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In order to clarify the suction characteristics of unsaturated clay under different conditions of water and salt, taking soil in western Jilin province, China as the research object, the suctions (matrix suction and osmotic suction) of samples with different water content, salt type, and salt content were determined by filter paper method. The results indicate that salt type and content have insignificant influence on the matrix suction. With the increase of water content, the matrix suction decreases at different rates in different suction regimes. When water content is constant, the osmotic suction increases with the increase of salt content, and under the condition of a constant salt content, the osmotic suction first increases and then decreases with the increase of ion concentration of the pore water, and can reach tens of MPa. The concept of suction equilibrium water content is proposed. When water content of sample is higher than this value, the magnitude of osmotic suction will always be greater than that of matrix suction. This indicates the necessity to consider osmotic suction in the presence or change of salt in soil. The applicability of the traditional models of matrix suction and osmotic suction in the full suction range of clay is discussed, and it is found that the traditional models cannot make a full explanation to the variation in suction. Based on the experimental data, an improved van Genuchten matrix suction model and an osmotic suction model, transformed by the Planck blackbody radiation formula, are proposed. [ABSTRACT FROM AUTHOR]

A time‐varying lighting regime was formulated based on the action spectrum of the circadian and photopic lights. Using LED panels, the regime was implemented, tested and evaluated in classroom environment. The circadian to photopic ratio C/P was identified as one of the key parameters along with standard photometric and spectrometric quantities. The circadian rhythm of the human body as decomposed into time intervals of the day. By the continuous monitoring of the light output from the LED panels, we obtained instantaneous values and variation in the parameters, such as luminous flux, correlated color temperatures, color rendering indices, luminous efficiency and CS value. Based on these measurement data, we derived the variation of color temperature versus that of black body radiation and that of the color coordinates of the sun light. we also calculated the circadian stimulus curve and found it consistent with the one suggested by Mark Rea et al. [ABSTRACT FROM AUTHOR]

Modeling analysis of underwater pulsed arc discharge can predict the characteristics of plasma channels, providing theoretical guidance for the practical application of underwater pulsed discharge. Due to the complexity of experimental diagnostics for 'kA'-level underwater pulsed discharge, there is currently a lack of precise experimental data to support the initial value selection and result optimization of the modeling. This paper established a plasma channel model for underwater pulsed arc discharge. In conjunction with the Saha ionization equilibrium equation, the model was capable of simulating the current, pressure, temperature, and electron density of the channel after gap breakdown. By utilizing spectroscopic diagnostic data and a multi-objective optimization algorithm, the initial values and key parameters of the model were reasonably determined. The simulation results were in good agreement with the experimental diagnostic results, reasonably representing the trends in electron density and blackbody radiation temperature. Moreover, the model was applicable for reasonably explaining the emission spectral mechanism of the arc channel and shock waves prediction under different discharge conditions. [ABSTRACT FROM AUTHOR]

If our thinking is socially conditioned, then how, at the end of 1900, did Max Planck, whose thinking was shaped by classical mechanics, manage to think that energy is quantized? After all, the idea was incommensurable with the principles of Newton's mechanics. My thesis is that Planck did not intend to think about it. Trying to reconcile the time reversibility of the laws of mechanics with the time irreversibility of the laws of classical thermodynamics, he was constantly thinking according to rules inherited from others. Trying to find a theoretical explanation of the formula describing the distribution of the energy of black-body radiation -- arrived at by fitting theoretical parameters to new experimental data -- he in "an act of despair" applied Boltzmann's statistical concept of entropy. Then he noticed -- on a sheet of paper -- that classical and statistical formulas are identical if and only if the energy of resonators was a multiple of h?. What cannot appear in the human mind -- as the mind is socially conditioned -- can appear on paper. This gives a clear example of how computations in a "world on paper" (Olson 1994) can create new concepts. [ABSTRACT FROM AUTHOR]

During the high-speed flight of a vehicle in the atmosphere, surface friction with the air generates aerodynamic heating. The aerodynamic heating phenomenon can create extremely high temperatures near the surface. These high temperatures impact material properties and the structure of the aircraft, so thermal deformation measurement is essential in aerospace engineering. This paper revisits high-temperature deformation measurement using the digital image correlation (DIC) technique under high-intensity blackbody radiation with a precise speckle pattern fabrication and a heat haze reduction method. The effects of the speckle pattern on the DIC measurement have been thoroughly studied at room temperature, but high-temperature measurement studies have not reported such effects so far. We found that the commonly used methods to reduce the heat haze effect could produce incorrect results. Hence, we propose a new method to mitigate heat haze effects. An infrared radiation heater was employed to make an experimental setup that could heat a specimen up to 950 °C. First, we mitigated image saturation using a short-wavelength bandpass filter with blue light illumination, a standard procedure for high-temperature DIC deformation measurement. Second, we studied how to determine the proper size of the speckle pattern in a high-temperature environment. Third, we devised a reduction method for the heat haze effect. As proof of the effectiveness of our developed experimental method, we successfully measured the deformation of stainless steel 304 specimens from 25 °C to 800 °C. The results confirmed that this method can be applied to the research and development of thermal protection systems in the aerospace field. [ABSTRACT FROM AUTHOR]

The modern textbook analysis of the thermal state of photons inside a three-dimensional reflective cavity is based on the three quantum numbers that characterize photon's energy eigenvalues coming out when the boundary conditions are imposed. The crucial passage from the quantum numbers to the continuous frequency is operated by introducing a three-dimensional continuous version of the three discrete quantum numbers, which leads to the energy spectral density and to the entropy spectral density. This standard analysis obscures the role of the multiplicity of energy eigenvalues associated to the same eigenfrequency. In this paper we review the past derivations of Bose's entropy spectral density and present a new analysis of energy spectral density and entropy spectral density based on the multiplicity of energy eigenvalues. Our analysis explicitly defines the eigenfrequency distribution of energy and entropy and uses it as a starting point for the passage from the discrete eigenfrequencies to the continuous frequency. [ABSTRACT FROM AUTHOR]

In order to solve the problem of inaccurate emissivity obtained by empirical or experimental measurements in traditional volcanic inversion methods, which leads to the discrepancy between the temperature inversion results and the actual temperature, this paper constructs a joint inversion model of volcanic temperature and emissivity, and solves the volcanic temperature and emissivity simultaneously from the image element scale.In order to obtain the two unknown parameters of volcanic temperature and emissivity simultaneously, the study image element is assumed to be a pure image element and Lambertian body, and based on the blackbody radiation law and energy conservation law, the volcanic radiation energy transfer equation under different irradiance conditions is established and solved jointly. In this paper, the study area is Halemaʻumaʻu crater in Hawaii, and the short-wave infrared band of Landsat 8 satellite day and night remote sensing images with an imaging interval of 36 hours are used as the study data, and the temperature and emissivity are calculated using the golden mean and parabolic interpolation method with the same emissivity of the same image element in both scenes and the temperature approximation as the constraints. The results are as follows: the temperature inversion of the study area has a banding phenomenon, the temperature of the lava lake is 800–1050 K and the emissivity is 0.5–0.7; the temperature of the crater surface outside the lava lake is 500–800 K and the emissivity is 0.7–1.0. The inversion results are consistent with the actual situation. The results show that the method can realize the simultaneous inversion of volcanic temperature and emissivity parameters on the image element scale, which provides a new method for the inversion of volcanic temperature and emissivity. [ABSTRACT FROM AUTHOR]

