Thermal Equilibrium Distribution Research Articles

A new kinetic model on hydrolysis of sulfur mustard non-dissolved and dissolved in aqueous solution

This paper aims to establish a hydrolysis extent equation and rate dependence of initial and boundary conditions for sulfur mustard (HD) non-dissolved and dissolved in water by the following work. Firstly, non-homogeneous hydrolysis extent was found to be accurately described by a product of logistic with exponential convex growth function because of slow collision-complex formation between activated H2O and HD molecule to non-linearly couple with transition state decay, while the homogeneous has grown up only in an exponential convex function because of fast collision-complex formation to make its initial extent ratio extremely quickly close to unity. Secondly, initial non-temperature effects from (ethanol, acid, base) additives, HD concentration and droplet size, and rotation speed on hydrolysis rate could be summarized into a Boltzmann function of rate constant with initial molar free energy because of a thermal equilibrium distribution of internal quantum state at a given energy for bi-molecular structures before and after complexing. The results from 5 mL solution under vortex was nearly similar to the stirring 100 mL solution and would helpfully clarify the detoxification kinetics to establish a standard method for evaluating reactivity of aqueous decontaminants against chemical warfare agents at necessarily specified conditions.

A Linkage Factors Between Nucleation and Atomic Physics as a Isomers Bases

The radioactive isomer was initially used to characterize persistent excited atomic states, much like molecular isomers, more than a century ago. Otto Hahn made the first atomic isomer discovery in 1921. Subsequently, it was gradually discovered that there are several kinds of nuclear isomers, such as spin isomer, K isomer, seniority isomer, and “shape and fission” isomer. Isomers are essential to the nucleosynthesis of astrophysical materials. High-accuracy nuclear reaction rate inputs are anticipated while carrying out a celestial nucleosynthesis net computation, even though a single reaction rate can have a significant impact on the whole astronomical evolutionary network. The isotopes are often considered to be in their initial state or to have levels populated in accordance with the thermal-equilibrium distribution of chances when computing nuclear synthesis rates. After all, certain isomers may have lives that reach millions of years or perhaps beyond the age of the cosmos. Thus, in an astrophysics event, such isomers might not be thermally equilibrium. Some atomic isomers—that is, astrometry—should be considered special isotopes since they are crucial to nucleosynthesis. Nuclear batteries can also be produced using nuclear isomers. Similar to the weak force, in certain specific cases such as isomer decays, the electromagnetic force could be crucial for nuclear changes. It is important to note that radioactive isomer states and radioactive ground states are not the same thing. Durable nuclear states of excitement provide insight into the nuclear framework and potential uses. Atomic and molecular changes become interconnected when the connection to the electrons in atoms is made possible by the existence of em decay routes from isomers. Notably renowned chemical decay process is inner conversion. Its inverted, nuclear excitement by free capture of electrons has been observed; however, it is debatable and needs more investigation. This study describes the connection connecting radioactive and molecular changes and discusses instances of manipulating nuclear moves related to isomers using external electromagnetic fields.

Variational autoencoder analysis of Ising model statistical distributions and phase transitions

Variational autoencoders employ an encoding neural network to generate a probabilistic representation of a data set within a low-dimensional space of latent variables followed by a decoding stage that maps the latent variables back to the original variable space. Once trained, a statistical ensemble of simulated data realizations can be obtained by randomly assigning values to the latent variables that are subsequently processed by the decoding section of the network. To determine the accuracy of such a procedure when applied to lattice models, an autoencoder is here trained on a thermal equilibrium distribution of Ising spin realizations. When the output of the decoder for synthetic data is interpreted probabilistically, spin realizations can be generated by randomly assigning spin values according to the computed likelihood. The resulting state distribution in energy-magnetization space then qualitatively resembles that of the training samples. However, because correlations between spins are suppressed, the computed energies are unphysically large for low-dimensional latent variable spaces. The features of the learned distributions as a function of temperature, however, provide a qualitative indication of the presence of a phase transition and the distribution of realizations with characteristic cluster sizes.

