Non-equilibrium Model Research Articles

Asynchronism and nonequilibrium phase transitions in (1+1)-dimensional quantum cellular automata.

Probabilistic cellular automata provide a simple framework for exploring classical nonequilibrium processes. Recently, quantum cellular automata have been proposed that rely on the propagation of a one-dimensional quantum state along a fictitious discrete time dimension via the sequential application of quantum gates. The resulting (1+1)-dimensional space-time structure makes these automata special cases of recurrent quantum neural networks which can implement broad classes of classical nonequilibrium processes. Here, we present a general prescription by which these models can be extended into genuinely quantum nonequilibrium models via the systematic inclusion of asynchronism. This is illustrated for the classical contact process, where the resulting model is closely linked to the quantum contact process (QCP), developed in the framework of open quantum systems. Studying the mean-field behavior of the model, we find evidence of an "asynchronism transition," i.e., a sudden qualitative change in the phase transition behavior once a certain degree of asynchronicity is surpassed, a phenomenon we link to observations in the QCP.

Construction of Unbalanced Engineering Cost Management and Multivariate Statistics System Based on Random Matrix Weight Algorithm

The informatization of engineering cost plays an important role in the cost management and is also one of the important subjects of the informatization in the engineering field. It is the direction of the future project cost management. There is a trend of exponential increase in the information about project cost, which brings a great challenge to cost informatization. On the basis of the construction quantity and cost composition in the process of analyzing the present situation of the project cost, the overall index of the construction quantity and cost is constructed. For bridges and tunnels and to achieve a reasonable index of roadbed, on the basis of considering project at different stages and the demand for different levels of cost management personnel, adopt the method of statistical analysis and neural network, respectively, and set up the project cost fast estimation method and cost prediction model: intelligent prediction model and index system forecasting model. The error analysis and checking calculation of the two models provide the possibility for correctly estimating the engineering quantity and engineering cost in the preliminary design stage. Aiming at the low accuracy of the traditional unbalanced cost data classification algorithm, the dimension of random matrix weight was introduced into the cost data classification. On the basis of analyzing the spatial and temporal characteristics of WAMS measurement data, a high-dimensional random matrix model of WAMS measurement big data was constructed according to the high-dimensional random matrix theory, and a nonequilibrium cost data classification model based on the weighted algorithm of improved fuzzy rules was established. The model is applied to a unit project cost data classification, which verifies the operability of the model and provides a new idea for other units to carry out similar work. Finally, other common problems that should be paid attention to when using multivariate statistical analysis method are put forward.

Pore-scale numerical simulation of the heat transfer and fluid flow characteristics in metal foam under high Reynolds numbers based on tetrakaidecahedron model

In this paper, the pressure drops and interfacial heat transfer coefficient in metal foam with different pore density which was constructed by tetrakaidecahedron models were numerically studied under high velocity by Computational Fluid Dynamics (CFD). The velocity fields, temperature fields and pressure fields in the computational domain of metal foam were investigated. The equation of pore density and hydraulic diameter of metal foam was obtained. Influence of flow rate on the whole porous zone was also studied and obtaining the fitting formula to predict pressure loss in porous metal which was applied to the pore density range from 10PPI(Pore Per Inch)to 40PPI at high flow rate. Comparing with the previous literatures, the maximum error of pressure drop value was 12.23%. Meanwhile, the relationship between Reynolds number and interfacial heat transfer coefficient was studied, the results shown that the values of heat transfer coefficient increase with the rising of Reynolds number, but the lifting rate decreases gradually. And according to the data points, the numerical formula of interfacial heat transfer coefficient in porous metal was obtained which had a great correctness through contrasting with other data. As a result, the fitting formula could accurately predict the convection heat transfer coefficient of the metal foam interface and provide relevant data for the Thermal Non-equilibrium Model.

A non-equilibrium slip wall model for large-eddy simulation with an immersed boundary method

A non-equilibrium wall model for large-eddy simulation with the immersed boundary (IB) method is proposed to reduce the required number of grid points in simulating wall-bounded turbulence. The proposed wall model is presented as an appropriate slip velocity on the wall. The slip velocity is constructed by integrating the simplified turbulent boundary layer (TBL) equation along the wall-normal direction, which enhances the integral momentum balance near the wall on a coarse grid. The effect of pressure gradient on the near wall flow is taken into account by retaining the pressure gradient term in the simplified TBL equation. The proposed model is implemented in the form of a direct-forcing IB method with moving-least-square reconstruction near the wall. The benchmarks of plane channel turbulence and the flows over a backward-facing step are used for validation. The proposed model improves the wall stresses and velocity profiles in the region where the pressure gradient dominates the near wall flows.