This paper presents an FPGA-based lightweight and real-time infrared image processor based on a series of hardware-oriented lightweight algorithms. The two-point correction algorithm based on blackbody radiation is introduced to calibrate the non-uniformity of the sensor. With precomputed gain and offset matrices, the design can achieve real-time non-uniformity correction with a resolution of 640 × 480 . The blind pixel detection algorithm employs the first-level approximation to simplify multiple iterative computations. The blind pixel compensation algorithm in our design is constructed on the side-window-filtering method. The results of eight convolution kernels for side windows are computed simultaneously to improve the processing speed. Due to the proposed side-window-filtering-based blind pixel compensation algorithm, blind pixels can be effectively compensated while details in the image are preserved. Before image output, we also incorporated lightweight histogram equalization to make the processed image more easily observable to the human eyes. The proposed lightweight infrared image processor is implemented on Xilinx XC7A100T-2. Our proposed lightweight infrared image processor costs 10,894 LUTs, 9367 FFs, 4 BRAMs, and 5 DSP48. Under a 50 MHz clock, the processor achieves a speed of 30 frames per second at the cost of 1800 mW. The maximum operating frequency of our proposed processor can reach 186 MHz. Compared with existing similar works, our proposed infrared image processor incurs minimal resource overhead and has lower power consumption. [ABSTRACT FROM AUTHOR]

Thermography is probably the most used method of measuring surface temperature by analyzing radiation in the infrared part of the spectrum which accuracy depends on factors such as emissivity and reflected radiation. Contrary to popular belief that thermographic images represent temperature maps, they are actually thermal radiation converted into an image, and if not properly calibrated, they show incorrect temperatures. The objective of this study is to analyze commonly used image processing techniques and their impact on radiometric data in thermography. In particular, the extent to which a thermograph can be considered as an image and how image processing affects radiometric data. Three analyzes are presented in the paper. The first one examines how image processing techniques, such as contrast and brightness, affect physical reality and its representation in thermographic imaging. The second analysis examines the effects of JPEG compression on radiometric data and how degradation of the data varies with the compression parameters. The third analysis aims to determine the optimal resolution increase required to minimize the effects of compression on the radiometric data. The output from an IR camera in CSV format was used for these analyses, and compared to images from the manufacturer's software. The IR camera providing data in JPEG format was used, and the data included thermographic images, visible images, and a matrix of thermal radiation data. The study was verified with a reference blackbody radiation set at 60 ° C. The results highlight the dangers of interpreting thermographic images as temperature maps without considering the underlying radiometric data which can be affected by image processing and compression. The paper concludes with the importance of accurate and precise thermographic analysis for reliable temperature measurement. [ABSTRACT FROM AUTHOR]

In order to show how formal analogies between different physical systems play an important conceptual work in physics, this paper analyzes the evolution of Einstein's thoughts on the structure of radiation from the point of view of the formal analogies he used as 'lenses' to 'see' through the 'black box' of Planck's blackbody radiation law. A comparison is also made with his 1925 paper on the quantum gas where he used the same formal methods. Changes of formal points of view are most of the time taken for granted or passed over in silence in studies on the mathematization of physics as if they had no special significance. Revisiting Einstein's classic papers on the nature of light and matter from the angle of the various theoretical tools he used, namely entropy and energy fluctuation calculations, helps explain why he was in a unique position to make visible the particle structure of radiation and the dual (particle and wave) nature of light and matter. Finally, this case study calls attention to the more general question of the surprising creative power of formal analogies and their frequent use in theoretical physics. This aspect of intellectual creation can be useful in the teaching of physics. [ABSTRACT FROM AUTHOR]

This manuscript serves as an addendum to our previous paper, ‘Change of Exposure Time Mid-Test in High Temperature DIC Measurement,’ published in 2020 (Thai et al 2020 Meas. Sci. Technol. 31 075402). Since publishing that paper, we have since discovered that our two sources of lighting affect the brightness and contrast of high-temperature images differently. While it is broadly understood that changes in camera sensitivity (for example, by reducing exposure time) produce linear scaling in lighting, here we show that changes in temperature (which produce blackbody radiation) instead produce uniform offsets in lighting. This has important implications for the correlation algorithm, as the normalized sum of squared differences (NSSD) function compensates only for linear scaling, not uniform offsets. Here, we repeat the analysis for three different temperatures (1300 °C, 1450 °C, and 1600 °C) and correlate using three different algorithms: the sum of squared differences, NSSD, and zero-normalized sum of squared differences (ZNSSD). Our findings reinforce the consensus that, when performing digital image correlation (DIC) at extreme temperatures, it is important to always select the ZNSSD algorithm due to its ability to correct for both offsets and linear scaling in lighting. [ABSTRACT FROM AUTHOR]

Stefan–Boltzmann law, stating the fourth power temperature dependence of the radiation emission by a black-body, was empirically formulated by Stefan in 1874 by fitting existing experiments and theoretically validated by Boltzmann in 1884 on the basis of a classical physical model involving thermodynamics principles and the radiation pressure predicted by Maxwell equations. At first sight the electromagnetic (EM) gas assumed by Boltzmann and following Rayleigh (1900) identifiable as an ensemble of N classical normal-modes, looks like an extension of the classical model of the massive ideal-gas. Accordingly, for this EM gas the internal total energy, U, was assumed to be function of volume V and temperature T as U = U (V , T) , and the equation of state was given by U = 3 P V , with P the radiation pressure. In addition, Boltzmann implicitly assumed that, for given values of V and T, U and the number of modes N would take finite values. However, from one hand these assumptions are not justified by Maxwell equations and classical statistics since, in vacuum (i.e., far from the EM sources), the values of N and U diverge, the so-called ultraviolet catastrophe introduced by Ehrenfest in 1911. From another hand, Boltzmann derivation of Stefan law is found to be macroscopically compatible with its derivation from quantum statistics announced by Planck in 1901. In this paper, we present a justification of this puzzling classical/quantum compatibility by noticing that the implicit assumptions made by Boltzmann is fully justified by Planck quantum statistics. Furthermore, we shed new light on the interpretation of recent classical simulations of a black body carried out by Wang, Casati, and Benenti in 2022 who found an analogous puzzling consistency between Stefan–Boltzmann law and their simulations to induce speculations on classical physics and black body radiation that are claimed to require a critical reconsideration of the role of classical physics for the understanding of quantum mechanics. [ABSTRACT FROM AUTHOR]

