Energy Density Rate Research Articles

Development of Mass and Energy Rate (Density) of Dissipative Systems Over Their Lifetimes: A Comparison of a Low-Mass Star, Like Our Sun, a Human and the Roman Empire

Energy rate density (ERD) corresponds to the energy flow through a dissipative system to maintain its energy gradient and is defined as the energy rate (ER), normalised to mass. ERD has been proposed by Chaisson [2002] as a single, simple metric for complexity of a wide variety of systems over big time. The main objective of this study is to assess the usefulness of this metric over the lifetimes of dissipative systems. For this purpose, mass and ER(D) data have been collected over the lifetimes of a low-mass star, like our Sun, a human, and the Roman Empire, as representative examples of dissipative systems from the cosmological, biological, and cultural realms. Proxies are very useful for further interpretation of the ER(D) time profiles. ER(D) of a low-mass star as a contracting proto-star (< 0.05 Gyr) as well as during its red giant stage and helium flashes (11 to 12.5 Gyr) is much larger than during its stable appearance as a yellow dwarf star in its main sequence (0.05 to 11 Gyr). ERD of a human peaks at 1.5 yr, reflecting the large relative growth of a baby. ER of a human represents the biochemical activities of the human body, especially of physical activities, and reaches a maximum when a human is in the prime of its life between 20 and 30 yr. Cognitive and emotional performance do not impose any additional energy requirements. For the Roman Empire ERD decreased over time, because the growth rate of the total mass including that of man-made constructs (note that Chaisson only uses mass of humans) was larger than that of ER. ER per capita hardly varied, because human (slave) labour was the main energy source powering the empire. The Roman Empire was at the height of its power between 100 and 200 CE, which is best reflected by ER or simply population. Thus, it is concluded that ERD runs in to several issues, when it is applied as a metric of complexity of systems over their lifetimes. ERD does not capture information processing and, as a result, underestimates the complexity of biological and cultural systems. This hampers its application in a BH context, including the issues of the Big History periodization. Alternative complexity metrics related to information processing need to be developed.

Thermodynamic Approach to Modeling Complexity of Regional Hewett-Hubbert Resource Bubbles and Large Dynasties

This paper examines how the phenomena of emergence and complexity can be applied to the analysis of physical Hewett-Hubbert resource bubbles and historical dynasties. Concepts and definitions of energy, the laws of thermodynamics, efficiency, power and other useful terminology are introduced. Relevant proposed extensions of the Second Law of Thermodynamics are discussed. Several definitions of complexity are discussed and critiqued, including the energy rate density approach. Approaches between energy rate density and entropy approaches are compared. The divergence between energy rate density and complexity artifacts is explored. Principles of extended thermodynamics are then applied to the emergence of medium-term dissipative structures, such as the rise and fall of physical resource bubbles and historical dynasties. Changes in complexity are discussed when resource bubbles and historical dynasties progress through their processes of emergence. Patterns in complexity change are identified and a characteristic complexity profile for resource bubbles and historical dynasties is articulated.

Energy Flow and Complexity in the Cosmic Structure Development Phase

The structural development of the universe differs significantly from the initial rapid cooling after the Big Bang and the later rise of life on Earth. These structures span a vast range, from the cosmic web and galaxies to stars and planets. Earlier studies on free energy rate density (FERD) flows suggested a trend of increasing energy density through cosmic and life systems over time. According to this, galactic structures were indicated to be less complex than stellar ones due to the estimated energy flow per mass. However, recent findings in cosmic evolution reveal that large energy flows, including those from gravitational collapse in the cosmic web and active galactic nuclei (AGN or quasars), played a key role in forming these dissipative structures, often in stages of smaller sizes. For example, if we include the energy flow from the cosmic web’s collapse, the AGN phase of younger galaxies, stellar energy processes, and Earth's own cooling from gravitational collapse and radioactive decay, it appears that the FERD might actually decrease during this phase as the energy gradients dissipate and the system cools, creating more stable conditions conducive to life. However, during this cosmic structural development phase, the cascade of energy flow, much like turbulent fluid dynamics, seems to serve as a better analogy for understanding the evolution of these complex structures.

