Variable Absorption Coefficient Research Articles

Radiative transfer for variable three-dimensional atmospheres

To study the temperature in a gas subjected to electromagnetic radiations, one may use the Radiative Transfer equations coupled with the Navier-Stokes equations. The problem has 7 dimensions; however with minimal simplifications it is equivalent to a small number of integro-differential equations in 3 dimensions. We present the method and a numerical implementation using an H-matrix compression scheme. The result is very fast: 240K physical points, all directions of radiation and 683 frequencies require less than 35 minutes on an Apple M1 Laptop. The method is capable of handling variable absorption and scattering functions of spatial positions and frequencies.The implementation is done using htool,1 a matrix compression library interfaced with the PDE solver freefem++. Applications to the temperature in the French Chamonix valley are presented at different hours of the day with and without snow or cloud and with a variable absorption coefficient taken from the Gemini measurements. The software is precise enough to assert temperature differences due to increased absorption in the vibrational frequency subrange of greenhouse gases.

Stability for an inverse source problem of the diffusion equation

We prove an increasing stability estimate for an inverse source problem of the diffusion equation with a nontrivial variable absorption coefficient in . The stability estimate consists of two parts: the Lipschitz type data discrepancy and the high frequency tail of the source function. The latter decreases when the upper bound of the frequency increases. The proof is based on an exact observability bound for the heat equation and the resolvent estimates for the elliptic operator. In particular, to justify the Fourier transform and obtain Plancherel’s theorem for the time-domain Cauchy data on the boundary, we derive certain appropriate time decay estimates for the heat equation using semigroup theory.

Fine Tunable, Redox Active Octapalladium Chains Supported by Linear Tetraphosphines, Leading to Dynamically 1D Self-Assembled Coordination Polymers.

A series of the octapalladium chains supported by meso-Ph2 PCH2 P(Ph)CH2 P(Ph)CH2 PPh2 (meso-dpmppm) ligands, [Pd8 (meso-dpmppm)4 (L)2 ](BF4 )4 (L=none (1), solvents: CH3 CN (2 a), dmf (2 b), dmso (2 c), RN≡C: R=Xyl (3 a), Mes (3 b), Dip (3 c), t Bu (3 d), Cy (3 e), CH3 (CH2 )7 (3 f), CH3 (CH2 )11 (3 g), CH3 (CH2 )17 (3 h)) and [Pd8 (meso-dpmppm)4 (X)2 ](BF4 )2 (X=Cl (4 a), N3 (4 b), CN (4 c), SCN (4 d)), were synthesized by using 2 a as a stable good precursor, and characterized by spectroscopic (IR, 1 H and 31 P NMR, UV-vis-NIR, ESI-MS) measurements and X-ray crystallographic analyses (for 1, 2 a, b, 3 a, b, e, f, 4 a-d). On the basis of DFT calculations on the X-ray determined structure of 2 b ([2b-Pd8 ]4+ ) and the optimized models [Pd8 (meso-Ph2 PCH2 P(H)CH2 P(H)CH2 PH2 )4 (CH3 CN)2 ]4+ ([Pd8 Ph8 ]4+ ) and [Pd8 (meso-H2 PCH2 P(H)CH2 P(H)CH2 PH2 )4 (CH3 CN)2 ]4+ ([Pd8 H8 ]4+ ), with and without empirically calculating dispersion force stabilization energy (B3LYP-D3, B3LYP), the formation energy between the two Pd4 fragments is assumed to involve mainly noncovalent interactions (ca. -70 kcal/mol) with four sets of interligand C-H/π interactions and Pd⋅⋅⋅Pd metallophilic one, while electron shared covalent interactions are almost canceled out within the Pd8 chain. All the compounds isolated are stable in solution and exhibit characteristic absorption at ∼900 nm, which is assignable to a spin allowed HOMO to LUMO transition, and shows temperature dependent intensity change with variable absorption coefficients presumably due to coupling with some thermal vibrations. The structures and electronic states of the Pd8 chains are found finely tunable by varying the terminal capping ligands. In particular, theoretical calculations elucidated that the HOMO-LUMO energy gap is systematically related to the central Pd-Pd distance (2.7319(6)-2.7575(6) Å) by two ways with neutral ligands L (1, 2, 3) and with anionic ligands X (4), which are reflected on the NIR absorption energy of 867-954 nm. The isocyanide terminated Pd8 complexes (3) further reacted with excess of RNC (6 eq) to afford the Pd4 complexes, [Pd4 (meso-dpmppm)2 (RNC)2 ](BF4 )2 (13), and the cyclic voltammograms of 2 a (L=CH3 CN), 3, and 13 (R=Xyl, Mes, t Bu, Cy) demonstrated wide range redox behaviors from 2{Pd4 }4+ to 2{Pd4 }0 through 2{Pd4 }2+ ↔{Pd8 }4+ , {Pd8 }3+ , and {Pd8 }2+ strings. The oxidized complexes, [Pd4 (meso-dpmppm)2 (RNC)3 ](BF4 )4 (16), were characterized by X-ray analyses, and the two-electron reduced chain of [Pd8 (meso-dpmppm)4 ](BF4 )2 (7) was analyzed by spectroscopic and electrochemical techniques and DFT calculations. Reactions of 2 a with 1 equiv. of aromatic linear bisisocyanide (BI) in CH2 Cl2 deposited insoluble coordination polymers, {[Pd8 (meso-dpmppm)4 (BI)](BF4 )4 }n (5), and interestingly, they were soluble in acetonitrile, 31 P{1 H} and 1 H DOSY NMR spectra as well as SAXS curves suggesting that the coordination polymers may exist in acetonitrile as dynamically 1D self-assembled coordination polymers comprising ca. 50 units of the Pd8 rod averaged within the timescale.