Physics education has been identified as one of the public sectors that are mostly influenced by technological developments. This paper adopted the quasi-experimental pre- and post-test design to assess the effects of multimedia-aided technologies (MAT) on undergraduate students' performance in quantum physics (QP) at the University of Rwanda College of Education (UR-CE). The researcher used purposive sampling to get 385 undergraduate students. Participants were randomly allocated into experimental (group A) and control (group B) groups. Group A (187 students) students were taught selected topics of quantum physics (blackbody radiation, photoelectric effect, Compton effect, wave aspects of particles, De Broglie's hypothesis, diffraction, interference and double-slit experiment, model of the atom, uncertainty relations, wave function, and Schrodinger equations) for 6 weeks using multimedia-aided technologies and engage, predict, observe, and explain (EPOE) method, whereas group B (187 students) was taught same topics during the same period with a lecture method. The results of ANCOVA revealed that the group's performance was the same (p >.05) before learning with no effect size (.000), while they diverged after learning with different teaching interventions. The significance was very high and statistically different (p <.001) with a large effect size (>.5). This implies that students taught with multimedia-aided technologies (experimental group) outperformed those students taught with lecture teaching methods (control group). Thus, the study recommends that educators should adapt teaching using MAT and EPOE strategy not only in QP but also in other domains of physics to improve active engagement, understanding levels, and academic achievement. [ABSTRACT FROM AUTHOR]

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For hot and shiny forging, rapid optical three-dimensional (3D) shape measurement can find the defects in time, improve manufacturing efficiency and reduce manufacturing cost. Optical 3D measurement of hot and shiny forging faces following three challenges. (a) Influence of blackbody radiation on the red band of visible light leads to saturation of captured fringe pattern. (b) Infrared band of blackbody radiation causes the camera to heat up. (c) Specular reflection of shiny forging leads to local saturation of captured fringe pattern. To address the above issues, we propose an effective optical 3D measurement scheme for hot and shiny forging in this paper. Firstly, the experiments demonstrate that the influence of blackbody radiation on visible light is concentrated in red light band and has no crosstalk in the blue light band, so we adopt blue light projection and blue light band-pass filter (BBF) to capture clear fringe pattern. Secondly, since the BBF cannot block the near-infrared component, we use an infrared light cutoff filter (ICF) to reduce the thermal effect of blackbody radiation. Finally, we analyze the Fourier transform (FT) spectrum of saturated fringe pattern caused by specular reflection, and propose an efficient Butterworth low-pass filtering (BLPF) method that does not require additional hardware, algorithm processing, and image assistance. The experimental results verify the effectiveness of the proposed scheme. • 3D measurement for hot and shiny forging based on blue light projection and blue light band-pass filter is proposed. • An effective infrared light cutoff filter is adopted to reduce the thermal effect on the camera. • Butterworth low-pass filter is adopted to suppress high-order harmonics introduced by shiny forging. [ABSTRACT FROM AUTHOR]

The present age, which can be called the Information Age, has a core technology constituted by bits transported by photons. Both concepts, bit and photon, originated in the past century: the concept of photon was introduced by Planck in 1900 when he advanced the solution of the blackbody spectrum, and bit is a term first used by Shannon in 1948 when he introduced the theorems that founded information theory. The connection between Planck and Shannon is not immediately apparent; nor is it obvious that they derived their basic results from the concept of entropy. Examination of other important scientists can shed light on Planck's and Shannon's work in these respects. Darwin and Fowler, who in 1922 published a couple of papers where they reinterpreted Planck's results, pointed out the centrality of the partition function to statistical mechanics and thermodynamics. The same roots have been more recently reconsidered by Jaynes, who extended the considerations advanced by Darwin and Fowler to information theory. This paper investigates how the concept of entropy was propagated in the past century in order to show how a simple intuition, born in the 1824 during the first industrial revolution in the mind of the young French engineer Carnot, is literally still enlightening the fourth industrial revolution and probably will continue to do so in the coming century. [ABSTRACT FROM AUTHOR]

The COBE/FIRAS dataset is used to calculate the Cosmic Microwave Background temperature and the uncertainty using the Blackbody Radiation Inversion (BRI) method. In this research work, the procedure is somewhat comparable to the mixing of weighted blackbodies in the case of the dipole. The temperature and its spreading for the monopole and dipole, respectively, are 2.741 ± 0.018 K and 2.748 ± 0.270 K. This dipole spreading exceeds the spreading predicted by taking relative motion into account (i.e., 3.3 × 10−3 K). The comparison of the probability distributions for the monopole spectrum, dipole spectrum, and their resultant is also displayed. It is shown that the distribution is symmetrically orientated. We estimated the µ and y-distortions by interpreting the spreading as the distortion and found that they are of the order of 10−4 and 10−5, respectively, for the monopole spectrum and 10−2 for the dipole spectrum. The paper also highlights the effectiveness of the BRI method and hints at future applications in the thermal nature of the early universe. [ABSTRACT FROM AUTHOR]

Classical statistical mechanics has long relied on assumptions such as the equipartition theorem to understand the behavior of the complicated systems of many particles. The successes of this approach are well known, but there are also many well-known issues with classical theories. For some of these, the introduction of quantum mechanics is necessary, e.g., the ultraviolet catastrophe. However, more recently, the validity of assumptions such as the equipartition of energy in classical systems was called into question. For instance, a detailed analysis of a simplified model for blackbody radiation was apparently able to deduce the Stefan–Boltzmann law using purely classical statistical mechanics. This novel approach involved a careful analysis of a "metastable" state which greatly delays the approach to equilibrium. In this paper, we perform a broad analysis of such a metastable state in the classical Fermi–Pasta–Ulam–Tsingou (FPUT) models. We treat both the α -FPUT and β -FPUT models, exploring both quantitative and qualitative behavior. After introducing the models, we validate our methodology by reproducing the well-known FPUT recurrences in both models and confirming earlier results on how the strength of the recurrences depends on a single system parameter. We establish that the metastable state in the FPUT models can be defined by using a single degree-of-freedom measure—the spectral entropy (η)—and show that this measure has the power to quantify the distance from equipartition. For the α -FPUT model, a comparison to the integrable Toda lattice allows us to define rather clearly the lifetime of the metastable state for the standard initial conditions. We next devise a method to measure the lifetime of the metastable state t m in the α -FPUT model that reduces the sensitivity to the exact initial conditions. Our procedure involves averaging over random initial phases in the plane of initial conditions, the P 1 - Q 1 plane. Applying this procedure gives us a power-law scaling for t m , with the important result that the power laws for different system sizes collapse down to the same exponent as E α 2 → 0 . We examine the energy spectrum E (k) over time in the α -FPUT model and again compare the results to those of the Toda model. This analysis tentatively supports a method for an irreversible energy dissipation process suggested by Onorato et al.: four-wave and six-wave resonances as described by the "wave turbulence" theory. We next apply a similar approach to the β -FPUT model. Here, we explore in particular the different behavior for the two different signs of β. Finally, we describe a procedure for calculating t m in the β -FPUT model, a very different task than for the α -FPUT model, because the β -FPUT model is not a truncation of an integrable nonlinear model. [ABSTRACT FROM AUTHOR]