Phenomenological study of quarkonium suppression and the impact of the energy gap between singlets and octets

The study of heavy quarkonium suppression in heavy-ion collisions represents an important source of information about the properties of the quark-gluon plasma produced in such collisions. In a previous paper, we have considered how to model the evolution of a quarkonium in such a way that the solution of the resulting equations evolves toward the correct thermal equilibrium distribution for a homogeneous and static medium. We found that it is crucial to take into account the energy gap between singlet and octet configurations when the temperature is not much greater than this energy gap. In this paper, we explore in more detail the phenomenological consequences of this observation in the more realistic situation of an expanding system. We consider two different scenarios, based on the same approximation scheme, but on different choices of parameters. In the first case, we rely on a Hard Thermal Loop approximation, while the second case is based on a recent determination of the static potential in lattice QCD. In both cases, we compute the decay width and the nuclear modification factor, both taking the energy gap into account and ignoring it. We find that the impact on the predictions is as large in the expanding medium as it is in the static case. Our conclusion is that this energy gap should be taken into account in phenomenological studies.

Quantum impedance Lorentz oscillator and its 1- and 2-photon-absorption applications

In this paper, a classical Lorentz oscillator is quantized via Bohr–Sommerfeld quantum theory and 1- and 2-photon absorption (1PA and 2PA) selection rules of quantum mechanics. Based on the Bohr–Sommerfeld model of a hydrogen-like atom in the adiabatic approximation, the computational formulas of the linear and nonlinear parameters and the damping coefficient of the quantized oscillator are derived and further expressed in terms of microphysical quantities, such as electronic charge and mass, Bohr radius, and effective quantum number. In accordance with Boltzmann thermal equilibrium distribution, here, the atom number density in general electric susceptibility is changed to the energy level transition one from the initial to the final state at equilibrium between atomic emission and absorption under light field. A new relationship is proposed to determine the transition eigenfrequency according to the peak frequency and full width at half maximum of an absorption spectrum. Our theoretical simulations of the 1PA spectra of atomic hydrogen and lithium and 1PA and 2PA spectra of two kinds of organic molecules turn out to be in good agreement with the experimental ones. These results suggest that our advancement in the quantization of the Lorentz oscillator is likely successful to make it available for use in the quantitative description of atomic or molecular 1PA and 2PA processes. Generally, the improved Lorentz oscillator may also be more suitable for approximating both linear and nonlinear properties of many dielectric or optoelectronic materials due to its relative simplicity.

Space charge limited current with distributed velocity of initial electrons in planar diode

The research on the space-charge limited current is of great importance for developing insight into the high current diodes. The Child-Langmuir law presents one-dimensional (1D) space-charge limited current density by considering a full electrostatic solution. Jaffe investigated the 1D space-charge limited current density modified by the uniform initial velocity of electrons emitted from the cathode by using the equation of motion for the individual electron. Luginsland et al. presented the two-dimensional (2D) space-charge limited current density by using the particle-in-cell (PIC) codes neglecting initial velocity distribution of the emitted electrons. In this Letter, the effects of initial electrons with the uniform energy distribution and thermal equilibrium distribution on the space charge limited current density are studied by using the full electromagnetic PIC method; the 2D modification factors to the space charge limited current density for the two cases are presented and discussed.

Photon thermalization and a condensation phase transition in an electrically pumped semiconductor microresonator.

We report on an experimental study of photon thermalization and condensation in a semiconductor microresonator in the weak-coupling regime. We measure the dispersion relation of light and the photon mass in a single-wavelength, broad-area resonator. The observed luminescence spectrum is compatible with a room-temperature, thermal-equilibrium distribution. A phase transition, identified by a saturation of the population at high energies and a superlinear increase of the occupation at low energy, takes place when the phase-space density is of order unity. We explain our observations by Bose-Einstein condensation of photons in equilibrium with a particle reservoir and discuss the relation with laser emission.

