Boltzmann Distribution Model Research Articles

Thermometry of stored molecular ion beams

The radiative cooling of a stored, initially rotationally hot OH^{-} ion beam is probed by photodetachment using an electrostatic ion beam trap combined with an in-trap velocity map imaging spectrometer, providing direct measurement of the time-dependent rotational population. The rotational temperatures are estimated from photodetached electron spectra as a function of time using a Boltzmann distribution model and further verified by a rate law model using known Einstein coefficients. We demonstrate that during the entire cooling time, the rotational population can be well described by a Boltzmann distribution.

In situ characterisation of absorbing species in stationary premixed flat flames using UV\u2013Vis absorption spectroscopy

A one-dimensional premixed ethylene–air flame is investigated regarding the presence of various combustion intermediates and products relevant for the formation of carbonaceous particles for various equivalence ratios and spatial positions using in situ UV–Vis absorption spectroscopy. A laser driven light source in combination with a fast spectrometer allow to record absorption spectra at a high rate required for practical combustion devices. The approach is coupled with a least squares regression procedure using a database of several absorbing species in the flame. To account for the high temperature flame conditions, the absorption spectra are convoluted by a simplified Maxwell–Boltzmann distribution model. While the approach is based on several assumptions and a verification requires future detailed intercomparison with other techniques, a first semi-quantitative evaluation can be obtained. This novel approach opens a potential route to the in situ measurement of the evolution of polycyclic aromatic hydrocarbons (PAHs) in flames.

Carrier phase recovery friendly probabilistic shaping scheme based on a quasi-Maxwell-Boltzmann distribution model.

A novel probabilistic shaping (PS) scheme based on the quasi-Maxwell-Boltzmann (quasi-MB) distribution model is proposed in order to solve the incompatibility between PS and carrier phase recovery (CPR) algorithms, such as blind phase search (BPS) and principal component-based phase estimation (PCPE). In the proposed quasi-MB model, the same occurrence probability is assigned to each constellation point on the same square-ring, rather than on the same circle. Signals obeying the quasi-MB model have superior CPR friendliness compared to traditional PS signals. For a PS 64 quadrature amplitude modulation system, the simulation results indicate up to 51% and 21% normalized generalized mutual information (NGMI) improvements for PCPE and BPS, respectively. Experimental verification of the proposed quasi-MB scheme was demonstrated in a 10 Gbaud coherent detection system. The results show that when the optical signal-to-noise ratio (OSNR) is low, the quasi-MB model can help the BPS algorithm to achieve better NGMI performance and, when the OSNR is high, the proposed model can also solve the incompatibility between the PCPE algorithm and PS.

State-to-state chemical kinetic mechanism for HF chemical lasers

State-to-state rotational relaxation processes play a critical role in predicting rotational nonequilibrium, which can significantly affect total laser power and spectral distribution. In this paper, the state-to-state rotational relaxation rate coefficients for the pumping reaction of F + H2, the rotational energy transfer processes of HF(υ, j = 0–10) + HF(υ′, j′ = 0–10) and HF(υ, j = 0–10) + H2 are calculated. Subsequently, a detailed state-to-state chemical kinetic mechanism is constructed including 61 species and 124,482 elementary reactions for HF chemical lasers. All of these rotational relaxation rate coefficients have been expressed with Arrhenius-like formulas. A comparison of the Boltzmann distribution model with the detailed state-to-state chemical mechanism has been analysed and discussed. These results show that rotational nonequilibrium processes can significantly affect the distribution of ro-vibrational excited HF molecules. The rotational distributions of HF(υ = 0–2, j) are far from equilibrium distribution. Conversely, the distributions of HF(υ = 3, 4, j) seem to be a Boltzmann distribution. These results indicate that numerical models must include the rotational nonequilibrium processes and numerical models using a Boltzmann distribution for the rotational populations cannot predict performance of real HF chemical lasers.

