux and Velocity Variances in the Marine Atmospheric Boundary Layer

AbstractThe wave-coherent momentum flux and velocity variances are investigated using a theoretical model and open-ocean measurements. The spectrum-integrated wave-coherent (SIWC) momentum flux and velocity variances decay roughly exponentially with height. The exponential decay coefficients of the SIWC momentum flux and velocity variances decrease with increasing peak wavenumber. The phases of the wave-coherent horizontal (vertical) velocity fluctuations are approximately 180° (90°) under waves with wind-wave angle |α1| &lt; 90°. In general, the ratio of the SIWC momentum flux to the total momentum flux under swell conditions is higher than that under wind-wave conditions at the same height. At a height of 9.9 m, the SIWC vertical (horizontal) velocity variances can exceed 30% (10%) of the total vertical (horizontal) velocity variances at high wave ages. The impact of SIWC momentum flux on wind profiles is determined mainly by the surface SIWC momentum flux ratio, the decay coefficient of the SIWC momentum flux, and the sea surface roughness length, with the first two factors being dominant. The results of this study suggest a methodology for parameterizing the SIWC momentum flux and the total momentum flux over the ocean. These results are important for simulating the marine atmospheric boundary layer and should be used in model development.

Emergence of the Reactivity Continuum of Organic Matter from Kinetics of a Multitude of Individual Molecular Constituents.

The reactivity continuum (RC) model is a powerful statistical approach for describing the apparent kinetics of bulk organic matter (OM) decomposition. Here, we used ultrahigh resolution mass spectrometry data to evaluate the main premise of the RC model, namely that there is a continuous spectrum of reactivity within bulk OM, where each individual reactive type undergoes exponential decay. We performed a 120 day OM decomposition experiment on lake water, with an untreated control and a treatment preexposed to UV light, and described the loss of bulk dissolved organic carbon with RC modeling. The behavior of individual molecular formulas was described by fitting the single exponential model to the change in peak intensities over time. The range of the empirically derived apparent exponential decay coefficients (kexp) was indeed continuous. The character of the corresponding distribution, however, differed from the conceptual expectations, due to the effects of intrinsic averaging, overlaps in formula-specific loss and formation rates, and the limitation of the RC model to include apparently accumulating compounds in the analysis. Despite these limitations, both the RC model-simulated and empirical (mass spectrometry-derived) distributions of kexp captured the effects of preexposure to UV light. Overall, we present experimental evidence that the reactivity continuum within bulk OM emerges from a range of reactivity of numerous individual components. This constitutes direct empirical support for the major assumption behind the RC model of the natural OM decomposition.

Wave attenuation in the shallows of San Francisco Bay

Waves propagating over broad, gently-sloped shallows decrease in height due to frictional dissipation at the bed. We quantified wave-height evolution across 7km of mudflat in San Pablo Bay (northern San Francisco Bay), an environment where tidal mixing prevents the formation of fluid mud. Wave height was measured along a cross-shore transect (elevation range −2m to +0.45m MLLW) in winter 2011 and summer 2012. Wave height decreased more than 50% across the transect. The exponential decay coefficient λ was inversely related to depth squared (λ=6×10−4h−2). The physical roughness length scale kb, estimated from near-bed turbulence measurements, was 3.5×10−3m in winter and 1.1×10−2m in summer. Estimated wave friction factor f̂w determined from wave-height data suggests that bottom friction dominates dissipation at high Rew but not at low Rew. Predictions of near-shore wave height based on offshore wave height and a rough formulation for fw were quite accurate, with errors about half as great as those based on the smooth formulation for fw. Researchers often assume that the wave boundary layer is smooth for settings with fine-grained sediments. At this site, use of a smooth fw results in an underestimate of wave shear stress by a factor of 2 for typical waves and as much as 5 for more energetic waves. It also inadequately captures the effectiveness of the mudflats in protecting the shoreline through wave attenuation.

