Thermal Rate Equations Research Articles

Non-relativistic susceptibility and a dark matter application

When thermal rate equations are derived for the evolution of slow variables, it is often practical to parametrize the right-hand side with chemical potentials. To close the system, the chemical potentials are subsequently re-expressed in terms of the slow variables, which involves the consideration of a “susceptibility”. Here we study a non-relativistic situation in which chemical potentials are large compared with the temperature, as is relevant for late-time pair annihilations in dark matter freeze-out. An order-of-magnitude estimate and a lattice simulation are presented for a susceptibility dominated by bound states of stop-like mediators. After this “calibration”, the formalism is applied to a model with Majorana singlet dark matter, confirming that masses up to the multi-TeV domain are viable in the presence of sufficient (though not beyond a limit) mass degeneracy in the dark sector.

Formation of massive protostars in atomic cooling haloes

We present the highest-resolution three-dimensional simulation to date of the collapse of an atomic cooling halo in the early Universe. We use the moving-mesh code arepo with the primordial chemistry module introduced in Greif (2014), which evolves the chemical and thermal rate equations for over more than 20 orders of magnitude in density. Molecular hydrogen cooling is suppressed by a strong Lyman-Werner background, which facilitates the near-isothermal collapse of the gas at a temperature of about $10^4\,$K. Once the central gas cloud becomes optically thick to continuum emission, it settles into a Keplerian disc around the primary protostar. The initial mass of the protostar is about $0.1\,{\rm M}_\odot$, which is an order of magnitude higher than in minihaloes that cool via molecular hydrogen. The high accretion rate and efficient cooling of the gas catalyse the fragmentation of the disc into a small protostellar system with 5-10 members. After about 12 yr, strong gravitational interactions disrupt the disc and temporarily eject the primary protostar from the centre of the cloud. By the end of the simulation, a secondary clump has collapsed at a distance of $\simeq 150\,$au from the primary clump. If this clump undergoes a similar evolution as the first, the central gas cloud may evolve into a wide binary system. High accretion rates of both the primary and secondary clumps suggest that fragmentation is not a significant barrier for forming at least one massive black hole seed.

Study on Thermal Decomposition of AP/HTPB Base Bleed Propellant after Depressurization and Flameout Conditions

In order to analyze the characteristics of secondary ignition of AP/HTPB base bleed propellant, the quenched samples of AP/HTPB base bleed propellant are made under the condition of transient depressurization, and experiments on thermal decomposition of this micro sample are carried by means of differential scanning calorimeter (DSC). The experimental results are obtained under two heating rates of 20°C/min and 40°C/min. They are analyzed and compared with the original sample of AP/HTPB. The kinetic parameters are estimated according to thermal decomposition rate equation and thermograms.

English

In this paper, a micro electromechanical systems vertical-cavity surface-emitting laser (MEMS-VCSEL) with asymmetric double oxide aperture and highly strained GaInNAsSb quantum wells for widely tunable, single mode and high temperature operation has been investigated. The MEMS-VCSEL is based on an integrated two-chip concept which allows us to extend the single wavelength performance to a continuously tunable, selectively wavelength-addressable spectrum of 40 nm. It has a much larger tuning range as compared with previous works. We present a comprehensive model including electrostatic membrane equation coupled with thermal, spatial and temporal rate equations considering Shockley Read Hall (SRH), Auger and carrier diffusion effects. These coupled equations are solved numerically by finite difference method (FDM). Using the simulation results, we design a single mode, high power, high temperature and tunable VCSEL, which is suitable for C-band dense-wavelength-division- multiplexing (DWDM) optical communication systems.   Key words: Micro electromechanical systems (MEMS), tunable vertical-cavity surface-emitting laser (VCSELs), strained GaInNAsSb QWs, single mode operation.