Multispectral thermometry is based on the law of blackbody radiation and is widely used in engineering practice today. Temperature values can be inferred from radiation intensity and multiple sets of wavelengths. Multispectral thermometry eliminates the requirements for single-spectral and spectral similarity, which are associated with two-colour thermometry. In the process of multispectral temperature inversion, the solution of spectral emissivity and multispectral data processing can be seen as the keys to accurate thermometry. At present, spectral emissivity is most commonly estimated using assumption models. When an assumption model closely matches an actual situation, the inversion of the temperature and the accuracy of spectral emissivity are both very high; however, when the two are not closely matched, the inversion result is very different from the actual situation. Assumption models of spectral emissivity exhibit drawbacks when used for thermometry of a complex material, or any material whose properties dynamically change during a combustion process. To address the above problems, in the present study, we developed a multispectral thermometry method based on optimisation ideas. This method involves analysing connections between measured temperatures of each channel in a multispectral temperature inversion process; it also makes use of correlations between multispectral signals at different temperatures. In short, we established a multivariate temperature difference correlation function based on the principles of multispectral radiometric thermometry, using information correlations between data for each channel in a temperature inversion process. We then established a high-precision thermometry model by optimising the correlation function and correcting any measurement errors. This method simplifies the modelling process so that it becomes an optimisation problem of the temperature difference function. This also removes the need to assume the relationships between spectral emissivity and other physical quantities, simplifying the process of multispectral thermometry. Finally, this involves correction of the spectral data so that any impact of measurement error on the thermometry is reduced. In order to verify the feasibility and reliability of the method, a simple eight-channel multispectral thermometry device was used for experimental validation, in which the temperature emitted from a blackbody furnace was identified as the standard value. In addition, spectral data from the 468–603 nm band were calibrated within a temperature range of 1923.15–2273.15 K, resulting in multispectral thermometry based on optimisation principles with an error rate of around 0.3% and a temperature calculation time of less than 3 s. The achieved level of inversion accuracy was better than that obtained using either a secondary measurement method (SMM) or a neural network method, and the calculation speed achieved was considerably faster than that obtained using the SMM method. [ABSTRACT FROM AUTHOR]

In this paper, using automated optical inspection equipment and a thermal imager, the position and the temperature of the heat source or measured object can effectively be grasped. The high-resolution depth camera is with the stereo vision distance measurement and the low-resolution thermal imager is with the long-wave infrared measurement. Based on Planck's black body radiation law and Stefan–Boltzmann law, the binocular stereo calibration of the two cameras was calculated. In order to improve the measured temperature error at different distances, equipped with Intel Real Sense Depth Camera D435, a compensator is proposed to ensure that the measured temperature of the heat source is correct and accurate. From the results, it can be clearly seen that the actual measured temperature at each distance is proportional to the temperature of the thermal image vanadium oxide, while the actual measured temperature is inversely proportional to the distance of the test object. By the proposed compensation function, the compensation temperature at varying vanadium oxide temperatures can be obtained. The errors between the average temperature at each distance and the constant temperature of the test object at 39 °C are all less than 0.1%. [ABSTRACT FROM AUTHOR]

GaInAsSb cells may show better performance than GaSb cells in low-temperature thermophotovoltaic systems due to their lower bandgap energies. In this paper, numerical simulation is used to evaluate GaInAsSb and GaSb cells with similar structures under different radiation temperatures. We find that GaInAsSb cells with n-type emitters show slightly higher output power densities compared with those for GaSb cells with n-type emitters below 1500 K given-blackbody radiation, but the power density of the GaSb cells will surpass the former’s above this temperature point. Furthermore, over the temperature range of $1200\sim 2000$ K, the efficiencies of GaSb cells with n-emitters are $1.31\sim 2.32$ times higher than those of GaInAsSb cells with n-emitters if filters with 10% subbandgap losses are used. Several parameters that affect the GaInAsSb cell were analyzed, such as doping profiles, thicknesses of GaInAsSb epitaxial layer and surface recombination velocity. The n-on-p junctions, i.e., n-type emitters vs p-type emitters are better for GaInAsSb cell fabrication, which is similar to that for the GaSb cell. [ABSTRACT FROM AUTHOR]

High-temperature measurements above 1000 °C are critical in harsh environments such as aerospace, metallurgy, fossil fuel, and power production. Fiber-optic high-temperature sensors are gradually replacing traditional electronic sensors due to their small size, resistance to electromagnetic interference, remote detection, multiplexing, and distributed measurement advantages. This paper reviews the sensing principle, structural design, and temperature measurement performance of fiber-optic high-temperature sensors, as well as recent significant progress in the transition of sensing solutions from glass to crystal fiber. Finally, future prospects and challenges in developing fiber-optic high-temperature sensors are also discussed. [ABSTRACT FROM AUTHOR]

This paper is aimed at the investigation of the acoustic and spectral characteristics of underwater electric sparks generated between two plate electrodes, using synchronized gas bubble injection. There are two purposes served by discharge initiation in the bubble. Firstly, it creates a favorable condition for electrical breakdown. Secondly, the gas bubble provides an opportunity for the direct spectroscopy of plasma light emission, avoiding water absorption. The effect of water absorption on captured spectra was studied. It was observed that the emission intensity of the Ha line and a shockwave amplitude generated by discharge strongly depend on the size of the gas bubble in the moment of the discharge initiation. It was found that the plasma in the underwater spark channel does not correspond to a source of black-body radiation. This study can be also very useful for understanding the difference between discharges produced directly in a liquid and discharges produced in gas/vapor bubbles surrounded by a liquid. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct the thermodynamics of open quantum systems of elementary Bose-gas particles in the framework of nonextensive Tsallis statistics based on modified quantum entropy, which depends on the real deformation parameter We obtain generalized expressions for the thermodynamic potential, internal energy, free energy, specific heat, and pressure, as well as the basic thermodynamic equations. Modified equilibrium Bose–Einstein distributions for massive particles and generalized Planck, Rayleigh–Jeans, and Wien laws for photons that can be applied to various physical problems, in particular, to the description of cosmic blackbody radiation, are discussed. The initial basis for such a consideration of a photon gas is the assumption that the photon distribution of the cosmic background radiation (in thermal equilibrium) may differ from the classical Planck distribution due to the influence of long-range gravitational effects at large distances. This influence is probably a reflection of the fact that in remote time matter and light were strongly interconnected. The generalized thermodynamics of a photon gas can be used, in particular, as a theoretical justification for experimental studies of blackbody radiation inside various astrophysical objects. [ABSTRACT FROM AUTHOR]