Comparing different charge-state models with experimental data of ion beams penetrating fully and partially ionized plasmas

In the present work, we have conducted a study to investigate the validity of three different charge-state models of ion beams penetrating plasma targets through a comparison with a total of five experiments from the literature. We have applied two alternative theoretical approaches. On the one hand, we have used a further extension of our cross-sectional model (CSM) code based on projectile electron loss and capture cross sections (rate equations) that was developed previously [Morales et al., Phys. Plasmas 24, 042703 (2017); R. Morales, Ph.D. thesis (Universidad de Castilla-La Mancha, 2019)]. On the other hand, we also used two charge-state models based on a semi-empirical formalism adapted to the plasma case: the Kreussler model [Kreussler et al., Phys. Rev. B 23, 82 (1981)] and the Gus'kov model [Guskov et al., Plasma Phys. Rep. 35, 709 (2009)]. Specifically, we present the predictions and the interpretation of the charge state of light to heavier ions at high, intermediate, and low velocities in Z-pinch and laser-produced partially and fully ionized plasmas. We are showing that experimental data support our new CSM code based on the cross-sectional formalism. In contrast, the framework based on semi-empirical formulas is less accurate for a precise charge-state prediction, but it can be applied for a reasonable stopping power calculation. Overall, results denote that the Gus'kov model is better suited to stopping power calculations at low projectile velocities and the Kreussler model fits better the energy loss data at intermediate velocities. Additionally, we propose a simple non-equilibrium charge model, derived from the semi-empirical framework, as a function of the ion path and equilibrium charge state.

Numerical Approximation of the Nonequilibrium Model of Gradient Elution Chromatography Considering Linear and Nonlinear Solvent Strength Models.

In both linear and nonlinear chromatography, the lumped kinetic model is a suitable model for predicting elution bands when appropriate equilibrium functions and mass transfer coefficients are accessible. This model also works well in the case of gradient elution chromatography if variations in the equilibrium functions due to changes in the mobile phase composition are known. The rational selection of an optimum gradient is explored in this study from three different perspectives using the lumped kinetic model. Elution profiles generated by using (a) linear solvent strength, (b) quadratic solvent strength, and (c) power law are investigated. The effectiveness and reliability of the suggested numerical approach, utilizing the flux-limiting finite volume method, are demonstrated through numerical simulations. The impacts of axial dispersion, nonlinearity coefficient, Henry’s constant, mass transfer coefficient, and gradient parameters are studied on single and two-component elution profiles.

Turbulence Model Comparative Study for Complex Phenomena in Supersonic Steam Ejectors with Double Choking Mode.

Scholars usually ignore the non-equilibrium condensing effects in turbulence-model comparative studies on supersonic steam ejectors. In this study, a non-equilibrium condensation model considering real physical properties was coupled respectively with seven turbulence models. They are the k-ε Standard, k-ε RNG, k-ε Realizable, k-ω Standard, k-ω SST, Transition SST, and Linear Reynolds Stress Model. Simulation results were compared with the experiment results globally and locally. The complex flow phenomena in the steam ejector captured by different models, including shock waves, choking, non-equilibrium condensation, boundary layer separation, and vortices were discussed. The reasons for the differences in simulation results were explained and compared. The relationship between ejector performance and local flow phenomena was illustrated. The novelty lies in the conclusions that consider the non-equilibrium condensing effects. Results show that the number and type of shock waves predicted by different turbulence models are different. Non-equilibrium condensation and boundary layer separation regions obtained by various turbulence models are different. Comparing the ejector performance and the complex flow phenomena with the experimental results, the k-ω SST model is proposed to simulate supersonic steam ejectors.

