Logarithmic Decay Research Articles

Towards a Non-Destructive Method of Mapping the E-J Relation Using Force Decay Measurements on Superconducting Bulks

In many applications of high-temperature superconductivity, such as superconducting magnetic bearings, precise knowledge of the non-linear voltage-current (E-J) relation is necessary for making accurate quantitative predictions of performance. Magnetic microscopy allows the spatial mapping of coated conductor superconducting properties. There is no equivalent spatial mapping technique for bulk superconductors. A convenient method of mapping the E-J relation for superconductor bulks to be used in superconducting magnetic bearings is desired. The maglev force in a superconducting bearing decays logarithmically over time due to flux creep. The non-linear E-J behaviour describes this flux-creep behaviour and maximum force. It should, therefore, be possible to map the E-J power law of a bulk superconductor using levitation force decay characteristics. Using the H-formulation finite-element method we have simulated the levitation force decay under zero field cooled conditions and identified a relation between the logarithmic force decay parameters and the n-index of the E-J power law. This potentially offers a non-destructive method of determining the E-J relation in large superconducting bulks.

Surface properties of semiconductors from post-illumination photovoltage transient

Free surfaces of semiconductors respond to light by varying their surface voltage (surface band bending). This surface photovoltage may be easily detected using a Kelvin probe. Modeling the transient temporal behavior of the surface photovoltage after the light is turned off may serve as a means to characterize several key electronic properties of the semiconductor, which are of fundamental importance in numerous electronic device applications, such as transistors and solar cells. In this paper, we develop a model for this temporal behavior and use it experimentally to characterize layers and nanowires of several semiconductors. Our results suggest that what has previously been considered to be a logarithmic decay is a rather rough approximation. Due to the known limited frequency bandwidth of the Kelvin probe method, most previous Kelvin-probe-based methods have been limited to “slow responding” semiconductors. The model we propose extends this range of applicability.

Stability and Logarithmic Decay of the Solution to Hadamard-Type Fractional Differential Equation

In this paper, we study the stability and logarithmic decay of the solutions to fractional differential equations (FDEs). Both linear and nonlinear cases are included. And the fractional derivative is in the sense of Hadamard or Caputo–Hadamard with order $$\alpha \,(0<\alpha <1)$$ . The solutions can be expressed by Mittag–Leffler functions through applying the modified Laplace transform. In view of the asymptotic expansions of Mittag–Leffler function, we discuss the stability and logarithmic decay of the solution to FDEs in great detail.

Nitrogen in Atmospheric Wet Depositions Over the East Indian Ocean and West Pacific Ocean: Spatial Variability, Source Identification, and Potential Influences

Atmospheric deposition is the dominant pathway for the loading of exogenous nitrogen (N) to open ocean. Here, rainwater samples were collected from 31 stations in the equatorial East Indian Ocean (EIO) and West Pacific Ocean (WPO) to explore the spatial variability of N species, potential sources, and related ecological influences. Among two oceans, nitrate (NO3–) and ammonium (NH4+) were the main components in the rainwater N inventory. NO3–concentrations varied from 0.19 to 100.5 μM, whereas NH4+concentrations ranged from 0.54 to 110.6 μM. Among all stations, low concentrations of NO3–and NH4+appeared in the remote ocean, whereas high concentrations were observed at the stations near the Malacca Strait and New Guinea, coupled with an enhancement of non-sea salt major ions, e.g., calcium ions (Ca2+) and sulfate (SO42–), revealing the influence from coastal human activities, such as coal and gasoline combustion. In the remote ocean, δ15N–NH4+ranged from −5.7 to −9.3‰, whereas it dropped to -15.5‰ near coasts. A logarithmic decay between δ15N–NH4+and NH4+concentrations in rainwater samples was obtained, suggesting a shift from natural source (seawater emission) in oceanic precipitation events to anthropogenic source (chemical fertilizer volatilization and vehicle exhaust) in coastal rainwaters. δ15N–NO3–in the remote ocean varied between −1.7 and 0.4‰ with low levels found in the WPO, likely related to the ascending air flow driven by the Walker Circulation. In coastal oceans, δ15N–NO3–ranged from 1.5 to 3.5‰. The linkage between δ15N–NO3–and NO3–concentrations varied in two oceans, resulting from difference in biological and fossil fuel combustion contributions. Compared with ocean surface water, N in the rainwater was markedly enriched, suggesting that N from atmospheric wet depositions could rapidly enhance the dissolved N availability in ocean surface water. However, the N redundancy according to the Redfield–Brzezinski ratio (N:Si:P = 16:16:1) in the rainwater might benefit from the growth of N-preference phytoplankton species and microbes. As the first study on N concentrations, sources, and stoichiometry balance in rainwater over the equatorial WPO and EIO, the results could be a support to the global N budget estimation and oceanic primary production modeling.