A Monte Carlo simulation of water + oil + ABA triblock copolymer ternary system II. Rheology under shear flow field by Monte Carlo Brownian Dynamics method

A water/oil/amphiphilic polymer ternary system is analyzed by Monte Carlo (MC) method using a lattice model to determine the thermal equilibrium distribution by changing the component ratio. Particularly the rheological properties such as shear stress and viscosity are evaluated via Monte Carlo Brownian Dynamics (MCBD) simulation, in which the flexibility of polymer movement is considered by the bond fluctuation model and the shear force is expressed by the Kramers potential. Our analysis on the micelle pattern for each concentration ratio shows that, the increase of polymer concentration decreases the solute (water, polymer) mobility, and exponentially increases the viscosity. These results in our simulation reflect general phenomena in concentrated colloid system. By assuming that the polymer orientation dominates the stress of system by the elasticity between polymer bonds, we newly find that from the polymer placement under the shear field, the shear stress itself exponentially increases while raising the concentration. Even in the category of lattice model, our study indicates the possibility of acquiring new knowledge on Dynamics by using a polymer model with specific consideration on flexible mobility and MCBD method.

Thermal Equilibrium Distribution in Infinite-Dimensional Hilbert Spaces

The thermal equilibrium distribution over quantum-mechanical wave functions is a so-called Gaussian adjusted projected (GAP) measure, $GAP(\rho_\beta)$, for a thermal density operator $\rho_\beta$ at inverse temperature $\beta$. More generally, $GAP(\rho)$ is a probability measure on the unit sphere in Hilbert space for any density operator $\rho$ (i.e., a positive operator with trace 1). In this note, we collect the mathematical details concerning the rigorous definition of $GAP(\rho)$ in infinite-dimensional separable Hilbert spaces. Its existence and uniqueness follows from Prohorov's theorem on the existence and uniqueness of Gaussian measures in Hilbert spaces with given mean and covariance. We also give an alternative existence proof. Finally, we give a proof that $GAP(\rho)$ depends continuously on $\rho$ in the sense that convergence of $\rho$ in the trace norm implies weak convergence of $GAP(\rho)$.

Phonon mode potential and its contribution to anharmonism

We present systematic ab-initio study on the phonon mode potential as a source of anharmonicity in the crystal. As an example, the transverse optical (TO) mode potential in PbTe has been fitted to density-functional-theory calculated energies of phonons excited with different amplitudes of mode displacements. The corresponding equation of motion has been analytically and numerically solved in 1D and 2D space, respectively. The solution is used for constructing the ensemble of 10,000 systems with potential and kinetic energies selected according to the thermal equilibrium distributions. The velocity auto-correlation function derived from the computed trajectories is then used to calculate the profile of the phonon spectrum for the TO an LA modes at three temperatures of 100, 300, and 600 K. This technique allows for determination of the contribution of non-quadratic potential of the phonon mode to the anharmonicity in the crystal and its effect on the phonon spectrum.

An efficient lattice Boltzmann method for compressible aerodynamics on D3Q19 lattice

An efficient lattice Boltzmann (LB) model relying on a hybrid recursive regularization (HRR) collision operator on D3Q19 stencil is proposed for the simulation of three-dimensional high-speed compressible flows in both subsonic and supersonic regimes. An improved thermal equilibrium distribution function on D3Q19 lattice is derived to reduce the complexity of correcting terms. A simple shock capturing scheme and an upwind biased discretization of correction terms are implemented for supersonic flows with shocks. Mass and momentum equations are recovered by an efficient streaming, collision and forcing process on D3Q19 lattice. Then a non-conservative formulation of the entropy evolution equation is used, that is solved using a finite volume method. The proposed method is assessed considering the simulation of i) 2D isentropic vortex convection, ii) 3D non-isothermal acoustic pulse, iii) 2D supersonic flow over a bump, iv) 3D shock explosion in a box, v) 2D vortex interaction with shock wave, vi) 2D laminar flows over a flat plate at Ma of 0.5, 1.0 and 1.5.