Method for finding optimal exponential decay coefficient in numerical Laplace transform for application to linear convolution

In this paper, a method based on the numerical Laplace transform is used for calculating the full linear convolution of real or complex signals. An algorithm for obtaining the last N values of the convolution is presented, along with a method for finding an optimal value for the decay coefficient of the transform. It is shown that the use of the numerical Laplace transform formulation allows the calculation of each half of the linear convolution independently, which has computational benefits. The numerical Laplace transform is expressed as the fast Fourier transform of signals that have been premultiplied by a decreasing exponential window characterized by decay coefficient c. The error of the resulting linear convolution depends on the value of the decay coefficient; undervalue results in the generation of wrap-around error whereas overvalue causes amplification of Gibbs phenomenon. In this paper, a formula that optimizes the value of the decay coefficient is developed. A trade-off value for c is obtained and error analysis shows that it outperforms other coefficients proposed in the literature when applied to the calculation of linear convolution. The relative errors obtained are of the order of 10−6% and 10−9% for single and double precisions.

Cotton-strip decomposition rate as a river condition indicator – Diel temperature range and deployment season and length also matter

Decomposition of organic matter, a fundamental ecological process, has been proposed to be used as a functional indicator of stream condition. A recently published protocol for the use of the cotton-strip assay as a standardized measure of decomposition rates provided a basis for the use of decomposition as an indicator. However, some factors that may influence the application of the cotton-strip assay, such as the deployment season, remain largely unexplored. To further establish the technique, we studied temporal and spatial variability in cotton-strip decomposition rates along small upland rivers in SE Australia. We found a consistent longitudinal pattern in decomposition rates throughout the year, in spite of large within-site and site-specific temporal variability. Results from the models of temporal variability in decomposition rates indicate that differences in the duration of incubation might have been a confounding variable. Models of spatial variability in decomposition rates explained 45% and 52% of the variability in decomposition rates across five rivers, with diel temperature range being the most important predictor, accounting for ca. 20% of the variability in decomposition rates. We have shown that additional considerations are needed, if decomposition rates are to be compared across spatial and temporal scales. First, large within-site variability in decomposition rates, found in our and other studies, might prevent comparisons with reference conditions. Second, the length (and therefore the season) of cotton-strip deployment needs to be specified, since the exponential decomposition coefficient appears not to be a constant throughout time. Third, diel temperature range needs to be considered when establishing sampling protocols, since the exponential decay coefficient appears to change non-linearly with changing temperature, and therefore, using only daily mean temperatures does not realistically reflect the effect of temperature. The importance of temperature range also has implications for stream rehabilitation, showing that restoring the temperature regime contributes to the restoration of a fundamental ecosystem process.

Myocardial strain imaging with radial acquisitions (SIRA) reduces tag fading compared to Cartesian sampling

Background Myocardial tagging is considered a gold-standard technique to derive myocardial strain using cardiac magnetic resonance (CMR) in large epidemiologic studies. Nevertheless technical limitations related to tag line fading (via T1 relaxation) limit generalizability and reproducibility of this technique. Our purpose was to test myocardial tagging with radial k-space acquisition against routinely utilized Cartesian k-space sampling techniques, in order to potentially minimize tag-line fading over the cardiac cycle. Methods We compared a new tagging sequence with radial acquisitions for cardiac MRI to a routinely-utilized clinical tagging sequence with Cartesian sampling. Both sequences were added pre-contrast to routine clinical scans of 14 patients. The per phase change in grayscale contrast due to T1 relaxation (tag fading”) of tagged myocardium was modeled using a non-linear fit with maximum likelihood estimation to an exponential decay curve and compared between groups. Peak Eulerian circumferential strain (Ecc) was compared using HARP software. Results 14 patients (mean age 54 ± 16 years and 36% were men) and mean left ventricular ejection fraction 53 ± 16% (LVEF) were included. Tag fading differed significantly between radial and Cartesian sampling; the exponential decay coefficient was -0.045 ± 0.011 for the Cartesian and significantly higher than the-decay coefficient value of 0.029 ± 0.007 for radial read-outs (p < 0.001). Due to less tag fading myocardial strain could be evaluated for more segments acquired with radial, compared to Cartesian read-outs (p < 0.001). The intra-observer reliability for Ecc was higher for radial (r = 0.99, p < 0.001) than Cartesian (r = 0.86, p=<0.001) images (p = 0.002 for comparison). The bias was 0.9% and limits of agreement -4.1 to 6.0% with concordance = 0.86 (p < 0.001) for Ecc-radial versus Ecc-Cartesian. Both tagging methods correlated with LVEF, r = -0.86 (p < 0.001) for Ecc-radial versus r = -0.83 (p < 0.001) for Ecc-Cartesian. Conclusions