Athermal sediment creep triggered by porous flow

Quasi-2D experiments of a submerged sediment layer creeping downward were performed, varying the channel tilt and a porous flow under the respective thresholds for yielding. Logarithmic decay rates of the deformation are observed, with the rate increasing with both control parameters. A new dimensionless parameter, $P^*$, accounting for both mean porous flow and gravity force effects on particle motion, allows a collapse of all the deformation results on a single curve. Two distinct creep regimes are identified, and correspond to a systematic change of the void size distribution as $P^*$ increases.

Slope filtrations of $F$-isocrystals and logarithmic decay

Slope filtrations of $F$-isocrystals and logarithmic decay

Logarithmic Decay for Linear Damped Hypoelliptic Wave and Schrödinger Equations

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 22 July 2020Accepted: 22 February 2021Published online: 20 May 2021Keywordsstability estimates, hypoelliptic operators, wave equation, resolvent estimates, approximate observabilityAMS Subject Headings35H10, 35B60, 35L05, 93B07, 93B05Publication DataISSN (print): 0363-0129ISSN (online): 1095-7138Publisher: Society for Industrial and Applied MathematicsCODEN: sjcodc

Proton Radioactivity of Heavy Nuclei of Atomic Number Range 72 &lt; Z &lt; 88

We have studied proton radioactivity of heavy nuclei of atomic number range 72 < Z < 88. We have calculated the energy released during the proton decay (QP) and half-lives of proton decay. To study the competition between different decay modes, we have compared the proton decay half lives with that of the decay modes such as alpha decay, beta decay, cluster decay and spontaneous fission. To check the Geiger–Nuttall law for proton decay, we have plotted the logarithmic proton decay half-lives versus 1/sqrt(Q). We have also highlighted possible proton emitters with the corresponding energies and half-lives in the atomic number range 72 < Z < 88.

On Cohesive Soil Damping Estimation by Free Vibration Method in Resonant Column Test

Abstract Measurement of soil properties under cyclic and dynamic loading conditions is a critical task in the solution of most geotechnical earthquake engineering problems. The main dynamic properties of soils are usually expressed in terms of shear modulus and damping ratio that are generally obtained from laboratory tests. To date, the resonant column test is considered one of the most accurate ways to determine dynamic soil properties at low to medium-strain levels. Because it allows for investigation of a wide range of strain amplitudes, it is a valuable tool for characterizing the shear soil behavior for a large number of practical geotechnical problems. One of the approaches followed in estimating the damping ratio from the resonant column test is the free vibration method (also called logarithmic decrement or amplitude decay method). It consists of analyzing the time history of the damped free vibrations of the specimen once harmonic loading is cut off after reaching the resonant conditions. The soil damping ratio is determined measuring the logarithmic ratio of the amplitude of any two successive peaks of the system damped motion (logarithmic decrement). In this article, the influence on the damping ratio of the shear strain level, the plasticity index, the confining pressure, and the time interval between the peaks selected in calculating the logarithmic decrement is evaluated from the results of resonant column tests performed on 51 undisturbed isotropically consolidated fine-grained soil specimens.