Precision early universe thermodynamics made simple: Neff and neutrino decoupling in the Standard Model and beyond

Precision measurements of the number of effective relativistic neutrino species and the primordial element abundances require accurate theoretical predictions for early Universe observables in the Standard Model and beyond. Given the complexity of accurately modelling the thermal history of the early Universe, in this work, we extend a previous method presented by the author in [1] to obtain simple, fast and accurate early Universe thermodynamics. The method is based upon the approximation that all relevant species can be described by thermal equilibrium distribution functions characterized by a temperature and a chemical potential. We apply the method to neutrino decoupling in the Standard Model and find NeffSM = 3.045—a result in excellent agreement with previous state-of-the-art calculations. We apply the method to study the thermal history of the Universe in the presence of a very light (1 eV<mϕ < 1 MeV) and weakly coupled (λ ≲ 10−9) neutrinophilic scalar. We find our results to be in excellent agreement with the solution to the exact Liouville equation. Finally, we release a code: NUDEC_BSM (available in both Mathematica and Python formats), with which neutrino decoupling can be accurately and efficiently solved in the Standard Model and beyond: https://github.com/MiguelEA/nudec_BSM.

Thermal optimization of square pin-fins in crossflow using the Lattice Boltzmann Method with quadratic thermal equilibrium

The geometric spacing and operating Reynolds number (Re) for the best thermal performance of square pin-fin heat sinks is found numerically at a Prandtl number of 0.7. The numerical model used is the double population thermal Multiple-Relaxation-Time Lattice Boltzmann Method (MRT LBM). The Nusselt number (Nu), friction factor (f) and the Thermal Performance Factor (TPF) are calculated for a range of streamwise (0.5 to 3) and cross-streamwise (1 to 2) spacing ratios at Re numbers from 20 to 140. A quadratic thermal equilibrium distribution function is used instead of the commonly used linear function to enhance the simulation accuracy. It is found that the Nu number of each row of the pin-fins array increases with the increase in the spacing in the streamwise direction and the reduction of the spacing in the cross-streamwise direction specially at higher Re numbers. The effect of the reduction in the cross-streamwise direction spacing is more significant than the increase in the streamwise direction one.

Overdamped langevin dynamics simulations of grain boundary motion

Macroscopic properties of structural materials are strongly dependent on their microstructure. However, the modeling of their evolution is a complex task because of the mechanisms involved such as plasticity, recrystallization, and phase transformations, which are common processes taking place in metallic alloys. This complexity led to a growing interest in atomistic simulations formulated without any auxiliary hypotheses beyond the choice of interatomic potential. In this context, we propose here a model based on an overdamped stochastic evolution of particles interacting through inter-atomic forces. The model settles to the correct thermal equilibrium distribution in canonical and grand-canonical ensembles and is used to study the grain boundary migration. Finally, a comparison of our results with those obtained by molecular dynamics shows that our approach reproduces the complex atomic-scale dynamics of grain boundary migration correctly.

Influence of non-Markovian dynamics in equilibrium uncertainty-relations.

Contrary to the conventional wisdom that deviations from standard thermodynamics originate from the strong coupling to the bath, it is shown that in quantum mechanics, these deviations originate from the uncertainty principle and are supported by the non-Markovian character of the dynamics. Specifically, it is shown that the lower bound of the dispersion of the total energy of the system, imposed by the uncertainty principle, is dominated by the bath power spectrum; therefore, quantum mechanics inhibits the system thermal-equilibrium-state from being described by the canonical Boltzmann's distribution. We show for a wide class of systems, systems interacting via central forces with pairwise-self-interacting environments; this general observation is in sharp contrast to the classical case, for which the thermal equilibrium distribution, irrespective of the interaction strength, is exactly characterized by the canonical Boltzmann distribution; therefore, no dependence on the bath power spectrum is present. We define an effective coupling to the environment that depends on all energy scales in the system and reservoir interaction. Sample computations in regimes predicted by this effective coupling are demonstrated. For example, for the case of strong effective coupling, deviations from standard thermodynamics are present and for the case of weak effective coupling, quantum features such as stationary entanglement are possible at high temperatures.

