Energy Decay Research Articles

Control of a nonlinear wave equation with a dynamic boundary condition

Existence, uniqueness, energy decay, and approximate numerical solution for the nonlinear wave equation with dynamic control at the boundary is being studied in this work. The theoretical analysis of the problem will be conducted using the Faedo-Galerkin method and compactness results. To obtain the approximate numerical solution, a combined approach of the finite element method and a finite difference method will be employed, known as the linearized Crank-Nicolson Galerkin method. This method optimizes the calculations and preserves the quadratic order of convergence in time. Finally, numerical experiments are performed, and tables and graphs are presented to illustrate the theoretical convergence rates and demonstrate the consistency between theoretical and numerical results.

Decay of secondary electron yield of MgO–Au composite film at different incident electron energies

The relationship between the incident electron energy and secondary electron yield (SEY) decay of MgO–Au composite film was investigated by the designed comparison experiments. Besides the incident current and the properties of the film, the SEY value and the incident electron energy were found to be the other two key factors affecting the SEY decay rate. The value of SEY and the incident electron energy have opposite influences on the SEY decay rate, which makes it necessary to analyze the curve of incident electron energy versus SEY decay rate by dividing it into three parts. In addition, the empirical formulas for SEY decay were derived from experimental data, enabling the estimation of the SEY and decay rate of the MgO–Au composite film at any moment during SEY decay. Furthermore, the cause of SEY decay was also analyzed based on the relationship between incident electron energy and the SEY decay rate. The thermal dissipation, surface roughness, and deposition of contaminants were proven not to be the determinants of SEY decay. The experiment results in this paper supported the inference that the charging effect was the primary cause of SEY decay.

Existence and stability of a weakly damped laminated beam with a nonlinear delay

AbstractA weakly damped laminated beam system with nonlinear time delay is studied. The existence and uniqueness are proved by Faedo–Galerkin approach. We prove that the system is stable under some specific conditions on the weight of the delay and the equal wave speeds of propagation. The general energy decay rate is established by using multiplier method and some properties of convex functions. This decay result is obtained without imposing any restrictive growth assumption on the damping term at the origin. In addition, our result improves and develops some existing results in the literature.

Long time behavior for the two-dimensional magnetohydrodynamic flows in a general domain

By utilizing spectral analysis methods and properties of fractional order operators, some new estimates have been established for the nonlinear terms appearing from the two-dimensional non-stationary magnetohydrodynamic flows in a general domain. Based on these, a series of energy decay properties are given. Furthermore, the large time decay behavior of the solution and that of its gradient have also been addressed in the L∞ and L2 spaces, respectively.

Unveiling Anomalies in Terrain Elevation Products from Spaceborne Full-Waveform LiDAR over Forested Areas

Anomalies displaying significant deviations between terrain elevation products acquired from spaceborne full-waveform LiDAR and reference elevations are frequently observed in assessment studies. While the predominant focus is on “normal” data, recognizing anomalies within datasets obtained from the Geoscience Laser Altimeter System (GLAS) and the Global Ecosystem Dynamics Investigation (GEDI) is essential for a comprehensive understanding of widely used spaceborne full-waveform data, which not only facilitates optimal data utilization but also enhances the exploration of potential applications. Nevertheless, our comprehension of anomalies remains limited as they have received scant specific attention. Diverging from prevalent practices of directly eliminating outliers, we conducted a targeted exploration of anomalies in forested areas using both transmitted and return waveforms from the GLAS and the GEDI in conjunction with airborne LiDAR point cloud data. We unveiled that elevation anomalies stem not from the transmitted pulses or product algorithms, but rather from scattering sources. We further observed similarities between the GLAS and the GEDI despite their considerable disparities in sensor parameters, with the waveforms characterized by a low signal-to-noise ratio and a near exponential decay in return energy; specifically, return signals of anomalies originated from clouds rather than the land surface. This discovery underscores the potential of deriving cloud-top height from spaceborne full-waveform LiDAR missions, particularly the GEDI, suggesting promising prospects for applying GEDI data in atmospheric science—an area that has received scant attention thus far. To mitigate the impact of abnormal return waveforms on diverse land surface studies, we strongly recommend incorporating spaceborne LiDAR-offered terrain elevation in data filtering by establishing an elevation-difference threshold against a reference elevation. This is especially vital for studies concerning forest parameters due to potential cloud interference, yet a consensus has not been reached within the community.