Semi-transient thermal analysis from MHD-Participating fluid into a square cavity with variable optical thickness

In this study, the effect of the variable radiative absorption coeeficient in a two-dimensional closed cavity containing an electrical conductor fluid under a uniform magnetic field on the heat transfer and the fluid flow is investigated. The governing equations for the laminar flow and the boundary conditions are solved numerically using the finite volume method. The dependence of the velocity and pressure field is solved using the SIMPLER algorithm and the radiative transfer equation using the discrete ordinates method. A semi-transient algorithm is used to solve both the magnetic convection and radiation equations. The impact of the effective parameters of the maximum optical thickness in the range of 0.1–5, Hartmann number in the range of 0–800 and Rayleigh number in the range of 104-106 in two modes of the average and variable absorption coefficient with the linear temperature are investigated. The results show that by increasing the optical thickness and the Hartmann number and by changing the absorption coefficient of the medium from the average to the variable, the average Nusselt number decreases by 10.5%. Moreover, the effect of Rayleigh number on the heat transfer and fluid flow is investigated. The study of the Rayleigh number shows that the maximum percentage of heat transfer reduction which was made by switching the absorption coefficient of the medium from average to variable does not alter by changing the Rayleigh number, so it is independent of the Rayleigh number. Also, the highest percentage of the reduction in small Hartmann numbers is related to the Rayleigh number 104. Besides, the results reveal that by increasing the Hartmann number from 400 onwards for Rayleigh number 106 and 200 onwards for Rayleigh numbers 104 and 105, the average Nusselt numbers difference in the mode of average and variable absorption coefficient is almost constant.