A 1-D non-isothermal dynamic model for the thermal decomposition of a gibbsite particle

A 1-D mathematical model describing the thermal decomposition, or calcination, of a single gibbsite particle to alumina has been developed and validated against literature data. A dynamic, spatially distributed, mass and energy balance model enables the prediction of the evolution of chemical composition and temperature as a function of radial position inside a particle. In the thermal decomposition of gibbsite, water vapour is formed and the internal water vapour pressure plays a significant role in determining the rate of gibbsite dehydration. A thermal decomposition rate equation, developed by closely matching experimental data reported previously in the literature, assumes a reaction order of 1 with respect to gibbsite concentration, and an order of −1 with respect to water vapour pressure. Estimated values of the transformation kinetic parameters were k0=2.5×1013mol/(m3s) for the pre-exponential factor, and Ea=131kJ/mol for the activation energy. Using these kinetic parameters, the gibbsite particle model is solved numerically to predict the evolution of the internal water vapour pressure, temperature and gibbsite concentration. The model prediction was shown to be very sensitive to the values of heat transfer coefficient, effective diffusivity, particle size and external pressure, but relatively less sensitive to the mass transfer coefficient and particle thermal conductivity. The predicted profile of the water vapour pressure inside the particle helps explain some phenomena observed in practice, including particle breakage and formation of a boehmite phase.

Internal cooling efficiency of a junction diode

The three thermal rate equations were built newly up at both ends and at the junction of a p–n diode, in order to derive analytically the temperature difference ΔT (between a junction and both ends) and the internal cooling efficiency η defined newly for a homojunction diode. The maxima ΔT and η of a diode were derived analytically as a function of Vj within the short-length approximation and calculated numerically as a function of Vj or Vbi, where Vj is a voltage across the junction and Vbi is a built-in voltage at the junction. As a result, ΔT increases abruptly with an increase of Vj below Vj=0.050 V or of Vbi below Vbi=0.10 V, while above their values, it increases slowly with an increase of Vj or Vbi to saturate a certain value. For example, ΔT was estimated as 14.6 K for Hg0.8Cd0.2Te diode with Vbi=0.36 V. η has a local maximum of 63% at Vj≈0.01 V or at Vbi≈0.03 V, while above their respective values, it decreases abruptly with an increase of Vj or Vbi and falls to 4.4% at Vbi=0.80 V which is equivalent to that of a diode emitting a laser for fiber optical communication. However, the greater enhancements in ΔT and η of a diode are required to apply the internal cooling system to a laser-emitting diode which needs the exact control of temperature. These results should be useful for the application of the internal cooling system to the double heterojunction diode used in the optical communication.

Charmonium in medium: From correlators to experiment

We set up a framework in which in-medium charmonium properties are constrained by thermal lattice quantum chromodynamics and subsequently implemented into a thermal rate equation enabling the comparison with experimental data in heavy-ion collisions. Specifically, we evaluate phenomenological consequences for charmonium production originating from two different scenarios in which either the free or the internal energy are identified with the in-medium two-body potential between charm and anticharm quarks. These two scenarios represent $J/\ensuremath{\psi}$ ``melting temperatures'' of approximately $1.25{T}_{c}$ (``weak binding'') and $2{T}_{c}$ (``strong binding''), respectively. Within current uncertainties in dissociation rates and charm-quark momentum spectra, both scenarios can reproduce the centrality dependence of inclusive $J/\ensuremath{\psi}$ yields in nuclear collisions at the Super Proton Synchrotron (SPS) and the Relativistic Heavy-Ion Collider (RHIC) reasonably well. However, the ``strong-binding'' scenario associated with the internal energy as the potential tends to better reproduce current data on transverse momentum spectra at both SPS and RHIC.

Interplay effects of temperature and injection power on photoluminescence of InAs/GaAs quantum dot with high and low areal density

In this report, we have investigated the temperature and injection power dependent photoluminescence in self-assembled InAs/GaAs quantum dots (QDs) systems with low and high areal density, respectively. It was found that, for the high-density samples, state filling effect and abnormal temperature dependence were interacting. In particular, the injection power-induced variations were most obvious at the temperature interval where carriers transfer from small quantum dots (SQDs) to large quantum dots (LQDs). Such interplay effects could be explained by carrier population of SQDs relative to LQDs, which could be fitted well using a thermal carrier rate equation model. On the other hand, for the low density sample, an abnormal broadening of full width at half maximum (FWHM) was observed at the 15–100 K interval. In addition, the FWHM also broadened with increasing injection power at the whole measured temperature interval. Such peculiarities of low density QDs could be attributed to the exciton dephasing processes, which is similar to the characteristic of a single quantum dot. The compared interplay effects of high- and low-density QDs reflect the difference between an interacting and isolated QDs system.