Eliminating Charge Transfer at Cathode-Electrolyte Interface for Ultrafast Kinetics in Na-Ion Batteries.

Sodium-ion batteries suffer from kinetic problems stemming from sluggish ion transport across the electrode-electrolyte interface, causing rapid energy decay during fast-charging or low-temperature operation. One exciting prospect to enhance kinetics is constructing neuron-like electrodes that emulate fast signal transmission in a nervous system. It has been considered that these bioinspired designs enhance electron/ion transport of the electrodes through carbon networks. However, whether they can avoid sluggish charge transfer at the electrode-electrolyte interface remains unknown. By connecting the openings of carbon nanotubes with the surface of carbon-coated Na3V2O2(PO4)2F cathode nanoparticles, here we use carbon nanotubes to trap Na+ ions released from the nanoparticles during charge. Therefore, Na+ movement is confined only inside the neuron-like cathode, eliminating ion transport between the electrolyte and cathode, which has been scarcely achieved in conventional batteries. As a result, a 14-fold reduction in interfacial charge transfer resistance is achieved when compared to unmodified cathodes, leading to superior fast-charging performance and excellent cyclability up to 200C, and surprisingly, reversible operation at low temperatures down to -60 °C without electrolyte modification, surpassing other Na3V2O2(PO4)2F-based batteries reported to date. As battery operation has relied on charge transfer at the electrode-electrolyte interface for over 200 years, our approach departs from this traditional ion transport paradigm, paving the way for building better batteries that work under harsh conditions.

Data-driven room acoustic modeling via differentiable feedback delay networks with learnable delay lines

Over the past few decades, extensive research has been devoted to the design of artificial reverberation algorithms aimed at emulating the room acoustics of physical environments. Despite significant advancements, automatic parameter tuning of delay-network models remains an open challenge. We introduce a novel method for finding the parameters of a feedback delay network (FDN) such that its output renders target attributes of a measured room impulse response. The proposed approach involves the implementation of a differentiable FDN with trainable delay lines, which, for the first time, allows us to simultaneously learn each and every delay-network parameter via backpropagation. The iterative optimization process seeks to minimize a perceptually motivated time-domain loss function incorporating differentiable terms accounting for energy decay and echo density. Through experimental validation, we show that the proposed method yields time-invariant frequency-independent FDNs capable of closely matching the desired acoustical characteristics and outperforms existing methods based on genetic algorithms and analytical FDN design.

Modelling uncertainty in P-wave arrival-times retrieved from DAS data: case-studies from 15 fibre optic cables

SUMMARY Distributed acoustic sensing (DAS) technology enables the detection of waves generated by seismic events, generally as uniaxial strain/strain rate time-series observed for dense, subsequent, portions of a Fibre Optic Cable (FOC). Despite the advantages in measurement density, data quality is often affected by uniaxial signal polarization, site effects and cable coupling, beyond the physical energy decay with distance. To better understand the relative importance of these factors for data inversion, we attempt a first modelling of noise patterns affecting DAS arrival times for a set of seismic events. The focus is on assessing the impact of noise statistics, together with the geometry of the problem, on epicentral location uncertainties. For this goal, we consider 15 ‘real-world’ cases of DAS arrays with different geometry, each associated with a seismic event of known location. We compute synthetic P-wave arrival times and contaminate them with four statistical distributions of the noise. We also estimate P-wave arrival times on real waveforms using a standard seismological picker. Eventually, these five data sets are inverted using a Markov chain Monte Carlo method, which offers the evaluation of the relative event location differences in terms of posterior probability density (PPD). Results highlight how cable geometry influences the shape, extent and directionality of the PPDs. However, synthetic tests demonstrate how noise assumptions on arrival times often have important effects on location uncertainties. Moreover, for half of the analysed case studies, the observed and synthetic locations are more similar when considering noise sources that are independent of the geometrical characteristics of the arrays. Thus, the results indicate that axial polarization, site conditions and cable coupling, beyond other intrinsic features (e.g. optical noise), are likely responsible for the complex distribution of DAS arrival times. Overall, the noise sensitivity of DAS suggests caution when applying geometry-only-based approaches for the a priori evaluation of novel monitoring systems.