Synthesis, characterization and thermodynamic stability of nanostructured ε-iron carbonitride powder prepared by a solid-state mechanochemical route

Nanostructured epsilon iron carbonitride (ε-Fe3CxN1-x, x ∼ 0.05) powder with high purity (>97 wt%) was synthesized through a simple mechanochemical reaction between metallic iron and melamine. Various characterization techniques were employed to investigate the chemical and physical characteristics of the milling intermediates and the final products. The thermodynamic stability of the different phases in the Fe-C-N ternary system, including nitrogen and carbon doped structures were studied through density functional theory (DFT) calculations. A Boltzmann-distribution model was developed to qualitatively assess the stability and the proportion of the different milling products vs. milling energy. The theoretical and experimental results revealed that the milling products mainly comprise the ε-Fe3CxN1-x phase with a mean crystallite size of around 15 nm and a trace of amorphous carbon material. The thermal stability and magnetic properties of the milling products were thoroughly investigated. The synthesized ε-Fe3CxN1-x exhibited thermal stabilities up to 473 K and 673 K in air and argon atmospheres, respectively, and soft magnetic properties with a saturation magnetization of around 125 emu/g.

Regional-Level Allocation of CO2 Emission Permits in China: Evidence from the Boltzmann Distribution Method

To achieve the commitment of carbon emission reduction in 2030 at the climate conference in Paris, it is an important task for China to decompose the carbon emission target among regions. In this paper, entropy maximization is brought to inter-provincial carbon emissions allocation via the Boltzmann distribution method, which provides guidelines for allocating carbon emissions permits among provinces. The research is mainly divided into three parts: (1) We develop the CO2 influence factor, including per capita GDP, per capita carbon emissions, carbon emission intensity and carbon emissions of per unit industrial added value; the proportion of the second industry; and the urbanization rate, to optimize the Boltzmann distribution model. (2) The probability of carbon emission reduction allocation in each province was calculated by the Boltzmann distribution model, and then the absolute emission reduction target was allocated among different provinces. (3) Comparing the distribution results with the actual carbon emission data in 2015, we then put forward the targeted development strategies for different provinces. Finally, suggestions were provided for CO2 emission permits allocation to optimize the national carbon emissions trading market in China.

A combined experimental and theoretical investigation of the Al-Melamine reactive milling system: A mechanistic study towards AlN-based ceramics

A versatile ball milling process was employed for the synthesis of hexagonal aluminum nitride (h-AlN) through the reaction of metallic aluminum with melamine. A combined experimental and theoretical study was carried out to evaluate the synthesized products. Milling intermediates and products were fully characterized via various techniques including XRD, FTIR, XPS, Raman and TEM. Moreover, a Boltzmann distribution model was proposed to investigate the effect of milling energy and reactant ratios on the thermodynamic stability and the proportion of different milling products. According to the results, the reaction mechanism and milling products were significantly influenced by the reactant ratio. The optimized condition for AlN synthesis was found to be at Al/M molar ratio of 6, where the final products were consisted of nanostructured AlN with average crystallite size of 11 nm and non-crystalline heterogeneous carbon.

U.S. stock market interaction network as learned by the Boltzmann machine

We study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning framework for statistical inference, we analyze historical behavior of the parameters inferred using exact and approximate learning algorithms. Since the model and inference methods require use of binary variables, effect of this mapping of continuous returns to the discrete domain is studied. The presented analysis shows that binarization preserves market correlation structure. Properties of distributions of external fields and couplings as well as industry sector clustering structure are studied for different historical dates and moving window sizes. We found that a heavy positive tail in the distribution of couplings is responsible for the sparse market clustering structure. We also show that discrepancies between the model parameters might be used as a precursor of financial instabilities.

