Time-dependent Energy Research Articles

A uniqueness theory on determining the nonlinear energy potential in phase-field system

Abstract The phase-field system is a nonlinear model that has significant applications in material sciences. In this paper, we are concerned with the uniqueness of determining the nonlinear energy potential in a phase-field system consisted of Cahn-Hilliard and Allen-Cahn equations. This system finds widespread applications in the development of alloys engineered to withstand extreme temperatures and pressures. The goal is to reconstruct the nonlinear energy potential through the measurements of concentration fields. We establish the local well-posedness of the phase-field system based on the implicit function theorem in Banach spaces. Both of the uniqueness results for recovering time-independent and time-dependent energy potential functions are provided through the higher order linearization technique.

Efficient and Lightweight Model-Predictive IoT Energy Management

Multi-sensor IoT devices often rely on renewable energy and batteries to support diverse field deployments. A device’s sensors use significant energy, so careful energy management is needed to maximize its operating time while meeting application requirements. Model Predictive Control (MPC), a successful energy management technique for other application domains, requires significant computational resources usually not available in typical IoT sensing devices. We develop and evaluate a low-complexity approximation to MPC for IoT device operations powered by renewable (solar) energy, where the approximation is guided by the charging characteristics of real batteries. The complex MPC optimization problem is solved by decomposing it into a time-dependent energy allocation problem, and a task-dependent sensor scheduling problem, each of which is solvable with cubic time complexity. We utilize a novel combination of an incremental max-min fair allocation method and a recursive dynamic programming-like procedure. This low-complexity predictive optimization step is integrated with a very simple parabola-based adaptive solar prediction to provide a full system solution, termed Predictive EneRgy Management for IoT (PERMIT) , that can be implemented in lightweight IoT devices. PERMIT is evaluated through experiments on a solar-powered Raspberry Pi device with multiple sensors. We also complement our evaluations with simulations based on real device data traces. Results show that PERMIT’s low-complexity algorithm approximates the exact MPC solution very closely. PERMIT also performs significantly better than Signpost, a comparable IoT energy management solution.

The progenitor star of SN 2023ixf: a massive red supergiant with enhanced, episodic pre-supernova mass loss

ABSTRACT We identify the progenitor star of SN 2023ixf in Messier 101 using Keck/NIRC2 adaptive optics imaging and pre-explosion Hubble Space Telescope (HST)/Advanced Camera for Surveys (ACS) images. The supernova, localized with diffraction spikes and high-precision astrometry, unambiguously coincides with a progenitor candidate of $m_\text{F814W}=24.87\pm 0.05$ (AB). Given its reported infrared excess and semiregular variability, we fit a time-dependent spectral energy distribution (SED) model of a dusty red supergiant (RSG) to a combined data set of HST optical, ground-based near-infrared, and Spitzer Infrared Array Camera (IRAC) [3.6], [4.5] photometry. The progenitor resembles an RSG of $T_\text{eff}=3488\pm 39$ K and $\log (L/\mathrm{L}_\odot)=5.15\pm 0.02$, with a $0.13\pm 0.01$ dex ($31.1\pm 1.7$ per cent) luminosity variation at a period of $P=1144.7\pm 4.8$ d, obscured by a dusty envelope of $\tau =2.92\pm 0.02$ at $1\, \mu \text{m}$ in optical depth (or $A_\text{V}=8.43\pm 0.11$ mag). The signatures match a post-main-sequence star of $18.2_{-0.6}^{+1.3}\, \mathrm{M}_\odot$ in zero-age main-sequence mass, among the most massive SN II progenitor, with a pulsation-enhanced mass-loss rate of $\dot{M}=(4.32\pm 0.26)\times 10^{-4} \, \mathrm{M}_\odot \, \text{yr}^{-1}$. The dense and confined circumstellar material is ejected during the last episode of radial pulsation before the explosion. Notably, we find strong evidence for variations of $\tau$ or $T_\text{eff}$ along with luminosity, a necessary assumption to reproduce the wavelength-dependent variability, which implies periodic dust sublimation and condensation. Given the observed SED, partial dust obscuration remains possible, but any unobstructed binary companion over $5.6\, \mathrm{ M}_\odot$ can be ruled out.