3D simulations of the RF wave propagation and power coupling in cold magnetized plasma near an ICRF antenna

Abstract The electromagnetic wave propagations and their coupling characteristics in magnetized plasma near the antenna of Ion Cyclotron Range of Frequencies (ICRF) is studied based on self-developed 3DFEM-IA code. This code effectively resolves the three-dimensional (3D) geometry and the electromagnetic field using the finite element method. Our findings reveal that the distributions of electromagnetic fields and energy flow density significantly depend on the antenna phases, surface current density on the antenna straps, and background plasma density. Notably, the non-uniform surface current density on the antenna straps, resulting from the presence of induced currents, contributes to a reduction in coupling power within the edge plasma. Furthermore, the calculated coupling impedance increases with plasma density, corroborating well with experimental measurements.

Dissipative systems have a maximum energy rate density of 105 W/kg

Dissipative systems have a maximum energy rate density of 105 W/kg

Modular Flat Structure with Miura Origami for Space Solar Power Station

To address the challenges associated with existing space solar power station (SSPS) concepts, including noncompact structural design, nonuniform solar energy flow density, and orbital deployment complexities, an integrated, highly modular, flat functional structure based on the Miura origami pattern is proposed. The flat functional structure consists of a flat quadrilateral Fresnel concentrator for solar energy collection, a photovoltaic array for photoelectric conversion, and a transmitting array for microwave power transmission. To optimize space utilization and enhance the deployment ratio, the Miura origami pattern is introduced, and the subarray composed of multiple flat functional structures can be packaged in a payload capsule before launch and unfold as a standard rectangle with uniform thickness and a flat surface in orbit, improving the transportability of the launch vehicle. Additionally, to solve the nonuniform solar energy flow density, a Fresnel concentrator was employed to achieve uniform irradiation, while the transmitting array was designed to achieve good electrical performance. Finally, the structural parameters and efficiency of the SSPS system composed of multiple subarrays are presented in detail.

Dual cation Kgu/PAM Gel polymer electrolyte with high ionic conductivity and mechanical strength for flexible All-Solid-State supercapacitors

Gel polymer electrolytes (GPEs) have attracted much attention due to their excellent flexibility, good interface contact, and high safety in solid-state supercapacitors (SSCs). However, in practical applications, GPEs still face low ionic conductivity and poor mechanical strength. This study delineates a novel dual-cationic Kgu/PAM GPE, the ion diffusion coefficients in which are 1.51 × 10-8 cm2 s−1 (K+) and 4.77 × 10-9 cm2 s−1 (Na+), respectively. Radial distribution function and in-situ Fourier transform infrared spectroscopy have confirmed that the migration mechanism of dual-cations in Kgu/PAM is through the long-range hydration channels, which is depended on the continuous formation of binding water facilitated by movement of Kgu and PAM chain segments. When assembled dual-cationic Kgu/PAM GPE to a flexible solid-state asymmetric supercapacitor, it delivers a high ionic conductivity (86.9 mS cm−1), an excellent energy rate density (86.1 Wh kg−1) and outstanding power density (476 W kg−1). In addition, dual-cationic Kgu/PAM GPE exhibits an excellent strain threshold of 910 % and remarkable mechanical strength of 35 KPa, good flexibility and flame retardant, highlighting the potential for its practical application in various fields. Collectively, these findings herald a novel paradigm in the development of secure and efficacious flexible wearables.