Lattice Boltzmann Method for Numerical Simulation of Circular Tube Forced Convection

This paper established the thermal Lattice Boltzmann model of fluid flow and heat transfer, which is based on double lattice Boltzmann distribution model [. The temperature distribution adopted the higher accuracy velocity model. Based on this thermal lattice Boltzmann model, this paper simulated forced convection of circular tube fluid. Comparing the simulation results with the traditional CFD calculation results, we could find that the thermal lattice Boltzmann method have unique advantages in effectiveness and flexibility than the traditional calculation method.

Temperature-dependent Emission of Copper(I) Phenanthroline Complexes with Bulky Substituents: Estimation of an Energy Gap between the Singlet and Triplet MLCT States

Abstract Temperature dependence of emission from bis(2,9-di-tert-butyl-1,10-phenanthroline)copper(I) ([Cu(dtbp)2]+) as well as several other copper(I) bis(phenanthroline) complexes was measured between 190 and 300 K. An analysis based on a Boltzmann distribution model gives an energy gap between 1MLCT and 3MLCT excited states as 790 cm−1 for [Cu(dtbp)2]SbF6. The contribution of the delayed fluorescence largely depends on the ligand substituents.

Synchrotron Mossbauer spectroscopic study of ferropericlase at high pressures and temperatures

The electronic spin state of Fe 2+ in ferropericlase, (Mg 0.75 Fe 0.25) O, transitions from a high-spin (spin unpaired) to low-spin (spin paired) state within the Earth’s mid-lower mantle region. To better understand the local electronic environment of high-spin Fe 2+ ions in ferropericlase near the transition, we obtained synchrotron Mössbauer spectra (SMS) of (Mg 0.75 ,Fe 0.25 )O in externally heated and laser-heated diamond anvil cells at relevant high pressures and temperatures. Results show that the quadrupole splitting (QS) of the dominant high-spin Fe 2+ site decreases with increasing temperature at static high pressure. The QS values at constant pressure are fitted to a temperature-dependent Boltzmann distribution model, which permits estimation of the crystal-field splitting energy (Δ 3 ) between the d xy and d xz or d zy orbitals of the t 2g states in a distorted octahedral Fe 2+ site. The derived Δ 3 increases from approximately 36 meV at 1 GPa to 95 meV at 40 GPa, revealing that both high pressure and high temperature have significant effects on the 3d electronic shells of Fe 2+ in ferropericlase. The SMS spectra collected from the laser-heated diamond cells within the time window of 146 ns also indicate that QS significantly decreases at very high temperatures. A larger splitting of the energy levels at high temperatures and pressures should broaden the spin crossover in ferropericlase because the degeneracy of energy levels is partially lifted. Our results provide information on the hyperfine parameters and crystal-field splitting energy of high-spin Fe 2+ in ferropericlase at high pressures and temperatures, relevant to the electronic structure of iron in oxides in the deep lower mantle.

Nuclear magic numbers based on a quarklike model is compared with the Boltzmann distribution model from nuclear abundance in the universe and low energy nuclear reactions

Nuclear magic numbers based on a quarklike model is compared with the Boltzmann distribution model from nuclear abundance in the universe and low energy nuclear reactions

Behavior of excitons and trions in CdTe/CdMgTe quantum-well structures with variations in temperature

The temperature-induced variations in the photoluminescence spectra measured in a magnetic field of trions and excitons in CdTe/CdMgTe quantum wells with modulated doping are studied. It is found that the temperature-induced redistribution of the intensity between the exciton and trion emission lines in a magnetic field is opposite to that expected from the simple Boltzmann distribution model. Coupled rate equations for the trion-exciton system are solved to construct the temperature dependences of the exciton and trion emission line intensities. The relations thus calculated are in good agreement with experiment.

A Two-State Boltzmann Model for Polar A-Smectics

Abstract Assuming a head to head and side by side association of the molecules, a two-state Boltzmann distribution model is proposed which explains the temperature dependence of the thickness of the smectic-A layers observed with polar single-tailed mesogens.