Understanding molecular geometric phase effects with exact effective force: case study of a model system

In this work, molecular geometric phase effects are studied using the idea of exact factorization (EF) (Abediet al2010Phys. Rev. Lett.105123002) and exact effective force (Liet al2022Phys. Rev. Lett.128113001). In particular, we performed dynamics simulations for a two-state vibronic coupling model, and interpreted the results in three different perspectives: the Born-Huang expansion, the exact time-dependent potential energy surface (TDPES) and the exact effective force. We find that (i) at particular moment, while the vanishing nuclear density that occurs periodically in space is conventionally attributed to destructive interference of the nuclear wave packet owing to the geometric phase, such phenomenon can be equally well interpreted through the energy perspective, as manifested in the exact TDPES in the EF scheme; (ii) when combined with trajectory-based classical dynamics, the exact effective force obtained through EF qualitatively reproduces the correct nuclear density, while the adiabatic force gives the wrong density, particularly in the interference region. Our results suggest that the exact effective force is a potential starting point for making approximations and improving trajectory-based computational methods towards an accurate description of geometric phase effects.

Fitting the DESI BAO data with dark energy driven by the Cohen-Kaplan-Nelson bound

Gravity constrains the range of validity of quantum field theory. As has been pointed out by Cohen, Kaplan, and Nelson (CKN), such effects lead to interdependent ultraviolet (UV) and infrared (IR) cutoffs that may stabilize the dark energy of the universe against quantum corrections, if the IR cutoff is set by the Hubble horizon. As a consequence of the cosmic expansion, this argument implies a time-dependent dark energy density. In this paper we confront this idea with recent data from DESI BAO, Hubble and supernova measurements. We find that the CKN model provides a better fit to the data than the ΛCDM model and can compete with other models of time-dependent dark energy that have been studied so far.

Heating mode transitions in capacitively coupled CF4 plasmas at low pressure

Abstract Capacitively coupled plasmas operated in CF4 at low pressure are frequently used for dielectric plasma etching. For such applications the generation of different ion and neutral radical species by energy dependent electron impact ionization and dissociation of the neutral background gas is important. These processes are largely determined by the space and time dependent electron energy distribution function and, thus, by the electron power absorption dynamics. In this work and based on a particle-in-cell/Monte Carlo collision model, we show that the electron heating mode in such plasmas is sensitive to changes of the gap at a constant pressure of 3 Pa. At a gap of 1.5 cm, the dominant mode is found to be a hybrid combination of the Drift-Ambipolar (DA) and the α-mode. As the gap is increased to 2 cm and 2.5 cm, the bulk power absorption and ambipolar power absorption decreases, and the DA mode decays. When the gap reaches 3 cm, the α-mode becomes more prominent, and at a gap of 3.75 cm the α-mode is dominant. These mode transitions are caused by a change of the electronegativity and are found to affect the discharge characteristics. The presence of the DA-mode leads to significant positive electron power absorption inside the bulk region and negative power absorption within the sheaths on time average, as electrons are accelerated from the bulk towards the collapsed sheath. The heating mode transitions result in a change from negative to positive total electron power absorption within the sheaths as the gap increases. When accounting for secondary electron emission, the transition of the heating mode can occur at shorter gaps due to the enhanced plasma density and decreased electronegativity.

Energy efficient F atom generation and control in CF4 capacitively coupled plasmas driven by tailored voltage waveforms