Multi objective optimization of the amines- CO2 capture absorption-desorption process by a non-equilibrium rate model

The global concentration of CO2 in the atmosphere is increasing rapidly. CO2 emissions have an impact on global climate change. Carbon dioxide capture technologies have been proposed as a promising alternative to reducing CO2 emissions from fossil fuel power plants with post-combustion capture. Amine-based chemical absorption is considered the most industrially developed technology for this kind of process. In this work, a strategy for defining the relationships between design and the operational policies in CO2 capture technologies is addressed. The solution to the problem consists in maximizing the percentage of the CO2 removal, while the stripper reboiler duty is minimized. Since both objective functions in conflict, a multi-objective optimization approach is proposed to achieve a trade-off. Moreover, due to the highly non-ideal behavior in the heat and mass transfer phase, a fully rigorous model was used to capture this strongly non-linear behavior. In addition, an economic evaluation of the heating and cooling utilities in the stripper according to the operation process is carried out. The results show the importance of considering the significance between the influence of operating variables (i.e., temperature, liquid solvent flow rate, and operating pressure) on the amount of CO2 removed and the associated reboiler duty. It shows that both optimal operating policies can be traded-off. Finally, with 30 wt% of MEA solvent, the compromise solution presents a 77% CO2 capture with an energy consumption of 4.98 GJ/t of CO2 for the reboiler service, a cost of heat utilities per year of $3971 capturing 142.29 kg/h of CO2.

Evaluation and development of a predictive model for conjugate phase change heat transfer of energy storage system partially filled with porous media

The present study proposes a predictive model to explore the effect of partially filled porous media on the conjugate heat transfer characteristic of phase change material (PCM) with interfacial coupling conditions between pure fluid region and porous region. The enthalpy-porosity method, local thermal non-equilibrium model and Darcy-Forchheimer law are comprehensively considered to describe the convective heat transfer process in porous media. The modified model is then validated by benchmark data provided by particle image velocimetry (PIV) experiments. The phase change behavior, heat transfer efficiency and energy storage performance are numerically investigated for different partial porous filling strategies in terms of filling content, position, height of porous foam and inclination angles of cavity. The results indicate that due to the resistance in porous region, the shear stress exerted by the main vortex (natural convection) in pure fluid region and the momentum transferred, a secondary vortex phenomenon appears in the porous region near the fluid/porous interface. Moreover, such discontinuity of permeability and fluid-to-porous thermal conductivity results in the cusp of phase change interface at the horizontal fluid/porous boundary. Among four partial porous filling cases, the lower porous filling one has more desirable heat transfer performance, and the 3/4H lower porous filling configuration is the best solution for optimization of the latent heat thermal energy storage (LHTES) systems. For tilted cavity, the increase of inclination angle positively affects the heat transfer efficiency as well as the energy storage rate of the LHTES system, where the performance of 3/4H lower porous filling configuration is further highlighted.

Heat to Hydrogen by Reverse Electrodialysis—Using a Non-Equilibrium Thermodynamics Model to Evaluate Hydrogen Production Concepts Utilising Waste Heat

The reverse electrodialysis heat engine (REDHE) is a promising salinity gradient energy technology, capable of producing hydrogen with an input of waste heat at temperatures below 100 °C. A salinity gradient drives water electrolysis in the reverse electrodialysis (RED) cell, and spent solutions are regenerated using waste heat in a precipitation or evaporation unit. This work presents a non-equilibrium thermodynamics model for the RED cell, and the hydrogen production is investigated for KCl/water solutions. The results show that the evaporation concept requires 40 times less waste heat and produces three times more hydrogen than the precipitation concept. With commercial evaporation technology, a system efficiency of 2% is obtained, with a hydrogen production rate of 0.38 gH2 m−2h−1 and a waste heat requirement of 1.7 kWh gH2−1. The water transference coefficient and the salt diffusion coefficient are identified as membrane properties with a large negative impact on hydrogen production and system efficiency. Each unit of the water transference coefficient in the range tw=[0–10] causes a −7 mV decrease in unit cell electric potential, and a −0.3% decrease in system efficiency. Increasing the membrane salt diffusion coefficient from 10−12 to 10−11 leads to the system efficiency decreasing from 2% to 0.6%.