In this paper, we consider the d -mode q -deformed bosonic Newton oscillators. Regarding photon and phonon as the particles obeying the multi-mode q -deformed bosonic Newton algebra, we discuss the blackbody radiation and Debye model. [ABSTRACT FROM AUTHOR]

In order to improve the absorption of stray radiation traps and thermal radiation detectors of blackbody radiators and enhance the thermal radiation transmission, large aperture and high-emissivity blackbody radiators or compact space-borne blackbody sources can be developed. The design of blackbody cavity with V-grooves is a method to change the effective emissivity of blackbody radiation source. At the design stage, the most important work is to evaluate its radiation characteristics in order to verify the effectiveness of this method. Two kinds of blackbody cavity models are designed in this paper. One is a cylindrical–conical blackbody cavity with a 2-mm deep 50° angle V-grooves (the cavity is 300 mm long and 80 mm in diameter, with a depth of 277 mm the cone part of the cavity is 23.09 mm long, the top angle of the cone is 120°, the wall thickness is 2 mm, and the surface will be painted with 0.95 emissivity coating). The other is the blackbody cavity model with the same structure and smooth inner wall. Using the special software based on Monte Carlo method, the radiation characteristics of the two blackbody cavity models are simulated under isothermal conditions. The average normal effective emissivity and right-conical effective emissivity of the blackbody cavity with different observation radius are obtained, respectively. The results show that the average normal effective emissivity and right-conical effective emissivity of the blackbody cavity with V-grooves on the inner wall are increased. In addition, the experimental results of radiative properties of the blackbody radiator having the V-grooved cavity measured by thermal cavity reflectometry method agree with the theoretical simulation results. Therefore, it is proved that the blackbody cavity with V-grooves on the inner wall (except for special angles) can be an effective way to improve the emissivity of the blackbody source. [ABSTRACT FROM AUTHOR]

• Studied the impact of coating emissivity, base-height ratio, and reflection characteristics on the performance of plane blackbodies with various pyramid array structures. • Investigated various pyramid array structures, analysed their effects on emissivity, and evaluated the temperature field distributions of radiation surfaces with different blackbodies. • Emphasized the optimization of surface structures and the use of high-emissivity coatings to significantly improve the radiation capabilities of plane blackbodies. • Developed a light transmission model using the Monte Carlo Method to simulate emissivity and conducted experimental validations with fabricated specimens, demonstrating strong alignment with the simulation results. • Provided crucial data and insights for exploring the plane blackbody emissivity of different array structures and coating materials. The plane blackbody radiation source is pivotal to the infrared remote sensing detection system, with emissivity serving as a critical metric for its performance evaluation. This metric is predominantly influenced by the surface structure and coating properties. To improve emissivity, existing works have utilized pyramid structures to expand the contact area between the radiation surface and light, thereby augmenting light absorption. Nonetheless, there is relatively little research exploring the impact of pyramid structure on emissivity, leading to a scarcity of related emissivity data for plane blackbody. In this paper, we explored the impact on the blackbody emissivity induced by different pyramid structures, including the triangular pyramid array (TPA), the quadrangular pyramid array (QPA), the pentagonal pyramid array (PPA), and the hexagonal pyramid array (HPA). Also, the effects involving coating properties, the base-height ratio of the pyramid, and reflection characteristics on emissivity were investigated based on the Monte Carlo Method. Then, the specimens with diffuse reflection (DR) and near-specular reflection (NSR) were fabricated and tested experimentally. The uncertainties of simulation and experiment were maintained below 0.21 % and 0.50 %, respectively. Experimental results are well aligned with the corresponding simulation results, indicating that the normal emissivity of the TPA blackbody is 0.12 % higher than the QPA blackbody, and the directional emissivity uniform of the TPA blackbody is superior to that of the QPA blackbody for the DR model in the 8–14 μm waveband. Furthermore, the temperature field distributions of radiation surface for TPA and QPA blackbody were analysed, noting a maximum temperature difference of 50 mK and 30 mK, respectively. This paper provides experimental support and design references for further improving the emissivity of plane blackbodies. [ABSTRACT FROM AUTHOR]

The study of radiation exergy has important significance for solar energy and high-temperature engineering. In this paper, several exergy expressions of blackbody radiation were discussed and the differences between Petela's expression of exergy and two other expressions were analyzed. Considering that radiant energy and thermal energy are different, the radiation machine model was established; furthermore, the validity of Petela's formula was indicated by this model. Based on the concept of radiation equivalent temperature, the integral form expression of monochromatic photon exergy was put forward by establishing the infinite-staged Carnot heat engine model. At the same time, an approximate relation between equivalent temperature and radiation wavelength was given. The error of this relation is negligible when calculating the exergy of blackbody radiation within the temperature range of the engineering field. Finally, the monochromatic photon entropy was discussed by considering the infinite-staged Carnot heat engine model, and an expression of photon entropy with integral form was given. The monochromatic photon entropy and exergy proposed in our paper satisfy the thermodynamic relation and can reflect the differences between radiant energy and thermal energy. [ABSTRACT FROM AUTHOR]

Advances in green nano-technologies is the main field under which the present paper series is firstly envisaged; therefore, advanced, research-progressive nano-science is aimed to shorten the distance from fundamental concepts to applications, devices and their implementations. It however would gather both physics and chemistry fundamental and applicative fields in dealing with solar/black body radiation as well as with new materials based on inorganic-organic hybrids, composites and electron quantum features (excitons, bondons, diffusion, electrical circuits, semiconductors, quantum dots, etc.). Such research is therefore equally highly necessary for both communities (physical engineering and chemical engineering) enlightening the dedicated international forums on quantum-dots based solar cells, as well as for giving further impetus to this new field of photovoltaics by gathering active international scientists in solar energy. The present paper offers a review on the progresses regarding the application of defective graphene and other defect-doped carbon nanostructures in the construction of solar cells devices towards introducing the semiconductor based graphenes. Competitiveness and eco-ecological aspects of such projects are also considered in a resumed scientific and innovative research. [ABSTRACT FROM AUTHOR]