Localized Afterslip at Geometrical Complexities Revealed by InSAR After the 2016 Central Italy Seismic Sequence

AbstractThe Mw 6.5 Norcia earthquake occurred on 30 October 2016, along the Mt Vettore fault (Central Apennines, Italy), it was the largest earthquake of the 2016–2017 seismic sequence that started 2 months earlier with the Mw 6.0 Amatrice earthquake (24 August). To detect potential slow slip during the sequence, we produced Interferometric Synthetic Aperture Radar (InSAR) time series using 12‐ to 6‐day repeat cycles of Sentinel‐1A/1B images. Time series indicates that centimeter‐scale surface displacements took place during the 10 weeks following the Norcia earthquake. Two areas of subsidence are detected: one in the Castelluccio basin (hanging wall of the Mt Vettore fault) and one in the southern extent of the Norcia earthquake surface rupture, near an inherited thrust. Poroelastic and viscoelastic models are unable to explain these displacements. In the Castelluccio basin, the displacement reaches 13.2 ± 1.4 mm in the ascending line of sight on 6 January 2017. South of the Norcia earthquake surface rupture (a zone between the Norcia and Amatrice earthquakes), the postseismic surface displacements affect a smaller area but reach 35.5 ± 1.7 mm in ascending line of sight by January 2017 and follow a logarithmic temporal decay consistent with postseismic afterslip. Our analysis suggests that the structurally complex area located south of the Norcia rupture (30 October) is characterized by a conditionally stable frictional regime. This geometrical and frictional barrier likely halted rupture propagation during the Amatrice (24 August) and Norcia (30 October) earthquakes at shallow depth (&lt;3–4 km).

Mathematical Analysis and the Local Discontinuous Galerkin Method for Caputo–Hadamard Fractional Partial Differential Equation

In this paper, we study the Caputo–Hadamard fractional partial differential equation where the time derivative is the Caputo–Hadamard fractional derivative and the space derivative is the integer-order one. We first introduce a modified Laplace transform. Then using the newly defined Laplace transform and the well-known finite Fourier sine transform, we obtain the analytical solution to this kind of linear equation. Furthermore, we study the regularity and logarithmic decay of its solution. Since the equation has a time fractional derivative, its solution behaves a certain weak regularity at the initial time. We use the finite difference scheme on non-uniform meshes to approximate the time fractional derivative in order to guarantee the accuracy and use the local discontinuous Galerkin method (LDG) to approximate the spacial derivative. The fully discrete scheme is established and analyzed. A numerical example is displayed which support the theoretical analysis.

On the derivative nonlinear Schrödinger equation with weakly dissipative structure

We consider the initial value problem for cubic derivative nonlinear Schr\"odinger equation in one space dimension. Under a suitable weakly dissipative condition on the nonlinearity, we show that the small data solution has a logarithmic time decay in $L^2$.

Parametric imaging of ultrasonic backscatter of fixed sheep brain

Ultrasound backscatter properties of aggregate brain tissue are available in the literature, however, reporting on the spatial variation of backscatter over tissue volumes is limited. The spatial variation of the apparent integrated backscatter (AIB) and the logarithmic backscatter amplitude decay constant (BADCL) was characterized for 1-cm thick samples from the coronal, sagittal and transverse anatomic planes of fixed sheep brain. Submerged samples were exposed to ultrasound using broadband transducers with center frequencies of 3.5, 5.0, 7.5, and 10 MHz by scanning over the samples in half-beamwidth step sizes to measure the backscattered signal. Parametric images of the AIB and BADCL showed a clear correlation between morphological features in the tissue samples and the images with the AIB giving the better representation of the overall tissue structure. Over all samples and frequencies, the range of the spatial mean of the AIB was −77.7 to −59.8 dB with the standard deviation ranging from 3.14 to 6.99 dB. The spatial mean of the BADCL ranged from 0.0350 to 0.152 μs−1 with standard deviations ranging from 0.0820 to 0.111 μs−1. For both parameters, morphological features of the tissue become more distinctive with increasing frequency.