Study on saline-alkali water distillation system by reflection enhanced solar heating

A saline-alkali water distillation system by reflection enhanced solar heating is proposed to treat the saline-alkali soil washing water. In this system, the heat concentration collector employs heat collecting plate to receive solar radiation energy, and converges to small-area steam generating tube through efficiently heat transfer. Without expensive optical tracking equipment, the system also employs an external reflector to reflect the solar radiation to the surface of the heat concentration collector. Thereby the energy flow density is further increased, and the useful energy and vaporization intensity is promoted. The latent heat of the steam is reused by heat recovery to enhance the energy utilization efficiency. The optimal inclination angles of reflector in different seasons and system performance were theoretically calculated. In the spring equinox, summer solstice, autumn equinox, and winter solstice, the optimal inclination angles of the reflector were 30°, 45°, 30°, and 15°, respectively. The freshwater production, useful energy, and heat recovery efficiency of the system were investigated by experiments. The daily freshwater production of the system was 17.04 kg, and the maximum production rate was 3.44 kg/h. The reflector increased the useful energy and freshwater production of the system by 33.68% and 35%, respectively. With heat recovery, the initial temperature of the saline-alkali water was increased to 53.8 °C and the freshwater production was increased by 13.16%.

Dynamic evolution of temperature field, flow field, and solidification behavior during multilayer multitrack laser cladding

During multilayer multitrack laser cladding, secondary melting and solidification in the interlayer lap zone have a significant impact on the mechanical properties of cladding coatings. However, mathematical modeling of the melt flow and solidification behavior of multilayer, multitrack laser cladding interlayer lap zones is lacking. In this paper, a 3D finite element model was established to investigate the mass and heat transfer processes in both lap and non-lap zones during the laser cladding of multilayer multitrack Fe-Cr-based alloys on 45# steel surface. A dynamic grid is used to track the free surface of the melt pool, while the enthalpy method is used to simulate the solid-liquid phase transition. The change in thermophysical properties with temperature, as well as the change in laser energy and alloy powder flow density in the lap zone, were taken into consideration. The influence of the number of cladding layers on the heat and mass transfer in the molten pool, remelting, and solidification in the lap zone was investigated, along with its intrinsic mechanism. The results show that the model can accurately predict the size and microstructural change law of coating layers, including the grain size of the lap region between layers. The melt pool temperature and grain size increase with the number of cladding layers, while the convection and cooling velocities decrease. In addition, the grain size in the lap zone of the cladding is larger than that in the nearby non-lap zone. Using solidification parameters extracted from the solidification front of the molten pool, changes in grain size and morphology were predicted for both the interlayer lap and non-lap zones. The numerical calculation results were consistent with the experimental measurements.

Interstage transmission and differential analysis of pressure fluctuations in multistage centrifugal pump-as-turbine

Pumps as turbines (PATs) are used in petroleum and chemical industries to recover high-pressure residual energy. Multistage PATs allow for a wider energy recovery interval and wider range of applications. However, because multistage centrifugal pumps were not originally designed for turbine conditions, complex pressure fluctuations occur, impacting the stable operation and performance of multistage PAT. Pressure fluctuation is essentially a wave, and by analogy with the wave intensity definition, pressure fluctuations were quantified using the pressure wave energy flow density, and the pressure fluctuation patterns at different stages were investigated. The findings reveal significant differences in the intensity of pressure fluctuations at different locations within the multistage PAT. Specifically, the pressure fluctuation intensity is significantly higher from the second to the final stage, compared to the first stage. The difference in inlet flow conditions is the main reason for this difference in pressure fluctuations between stages. The inlet inflow from the second to the final stage is subject to rotational effects that exacerbate the difference in pressure fluctuation intensity between stages. Pressure fluctuations are found to be negatively related to the distance from the source of fluctuations and positively related to the flow state. Different flow conditions and interaction regions of the impeller affect the distribution of pressure fluctuation intensity and the distribution of pressure fluctuation energy across different frequency domains within the guide vanes. The main source of fluctuations in the shaft frequency and four times the shaft frequency is the impeller inlet interaction region, whereas the fluctuations in the blade passing frequency originate from the impeller outlet interaction region. This paper provides a reference for improving the stable operation of multistage PATs.