This paper presents a study of near-field radiometry for internal temperature measurements of the human body. The radiometer has a Dicke architecture and operates in the 1.4-GHz quiet band for centimeter penetration into tissues with minimized radio frequency interference (RFI). The total blackbody power from a tissue stack is received by a probe placed on the skin, designed to receive a high percentage of the total power from a buried tissue layer. Temperature retrieval for subsurface tissue layers is performed using near-field weighting functions obtained from full-wave simulations. The calibrated radiometer is demonstrated to track the temperature of a phantom muscle tissue layer under phantom fat and skin layers within a fraction of a degree. It is shown that RFI can be reduced through the use of a second probe and adaptive processing. Measurements on the human cheek show good agreement with independent thermocouple measurements inside the mouth. [ABSTRACT FROM PUBLISHER]

Hawking radiation is emitted from black holes. At the black hole event horizon, the Hawking radiation is the exact blackbody radiation. However, while propagating, the Hawking radiation is modified by the curvature of spacetime. Therefore, it is not considered as blackbody radiation when travelling out of the event horizon. Greybody factors are the transmission probabilities with which the Hawking radiation can be transmitted by gravitational potential to spatial infinity. This potential is the curvature of spacetime generated by a black hole. In this paper, the greybody factors for various black holes in perfect fluid spheres are calculated. The formula of the lower bound on the transmission probability is used to obtain the greybody factors. The bounds can give us a qualitative understanding of the quantum nature of black holes. Finally, we calculate the Hawking temperature and entropy of blackholes. [ABSTRACT FROM AUTHOR]

Infrared (IR) radiometry technology is an important method for characterizing the IR signature of targets, such as aircrafts or rockets. However, the received signal of targets could be reduced by a combination of atmospheric molecule absorption and aerosol scattering. Therefore, atmospheric correction is a requisite step for obtaining the real radiance of targets. Conventionally, the atmospheric transmittance and the air path radiance are calculated by an atmospheric radiative transfer calculation software. In this paper, an improved IR radiometric method based on constant reference correction of atmospheric attenuation is proposed. The basic principle and procedure of this method are introduced, and then the linear model of high-speed calibration in consideration of the integration time is employed and confirmed, which is then applicable in various complex conditions. To eliminate stochastic errors, radiometric experiments were conducted for multiple integration times. Finally, several experiments were performed on a mid-wave IR system with F600 mm aperture. The radiometry results indicate that the radiation inversion precision of the novel method is 4.78-4.89%, while the precision of the conventional method is 10.86-13.81%. [ABSTRACT FROM AUTHOR]

Shadows are evident in most aerial images with high resolutions, particularly in urban scenes, and their existence obstructs the image interpretation and the following application, such as classification and target detection. Most current shadow removal methods were proposed for natural images, whereas shadows in remote sensing images show distinct characteristics. We have therefore analyzed the characteristics of shadows in aerial images, and in this paper, we propose a new shadow removal method for aerial images, using nonlocal (NL) operators. In the proposed method, the soft shadow is introduced to replace the traditional binary hard shadow. NL operators are used to regularize the shadow scale and the updated shadow-free image. Furthermore, a spatially adaptive NL regularization is introduced to handle compound shadows. The combination of the soft shadow and NL operators yields satisfying shadow-free results, preserving textures and holding regular color. Different types of shadowed aerial images are employed to verify the proposed method, and the results are compared with two other methods. The experimental results confirm the validity of the proposed method and the advantage of the soft-shadow approach. [ABSTRACT FROM AUTHOR]

The Gimballed Limb Observer for Radiance Imaging of the Atmosphere (GLORIA) is a prototype of an imaging Fourier Transform Spectrometer (FTS) for PREMIER, a former candidate mission for ESA's Earth Explorer 7. GLORIA is deployed on board various research aircraft such as the Russian M55 Geophysica or the German HALO. The instrument provides detailed infrared images of the Upper Troposphere/Lower Stratosphere (UTLS) region, which plays a crucial role in the climate system. GLORIA uses a two-dimensional detector array for infrared limb observations in emission and therefore needs large-area blackbody radiation sources (126mm×126 mm) for calibration. In order to meet the highly demanding uncertainty requirements for the scientific objectives of the GLORIA missions and due to the sophisticated tomographic evaluation scheme, the spatial distribution of the radiance temperature of the blackbody calibration sources has to be determined with an uncertainty of about 0.1 K. Since GLORIA is exposed to the hostile environment of the UTLS with mutable low temperature and pressure, an in-flight calibration system has to be carefully designed to cope with those adverse circumstances. The GLORIA in-flight calibration system consists of two identical weight-optimised high-precision blackbody radiation sources, which are independently stabilised at two different temperatures. The two point calibration is in the range of the observed atmospheric infrared radiance emissions with 10K below and 30K above ambient temperature, respectively. Thermo-Electric Coolers are used to control the temperature of the blackbody radiation sources offering the advantage of avoiding cryogens and mechanical coolers. The design and performance of the GLORIA in-flight calibration system is presented. The blackbody calibration sources have been comprehensively characterised for their spatially (full aperture) and spectrally (7 to 13 μm) resolved radiation properties in terms of radiance temperatures traceable to the International Temperature Scale (ITS-90) at the Physikalisch- Technische Bundesanstalt (PTB), the national metrology institute of Germany. [ABSTRACT FROM AUTHOR]

The blackbody radiation can provide light source for the fiber Fabry-Perot sensor system, but the output signal is difficult to demodulate. Because the signal of Fabry-Perot sensor is modulated by spectrum of blackbody radiation and SNR of signal is low. In this paper, the characteristics of the fiber Fabry-Perot sensor signal based on the blackbody light source were investigated. Effect of spectrum of blackbody radiation and low SNR on demodulation was analyzed. Strain experimental results show that correlation-like algorithm can accurately demodulate the signal when the temperature of the blackbody light source is equal to or higher than 800 °C. The maximum mean square error is $8.375~\mu \varepsilon $ after separating influence of temperature by the relationship between center wavelength of blackbody radiation and temperature. Higher the temperature, higher the demodulation accuracy. [ABSTRACT FROM AUTHOR]

Blackbody radiation inversion is a mathematical process for the determination of probability distribution of temperature from measured radiated power spectrum. In this paper a simple and stable blackbody radiation inversion is achieved by using an analytical function with three determinable parameters for temperature distribution. This inversion technique is used to invert the blackbody radiation field of the cosmic microwave background, the remnant radiation of the hot big bang, to infer the temperature distribution of the generating medium. The salient features of this distribution are investigated and analysis of this distribution predicts the presence of distortion in the cosmic microwave background spectrum. [ABSTRACT FROM AUTHOR]