On the boundedness of Toeplitz operators with radial symbols over weighted sup-norm spaces of holomorphic functions

We prove sufficient conditions for the boundedness and compactness of Toeplitz operators Ta in weighted sup-normed Banach spaces Hv∞ of holomorphic functions defined on the open unit disc D of the complex plane; both the weights v and symbols a are assumed to be radial functions on D. In an earlier work by the authors it was shown that there exists a bounded, harmonic (thus non-radial) symbol a such that Ta is not bounded in any space Hv∞ with an admissible weight v. Here, we show that a mild additional assumption on the logarithmic decay rate of a radial symbol a at the boundary of D guarantees the boundedness of Ta. The sufficient conditions for the boundedness and compactness of Ta, in a number of variations, are derived from the general, abstract necessary and sufficient condition recently found by the authors. The results apply for a large class of weights satisfying the so called condition (B), which includes in addition to standard weight classes also many rapidly decreasing weights.

Logarithmic and exponential transients in GNSS trajectory models as indicators of dominant processes in postseismic deformation

Models for postseismic transient displacements can be formulated using logarithmic and exponential decay formulas with single or multiple timescales. The logarithmic form is associated with rate and state friction theory and afterslip, while the exponential form is associated with bulk viscoelastic relaxation of coseismic stresses. It is now quite widely understood that one can model GPS/GNSS time series manifesting postseismic transient displacements almost equally well using trajectory models constructed using logarithmic or exponential transients. This is consistent with the consensus established by the late 1970s that it is difficult to use geodetic observations to distinguish between deep aseismic afterslip and more diffuse viscoelastic relaxation as the primary mechanism of postseismic deformation. In this paper, we assess the relative explanatory value of both logarithmic and exponential forms by focusing on GNSS time series measured with better than typical signal-to-noise ratios. We find that the double logarithmic transient typically provides much better fits than double exponential transient, when both models are given equal degrees of freedom. We also discuss the relative utility of the hybrid transient formulas in which the logarithmic component is assigned shorter decay timescale parameters than the exponential component. These models fit observed postseismic displacements almost as well as double logarithmic transients.

Establishment of a hemiparasite Rhinanthus alectorolophus and its density‐dependent suppressing effect on a grass: A case study from golf roughs

AbstractSuppression effect of hemiparasites on grasses is a phenomenon, that can be utilized to increase biodiversity of various grassland systems. Host suitability, environmental effects, and hemiparasite abundance most likely influence the impact of parasitism on host height and biomass. However, the role of these factors is unclear in field conditions. We studied host suitability, establishment rates, and effects of a hemiparasitic plant Greater yellow rattle [ Rhinanthus alectorolophus (Scop.)] (RA) on canopy height and biomass of a grass tall fescue (Festuca arundinacea Schreb.) in five trials with manipulated fertilization conducted in golf roughs. Particularly, we examined how grass height and biomass changed with increasing hemiparasite abundance. On average, grasses (nine in total) were better hosts than legumes (four in total). Tall fescue belonged to the group of better hosts. The average establishment rate of Rhinanthus plants ranged from 4.4 to 24.8% regardless of fertilization treatments. In fertilization trials, Rhinanthus did not affect grass height but weakly suppressed grass biomass in non‐fertilized plots. The relationship between grass height/biomass and Rhinanthus abundance was best described by a logarithmic decay model. The suppressive effect tended to saturate (negative density dependence) in plots where the Rhinanthus abundance was very high. However, such high densities were quite rare and low Rhinanthus abundances were usually insufficient to substantially suppress grass growth. Our results indicate that we should aim for at least 50 Rhinanthus plants per 1 m2 to achieve desirable effects on biodiversity and that Rhinanthus performance will be better when nutrients are rather limiting.