Abstract Neutral radicals generated by electron impact dissociation of the background gas play important roles in etching and deposition processes in low pressure capacitively coupled plasmas (CCPs). The rate and energy efficiency of producing a given radical depend on the space- and time-dependent electron energy distribution function (EEDF) in the plasma, as well as the electron energy dependent cross sections of the electron-neutral collisions that result in the generation of the radical. For the case of a CCP operated in CF4 gas, we computationally demonstrate that the energy efficiency of generating neutral radicals, such as F atoms can be improved by controlling the EEDF by using tailored voltage waveforms (TVW) instead of single-frequency driving voltage waveforms and that separate control of the radical density and the ion energy can be realized by adjusting the waveform shape at constant peak-to-peak voltage. Such discharges are often used for industrial etching processes, in which the F atom density plays a crucial role for the etch rate. Different voltage waveform shapes, i.e. sinusoidal waveforms at low (13.56 MHz) and high (67.8 MHz) frequencies, peaks- and sawtooth-up TVWs, are used to study their effects on the energy cost / energy efficiency of F atom generation by PIC/MCC simulations combined with a stationary diffusion model. The F atom density is enhanced by increasing the voltage amplitude in the single frequency cases, while the energy cost per F atom generation increases, i.e. the energy efficiency decreases, because more power is dissipated to the ions, as the sheath voltages and the ion energy increase simultaneously. In contrast, using TVWs can result in a lower energy cost and provide separate control of the F atom density and the ion energy. This is explained by the fact that tailoring the waveform shape in this way allows to enhance the high-energy tail of the EEDF during the sheath expansion phase by inducing a non-sinusoidal sheath motion, which results in acceleration of more electrons to high enough energies to generate F atoms via electron-neutral collisions compared to the single frequency cases. Similar effects of TVWs are expected for the generation of other neutral radicals depending on the electron energy threshold and the specific consequences of TVWs on the EEDF under the discharge conditions of interest.

Time-dependent dynamical energy analysis via convolution quadrature

Dynamical Energy Analysis was introduced in 2009 as a novel method for predicting high-frequency acoustic and vibrational energy distributions in complex engineering structures. In this paper we introduce the first time-dependent Dynamical Energy Analysis method. Time-domain models are important in numerous applications including sound simulation in room acoustics, predicting shock-responses in structural mechanics and modelling electromagnetic scattering from conductors. The first step is to reformulate Dynamical Energy Analysis in the time-domain by means of a convolution integral operator. We are then able to employ the Convolution Quadrature method to provide a link between the previous frequency-domain implementations of Dynamical Energy Analysis and fully time-dependent solutions by means of the Z-transform. By combining a modified multistep Convolution Quadrature approach for the time discretisation, together with Galerkin and Petrov-Galerkin methods for the space and momentum discretisations, respectively, we are able to accurately track the propagation of high-frequency transient signals through phase-space. The implementation here is detailed for finite two-dimensional spatial domains and we demonstrate the versatility of our approach by performing a range of numerical experiments for regular, non-convex and irregular geometries as well as different types of wave source.

Tracking the size of the estimation window in time-series data

PurposeThis paper introduces a novel method, Variance Rule-based Window Size Tracking (VR-WT), for deriving a sequence of estimation window sizes. This approach not only identifies structural change points but also ascertains the optimal size of the estimation window. VR-WT is designed to achieve accurate model estimation and is versatile enough to be applied across a range of models in various disciplines.Design/methodology/approachThis paper proposes a new method named Variance Rule-based Window size Tracking (VR-WT), which derives a sequence of estimation window sizes. The concept of VR-WT is inspired by the Potential Scale Reduction Factor (PSRF), a tool used to evaluate the convergence and stationarity of MCMC.FindingsMonte Carlo simulation study demonstrates that VR-WT accurately detects structural change points and select appropriate window sizes. The VR-WT is essential in applications where accurate estimation of model parameters and inference about their value, sign, and significance are critical. The VR-WT has also helped us understand shifts in parameter-based inference, ensuring stability across periods and highlighting how the timing and impact of market shocks vary across fields and datasets.Originality/valueThe first distinction of the VR-WT lies in its purpose and methodological differences. The VR-WT focuses on precise parameter estimation. By dynamically tracking window sizes, VR-WT selects flexible window sizes and enables the visualization of structural changes. The second distinction of VR-WT lies in its broad applicability and versatility. We conducted empirical applications across three fields of study: CAPM; interdependence analysis between global stock markets; and the study of time-dependent energy prices.