Optimizing thermal load and power scaling in [formula omitted]-doped ZBLAN fiber lasers

Thanks to characteristics such as high beam qualities and high average powers, largely founded on the outstanding characteristics of fibers as an active medium, fiber lasers have become one of the most popular laser technologies. Although most of the advantages of fiber lasers stem from their geometry, the same geometry is the main source of the limitations. In this study, we focused on managing the thermal load by variable absorption coefficient in order to increase the thermal limits, which are an important limitation of further development in fiber technology. Metaheuristic optimization approaches can be used to improve the performance of fiber technologies with physical constraints. The main aim of metaheuristic optimization is to improve the output of the function with respect to the parameters considered as significant. Swarm Optimization approach is one of the powerful metaheuristic approaches proven to be quite promising to address the above issues. In this study, the optimization of the thermal management of the Er3+-doped ZBLAN fiber laser is performed using Artificial Bee Colony Algorithm (ABC). Additionally, this paper proposes four new strategies of initial parameter setting, repair parameter values, and fitness function for the thermal load of the Er3+-doped ZBLAN fiber laser with respect to the output power. The results show that the absorption coefficient functions obtained by ABC algorithm give more effective and efficient results than the obtained rising functions.

Performance assessment of time-domain optical brain imagers, part 2: nEUROPt protocol.

The nEUROPt protocol is one of two new protocols developed within the European project nEUROPt to characterize the performances of time-domain systems for optical imaging of the brain. It was applied in joint measurement campaigns to compare the various instruments and to assess the impact of technical improvements. This protocol addresses the characteristic of optical brain imaging to detect, localize, and quantify absorption changes in the brain. It was implemented with two types of inhomogeneous liquid phantoms based on Intralipid and India ink with well-defined optical properties. First, small black inclusions were used to mimic localized changes of the absorption coefficient. The position of the inclusions was varied in depth and lateral direction to investigate contrast and spatial resolution. Second, two-layered liquid phantoms with variable absorption coefficients were employed to study the quantification of layer-wide changes and, in particular, to determine depth selectivity, i.e., the ratio of sensitivities for deep and superficial absorption changes. We introduce the tests of the nEUROPt protocol and present examples of results obtained with different instruments and methods of data analysis. This protocol could be a useful step toward performance tests for future standards in diffuse optical imaging.

Assessment of simplified thermal radiation models for engineering calculations in natural gas-fired furnace

The paper assesses the significance of thermal radiation in turbulent non-premixed natural gas flames confined in axisymmetric furnaces. The in–house developed computational model includes simulation of the turbulent flow characteristics, the controlling mixing and chemical mechanisms as well as radiation modeled via the six-flux and of the P-1 models. A variable absorption coefficient is taken into account for the gaseous combustion mixture based on temperature and composition of the mixture. The results with and without radiation are evaluated as part of the complete prediction procedure involving flow, combustion, convection, and radiation phenomena. The comparative assessment of the two radiation models against experimental data indicates that they can be easily applied in engineering cases, with the P-1 model yielding more accurate results in the case considered.

Correction method for absorption-dependent signal enhancement by a liquid-core optical fiber

The enhancement of a dissolved chemical's Raman scattering by a liquid-core optical fiber (LCOF) geometry is absorption dependent. This dependence leads to a disruption of the usual linear correlation between chemical concentration and Raman peak area. To recover the linearity, we augmented a standard LCOF Raman spectroscopy system with spectrophotometric capabilities, permitting sequential measurements of Raman and absorption spectra within the LCOF. Measurements of samples with identical Raman-scatterer concentrations but different absorption coefficients are described. Using the absorption values, we reduced variations in the measured Raman intensities from 60% to less than 1%. This correction method should be important for LCOF-based Raman spectroscopy of sample sets with variable absorption coefficients, such as urine and blood serum from multiple patients.

Photochemical decomposition of 2,4-dichlorophenoxy acetic acid (2,4-D) in aqueous solution. I. Kinetic study

The intrinsic kinetics of the photochemical decomposition of 2,4-dichlorophenoxyacetic acid in aqueous solution has been studied using light of 253.7 nm. Experiments were carried out in a well stirred batch reactor irradiated from its bottom by means of a tubular lamp and a parabolic reflector. Results were analyzed in terms of a very simple kinetic expression. Absorbed radiation effects were duly quantified by means of a one-dimensional radiation field model. This approach incorporates a variable absorption coefficient that is a function of the 2,4-D conversion. The decomposition kinetics can be properly represented with a point valued equation of the following form: RD, λ = − ΦD,λ eλ(y).

