Logarithmic Decay Research Articles

Clock Fields and Logarithmic Decay of Dark Energy

We investigate the physical measurability of the infrared instability of a de Sitter phase in the formalism recently proposed. We find that the logarithmic decay of the effective cosmological constant is only measurable if an additional clock field is introduced.

Early postseismic slip of the 21 November 2022 Mw 5.6 Cianjur, Indonesia, earthquake based on GPS measurements

ABSTRACT Global Positioning System (GPS) data after the 21 November 2022 Mw 5.6 Cianjur earthquake are crucial for understanding the physical processes during the postseismic phase. New continuous GPS stations were installed and recorded data for periods ranging from five to twenty-five days after the mainshock. The daily time series data at GPS stations shows an evolving logarithmic decay over time, as expected due to frictional afterslip. We inverted the postseismic displacement data to solve the postseismic slip distribution, utilising Akaike’s Bayesian information criterion. A cumulative aseismic slip moment of 1.54 × 1016 N·m, equivalent to Mw 4.7, is modelled during the period from five to twenty-five days after the mainshock. This aseismic slip moment is equivalent to approximately 7% of the seismic moment during the mainshock. Our analysis on the newly identified active fault using GPS displacements highlights the imperative need to identify active faults prior to future earthquake occurrences, especially when conducting hazard mitigation in populated regions in Indonesia.

Rail pad damping characteristics in track vibration reduction evaluated through hammer tests and theoretical analysis

Although the majority of existing research addresses the stiffness characteristics of rail pads, the considerable impact of damping on vibration reduction underscores its significant research importance. In this study, the hammer test and theoretical calculation are both employed to assess the damping capacity across three rail pad types: prismatic (PRP), grooved (GRP), and mesh-type high-damping (MTHDRP). Through the hammer test, the MTHDRP notably surpassed GRP and PRP, achieving higher damping ratios by 51.40 % and 49.71 %, respectively, leading to significant vibration reductions in the track bed and rail. Comparison tests between three types of rail pads highlighted the enhanced performance of the MTHDRP, as it not only reduced vibration amplitudes and enhanced decay rates but also decreased vibration levels by 2−5 dB. Moreover, we established a refined finite element model of the fastener system and integrated it with the Logarithmic Decay Rate (LDR) method. Our findings demonstrate that this combination facilitates the calculation of the damping ratio of the rail pad. Furthermore, we conducted a comparative analysis between the LDR method and the envelope method, confirming its superior efficiency and reliability. Finally, the LDR method is used to predict the damping ratio of the rail pad with varying stiffness, showing that the softer the rail pad, the higher the corresponding damping ratio. Overall, our insights bridge the gap in theoretical calculations and experimental studies on rail pad damping characteristics, offering crucial guidance for rail pad selection in track vibration mitigation.

Optimization of Pin Fins Using Computational Fluid Dynamics and Machine Learning

This paper presents a two-part study focusing on the optimization of pin-fin arrays for gas turbine blade cooling. The first part of the study examines the thermal performance of various pin-fin shapes and sizes using computational fluid dynamics. The study investigates circular, elliptical, hexagonal, and rectangular cross sections, with emphasis on the hydraulic diameter and Reynolds number. Two-dimensional simulations mimicked a confined, staggered array of uniform-sized pins under different inlet conditions. For a hydraulic diameter of 0.053 m and a Reynolds number of 5500, the rectangular pins showed the highest Nusselt number 8.98, 16.01, and 20.62% larger than circular, elliptical, and hexagonal pins, respectively, but also a pressure increase 68.30% higher on average. For a hydraulic diameter of 0.046 m and a Reynolds number of 1000–15,000, it was shown that all shapes have an exponential increase in pressure and a logarithmic decay in the Nusselt number. Standing out was the rectangular shape, which, at a maximum Reynolds number of 15,000, had a pressure increase of 108% larger than the next in line, the hexagonal pin. In the same range of inlet conditions, the Gee–Webb coefficient was the highest for the circular pin, which was selected as the main shape for the following segment. In the second part of the study, a machine learning framework based on a neural network architecture is presented. The neural network predicts the thermal performance of different pin-fin array configurations. At the end, this framework is used in an optimization process that explores the advantages of nonuniform arrays consisting of differently sized circular pins as opposed to the standard uniform structures of the first part. The model proves to be capable of accurately predicting the characteristic thermal performance coefficients across a wide range of input parameters. The nonuniform array managed a 23% reduction in pressure rise at a 0.2% exit temperature increase compared to a reference standard array of the same hydraulic diameter.