Analyzing the thermal performance of transient heat transfer mechanism due to the combined effects of solar energy and variable surface temperature: Growing applications of solar energy in co-axial pipes

The current analysis is carried out to study the laminar convective heat transfer characteristics that change with time in the co-axial pipes along the impact of heat radiation and variable surface temperature. The flow is assumed along the axial direction of the pipe, and variable boundary condition is assumed at the surface of the pipe due to the variable surface temperature. A two-dimensional mathematical model made up of non-linear partial differential equations is solved using the implicit finite difference method. The project involves predicting the thermal efficiency of a pipe's time dependent flow across a number of flow model-relevant parameter ranges. Graphical representations highlighted the derived predictions. After separating the numerical solutions into the time independent and the time dependent components, the time dependent energy and surface shearness were found using the data from the time independent component. Comprehensive detail of the obtained results for the non-dimensional parameters included in the flow formulation is predicted for steady state velocity, temperature distribution, time dependent surface sheerness, and time dependent energy sheerness, which is given in results and discussion section of the manuscript. Major focus is given on the influence of the radiation parameter on the above-mentioned primary measures. Furthermore, it is concluded that in all cases, the steady state flow is as R→∞ and velocity profile as U→1 and θ→0, which ensured the accuracy of the obtained results by satisfying the boundary conditions. For various values of the fluid's absorption parameter D = 1.0, 3.0, 5.0, and 10.0, the flow profile is increased and U→1 as R→∞. Simultaneously, thermal distribution also increases and θ→0 as R→∞.

Revisiting flares in Sagittarius A* based on general relativistic magnetohydrodynamic numerical simulations of black hole accretion

ABSTRACT High-resolution observations with GRAVITY-Very Large Telescope Interferometer (VLTI) instrument have provided abundant information about the flares in Sgr A*, the supermassive black hole in our Galactic centre, including the time-dependent location of the centroid (a ‘hotspot’), the light curve, and polarization. Yuan et al. (2009) proposed a ‘coronal mass ejection’ model to explain the flares and their association with the plasma ejection. The key idea is that magnetic reconnection in the accretion flow produces the flares and results in the formation and ejection of flux ropes. The dynamical process proposed in the model has been confirmed by three-dimensional general-relativistic magnetohydrodynamic simulations in a later work. Based on this scenario, in our previous works the radiation of the flux rope has been calculated analytically and compared to the observations. In the present paper, we develop the model by directly using numerical simulation data to interpret observations. We first identify flux ropes formed due to reconnection from the data. By assuming that electrons are accelerated in the reconnection current sheet and flow into the flux rope and emit their radiation there, we have calculated the time-dependent energy distribution of electrons after phenomenologically considering their injection due to reconnection acceleration, radiative and adiabatic cooling. The radiation of these electrons is calculated using the ray-tracing approach. The trajectory of the hotspot, the radiation light curve during the flare, and the polarization are calculated. These results are compared with the GRAVITY observations and good consistencies are found.

Dynamical quantum phase transitions following a noisy quench

We study how time-dependent energy fluctuations impact the dynamical quantum phase transitions (DQPTs) following a noisy ramped quench of the transverse magnetic field in a quantum Ising chain. By numerically solving the stochastic Schrödinger equation of the mode-decoupled fermionic Hamiltonian of the problem, we identify two generic scenarios: Depending on the amplitude of the noise and the rate of the ramp, the expected periodic sequence of noiseless DQPTs may either be uniformly shifted in time or else replaced by a disarray of closely spaced DQPTs. Guided by an exact noise master equation, we trace the phenomenon to the interplay between noise-induced excitations which accumulate during the quench and the near-adiabatic dynamics of the massive modes of the system. Our analysis generalizes to any one-dimensional fermionic two-band model subject to a noisy quench. Published by the American Physical Society 2024

Gyrotactic bio-magneto-convective combined impacts on magnetorheological hybrid nanoflow: Microbial life on surfaces’ application