Multi‐mode inversion of dispersive surface‐wave free fields in layered media

AbstractInversion of surface‐wave free fields is of great importance in providing seismic excitations for the finite element (FE) analysis of soil–structure interaction (SSI) systems. In the case of layered media, the propagating surface waves are characterized by their unique dispersion property, resulting in dispersive multi‐mode surface wavefields. Available studies primarily focus on only the fundamental mode and neglect the influence of higher modes, which fail to identify the real structural response characteristics. To enhance the precision of seismic excitations for SSI systems situated in layered media, a multi‐mode inversion method for dispersive surface‐wave free fields is proposed in this study. The proposed method employs the energy flow density to characterize the participation volume of dispersive modes, and further calculates corresponding modal participation factors by combining with the dispersion curve and dynamic‐stiffness matrix (DSM) method. The modal participation factors are then utilized to assign the ground surface components of each mode and invert respective single‐mode surface‐wave free fields. Based on the mode superposition theory, all the single‐mode surface‐wave free fields are finally superimposed to construct the multi‐mode wavefields. The accuracy of the proposed method is thoroughly verified and validated across various types of layered media. Furthermore, the engineering application of the proposed method is illustrated by performing the FE analysis on an SSI example. The analysis results highlight the significant participation of surface waves' higher modes in structural seismic responses, particularly in the weak‐interbed type media.

Transformations of the transverse Poynting vector distribution upon diffraction of a circularly polarized paraxial beam.

Usually, the structure of paraxial light beams is characterized by the intensity associated with distribution of the longitudinal energy flow density (Poynting momentum) across the transverse plane. In this work, special attention is paid to the distribution of internal energy flows described by the transverse Poynting momentum (TPM) components. This approach discloses additional polarization-dependent features of the vector beam transformations; in application to the edge diffraction of a circularly polarized (CP) Gaussian beam, it reveals the helicity-dependent asymmetry of the diffracted-field TPM profile characterized by the shifts of the TPM singularity, maximum, etc. These phenomena are confirmed experimentally and interpreted in terms of the spin-orbit interaction (SOI) and spin Hall effect of light. In contrast to the known SOI manifestations in the CP beams' diffraction originating from the small longitudinal component of a paraxial field, the new TPM-related effects stem from the transverse field components and are thus much higher in magnitude.

What can we learn from a master plot of energy rate versus mass for a very wide variety of (complex) systems?

Mass and energy rate (ER) data have been collected for a wide variety of (complex) systems from the biological, cultural, and cosmological realms. They range from the cytochrome oxidase protein (10-22 kg and 6x10-19 W) to the observable universe (1.5x1053 kg and 1048 W) and, thus, span 75 mass and 66 ER orders of magnitude. Many of these systems are relevant for the big history (BH) narrative, i.e., the development of complexity over “big time” from the Big Bang up to the human society on Earth of today. The purpose of this paper is not per se to describe their history though, but to explore a master plot of ER vs. mass. Notably, the development of systems over big time has followed a rather tortuous path criss-crossing over this ER vs. mass master plot. The true mass of the system as a whole is used (for example trees including the non-living wood, living organisms including their intrinsic water, and social systems including the built constructs), because these inactive parts are essential for the performance of the system and facilitate its ER. A double logarithmic master plot of all ER vs. mass data shows clusters of data points. To some extent, this provides quantitative support for the distinction between the (sub-)realms, which is based on a qualitative description of their material structure and energy processing. In the master plot, small systems with low mass and ER converge into larger systems with larger mass and ER, which is typically accompanied by a decrease of the energy rate density (ERD = ER/mass). Correlation of ER with mass for various groups of systems demonstrates both sub- and supra-linear scaling with the power law β constant varying between 0.5 and 4.0, showing that the mechanisms of self-organisation are quite different for the corresponding system groups. The combination of convergence and scaling with β always larger than zero explains why the ER & mass data points fall in a diagonal band with a width of 17 orders of magnitude.
 ER and mass have changed over wide ranges during the evolution of groups of systems, suggesting that evolution can be viewed as a process of systems exploring a larger ER vs. mass area until they run into ER and/or mass limitations. Indeed, there is a diagonal ER vs. mass limit for stable systems in all realms, corresponding to an ERD value of around 105 W/kg. Systems with ER & mass combinations above this limit, such as bombs, super-novae and cosmological transients, are unstable and “explosive”. This raises the interesting question of whether such an ERD maximum puts a limit on the development of complexity over big time. It seems that the low, right side of the master plot is empty. However, it is argued here that it is full of systems with low ER, such as dormant, living organisms, technological systems with their power adjusted or even switched off, as well as cooling, cosmological objects. Such systems are typically considered of less interest in a BH context, but they are viewed here as simple, complex systems which are out of equilibrium with matter, energy and information stored in their structure. While ERD appears to increase with the ‘advancement’ of systems over big time [5,51,52], there are quite some confounding factors regarding the efficacy of ERD as a metric for complexity in BH. For example, ERD decreases during the lifetime of a human and the human society (the mass of human-made constructs has grown faster than the global energy consumption), as well as during the evolution of living organisms and stars, whereas complexity is considered to increase. High ERD values of system parts may be illustrative for the complexity of the larger system, but are not representative for ERD of the system itself. Machines with an increased efficiency of energy conversion have a lower ERD, but could be considered more complex. The smallest and largest ERD values observed for the various realms appear to correlate with activity level and reciprocally with size, which do not per se reflect complexity. It is hoped that the raw data collected and the major trends observed in this paper will offer new insights into various aspects of the evolution of the universe over big time, and serve as an important resource for other related studies.