Effect of Oxygen Dissociation on Nitric Oxide Ultraviolet Emissions

Hypersonic flow over a cylinder was modeled using the direct simulation Monte Carlo method to study how nitric oxide (NO) Ultraviolet emission profiles are a test of high-fidelity thermochemical, nonequilibrium models. For pressures found in typical hypersonic ground facilities, it was shown that the ultraviolet radiation emission profiles are very close to those calculated by assuming Boltzmann equilibrium conditions. Therefore, the NO emission profiles can be tied directly to the ground state NO concentration and flow bulk temperature. Two chemical models differing in the manner in which molecular oxygen is dissociated were considered in this classic canonical-type flow. A comparison of the predicted flowfields with schlieren imagery and surface pressure measurements from previous experiments showed good agreement; however, the sensitivity of these measurements to change in different freestream species concentrations was not found to be strong. Instead, the shapes of the predicted NO integrated emission spatial profiles were observed to be highly sensitive to whether vibrational favoring was considered in the oxygen dissociation model for the same freestream conditions.

On Three “Anomalous” Measurements of Nonlinear QPC Conductance

Practical mesoscopic devices based on quantum point contacts (QPCs) must function at operating point involving large internal driving fields. Experimental evidence has accumulated to display anomalous nonlinear features of QPC response beyond the capacities of accepted tunnelling-based models of nonlinear quantum transport. Here, we recall the physical setting of three anomalous QPC experiments and review how, for two of them, a microscopically based nonequilibrium quantum kinetic description—the correct physical boundary conditions being crucial—has already overcome the predictive limitations of standard nonequilibrium mesoscopic models. The third experiment remains a significant challenge to all theorists.

State-to-state vibrational kinetics of diatomic molecules in laser-induced ignition of a syngas-air mixture: Modeling study

A thermally nonequilibrium model was created to describe the processes occurring in a syngas-air mixture when exposed to intense CO laser radiation. The model consistently describes the reactions of syngas oxidation in air and the state-to-state vibrational kinetics of CO, N2, O2, H2, and OH molecules and also takes into account the nonequilibrium vibrational excitation of polyatomic molecules in the mode approximation. Using the constructed model, the possibility of laser-induced ignition of syngas in air was analyzed. Special attention was paid to the influence of the efficiency of vibrational energy of CO molecules in overcoming the energy barriers of reactions on the simulation results. For the key reactions involving CO molecules, the values of the coefficients of vibrational energy usage were estimated employing the method of classical single-trajectory calculations. It was shown that these coefficients are the critical parameters determining the possibility of using the CO laser radiation to accelerate the ignition of syngas. In addition, we have shown that in the problem considered, because of the strong nonequilibrium excitation of CO vibrations, it is extremely important to take into account the deviation of the vibrational distribution functions of molecules from the Boltzmann one, which requires the use of a state-to-state model of vibrational nonequilibrium. The inaccuracy in calculating the laser-induced ignition time of syngas in air by means of a mode model can reach an order of magnitude.

Quantifying Chromosome Structural Reorganizations during Differentiation, Reprogramming, and Transdifferentiation.

We developed a nonequilibrium model to study chromosome structural reorganizations within a simplified cell developmental system. From the chromosome structural perspective, we predicted that the neural progenitor cell is on the neural developmental path and very close to the transdifferentiation path from the fibroblast to the neuron cell. We identified an early bifurcation of stem cell differentiation processes and the cell-of-origin-specific reprogramming pathways. Our theoretical results are in good agreement with available experimental evidence, promoting future applications of our approach.

Numerical analysis of hybrid nanofluid natural convection in a wavy walled porous enclosure: Local thermal non-equilibrium model

A numerical study of the Buoyancy-driven flow in a porous enclosure, having a bottom heated wavy wall, filled with Cu-Al2O3/water hybrid nanofluid is performed using the local thermal non-equilibrium model. The non-dimensional governing equations of fluid flow and heat transfer are solved using the Galerkin finite element method. The state variables change in the porous enclosure is represented using the Darcy-Brinkman model. The impacts of various effective parameters which include nanoparticle volume fraction (0 ≤ Φ ≤ 0.04), Darcy number (10−5 ≤ Da ≤ 10−2), modified conductivity ratio (0.1 ≤ γ ≤ 1000), the number of undulations (1≤ N ≤ 5) and the amplitude of waviness (0.05 ≤ A ≤ 2). The results showed that the Darcy number is the first controlling parameter on the fluid flow and temperature distributions followed by A, N and γ. Additionally, the heat transfer rate is increased by increasing the thermal conductivity of the nanoparticles reaching its maximum value at Φ = 0.04. Furthermore, by comparing the temperature fields of the fluid phase and solid matrix, it is clear that the effects of the local thermal non-equilibrium are significant at a low modified thermal conductivity ratio and high Darcy number.