In this paper, we present the SDSS g′-, the Cousins Rc-, and Ic-band magnitudes and associated colors of Starlink's STARLINK-1113 (one of the standard Starlink satellites) and 1130 (Darksat) with a darkening treatment to its surface. Using the 105 cm Murikabushi telescope/MITSuME, simultaneous multicolor observations for the above satellites were conducted four times: on 2020 April 10 and May 18 (for Darksat), and 2020 June 11 (for Darksat and STARLINK-1113). We found that (1) the SDSS g′-band apparent magnitudes of Darksat (6.95 ± 0.11–7.65 ± 0.11 mag) are comparable to or brighter than that of STARLINK-1113 (7.69 ± 0.16 mag), (2) the shorter the observed wavelength is, the fainter the satellite magnitudes tend to become, (3) the reflected flux by STARLINK-1113 is extremely (>1.0 mag) redder than that of Darksat, (4) there is no clear correlation between the solar phase angle and orbital altitude-scaled magnitude, and (5) by flux model fitting of the satellite trails with the blackbody radiation, it is found that the albedo of Darksat is about half that of STARLINK-1113. In particular, result (1) is inconsistent with previous studies. However, considering both solar and observer phase angles and atmospheric extinction, the brightness of STARLINK-1113 can be drastically reduced in the SDSS g′ and the Cousins Rc band. Simultaneous multicolor–multispot observations of more than three colors would give us more detailed information regarding the impact of low-Earth-orbit satellite constellations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to predict total emissivity of CO near earth atmospheric conditions. Due to lack of total emissivity information in this temperature range, it was predicted from line data or spectral emissivity data. The results have been compared with several methods in this paper. The models compared are by Bliss [2], Hottel [4], Atwater and Ball [5, 7], wide band model by Edwards [6], Yamamoto and Sasamori [7, 8], and using HITRAN data base [12]. For spectral emissivity, the results by Yamamoto and Sasamori match well with predictions using HITRAN data base. For total emissivity, the deviations between models are rather large and sometimes more than about 0.05 at the upper bound value around 0.2. In general, for a given condition, the upper bound of total emissivity is given by Hottel, and lower bound is given by HITRAN. The predictions by Edwards are in between but near to those of Hottel. [ABSTRACT FROM AUTHOR]

Purpose – This paper aims to demonstrate that fundamental aspects of quantum theory can be applied to work in information studies (IS). Design/methodology/approach – The field of information studies is so broad and extensive that it requires similar breadth of epistemic and methodological features in order to fulfill its inherent promise as a human enterprise. Quantum theory holds promise as a way to shape questions and inquiry in information studies (IS). Findings – The revolutionary elements of quantum theory, such as entanglement, nonlocality, etc. can be applied to information, especially language-based communication. Research limitations/implications – Perhaps most especially, the non- or extra-mathematical components of quantum theory offer ontological and epistemic modes of thought which apply to information. Those modes of thought are ripe with conceptual promise for examination of, for example, information as objective entity and as complex material substance. This paper explores some of the potentially promising ways to explore information as a complex phenomenon. Originality/value – While some work in IS has considered quantum phenomena, there has not been a thorough investigation of the theory's application to inquiry in IS. [ABSTRACT FROM AUTHOR]

In this paper, Wien's displacement law as one of the most important laws of thermal radiation, for which Wien has won the Nobel Prize in Physics, is studied and derived from the perspective of phase transition by using catastrophe theory. This paper describes in detail how the control variable causes the phase transition of the system potential function and the main indexes for judging whether the phase transition occurs. By extending the control variable in the catastrophe theory affecting the thermal radiation into multi-parameters form, the function equilibrium curve of the blackbody radiation is solved, and then the two expressions of Wien's displacement law including wavelength-temperature and wavelength-temperature are derived theoretically. Furthermore, a phase transition method is proposed to study the thermal radiation of blackbody. This not only provides a new perspective for the research of thermal radiation, but also provides a new idea for the study of other phase transitions. [ABSTRACT FROM AUTHOR]

Teaching blackbody radiation within the framework of astrophysics can motivate students to learn and obtain a more profound and qualitative understanding of the subject. In this paper we present a teaching module that intertwines teaching blackbody radiation via the continuous spectrum of hot objects, especially the stars. The module's approach was that of guided inquiry. Students of upper secondary education carried out experimental activities that included a combination of hands-on activities and computer processing. They actively and creatively engaged in the activities which helped them develop a more complex and structured knowledge of the subject. A ten-multiple choice questionnaire was administered before and after the implementation and the data were qualitatively and quantitatively analyzed. The results showed that the intervention had a significant impact on students' learning outcomes. [ABSTRACT FROM AUTHOR]

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Many of the processes involved in the creation of semiconductor devices involve high-temperature processing of silicon wafers. The benefits of reduced thermal budget and faster cycle time make rapid thermal processing (RTP) a possible key technology for semiconductor manufacturing. However, the problem of nonuniform wafer temperature has prevented it from further spread among the industry. The first step in developing controls to maintain a uniform wafer temperature is accurate temperature measurement during processing. In this paper, a system was developed to exploit the specular reflectivity of silicon wafers and obtain a measurement of the wafer temperature profile. The spectral reflectivity is determined by measuring the intensity of an incident beam and the beam reflected from the wafer surface. With this measured reflectivity value the spectral-directional wafer emissivity was determined using Kirchhoff's law. The obtained emissivity then was used to calculate the wafer temperature profile from an image obtained with an infrared camera. An experimental study of the transmittance of an undoped silicon calibration wafer at an elevated temperature is also discussed. [ABSTRACT FROM AUTHOR]

Graphene is an attractive material for terahertz (THz) detectors due to its unique properties of extremely weak electron-phonon interaction and small electronic heat capacity. In this paper, we demonstrate a lens-antenna-coupled THz detector based on a diffusive superconductor-graphene-superconductor (SGS) junction, which has a sharp resistive transition at 1.4 K due to the proximity Josephson coupling. The SGS Josephson detector, measured with a dc superconducting quantum interference device (SQUID) readout, exhibits an electrical noise equivalent power (NEP) as low as 5 × 10−17 W/Hz0.5 at 0.1 K, which is still limited by the readout noise. Furthermore, the optical performance of the SGS Josephson detector is measured with a cryogenic blackbody radiation source, giving an optical NEP of 2.5–5 × 10−16 W/Hz0.5 at 1.4 THz in the temperature range from 0.1 K to 0.6 K. [Display omitted] [ABSTRACT FROM AUTHOR]

The Advanced Technology Microwave Sounder (ATMS) on board the Suomi National Polar-orbiting Partnership (NPP) satellite is a total power radiometer and scans across the track with a range of ±52.77° from nadir. It has 22 channels and measures the microwave radiation at either quasi-vertical or quasi-horizontal polarization from the Earth's atmosphere. The ATMS scanning reflector is made of beryllium coated with gold and can have an emission due to the surface roughness. During prelaunch phase, an estimate of the reflector emissivity was not explored. In this paper, a new methodology is developed to assess the antenna emission from the ATMS pitch-over observations. It is found that the antenna emission is significant and dominates the scan-angle-dependent features in the ATMS antenna temperatures. Retrieved emissivity from K- to G-bands ranges from 0.002 to 0.006. An error model was also developed to assess the impact of antenna emissivity to calibration accuracy of antenna temperature products. Simulation results show that the calibration error is scene temperature dependent and can be as large as 2.5 K for space view. [ABSTRACT FROM PUBLISHER]