Solitary structures in an inhomogeneous plasma with pseudo-potential approach

The set of nonlinear partial differential equations for the coupled ion acoustic and drift waves is reduced to the KdV equation, which is finally transformed into the form of energy integral equation of a pseudo particle in small amplitude limit. It is pointed out that this approach is convenient for choosing appropriate plasma parameters and numerically obtaining drift solitary wave profiles as compared to the solution of the KdV equation, particularly, in non-uniform plasmas. Electrons are assumed to follow the Kappa distribution function. It is found that the solitons amplitude decreases corresponding to steeper density and temperature gradients because of the restriction on the validity of local approximation. Deviation of electrons from thermal equilibrium distribution is supportive for the formation of electrostatic solitary structures by the coupled nonlinear ion acoustic and drift waves. The estimates of the width of the solitons formed by these coupled nonlinear electrostatic waves in the F-region ionosphere are found to be a few meters in agreement with the satellite observations.

Numerical Simulation of Waste Heat Boiler for Copper Flash Smelting

Based on the results of a thermal equilibrium, temperature and velocity distributions of the waste heat boiler were simulated. Results show that the gas flow doesn’t rush to the top intensely when the first baffle-board is set in the front of the radiation chamber. Flue gas is so strongly disturbed by the second baffle-board that its residence time is increased. These two baffle-boards enhance the heat transfer intensity in the radiation chamber. The relative error of simulation results to experimental is less than 10%.

Relativistic diffusion model with nonlinear drift

The nonequilibrium-statistical Relativistic Diffusion Model (RDM) is extended to include a nonlinear drift term such that its stationary solution agrees exactly with the thermal equilibrium distribution. The underlying Fokker-Planck equation cannot be solved analytically in this case and we present a numerical solution in rapidity space. The difference to the analytical RDM solution is discussed, and the numerical result is compared to data for net-proton rapidity distributions in \(\sqrt{s_{NN}} = 17.3\) GeV PbPb and 200 GeV AuAu collisions.

The charge imbalance in ultracold plasmas

Ultracold plasmas are regarded as quasineutral but not strictly neutral. The results of charge imbalance in the expansion of ultracold plasmas are reported. The calculations are performed by a full molecular-dynamics simulation. The details of the electron velocity distributions are calculated without the assumption of electron global thermal equilibrium and Boltzmann distribution. Spontaneous evolutions of the charge imbalance from the initial states with perfect neutrality are given in the simulations. The expansion of outer plasma slows down with the charge imbalance. The influences of plasma size and parameters on the charge imbalance are discussed. The radial profiles of electron temperature are given for the first time, and the self-similar expansion can still occur even if there is no global thermal equilibrium. The electron disorder induced heating is also found in the simulation.

Effects of Displacement-Distortion of Potential Energy Surfaces on Nonadiabatic Electron Transfers via Conical Intersections: Application to SO2 and trans-1,3,5-Hexatriene.

We show that the time-correlation function formalism can be applied to calculate nonadiabatic electronic population dynamics on the two vibronically coupled diabatic displaced-distorted harmonic potential energy surfaces through conical intersection. We present general formulas for the time-evolved electronic populations at finite temperature with initial sampling from both initial thermal equilibrium and nonequilibrium nuclear distributions. The validity of our formalism is verified through comparison with previous work in a certain limit of our results for case of displaced harmonic oscillator. Finally for illustration, the derived expressions have been applied to determine the electronic population dynamics at conical intersections for SO2 and trans-1,3,5-hexatriene molecules.