Effect of linear and non-linear components in the temperature dependences of thermoelectric properties on the energy conversion efficiency

The new thermal rate equations were built up by taking the linear and non-linear components in the temperature dependences of the Seebeck coefficient α, the electrical resistivity ρ and thermal conductivity κ of a thermoelectric (TE) material into the thermal rate equations on the assumption that their temperature dependences are expressed by a quadratic function of temperature T. The energy conversion efficiency η for a single TE element was formulated using the new thermal rate ones proposed here. By applying it to the high-performance half-Heusler compound, the non-linear component in the temperature dependence of α among those of the TE properties has the greatest effect on η, so that η/ η 0 was increased by 11% under the condition of T = 510 K and Δ T = 440 K, where η 0 is a well-known conventional energy conversion efficiency. It was thus found that the temperature dependences of TE properties have a significant influence on η. When one evaluates the accurate achievement rate of η exp obtained experimentally for a TE generator, therefore, η exp should be compared with η the estimated from the theoretical expression proposed here, not with η 0, particularly when there is a strong non-linearity in the temperature dependence of TE properties.

Effect of linear and non-linear components in the temperature dependences of thermoelectric properties on the cooling performance

The relative cooling of performance of ϕ / ϕ 0 for a thermoelectric (TE) element was derived analytically by taking the linear and non-linear components in the temperature ( T z ) dependences of TE properties into the thermal rate equations (TRE) on the assumption that all of the TE properties are expressed by a quadratic function of T z at a position z along a TE element and the temperature profile along a TE element is linear or non-linear, where ϕ and ϕ 0 are the coefficients of performance (COP) derived from the new and conventional TRE, respectively. The linear and non-linear components in the T z -dependences of TE properties were estimated experimentally for Bi–Te alloys. When a TE element has a linear temperature profile, ϕ / ϕ 0 estimated using the linear and/or non-linear components in the T z -dependences of their TE properties increases with an increase of Δ T and reached great values of 1.3–1.6 at ZT = 1 under the condition of T = 300 K and Δ T = 80 k . As a result, it was found that the linear component in the electrical resistivity ρ and the non-linear one in the Seebeck coefficient α have a significant effect on ϕ / ϕ 0 . When ϕ / ϕ 0 was estimated for a non-linear temperature profile of a module fabricated using these Bi–Te alloys, however, it was slightly lower than that obtained for a linear temperature profile. The formulas obtained for ϕ and ϕ / ϕ 0 are applicable even for the practical TE coolers and refrigerators with a strong non-linearity in the temperature profile.

Effect of linear temperature dependence of thermoelectric properties on energy conversion efficiency

New thermal rate equations were developed by taking the temperature dependences of the electrical resistivity ρ and thermal conductivity κ of the thermoelectric (TE) materials into the thermal rate equations on the assumption that they vary linearly with temperature T. The relative energy conversion efficiency η/ η 0 for a single TE element was formulated by approximate analysis, where η and η 0 are the energy conversion efficiencies derived from the new and conventional thermal rate equations, respectively. Applying it to Si–Ge alloys, the temperature dependence of ρ is stronger than that of κ, so the former has a more significant effect on η/ η 0 than the latter. However, the degree of contribution from both of them to η/ η 0 was a little lower than 1% at the temperature difference Δ T of 600 K. When the temperature dependence of κ was increased to become equal to that of ρ, however, it was found that η/ η 0 is increased by about 10% at Δ T = 600 K. It is clarified here that the temperature dependences of ρ and κ are also important factors for an improvement in η.

Effect of temperature dependence of electrical resistivity on the cooling performance of a single thermoelectric element

The coefficients of performance (COP) φ 0 and φ for a single thermoelectric (TE) element welded with two metal plates were calculated as functions of temperature difference (Δ T) and thermoelectric figure of merit ( ZT) from the conventional thermal rate equations and the new thermal rate ones proposed here, respectively. We made an attempt to take the differences in the Seebeck coefficient α, electrical resistivity ρ and thermal conductivity κ of TE materials at the hot and cold sides of a TE element into the thermal rate equations on the assumption that their TE properties change linearly with temperature. However, the difference in κ was neglected even in the new thermal rate equations because its temperature dependence was too small when φ was applied to the high-performance Bi–Te alloys. The normalized temperature dependences at 300 K of α and ρ were denoted by A and B, respectively. The term of A in the thermal rate equations was canceled out by the Thomson coefficient, but that of B remained. When B > 0 K −1, φ/ φ 0 is enhanced more significantly with an increase of B at larger Δ T and lower ZT, and it reached about 1.20 at Δ T = 80 K for Bi–Te alloys with B ≈ 5 × 10 −3 K −1. It was thus found that the COP of a cooling module is also affected strongly by B as well as ZT.