Revision of Sabine's and Eyring's reverberation theories

Sabine's and Eyring's reverberation theories are still the most important theoretical frameworks for room acoustics. The important physical quantities derived from these theories are the average sound pressure level (sound energy density) and the reverberation time (sound energy decay). Eyring revised Sabine's theory to become the reverberation time zero in the perfect absorption condition. However, Eyring's theory has contradictions regarding the sound energy density in a steady state and the energy decay from the steady state. In this study, in order to resolve these contradictions, the theoretical framework for the consistent system is presented introducing the new concept of the average impulse response in a room, and the contradictions in the current room acoustic theory are clarified. Based on the theoretical framework, Sabine's reverberation theory is revised by a different way of Eyring's theory. The reverberation time of the revised theory is shorter than that of Sabine's theory and longer than that of Eyring's theory. Finally, ray-tracing computer simulations were performed to verify the revised theory. Results of sound ray tracing simulations were in better agreement with the values calculated using the revised theory rather than those calculated using Sabine's and Eyring's theories.

Experimental encircling of an exceptional point in a two degrees of freedom system: overview and application to noise control

When a resonator is added to an acoustic cavity or a vibrating structure, a new resonance frequency, or pole, is created in the system. When dissipation is present, this may breakdown when some parameters are finely tuned. This phenomenon, typical of non-Hermitian dynamics is called an exceptional point in the parametric space where two (or more) eigenvalues, as well as their associated eigenvectors, coalesce. In the recent years, EPs have gained interest in physics because of the counter-intuitive concepts associated with them. In the fields of acoustics and vibration, understanding EP may lead to a better comprehension of modal energy exchanges and decay. This work aims at exploring the key concepts related to EPs by revisiting the well-known coupled pendulums problem in the presence of damping. First, the free response of the experimental system is investigated after tuning it on an EP. Then an encircling is performed by varying the parameters through time. Our experimental results illustrate in a pedagogical manner nearly-optimal dissipation, energy exchange and chirality effects which have been recently evidenced in physics.

Evaluating the effect of dome geometry on acoustical quality of a pavilion

Acoustic performance of structures is an emerging field of research enquiry, with limited number of studies conducted in the Indian context. To address this gap, this study examines the effect of varied dome geometry on the acoustic quality of a pavilion. In-situ measurements pertaining to energy decay curve from impulse sound were collated at a historical 'Baradari'. The square shaped pavilion considered in the study is surmounted by a shallow dome and has three doorways on each side. Virtual simulation models of the pavilion were built thereafter and validated. In this study, dome geometries that emerged between the 15th-19th century (corbelled, shallow, single-shell, bulbous, and onion) in the Indian subcontinent are examined. Acoustic simulation was conducted on treble software to assess and compare the sound quality of each dome geometry. The study found that the reverberation, RT30, for the flat dome was approximately half to that of the single-shell dome. The study established that the choice of dome geometry is crucial as it impacts the reverberation time. The study findings vary with building typology, size, and architectural features. Nevertheless, this study should be viewed as a case-specific analysis that identifies optimal dome geometry for improved pavilion acoustics.

Proper orthogonal decomposition of wall-bounded high-pressure transcritical fluids

This study explores the principal modes of high-pressure transcritical channel flow from direct numerical simulation data. The four cases investigated correspond to CO2 at high-pressure conditions (P/Pc=1.5) confined between a cold/bottom wall (T/Tc=0.8−0.95) and a hot/top wall (T/Tc=1.1−1.4); Pc and Tc correspond, respectively, to the pressure and temperature of the critical point. The bulk velocity ranges between Ub=0.5−1.0 m/s with corresponding bulk Reynolds numbers of Reb≈1000−2500. The four cases considered are first characterized into laminar and turbulent regimes, followed by an analysis of energy decay using singular value decomposition. This method allows us to identify the most energetic modes of velocity, temperature, and specific isobaric heat capacity for the laminar and turbulent cases considered. The results reveal that fewer modes are needed to represent the hydrodynamics compared to the thermodynamics of the system. The findings also highlight that the pseudo-boiling region, prevalent in high-pressure transcritical systems, disrupts the coherent structures formed (especially) in the hotter region of the flow. Finally, a correlation analysis between the most energetic modes shows an interdependence between velocity and specific isobaric heat capacity modes when conditioned to focus solely on the pseudo-boiling affected regions. This correlation underscores the complex interplay between hydrodynamic and thermodynamic variables in such high-pressure transcritical environments.