Three-dimensional computational analysis of optical coherence tomography images for the detection of soft tissue sarcomas

We present a three-dimensional (3-D) computational method to detect soft tissue sarcomas with the goal of automatic surgical margin assessment based on optical coherence tomography (OCT) images. Three parameters are investigated and quantified from OCT images as the indicators for the tissue diagnosis including the signal attenuation (A-line slope), the standard deviation of the signal fluctuations (speckles), and the exponential decay coefficient of its spatial frequency spectrum. The detection of soft tissue sarcomas relies on the combination of these three parameters, which are related to the optical attenuation characteristics and the structural features of the tissue. Pilot experiments were performed on ex vivo human tissue samples with homogeneous pieces (both normal and abnormal) and tumor margins. Our results demonstrate the feasibility of this computational method in the differentiation of soft tissue sarcomas from normal tissues. The features of A-line-based detection and 3-D quantitative analysis yield promise for a computer-aided technique capable of accurately and automatically identifying resection margins of soft tissue sarcomas during surgical treatment.

Impacts of Prescribed Fire Frequency on Coarse Woody Debris Volume, Decomposition and Termite Activity in the Longleaf Pine Flatwoods of Florida

Longleaf pine (Pinus palustris) ecosystems have been reduced dramatically throughout their range. Prescribed burning is considered the best way to restore and maintain plant communities associated with longleaf pine, but little is known about its effects on coarse woody debris and associated organisms. We conducted a 5-year study on the Osceola National Forest in northeastern Florida to determine how dormant-season prescribed burns at different frequencies (annual, biennial, quadrennial or unburned) applied over a 40-year period affected coarse woody debris volume, decomposition and nitrogen content, and subterranean termite (Reticulitermes spp.) activity. Burn frequency had no effect on standing dead tree or log volumes. However, freshly cut longleaf pine logs placed in the plots for four years lost significantly less mass in annually burned plots than in unburned plots. The annual exponential decay coefficient estimate from all logs was 0.14 yr−1 (SE = 0.01), with the estimated times for 50 and 95% loss being 5 and 21.4 years, respectively. Termite presence was unaffected by frequent burning, suggesting they were able to survive the fires underground or within wood, and that winter burning did not deplete their food resources.

Applicability of TOPMODEL in the Catchments of Nepal: Bagmati River Basin

ABSTRACT TOPMODEL was applied to simulate runoff hydrograph in Bagmati River Basin. Digital Elevation Model (DEM), soil, land-use and other spatial data were analyzed using Geographic Information System (GIS). To account for spatial variability of precipitation, climate and land-use, the entire basin was divided into sub-basins and the model was run separately. Other additional computer codes have been developed for computing evapotranspiration and channel routing so as to apply TOPMODEL as a complete hydrological model for medium to large basin. Less sensitive or physically based parameters were directly measured from topographic and soil maps using looked up table, where as more sensitive parameters such as saturated transmissivity [ln(T0)] and exponential decay coefficient (m) to each sub-basin were calibrated by manual iterative method. However, subjective and objective methods were applied to test the goodness of fit of simulated hydro- graphs to observed hydrographs. The results are satisfactory with Nash efficiency as much as 84.8% in calibration and 82.5% in validation. The results showed annual peak, runoff volume, annual average wet and dry seasons flows simulation using the model were relatively reasonable. Most of the river basins of Nepal are steep to moderately steep sloped, densely vegetated and receives appreciable amount of frequent precipitation and hence TOPMODEL assumptions are valid. The limited available resources used to achieve these results showed that TOPMODEL will be applicable in medium to large spring fed catchments of Nepal.