Nine is the New Ten of Apgar Scores: An Observational Retrospective Cohort Study

Apgar scores of 10 were once common but are now rare. We aggregated scores from US term infants from 1978 to 2021. We found that scores of 10 decreased by logarithmic decay independent of demographic changes. We hypothesize that this trend was driven by improved appreciation of transitional physiology.

A Critical Review of the Propagation Models Employed in LoRa Systems.

LoRa systems are emerging as a promising technology for wireless sensor networks due to their exceptional range and low power consumption. The successful deployment of LoRa networks relies on accurate propagation models to facilitate effective network planning. Therefore, this review explores the landscape of propagation models supporting LoRa networks. Specifically, we examine empirical propagation models commonly employed in communication systems, assessing their applicability across various environments such as outdoor, indoor, and within vegetation. Our investigation underscores the prevalence of logarithmic decay in most empirical models. In addition, we survey the relationship between model parameters and environmental factors, clearing their nuanced interplay. Analyzing published measurement results, we extract the log-distance model parameters to decipher environmental influences comprehensively. Drawing insights from published measurement results for LoRa, we compare them with the model's outcomes, highlighting successes and limitations. We additionally explore the application of multi-slope models to LoRa measurements to evaluate its effectiveness in enhancing the accuracy of path loss prediction. Finally, we propose new lines for future research in propagation modelling to improve empirical models.

A Logarithmic Decay of the Energy for the Hyperbolic Equation with Supercritical Damping

A Logarithmic Decay of the Energy for the Hyperbolic Equation with Supercritical Damping

Photoswitchable Temperature Nanosensors Based on the Chemical Kinetics of Photochromic Naphthopyran for Live Cell Imaging.

Microscopic temperature imaging holds significant importance in various fields, particularly in the development of nanomaterials for photothermal therapy (PTT). In this study, we present an analytical method to probe cellular temperature based on chemical kinetics and additional luminescence quenching by photoswitchable naphthopyrans. Taking advantage of the rapid ring-closing reaction of naphthopyran, temperature sensing was realized with a linear relationship between the logarithmic decay time constant (ln τ) and the reciprocal temperature (T-1). To create luminescent temperature nanosensors, we harnessed the ability of ring-opened naphthopyran to quench the luminescence of a semiconducting polymer, resulting in a diverse array of probes. Structural modifications on the naphthopyran also provided a way to fine-tune the sensitivity and response window of the nanosensors. The method allowed cellular temperature imaging on a cost-effective fluorescence microscopic setup. As an application, the temperature increase induced by gold nanorods (AuNRs) in cell lysosomes was successfully monitored, laying the foundation for a new class of photoswitchable nanosensors with promising biological applications.

Minimax Regret Robust Screening with Moment Information

Problem definition: We study a robust screening problem where a seller attempts to sell a product to a buyer knowing only the moment and support information of the buyer’s valuation distribution. The objective is to maximize the competitive ratio relative to an optimal hindsight policy equipped with full valuation information. Methodology/results: We formulate the robust screening problem as a linear programming problem, which can be solved efficiently if the support of the buyer’s valuation is finite. When the support of the buyer’s valuation is continuous and the seller knows the mean and the upper and lower bounds of the support for the buyer’s valuation, we show that the optimal payment is a piecewise polynomial function of the valuation with a degree of at most two. Moreover, we derive the closed-form competitive ratio corresponding to the optimal mechanism. The optimal mechanism can be implemented by a randomized pricing mechanism whose price density function is a piecewise inverse function adjusted by a constant. When the mean and variance are known to the seller, we propose a feasible piecewise polynomial approximation of the optimal payment function with a degree of at most three. We also demonstrate that the optimal competitive ratio exhibits a logarithmic decay with respect to the coefficient of variation of the buyer’s valuation distribution. Managerial implications: Our general framework provides an approach to investigating the value of moment information in the robust screening problem. We establish that even a loose upper bound of support or a large variance can guarantee a good competitive ratio. Funding: The research of S. Wang is partially supported by the National Natural Science Foundation of China [Grant 72394395]. The research of S. Liu is partly supported by the National Natural Science Foundation of China [Grant NSFC-72072117]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0072 .

New energy decay for a nonlinearly damped system of wave equations

AbstractIn this paper, a nonlinearly damped system of wave equations is considered. Uniform energy decay was discussed in the previous work (Discrete Contin. Dyn. Syst. Ser. S, 2 (2009) 583–608) for if the space dimension is 3. New energy decay is proposed for by choosing appropriate multiplier related to a non‐increasing differential function. As an example, a logarithmic energy decay is also presented.