Reexamining “Free Energy Rate Density” as a Complexity Metric

Cosmic Evolution, by Eric J. Chaisson is arguably one of the original “core” texts of big history. Despite being published over 20 years ago, it is still relevant for its explanation of the cosmological and thermodynamic underpinnings of the evolution of complex systems over the span of time. It was also a pioneering work because it proposed that we can quantify the degree of complexity of systems by determining the quantity of the “free energy rate density” or FERD (abbreviated as “Ωm” in Cosmic Evolution) that flows through a system. Although Chaisson advises that his correlations of FERD to complexity degree is subject to various limitations and generalizations, careful analysis of the arguments and examples used to support FERD indicates that it is even less likely to be as reliable and quantifiable than he purports for at least the following reasons:1. The author offers a relatively short list of criteria for a system to qualify being “complex” that in turn results in the inclusion of systems that are not classified as complex by usual criteria. 2. Free energy rate density is not compared against other complexity metrics and subsequently seems to serve as its own “gold standard.” The lack of comparisons results in a tautological argument and sometimes questionable conclusions.3. The argument for FERD sometimes deviates from the hypothesis that FERD is a good way to measure the degree of a system’s complexity to a claim that it also measures complex functions and structures as well. 4. The FERD that he reports are often actually for the total energy flow through a system. Hence, a much more efficient complexity might only appear to be less complex. 5. Complex systems have many variables that can confound attempts to make reliable and precise generalizations, including good metrics for their degree.

Realization of elastic wave energy flow density based on MATLAB

Realization of elastic wave energy flow density based on MATLAB

Tidal current energy resources assessment in Zhoushan Archipelago, China

ABSTRACT Zhoushan Archipelago, the largest archipelago in China, harbors a significant tidal stream resource due to robust tidal currents coursing through numerous channels between its islands. Nevertheless, the tidal energy resource in the Zhoushan Archipelago has not been systematically characterized considering both topography and energy flow density. This study presents a modeling study aimed at characterizing the tidal energy resource in the whole Zhejiang coast, including Zhoushan Archipelago, employing a high-resolution tidal hydrodynamic model, i.e. MIKE 21. Through a comparison of the model output with observed data from two tidal stations and three current stations, the accuracy of the numerical model was confirmed. The study identified areas with robust currents and suitable water depths, both essential factors for the advancement of tidal current energy. The findings showed that many channels in Zhoushan Archipelago and Wenzhou Bay in Zhejiang experience the highest tidal power density, reaching nearly 5500 W/m2. Furthermore, the study estimated the theoretical tidal current energy production for the whole area, highlighting Loutou channel, Cezi channel, Taohuagang, and the channel between Xiushan island and Daishan island as regions with high potential.