Photochemical decomposition of 2,4-dichlorophenoxyacetic acid (2,4-D) in aqueous solution.I. kinetic study

The intrinsic kinetics of the photochemical decomposition of 2,4-dichlorophenoxyacetic acid in aqueous solution has been studied using light of 253.7 nm. Experiments were carried out in a well stirred batch reactor irradiated from its bottom by means of a tubular lamp and a parabolic reflector. Results were analyzed in terms of a very simple kinetic expression. Absorbed radiation effects were duly quantified by means of a one-dimensional radiation field model. This approach incorporates a variable absorption coefficient that is a function of the 2,4-D conversion. The decomposition kinetics can be properly represented with a point valued equation of the following form: RD, ; = − ΦD,; e;(y).

Microcavity dynamics during laser-induced spallation of liquids and gels

Photomechanical fracture induced by thermoelastic stress waves is an important mechanism of tissue ablation by short laser pulses. In this study, we present experimental investigations of the fracture process in ductile, water-containing materials and compare the results with a theoretical calculation. The model describes cavitation caused by the negative part of a bipolar thermoelastic stress wave. Pulses from aQ-switched, frequency-doubled Nd:YAG laser with 8 ns duration were used to irradiate dyed water and gelatine with variable absorption coefficient. Cavitation and ablation were observed with various time-resolved methods such as stress detection, video imaging and an optical pump-probe technique for the detection of individual cavities. Quantitative agreement between experiment and simulation could be achieved in the case of cavity lifetimes, especially at low laser fluence where the bubble density is low and no coalescence takes place. An increase of the threshold energy density for ablation with rising absorption coefficient and a distortion of the thermoelastic wave in the presence of cavitation were experimentally observed and could be qualitatively explained by use of the simulation. The results obtained in this study should facilitate the choice of the optimal laser parameters for photomechanical tissue ablation.

“Spectral ω2 model” and variable absorption coefficient

Aki's “spectral ω2 model”[1] is used to estimate the amplitude field at epicentral distances up to 1000 km in the case of an absorption coefficient of seismic waves which varies with distance. Velocity spectra, the periods of the maximum of these spectra and the maximum velocity amplitudes are obtained. The results are compared with[2] and it is shown that the divergence of the amplitude field decreases if a variable absorption coefficient is used. The theoretical results, obtained in this case, approach the results seen in practice. The possibility of determining the limits of epicentral distances, at which the amplitude field may be considered as linear, is given.

Radiating hydrogen flow in axisymmetric nozzles

A considerable number of studies published in recent years have been devoted to the study of gas in channels and pipes. In view of the complexity of the question and the lack of analytic techniques, individual aspects of the problem are generally considered. The determination of the radiant field characteristics in regions of simple geometric form filled with a stationary radiating-absorbing medium has been carried out in several studies. The articles [1–3] are devoted to the calculation of the radiant field and the temperature field for a given flow of a perfect inviscid nonheat-conducting radiating gas with constant absorption coefficient. The flow is assumed to be irrotational [1, 2] or nearly potential [3]. The authors investigated the accuracy of the solution obtained with the aid of various approximate methods and found that the diffusion approximation yields a small error in calculating the radiation density field and the values of the radiant thermal fluxes for a quite broad class of wall reflecting properties. We may note also [4, 5], in which a calculation is made of one-dimensional steady flow of a viscous heat-conducting radiating perfect gas with constant transport coefficients. In [1–5] the absorption coefficient is considered constant. This assumption simplifies the solution process considerably, since as the independent variables we can take the corresponding optical thicknesses. The study [3] contains a remark that the calculation method proposed there may be used with a variable absorption coefficient. However, this possibility was not used in the calculations presented. For a constant absorption coefficient these studies yield a rather complete analysis of the methods for solving two-dimensional problems in geometrically simple regions in the absence of mechanical motion and one-dimensional problems with motion. They contain results obtained for the exact integral or integrodlfferential equations and present an analysis of the approximate methods. The study [3] considers broader possibilities of solving two-dimensional problems (using the Monte-Carlo method), but the flow is assumed known ahead of time. In the following we present a method for calculating the two-dimensional equilibrium flow of an inviscid non-heat-conducting radiating gas with variable absorption coefficient. As an example, we consider the flow of radiating-absorbing hydrogen in axisymmetric nozzles. It is assumed that the radiation is gray and is in local thermodynamic equilibrium. The transport equation is considered in the diffusion approximation. The nozzles examined have a semi-infinite cylindrical inlet section. The initial gas flow in the cylindrical section is supersonic. In the solution process we determine the radiation density field and all the flow parameters within the nozzle.