Research on the Dynamic Characteristics of Cantilever Rotor System With ISFD

Aiming at the common vibration problem of the cantilever rotor system and the nonlinear problem of traditional squeeze film damper (SFD), an integral squeeze film damper (ISFD) for the cantilever rotor system was proposed based on the traditional SFD. In order to investigate the effect of the ISFD on the dynamic characteristics of the cantilever rotor system, the vibration reduction experiment of the rotor system was carried out. The mechanical model and finite element model of the cantilever rotor system were established. The first‐order critical speed, strain energy, stability, and steady‐state response of the cantilever rotor system were numerically analyzed. Experimental research on the vibration reduction of the cantilever rotor system by the ISFD under different unbalance conditions and different rotational speed conditions was carried out on the test rig of the cantilever rotor system. The results showed that the ISFD has remarkable performance, which can reduce the bending deformation and strain energy of the rotating shaft, increase the logarithmic decay rate, and improve the overall stability of the system. Under various working conditions, the ISFD can effectively suppress the unbalanced vibration of the rotor and the shaft center displacement of the rotor, and the amplitude of the rotor system at the working frequency (1X) is greatly reduced.

Equivalence between the energy decay of fractional damped Klein–Gordon equations and geometric conditions for damping coefficients

We consider damped s s -fractional Klein–Gordon equations on R d \mathbb {R}^d , where s s denotes the order of the fractional Laplacian. In the one-dimensional case d = 1 d = 1 , Green (2020) established that the exponential decay for s ≥ 2 s \geq 2 and the polynomial decay of order s / ( 4 − 2 s ) s/(4-2s) hold if and only if the damping coefficient function satisfies the so-called geometric control condition. In this note, we show that the o ( 1 ) o(1) energy decay is also equivalent to these conditions in the case d = 1 d=1 . Furthermore, we extend this result to the higher-dimensional case: the logarithmic decay, the o ( 1 ) o(1) decay, and the thickness of the damping coefficient are equivalent for s ≥ 2 s \geq 2 . In addition, we also prove that the exponential decay holds for 0 > s > 2 0 > s > 2 if and only if the damping coefficient function has a positive lower bound, so in particular, we cannot expect the exponential decay under the geometric control condition.

Water vapor transport through bioenergy grass residues and its effects on soil water evaporation

AbstractMiscanthus is a productive perennial grass that is suitable as a bioenergy crop in “marginal” lands (e.g., eroded soils) with low water holding capacity. However, little is known about the impact of miscanthus residues on vapor transport and soil water budgets. Laboratory experiments were conducted to measure the vapor conductance through miscanthus residues and its effect on soil water evaporation. The ranges for the length, width, and thickness of residue elements were 0.5–9.0, 0.1–0.5, and 0.1–0.5 cm, respectively. Average residue areal, bulk, and skeletal densities were 0.88 kg m−2, 24 kg m−3, and 1006 kg m−3, respectively, giving a porosity of 0.98 m3 m−3. A power function described the decrease in conductance with increasing residue load. The corresponding conductance for a residue load of 0.88 kg m−2 was 1.6 mm s−1. During the first days of a 60‐day drying experiment, cumulative evaporation showed logarithmic decay with increasing residue load. Conversely, cumulative evaporation during the last days of the study showed little difference between treatments. Measurements indicated that there is a “critical” residue load (∼1.0 kg m−2) beyond which evaporation no longer decreases appreciably when the soil is under the stage 1 evaporation regime. Results suggest that soil water conservation in marginal lands may be accomplished by maintaining moderate amounts of bioenergy grass residue covering the soil. Determining “critical” loads for different residue types is a knowledge gap that merits further research.

Experimental investigation and strength model of rough ice-filled joints under tensile and shear loading

Warming softening of ice-filled joints has caused many rockfall disasters in cold regions. A series tensile and shear strength tests were conducted to investigate the thawing softening mechanism of ice-filled joints by considering the effect of the joint opening, temperature and roughness. The joint opening has little influence on the tensile strength of ice-filled joints, but the temperature is a remarkable influencing factor. When the temperature increases from −15 °C to −0.5 °C, the average tensile strength of ice-filled joint reduces from 0.64 MPa to 0.22 MPa, which displays a constant logarithmic decay function against the freezing temperature and it is similar to the change rule of pure ice. The shear strength of the ice-filled joint decreases with increasing the infill thickness, and tends to be the shear strength of pure ice beyond the critical infilling thickness. In addition, all the tensile failures are inside the joint ice, however, the shear failure is mainly caused by the debonding of ice-rock interface when the temperature increases to −0.5 °C. It implies that the tensile bonding strength of ice-rock interface also is larger than that of the solid ice itself even at a high freezing temperature. Based on the experimental results, a new shear strength model of the ice-filled joint is proposed for Barton's joint profiles by considering the effect of temperature and infill thickness. It has been validated that this model is accurate to predict the shear strength of ice-filled joint, which may be used to estimate the stability of freezing joint rock slope in cold regions.