Development of a Machine Learning-Based Damage Identification Method Using Multi-Point Simultaneous Acceleration Measurement Results.

It is necessary to assess damage properly for the safe use of a structure and for the development of an appropriate maintenance strategy. Although many efforts have been made to measure the vibration of a structure to determine the degree of damage, the accuracy of evaluation is not high enough, so it is difficult to say that a damage evaluation based on vibrations in a structure has not been put to practical use. In this study, we propose a method to evaluate damage by measuring the acceleration of a structure at multiple points and interpreting the results with a Random Forest, which is a kind of supervised machine learning. The proposed method uses the maximum response acceleration, standard deviation, logarithmic decay rate, and natural frequency to improve the accuracy of damage assessment. We propose a three-step Random Forest method to evaluate various damage types based on the results of these many measurements. Then, the accuracy of the proposed method is verified based on the results of a cross-validation and a vibration test of an actual damaged specimen.

Logarithmic Decay of Wave Equation with Kelvin-Voigt Damping

In this paper, we analyze the longtime behavior of the wave equation with local Kelvin-Voigt Damping. Through introducing proper class symbol and pseudo-diff-calculus, we obtain a Carleman estimate, and then establish an estimate on the corresponding resolvent operator. As a result, we show the logarithmic decay rate for energy of the system without any geometric assumption on the subdomain on which the damping is effective.

Cycloidal Rotor-Blade Tip-Vortex Analysis at Low Reynolds Number

This study provides the first in-depth analysis of the formation, strength, and convection of cycloidal rotor tip vortices. The measurements of blade force and tip vortex using particle image velocimetry were conducted for different blade aspect ratios and pitch kinematics at a chord-based Reynolds number of 18,000. Particle image velocimetry was employed to investigate vortex development at increasing vortex ages and the early development for varying azimuthal locations. The instantaneous blade force measurements on the cycloidal rotor showed a decrease in nondimensional lift with decreasing blade aspect ratio. The aspect ratio of the blade did not affect the shape of the vortex convection trajectory. However, the rate of downward convection increased with increasing aspect ratio due to the higher thrust produced. The tip vortices showed self-similarity in the velocity and the circulation profiles. The measurements indicate that the vortex core experiences a logarithmic growth and the swirl velocity experiences a logarithmic decay due to viscous diffusion. The tip-vortex strength varied cyclically with blade azimuthal location due to the cyclic variation of blade pitch angle and the dynamic virtual camber effects. This periodic variation in the tip-vortex strength leads to a periodic variation in the induced flow velocity on the blade.

Assessing Long‐Term Postseismic Transients From GPS Time Series in Southern California

AbstractIn order to gain insight into long‐term plate boundary motion and to shed light on geodetic‐based fault slip rates and the seismic hazards they inform, we apply a forward modeling strategy to identify and reduce the short‐ and long‐term effects of viscoelastic postseismic deformation on modern GPS observations following large magnitude earthquakes in Southern California. We assess ongoing postseismic deformation in the southwestern United States by analyzing all magnitude ≥Mw6.0 earthquakes that have occurred there and in Baja California and Sonora, Mexico, since year 1800, finding that ongoing postseismic displacements from 12 events are potentially contributing to the modern day deformation field in Southern California. With a forward modeling step, we calculate postseismic displacements associated with these 12 events using a reference model consisting of a layered, laterally homogeneous, viscoelastic Earth structure; these displacements are then subtracted from processed horizontal GPS coordinate time series data to produce a postseismic‐reduced data set. In order to quantify the success of this forward modeling in reducing the postseismic signal, we estimate parameters representing logarithmic decay associated with the 2010 Mw7.2 El Mayor‐Cucapah earthquake using two different time series analysis methods. Variance reduction indicates we were able to reduce postseismic deformation in this test case by up to 60%. Anomaly maps produced using our assessment of deformation around the El Mayor‐Cucapah event highlight hot spots in which secondary processes may be occurring or where a more complex viscosity structure may be necessary.