On the Nature of the Eclipses of ζ Aurigae.

view Abstract Citations (9) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the Nature of the Eclipses of ζ Aurigae. Kopal, Zdenek Abstract An analysis of the light-changes observed photoelectrically during the ingress of the 1939 minimum of the eclipsing system of ~ Aurigae leads to the following conclusions: 1. The ratio of racffi le of its B and K components can be determined with considerable accuracy from the fractional loss of light during totality. The ensemble of photoelectric observations made at different effective wave lengths leads to k = 0.0145 ± 0.0003, which renders the K supergiant sixty-nine nine times as large as its companion. This ratio appears to be relatively the most dependable character- istic of the system that can so far be inferred from its light-changes. 2. The observed duration of the disappearance of the B star, coupled with the foregoing value of k, excludes the possibility of the orbital inclination ~ being less than 78°, this latter value corresponding to an eclipse of two sharp-edged disks. The actual light-curve at the respective phases bears, however, little resemblance to any theoretical light-curve of a bodily eclipse, whatever the limb darkening on the ap- parent disk of the B star may be. 3. If 1> 78°, the apparent distance by which the B star gets displaced by orbital motion between the first and the second contact of the eclipse exceeds the diameter of the B star, which suggests that this eclipse may have been partly due to the extinction of the B light in a semitransparent envelope surround- ing the K supergiant. In order to analyze the situation, a theory of eclipses of stellar disks of finite rela- tive dimensions by semitra~nsparent outer layers of their mates has been developed, and equations are set up which relate the observed loss of light with variable absorption coefficient of these layers. The practical problem has been reduced to the solution of a pair of integral equations, one of which admits of a formal inversion, while the other must be solved by numerical means. 4. An application of this type of analysis to the light-changes of ~ Aurigae exhibited during the gradual disappearance of the B component shows that the orbital inclination must be very close to 900 in order to make a solution possible. A detailed interpretation of the light-changes leads us to conclude that, at the beginning of the eclipse, the B star must have been obscured, first, by an almost completely opaque cloud of a width equal roughly to O.5TB, followed by a nearly transparent region O.6rB wide, before disappearing ultimately behind the limb of the K star, which, as far as we can tell, may have been quite sharp. Assuming that the depth of the cloud along the line of sight was equal to its width and that its continuous absorption was due to metallic ions, we find the density nece~sary to produce the observed effects to be of the order of 10" ions per cubic centimeter-i.e., a quantity of the same order of magnitude as the density of solar prominences. 5. The absolute radii of the K and B components of ~ Aurigae should be approximately 200 and 2.8 0; and their masses, 22 and 10 0, respectively. The observational errors of quantities from which these elements were derived make these radii and masses uncertain by about 10 per cent Publication: The Astrophysical Journal Pub Date: May 1946 DOI: 10.1086/144813 Bibcode: 1946ApJ...103..310K full text sources ADS |