A remark on the logarithmic decay of the damped wave and Schrödinger equations on a compact Riemannian manifold

In this paper, we consider a compact Riemannian manifold (M,g) of class C^1 \cap W^{2,\infty} and the damped wave or Schrödinger equations on M , under the action of a damping function a = a(x) . We establish the following fact: if the measure of the set \{ x \in M; \, a(x) \not = 0 \} is strictly positive, then the decay in time of the associated energy is at least logarithmic.

Comparative study of the dynamics of colloidal glass and gel.

We investigate and compare the difference in the dynamics of two arrested states: colloidal glass and colloidal gel. Real-space experiments reveal two distinct nonergodicity origins for their slow dynamics, namely, cage effects for the glass and attractive bondings for the gel. Such distinct origins lead to a faster decay of the correlation function and a smaller nonergodicity parameter of the glass than those of the gel. We also find that the gel exhibits stronger dynamical heterogeneity compared with the glass due to the greater correlated motions in the gel. Moreover, a logarithmic decay in the correlation function is observed as the two nonergodicity origins merge, consistent with the mode coupling theory.

Function Model Based on Nonlinear Transient Rheology of Rocks: An Analysis of Decadal GNSS Time Series After the 2011 Tohoku‐oki Earthquake

AbstractThe postseismic Global Navigation Satellite System (GNSS) time series after the 2011 Tohoku‐oki earthquake is often empirically explained by one or more logarithmic and exponential decay functions. However, a function model with these decay functions struggles to illuminate various deformation mechanisms. Here, we propose a new function model incorporating laboratory‐derived constitutive laws (power‐law flow and velocity‐strengthening friction) utilized in mechanical postseismic models of the last decade. We demonstrated that our function model accurately predicts the decade‐long time series of inland GNSS stations, including coastal areas where significant postseismic uplift continues now. Moreover, it decomposes them into displacements due to viscoelastic relaxation and afterslip, similar to results produced by previous stress‐dependent postseismic models of the 2011 Tohoku‐oki earthquake. This physics‐based function model is an effective tool to ease the process of forecasting long‐term GNSS time series by dividing them into two dominant mechanisms at the plate interface and the surrounding viscoelastic mantle.

Structural Damping Ratio Identification through Iterative Frequency Domain Decomposition

The frequency domain decomposition method (FDD) is a commonly used method to identify structural modal parameters and analyze the structural dynamic performance. Although FDD has a high identification accuracy in natural frequencies and mode shapes, damping ratios cannot be identified accurately. The logarithmic decay method to identify the damping ratio in FDD needs the transformation from a narrow frequency band to the time domain, which leads to the loss of the corresponding mode outside the narrow band and add other modes in the narrow band. In this paper, an iterative frequency domain decomposition method (iFDD) is proposed to identify the structural damping ratio in frequency domain. Firstly, the natural frequencies and mode shapes are obtained by the FDD method, and the damping ratios during this identification process are assumed to be unknowns. Then, the natural frequencies, mode shapes, and unknowns are substituted into the output power spectrum formula to construct nonlinear equations. The damping ratios are obtained by solving the equations using iterative optimization methods. Finally, a numerical example and benchmark model are employed to validate the effectiveness of the proposed method. The results showed that the proposed iFDD method can identify the damping ratio precisely in the frequency domain, which is better than the traditional FDD performance.

Logarithmic Stabilization of an Acoustic System with a Damping Term of Brinkman Type

We study the problem of stabilization for the acoustic system with a spatially distributed damping. Without imposing any hypotheses on the structural properties of the damping term, we identify logarithmic decay of solutions with growing time. Logarithmic decay rate is shown through a new Carleman estimate which allows us to carry out a special analysis for the resolvent.

A dynamic Bayesian-based comprehensive trust evaluation model for dispersed computing environment

Dispersed computing is a new resource-centric computing paradigm. Due to its high degree of openness and decentralization, it is vulnerable to attacks, and security issues have become an important challenge hindering its development. The trust evaluation technology is of great significance to the reliable operation and security assurance of dispersed computing networks. In this paper, a dynamic Bayesian-based comprehensive trust evaluation model is proposed for dispersed computing environment. Specifically, in the calculation of direct trust, a logarithmic decay function and a sliding window are introduced to improve the timeliness. In the calculation of indirect trust, a random screening method based on sine function is designed, which excludes malicious nodes providing false reports and multiple malicious nodes colluding attacks. Finally, the comprehensive trust value is dynamically updated based on historical interactions, current interactions and momentary changes. Simulation experiments are introduced to verify the performance of the model. Compared with existing model, the proposed trust evaluation model performs better in terms of the detection rate of malicious nodes, the interaction success rate, and the computational cost.