Band-division utilization of core-shell photocatalyst under condenser solar-light and enhancement of synergistic catalytic CO2 reduction

The synergistic effect of intrinsic photoelectrons and thermal effects, provided by intermediate- and long-wave solar energy, is considered as the linchpin in enhancing photo-thermal catalytic CO2 reduction performance. Recently, photocatalysts possessing photothermal conversion capabilities and photocatalytic systems with adjustable incident light energy flow density have garnered significant attention. The strong condensing property of the Fresnel lens was adopted in increasing the density of incident photoelectrons simultaneously, and raising the surface temperature of the photocatalyst significantly without an external heat source. A novel core–shell photocatalyst with the photothermal conversion effect was fabricated, consisting of amorphous TiO2 and CuxO active species on Fe3O4@SiO2 core. Under optimal incident energy flux density of 3200 mW cm−2, the photocatalyst was able to reduce CO2 to CO and CH4 with the production rate of 361.39 and 70.84 μmol g−1h−1, and the solar conversion efficiency reached 1.43 %. Furthermore, a simple reaction kinetic optimization based on Langmuir-Hinshelwood model well simulated the photothermal coupling effect under different incident energy flux densities. This work demonstrates an innovative technology for the full-spectrum utilization of photocatalysts and synergistic photothermal coupling catalysis. It proposes a future development scenario for the new field of efficient solar catalytic conversion to produce solar fuels.

A hydraulic energy flow within the moving Earth

We consider the Earth moving through empty space at 30 km s−1 (in the Sun’s frame of reference). Associated with this motion is a convective flow of kinetic and internal energy. Since there is high pressure inside the Earth, and since the Earth is moving, there is yet another ‘hydraulic’ energy flow. This latter is what this article is about. Although this energy flow is huge, it is not addressed in the textbooks. The reason is that for the explanation one needs a concept which is not introduced in traditional presentations of classical gravitation: the gravitomagnetic field. The corresponding theory, gravitoelectromagnetism, was formulated in 1893 by Heaviside in analogy to Maxwell’s theory of electromagnetism. We discuss the question of what are the sources and sinks of this hydraulic, non-convective energy flow. To answer the question, we need to study the energy flow density distribution within the gravitational field. In doing so, we will make some interesting observations. The energy flow within the field is twice as large as it should be to transfer the field energy from one side of the Earth to the other. The excess flow goes back through the matter of the Earth. Since our readers may not be familiar with Heaviside’s theory, we first treat the electromagnetic analogue of our problem and then translate the results to the gravitational situation.

Propagation properties of the Pearcey Gaussian vortex electron plasma wave

In this Letter, we present an analytical discussion about the propagation properties of the Pearcey Gaussian vortex electron plasma (PGVEP) wave in an unmagnetized, collision-free plasma. Specifically, we examine the intensity, potential, energy flow density, and angular momentum density of the wave. Our findings reveal that the PGVEP wave exhibits the property of self-focusing, and intriguingly, it also demonstrates self-acceleration. Furthermore, we investigate the influence of the topological charge on the aforementioned propagation characteristics, considering the cases when the charge is n = 1 and n = 2, respectively.

Self-healing properties of symmetrical power-exponent-phase vortices.

The self-healing properties of symmetrical power-exponent-phase vortices (SPEPVs) are analyzed in this paper. By placing an obstacle in the optical path of SPEPVs, we simulated the propagation of the obstructed SPEPVs and verified the self-healing of the beam theoretically. We also explored the influence of external factors (e.g.,obstacle size and position) and internal parameters (topological charge l and power exponent n) on the self-healing effect of obstructed SPEPVs. Furthermore, the energy flow density, similarity coefficient, effective self-healing distance, and diffraction efficiency of the obstructed SPEPVs were also discussed. The results demonstrated that the transverse energy flows around the obstructed region of SPEPVs will recover with the propagation distance increased, and the effective self-healing distance gradually increases linearly with the obstacle size r x increased. The self-healing characteristic gives the petal-like SPEPVs the ability to trap microparticles three-dimensionally.