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.

Analysis of vibration signals near ground surface during blasting excavation of a tunnel in fractured rock

This study aims to analyze the vibration signals near the ground surface due to the underneath drilling and blasting activities in a fissured rock tunnel. Blasting induced vibration on the ground surface was continuously monitored in a fissured rock tunnel drilling and blasting excavation project in field. Wavelet packet analysis of the vibration signals using Matlab was carried out for signal denoising, differential blasting delay time interval identification, and three-way time-frequency energy analysis. The results show that within a 30 m range from the palm face, the dominant frequency bands of blasting-induced vibrations on the ground surface were concentrated in the range of 0–130 Hz. Two prominent peak frequency bands were identified at 31.25–39.063 Hz (low-frequency band) and 93.75–101.56 Hz (high-frequency band), accounting for 12% of the total energy. Among the three directions of ground surface vibrations, the energy decay was the most significant in the x-direction (tunnel excavation direction), which amounted to 54.29% of the overall energy decay with increasing distance. The energy decay within the 50–80 Hz range was the most pronounced (more than 90%), when the angle between the vibration propagation direction and the fissure or joint direction was 75°. The conclusions provide the insights in the attenuation of blast-induced vibrations in fissured rock and can potentially assist in the design of blasting vibration control.

Polynomial decay of the energy of solutions of coupled wave equations with locally boundary fractional dissipation

In this paper, we investigate a system of coupled wave equations featuring boundary fractional damping applied to a portion of the domain. We first establish the well-posedness of the system, proving the existence and uniqueness of solutions through semi-group theory. While the system does not exhibit exponential stability, we demonstrate its strong stability. Furthermore, leveraging Arendt and Batty’s general criteria and certain geometric conditions, we prove a polynomial rate of energy decay for the solutions.

Physical-space estimates for axisymmetric waves on extremal Kerr spacetime

We study axisymmetric solutions to the wave equation on extremal Kerr backgrounds and obtain integrated local energy decay (or Morawetz estimates) through an analysis exclusively in physical-space. Boundedness of the energy and Morawetz estimates for axisymmetric waves in extremal Kerr were first obtained by Aretakis [13] through the construction of frequency-localized currents used in particular to express the trapping degeneracy. Here we extend to extremal Kerr a method introduced by Stogin [63] in the sub-extremal case, simplifying Aretakis' derivation of Morawetz estimates through purely classical currents.

Separation of Intrinsic and Scattering Seismic Wave Attenuation in the Crust of Central and South-Central Alaska

ABSTRACT Seismic hazard analysis is essential for evaluating the potential consequences and dangers linked to earthquakes, particularly in areas with regular seismic activity such as central and south-central Alaska. A detailed study of attenuation can help in better defining the wave behavior and so refine the ground-motion prediction. Here, we examined the scattering (Qs−1), intrinsic (Qi−1), and coda-wave (Qc−1) attenuation in central and south-central Alaska. To do so, we performed the multiple lapse time-window analysis (MLTWA) techniques and estimated the coda energy decay. We considered earthquakes that occurred between December 2014 and December 2020, with magnitudes between 2.0 and 6.5. We observed significant spatial variations in scattering loss (Qs−1) up to 3 Hz, which diminish at 6 and 12 Hz. The Wrangell block exhibits the most significant scattering loss at a frequency of 1.5 Hz. Another area of marked scattering loss was identified north of the Alaska Range (AR), where it was pronounced up to 6 Hz. The area around Anchorage registered the lowest intrinsic absorption across all the central frequencies, whereas the highest values were detected north of the AR, particularly at 3 and 6 Hz. The seismic albedo (B0) in central and south-central Alaska varies spatially and is mainly dominated by scattering loss up to 3 Hz. Both the Chugach mountains and Yakutat block (YB) area exhibit lower B0 values at all central frequencies showing the dominance of intrinsic absorption. Low values of Qc (high attenuation) are focused almost on all the frequencies along the Denali fault and YB, showing a strong influence of these structures on the attenuation. The results yield a comprehensive understanding of the unique attenuation characteristics of each region, underscoring the significance of investigating the behavior of seismic wave attenuation for seismic risk purposes.