Magnetorheological fluid with self-driven ubiquitous motile organisms was affected by various physical factors such as hydrodynamics, dispersion, and distribution of organisms. These fascinating properties attracted us to work on this paper, a Casson hybrid nanoflow model exploring the dynamic behavior of microorganisms along spongy extensible surfaces taking Ohmic heating and chemical reaction into account. Further, the heat transfer phenomena are analyzed in the presence of thermal radiation and space and time-dependent energy sources/sinks. The nanoflow has its base methanol and a mixture of iron and aluminum oxides is suspended. Flow obeying mathematical model is solved numerically using the Runge–Kutta–Fehlberg technique along with the shooting method after imposing self-similarity transformation. Results of various pertinent parameters on the flow characteristic quantities and engineering quantities are portrayed and presented through graphs and tables. Iron oxide methanol nanofluid shows supremacy over hybrid nanoflows as speed is considered, whilst the opposite phenomenon is observed in the case of energy. Hybrid nanoflow makes the surface friction-free. Microorganism concentration difference improvement also helps in the intensification of motile organism growth.

An analytic description of electron thermalization in kilonovae ejecta

ABSTRACT A simple analytic description is provided of the rate of energy deposition by β-decay electrons in the homologously expanding radioactive plasma ejected in neutron star mergers, valid for a wide range of ejecta parameters – initial entropy, electron fraction {s0, Ye}, and scaled (time-independent) density ρt3. The formulae are derived using detailed numerical calculations following the time-dependent composition and β-decay emission spectra (including the effect of delayed deposition). The deposition efficiency depends mainly on ρt3 and only weakly on {s0, Ye}. The time te at which the ratio between the rates of electron energy deposition and energy production drops to 1 − e−1, is given by $t_e=t_{0e}\Big (\frac{\rho t^3}{0.5(\rho t^3)_0}\Big)^a$, where $(\rho t^3)_0=\frac{0.05\, {\rm M}_{\odot }}{4\pi (0.2c)^3}$, t0e(s0, Ye) ≈ 17 d, and 0.4 ≤ a(s0, Ye) ≤ 0.5. The fractional uncertainty in te due to nuclear physics uncertainties is $\approx 10~{{\ \rm per\ cent}}$. The result a ≤ 0.5 reflects the fact that the characteristic β-decay electron energies do not decrease with time (largely due to ‘inverted decay chains’ in which a slowly decaying isotope decays to a rapidly decaying isotope with higher end-point energy). We provide an analytic approximation for the time-dependent electron energy deposition rate, reproducing the numerical results to better than 50 per cent (typically $\lt 30~{{\ \rm per\ cent}}$, well within the energy production rate uncertainty due to nuclear physics uncertainties) over a 3–4 orders-of-magnitude deposition rate decrease with time. Our results may be easily incorporated in calculations of kilonovae light curves (with general density and composition structures), eliminating the need to numerically follow the time-dependent electron spectra. Identifying te, e.g. in the bolometric light curve, will constrain the ejecta density distribution.

Time-dependent electron transfer and energy dissipation in condensed media.

We study a moving adsorbate interacting with a metal electrode immersed in a solvent using the time-dependent Newns-Anderson-Schmickler model Hamiltonian. We have adopted a semiclassical trajectory treatment of the adsorbate to discuss the electron and energy transfers that occur between the adsorbate and the electrode. Using Keldysh Green's function scheme, we found a non-adiabatically suppressed electron transfer caused by the motion of the adsorbate and coupling with bath phonons that model the solvent. The energy is thus dissipated into electron-hole pair excitations, which are hindered by interacting with the solvent modes and facilitated by the applied electrode potential. The average energy transfer rate is discussed in terms of the electron friction coefficient and given an analytical expression in the slow-motion limit.

WR21 marine gas turbine thermodynamic simulator for ship propulsion studies

An original modular mathematical model, based on physical laws, for steady state and dynamics performance simulation of the WR21 gas turbine is presented in the paper. The model, developed in Matlab-Simulink language, is organized in modular form. Each gas turbine component (i.e. compressor, turbine, combustor, heat exchanger) is modelled in a specific simulator block, that simulates the performance of its pertinent component by means of steady state performance maps and/or correlations, time dependent momentum, energy and mass equations, nonlinear algebraic equations. The great application flexibility of the component simulator modules, allows to modelling any gas turbine layout (i.e. axial or radial flow compressor and turbine, rotating shafts number, heat exchangers). The WR21gas turbine, developed mainly for marine propulsion application, is a three shafts gas turbine with thermal regeneration. It is characterized by a high thermodynamic efficiency, which remains high up to 30% of the design power. The WR21 simulator results are validated by comparison with manufacturer or literature data. The WR21 gas turbine main performances are compared to those of the LM 2500 gas turbine, obtained by a previously author paper. The LM 2500 is the gas turbine currently most used in naval propulsion plants. In the article, a comparison between the steady state working data of the two gas turbines is reported in tabular and graphical form and commented.