Strong-coupling expansion for bosons on the kagome lattice

We use series-expansion techniques for analyzing properties of the phase transition between the Mott insulating and superfluid phase for bosons on the kagome lattice. The multicritical point in the ground-state phase diagram for unit filling is calculated. It is seen that, in a bond expansion, of the clusters that contribute with nonzero weights to the ground-state energy, many contain rings. The exponential decay coefficients of ground-state correlations are also obtained within the Mott phase. For excited properties, quasiparticle dispersion and effective masses for particles and holes are computed. Furthermore, at eighth order, the coherence-length critical exponent $\ensuremath{\nu}$ is found to be comparably close to that of the three-dimensional $XY$ model.

Hydrological storage and transmission characteristics of an alpine talus

AbstractAlpine watersheds are the source region of some of the largest rivers in North America and elsewhere. Understanding of hydrological processes in alpine watersheds is important for understanding the response of river basins to meteorological forcing. Talus units in alpine watersheds have been suggested in the literature as potential reservoirs of groundwater, but relatively little is known about hydrological processes in talus. To develop conceptual understanding of alpine talus and determine its storage capacity and hydraulic properties, we investigated a talus unit in the Lake O'Hara watershed in the Canadian Rockies using ground‐penetrating radar, electrical resistivity tomography, measurements of talus discharge, tracer tests, and isotopic hydrograph separation. The study talus, consisting mainly of quartzite and carbonate rock fragments, had very high hydraulic conductivity (0·01–0·03 m s−1) and fast hydrograph recession (exponential decay coefficient of 1 d−1), suggesting that its storage capacity is limited to a time scale of less than a week. Groundwater flow through the talus occurs in a relatively thin (0·01–0·1 m) saturated zone at the base of the talus, which appears to have discrete flow paths rather than a single continuous sheet. A late‐lying snowpack, located at the top of the talus and cliff ledges above, sustains baseflow discharging from the talus, which provides moisture to alpine meadows downstream. Although this study indicates limited storage capacity of talus, further research is required to examine the storage and transmission characteristics of talus consisting of different types of geological materials or formed in different environments. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Long-time behavior of nuclear spin decays in various lattices

The transverse NMR decays of $^{129}\mathrm{Xe}$ in polycrystalline xenon were recently shown to have a universal property: in the long-time regime these decays all converge to the same sinusoidally modulated exponential function irrespective of the initial transverse spin configuration prepared by a sequence of one or more radio frequency pulses. The present work constitutes a more comprehensive survey of this phenomenon. It examines transverse decays for several different isotopic concentrations of $^{129}\mathrm{Xe}$, employs additional pulse sequences, and performs similar measurements in a different material: $^{19}\mathrm{F}$ in single-crystal and polycrystalline CaF${}_{2}$. With the possible exception of polycrystalline CaF${}_{2}$ where the observation of the long-time behavior is limited by the experimental resolution, all these systems display the long-time universal behavior characterized by particular values of the exponential decay coefficient and beat frequency that were unique for each lattice. This behavior has been theoretically predicted based on the notion of microscopic chaos.

Intermolecular electronic coupling in organic molecular thin films measured by temperature modulation spectroscopy

Temperature modulation spectroscopy is used to obtain the temperature dependences of oscillator strength, exciton transition energy, and linewidth for a copper phthalocyanine thin film. With increasing temperature, the oscillator strength exhibits a pronounced decrease for charge transfer (CT) excitons, making this technique suitable for differentiating exciton types. From the measured magnitude and temperature dependence of the CT oscillator strength, we obtain estimates for the intermolecular electronic coupling and its exponential decay coefficient.