Near‐Source Waveform Modeling to Estimate Shallow Crustal Attenuation and Radiated Energy of Mw 2.0–4.5 Earthquakes

AbstractEstimating the radiated energy of small‐to‐moderate (Mw < 5) earthquakes remains challenging because their energy decay significantly during wave propagation. Even when near‐source records are available, seismic waves pass through the shallow crust with strong attenuation, which can bias energy estimates. This study evaluated the degree of energy dissipation in the crust through modeling near‐source (<12 km) waveform data in northern Ibaraki Prefecture, Japan. High‐quality waveforms recorded at a downhole sensor confined by granite with high seismic velocity helped to investigate this issue. We first estimated the moment tensors for M1–4 events and computed their synthetic waveforms, assuming a tentative one‐dimensional attenuation (Q−1) model. We then modified the Q−1‐model in the 5–20 Hz range such that the frequency components of the synthetic and observed waveforms of microearthquakes (Mw < 1.7) matched. The results show that the Qs‐value is as low as 55 at depths of <4 km with no obvious frequency dependence. Using the derived Q−1‐model, we estimated the moment‐scaled radiated energy (eR) of 3,884 events with Mw 2.0–4.5. The median eR is 3.5 × 10−5, similar to the values reported for Mw > 6 events, with no obvious Mw dependence. If we use an empirically derived Qs‐model, the median eR becomes a one‐order underestimation (2.0 × 10−6). More than 70% of the energy is dissipated in the shallow crust for events with Mw < 4. These results demonstrate the need for an accurate understanding of shallow crustal attenuation for energy estimation of small events, even with near‐source high‐quality data.

A motivational-based learning model for mobile robots

Humans have needs motivating their behavior according to intensity and context. However, we also create preferences associated with each action’s perceived pleasure, which is susceptible to changes over time. This makes decision-making more complex, requiring learning to balance needs and preferences according to the context. To understand how this process works and enable the development of robots with a motivational-based learning model, we computationally model a motivation theory proposed by Hull. In this model, the agent (an abstraction of a mobile robot) is motivated to keep itself in a state of homeostasis. We introduced hedonic dimensions to explore the impact of preferences on decision-making and employed reinforcement learning to train our motivated-based agents. In our experiments, we deploy three agents with distinct energy decay rates, simulating different metabolic rates, within two diverse environments. We investigate the influence of these conditions on their strategies, movement patterns, and overall behavior. The findings reveal that agents excel at learning more effective strategies when the environment allows for choices that align with their metabolic requirements. Furthermore, we observe that incorporating pleasure as a component of the motivational mechanism affects behavior learning, particularly for agents with regular metabolisms depending on the environment. Our study also unveils that, when confronted with survival challenges, agents prioritize immediate needs over pleasure and equilibrium. These insights shed light on how robotic agents can adapt and make informed decisions in demanding scenarios, demonstrating the intricate interplay between motivation, pleasure, and environmental context in autonomous systems.

The Impact of Source Time Function Complexity on Stress-Drop Estimates

ABSTRACT Earthquake stress drop—a key parameter for describing the energetics of earthquake rupture—can be estimated in several different, but theoretically equivalent, ways. However, independent estimates for the same earthquakes sometimes differ significantly. We find that earthquake source complexity plays a significant role in why theoretically (for simple rupture models) equivalent methods produce different estimates. We apply time- and frequency-domain methods to estimate stress drops for real earthquakes in the SCARDEC (Seismic source ChAracteristics Retrieved from DEConvolving teleseismic body waves, Vallée and Douet, 2016) source time function (STF) database and analyze how rupture complexity drives stress-drop estimate discrepancies. Specifically, we identify two complexity metrics—Brune relative energy (BRE) and spectral decay—that parameterize an earthquake’s complexity relative to the standard Brune model and strongly correlate with the estimate discrepancies. We find that the observed systematic magnitude–stress-drop trends may reflect underlying changes in STF complexity, not necessarily trends in actual stress drop. Both the decay and BRE parameters vary systematically with magnitude, but whether this magnitude–complexity relationship is real remains unresolved.