Dynamic behavior of mixed convection heat transfer among horizontal co-axial fixed pipes at varying temperatures: Efficiency of cylindrical heat sink

The aim of the current research is to highlight the time-dependent properties of laminar convective thermal transmission inside a semi-infinite pipe, with an emphasis on flow frequencies that impact inter-fluid momentum and energy. The implicit finite difference approach is used to solve two-dimensional mathematical model composed of nonlinear partial differential equations. The research includes forecasting thermal performance of time-dependent flow in a pipe over several parameter ranges relevant to the flow model. The obtained forecasts were emphasized graphically. The numerical solutions were separated into steady and unsteady components, with the steady component yielding findings that were then used to determine the time dependent surface shearness and energy shearness in the time dependent phase. The stable component of the investigation revealed that raising the buoyancy force parameter and the impact of viscous dissipation significantly improved the flow velocity pattern and heat distributions throughout the flow domain. While the amplitude of time dependent surface shearness varied somewhat across various buoyancy force parameter values, the amplitude of time dependent heat transmission rates varied significantly. This study sheds light on the interaction of several characteristics, such as buoyancy force effects and internal energy loss, on time-dependent thermal energy flow inside a semi-infinite pipe subjected to laminar convective flow. It is worth noting that the amplitude of the time dependent rate of heat transmission shows more noticeable variations with different values of the buoyancy force parameter, in contrast to the minute change in the amplitude of the time dependent surface sheerness.

An efficient solution of the multi-term multi-harmonic electron Boltzmann equation for use in global models

Solving the electron Boltzmann equation is an essential but costly step in simulating low-temperature plasma kinetics. This work addresses the problem by introducing a solution of the general multi-term multi-harmonic Boltzmann equation (MTMH-BE) optimized for electrons in time-dependent non-equilibrium gases and electric fields. This is accomplished by configuring the numerical Jacobian as the product of a time-independent sparse matrix and an array of time-dependent coefficients. As this approach requires a fixed energy grid, the MTMH-BE is discretized using a finite volume scheme with support for non-uniform cell size, enabling robust solutions across a wide range of reduced field strengths. The new MTMH-BE solver is tested against a range of benchmarks, demonstrating excellent agreement with existing methods. Performance with time-dependent electron energy is evaluated using LoKI-B's pulsed electric field model, with the new solver demonstrating improved wall time scaling and an improvement in grid convergence of over three orders of magnitude. Alternatively, performance with quasi-stationary electrons in an evolving non-equilibrium gas is tested using a nitrogen cross-section set with up to 58 vibrational states and 3,570 processes. Here, the MTMH-BE solver achieves a wall time reduction of up to 99.6% over MultiBolt for error-controlled simulations in the two-term limit, reducing the average solution time from 1-2 seconds to less than 10 ms. These results indicate that the new MTMH-BE solver can improve accuracy and performance in state-to-state global models without the use of grid refinement, cross-section pruning, and other time-saving procedures.

Green inventory model with two-warehouse system considering variable holding cost, time dependent demand, carbon emissions and energy consumption

Green inventory model with two-warehouse system considering variable holding cost, time dependent demand, carbon emissions and energy consumption

Gravity induced shape effects on the time-dependent evaporation of pendant drops

The paper presents a method to model the time-dependent evaporation of pendant drops taking into account the effect of drop deformation induced by gravity. The model is based on the solution to the time-dependent drop mass and energy conservation equations, where the mass and energy fluxes through the gas mixture are numerically evaluated for a range of Bond numbers and contact angles. The evaporation characteristics of pendant and sessile drops on hydrophobic and hydrophilic substrates are compared in terms of evaporation times and evaporative cooling, for both constant contact angle and constant contact radius modes.