A behavioral approach to model thermal sensitivity of semiconductor lasers

A new method is proposed in this paper to model the effects of temperature on the steady state and large signal response of single mode edge emitting semiconductor laser. Traditionally, a separate thermal rate equation, in conjunction with the laser rate equation model is used to describe the thermal behavior [IEEE J. Quant. Electron., 31(10) (1995); J. Lightwave Technol., 17(9) (1999)] or, temperature dependence of the rate equation parameters is explicitly defined through their respective characteristic temperatures to model thermal behavior [IEEE Proc. J., 140(4) (1993); IEEE J. Quant. Electron., 4 (1968) 119; IEEE Photon. Technol. Lett., 1 (1989) 356]. However, these methods introduce a number of additional parameters that necessitate new measurements and rigorous numerical computations for their determination and impart more complexity to the model. In the work presented here, a new thermal threshold is defined for the external laser slope efficiency together with an output feedback function obtained through the rate equations-time dynamics. This inherently introduce the dominant thermal mechanisms into the model with the parameters extracted from steady state measurements in a self-consistent manner, providing considerable reduction in computation complexity. The resulting modified rate equations also account for high power gain saturation effects, which is otherwise only possible through higher-level (1D–3D) modeling methods. Measured results from two commercial single mode lasers have shown excellent conformance with simulations, using this approach.

ゴムの硫黄/CBS架橋過程の速度論的解析

The curing processes of SBR with sulfur and CBS at various concentrations are estimated using an oscillating rheometer. The curing reaction, which could be treated as chain reaction including CBS thermal decomposition, is modeled, and rate equations for the reactions are derived. The apparent reaction rates are calculated with a nonlinear least square approximation so that the summation of differential square of relative states obtained from the torque curve of rheometer and the estimated values may become the minimum. The curing processes are analyzed on the basis of simulated using the obtained concentration changes.It is elucidated that the temperature dependence of the apparent rate constants can be validly expressed with the Arrhenius equation, and this relation gives the rate constant in arbitrary temperature. Therefore, the rate constants of curing processes with sulfur and CBS can be evaluated at arbitrary temperatures, and the curing processes can be estimated even at unsteady temperature distributions in actual rubber products.

Threshold behavior in polyimide photoablation: Single-shot rate measurements and surface-temperature modeling

The ablation rate of Kapton™-type polyimide has been measured as a function of incident fluence and excimer laser wavelength using a sensitive quartz-crystal microbalance (QCM). The experiments were performed such that the fluence and the ablated depth were known for each laser pulse, avoiding the need to average rate and fluence data over many pulses. By limiting the investigations to the low-fluence regimes near ablation threshold, high precision and detailed curve shapes were obtained. It was found that the ablation rate increases smoothly and exponentially with increasing fluence for 248, 308, and 351 nm wavelengths. This exponential behavior was modeled using an Arrheniustype thermal rate equation. In contrast, the 193 nm curve is linear in fluence, displays a sharp threshold, and is consistent with a possible photochemical ablation mechanism. Using a sophisticated surface temperature modeling code, the maximum laser induced surface temperature at the fluence at which ablation can first be detected is found to be the same, ∼ 850° C, for all four wavelengths. This “ablation” temperature is significantly higher than the approximately 500° C temperature at which Kapton™ starts to degrade under isothermal heating conditions.

Transient effects during tensile tests in a model of correlated dislocation motion

A model of the glide mechanism in f.c.c. crystals oriented for easy glide during deformation in stage II of the stress-strain curve is developed. It is based on experimental results of the study of the growth of slip lines and dislocation structure. The model leads to a thermal rate equation for the strain-rate that implies an explicit time-dependence. It is tested by the quantitative description of stress transients during strain-rate change-, stress relaxation- and transient creep experiments. The numerical calculations show satisfying agreement with experimental curves.

Relation between the Petch “friction” stress and the thermal activation rate equation

Abstract : The discussion is addressed towards establishing a connection between two alternative constitutive equations that have been used in the past to describe the temperature (and strain rate) dependence of the yield stress of iron.