Spectral emissivity is one of the important physical properties of materials. Emissivity measurement is critical for accurate temperature measurements and the evaluation of the stealth performance for materials. In this paper, a Fourier transform infrared spectrometer and an energy comparison method are used to study material emissivity measurements. Two reference blackbodies are employed for real-time measurement and correction of the spectrometer background function to enhance the emissivity measurement accuracy, to improve the design of a three-parabolic-mirror optical system, and to enlarge the optical field of view to meet the measurement requirements. The linearity of the system is measured using a mercury cadmium telluride detector and a deuterated triglycine sulfate detector. The results indicate that the linear range of the system meets the emissivity measurement requirements for the temperature range from $$50\,^{\circ }\mathrm{C}$$ to $$1000\,^{\circ }\mathrm{C}$$ . The effective radiation surface is introduced as a parameter of the reference blackbodies to reduce the influence of the measurement distance. The Fourier transform infrared spectrometer is used to measure the spectral emissivity of a conductive silica film and SiC, respectively, at different temperatures in the wavelength range of $$1\ \upmu \mathrm{m}$$ to $$25\ \upmu \mathrm{m}$$ . The expanded uncertainty is less than 5 %. [ABSTRACT FROM AUTHOR]

We present Einstein coefficient spectra and a detailed-balance derivation of generalized Einstein relations between them that is based on the connection between spontaneous and stimulated emission. If two broadened levels or bands overlap in energy, transitions between them need not be purely absorptive or emissive. Consequently, spontaneous emission can occur in both transition directions, and four Einstein coefficient spectra replace the three Einstein coefficients for a line. At equilibrium, the four different spectra obey five pairwise relationships and one lineshape generates all four. These relationships are independent of molecular quantum statistics and predict the Stokes' shift between forward and reverse transitions required by equilibrium with blackbody radiation. For Boltzmann statistics, the relative strengths of forward and reverse transitions depend on the formal chemical potential difference between the initial and final bands, which becomes the standard chemical potential difference for ideal solutes. The formal chemical potential of a band replaces both the energy and degeneracy of a quantum level. Like the energies of quantum levels, the formal chemical potentials of bands obey the Rydberg-Ritz combination principle. Each stimulated Einstein coefficient spectrum gives a frequency-dependent transition cross-section. Transition cross-sections obey causality and a detailed-balance condition with spontaneous emission, but do not directly obey generalized Einstein relations. Even with an energetic width much less than the photon energy, a predominantly absorptive forward transition with an energetic width much greater than the thermal energy can have such an extreme Stokes' shift that its reverse transition cross-section becomes predominantly absorptive rather than emissive. [ABSTRACT FROM AUTHOR]

Nonlinear wave propagation in large extra spatial dimensions (on and above d = 2) is investigated in the context of nonlinear electrodynamics theories that depend exclusively on the invariant F (= − (1 / 4) F μ ν F μ ν) . In this vein, we consider propagating waves under the influence of external uniform electric and magnetic fields. Features related to the blackbody radiation in the presence of a background constant electric field such as the generalization of the spectral energy density distribution and the Stefan–Boltzmann law are obtained. Interestingly enough, anisotropic contributions to the frequency spectrum appear in connection to the nonlinearity of the electromagnetic field. In addition, the long wavelength regime and Wien's displacement law in this situation are studied. The corresponding thermodynamics quantities at thermal equilibrium, such as energy, pressure, entropy, and heat capacity densities are contemplated as well. [ABSTRACT FROM AUTHOR]

The fundamental plane of black hole activity is a very important tool to study accretion and jets. However, we found that the SEDs of AGNs and XRBs are different in the 2–10 keV energy band, and it seems inappropriate to use 2–10 keV X-ray luminosities to study the fundamental plane. In this work, we use the luminosity near the peak of the blackbody radiation of the active galactic nuclei and black hole binaries to replace the 2–10 keV luminosity. We re-explore the fundamental plane of black hole activity by using the 2500 A ˚ luminosity as the peak luminosity of the blackbody radiation of AGNs and 1 keV luminosity as the peak luminosity of the blackbody radiation of XRBs. We compile samples of black hole binaries and active galactic nuclei with luminosity near the peak luminosity of blackbody radiation and study the fundamental plane between radio luminosity ( L R ), the peak luminosity of blackbody radiation ( L peak ), and black hole mass ( M BH ). We find that the radio–peak luminosity correlations are L 5 GHz / L Edd ∝ (L 2500 A ˚ / L Edd) 1.55 and L 5 GHz / L Edd ∝ (L 1 keV / L Edd) 1.53 for AGN and XRB, respectively, in the radiatively efficient sample, and L 5 GHz / L Edd ∝ (L 2500 A ˚ / L Edd) 0.48 and L 5 GHz / L Edd ∝ (L 1 keV / L Edd) 0.53 in the radiatively inefficient sample, respectively. Based on the similarities in radio–peak correlations, we further propose a fundamental plane in radio luminosity, the peak luminosity of blackbody radiation, and black hole mass, which is radiatively efficient: log L 5 GHz = 1. 57 − 0.01 + 0.01 log L peak − 0. 32 − 0.16 + 0.16 log M BH − 27. 73 − 0.34 + 0.34 with a scatter of σ R = 0.48 dex, and radiatively inefficient: log L 5 GHz = 0. 45 − 0.01 + 0.01 log L peak + 0. 91 − 0.10 + 0.12 log M BH + 12. 58 − 0.38 + 0.38 with a scatter of σ R = 0.63 dex. Our results are similar to those of previous studies on the fundamental plane for radiatively efficient and radiatively inefficient black hole activity. However, our results exhibit a smaller scatter, so when using the same part of blackbody radiation (i.e., the peak luminosity of the blackbody radiation), the fundamental plane becomes a little bit tighter. [ABSTRACT FROM AUTHOR]

Requiring that the changes in kinetic energies associated with this recoil should in thermal equilibrium be consistent with the Maxwell velocity distribution, Einstein obtained the Planck spectrum for the radiation. If the equipartition theorem of classical statistical mechanics, which for Planck's oscillators implies I U i = I kT i , is used in this relation, one obtains the Rayleigh-Jeans spectrum. The rest of the book focuses on Planck's "fundamental relation", how he obtained the blackbody spectrum, and Einstein's much later derivation. [Extracted from the article]