Inverse estimation of heat flux under forced convection conjugate heat transfer in a vertical channel fully filled with metal foam

In this work, for the first time, a heat flux at the boundary is estimated for a conjugate heat transfer under forced convection in the presence of high porosity metal foams. For the forward problem a vertical channel experimental set up reported in the literature is considered. The metal foam placed in the vertical channel is subjected to constant heat flux through aluminum plate and airflow of various velocities is passed through vertical channel for removal of heat from the high porosity metal foam placed in the vertical channel. Six different velocities are considered and the required temperature distribution of the aluminum plate is obtained by solving Darcy extended Forchheimer and Local Thermal non-equilibrium models for metal foams. The forward problem, created using computational fluid dynamics in ANSYS-FLUENT, is substituted with Neural Network for faster computation of the forward problem. The maximum errors between the computational fluid dynamics and Artificial Neural Network models for the heat flux values of 466.66, 666.66 and 1133.3 W/m 2 are found to be 0.086, 0.043, 0.092 respectively. The heat flux to the forward problem is treated as unknown and the same is estimated using an inverse method that couples Particle Swarm Optimization with Bayesian framework. The result of inverse estimation of exact temperature data shows that for a heat flux of 1266.64 W/m 2 the error is found to be 1.6e−4%. Similarly, for the noise added temperature data, the absolute % error in heat flux of 599.985, 733.315 and 1266.635 W/m 2 is 4.80e−2%, 2.20e−2%, 2.30e−2% respectively. • Inverse estimation of boundary heat flux using particle swarm optimization method. • Forward problem is a conjugate heat transfer problem in a vertical channel. • Darcy–Forchheimer, Local Thermal Non-equilibrium models for modelling porous medium. • Different Artificial Neural Network models to facilitate faster computations. • Particle Swarm Optimization combined Bayesian framework to quantify modeling error.

Wave reflections in counter-current separation processes with unequal mass transfer coefficients

In this paper, the influence of finite mass transfer resistance on the steady state and dynamic behavior of spatially distributed counter-current separation processes is analyzed. Special attention is given to the pinch states, at which thermodynamic equilibrium between the phases prevails. In a classical paper, Sundaresan et al. (1987) have shown that these pinch states may depend on the mass transfer coefficients. It is shown that this apparent contradiction can be explained by means of wave reflections at the system boundaries, which are reported here to the best of our knowledge for the first time. As an application example, a counter-current adsorption process as introduced in the above reference is considered, and it is shown how these wave solutions can be constructed in the concentration phase space by using the characteristic curves of equilibrium theory in combination with the wave trajectories generated with a non-equilibrium model.

A simple semiempirical model for the static polarizability of electronically excited atoms and molecules

We present a semiempirical analytical model for the static polarizability of electronically excited atoms and molecules, which requires very few readily accessible input data, including the ground-state polarizability, elemental composition, ionization potential, and spin multiplicities of excited and ground states. This very simple model formulated in a semiclassical framework is based on a number of observed trends in polarizability of electronically excited compounds. To adjust the model, both accurate theoretical predictions and reliable measurements previously reported elsewhere for a broad range of multielectron species in the gas phase are utilized. For some representative compounds of general concern that have not yet attracted sufficient research interest, the results of our multireference second-order perturbation theory calculations are additionally engaged. We show that the model we developed has reasonable (given the considerable uncertainties in the reference data) accuracy in predicting the static polarizability of electronically excited species of arbitrary size and excitation energy. These findings can be useful for many applications, where there is a need for inexpensive and quick assessments of the static gas-phase polarizability of excited electronic states, in particular, when building the complex nonequilibrium kinetic models to describe the observed optical refractivity (dielectric permittivity) of nonthermal reacting gas flows.

Generalized non-equilibrium suspended sediment transport model with hindered settling effect for open channel flows

The present paper formulates a generalized model for non-equilibrium suspended sediment transport through an open channel turbulent flow that contains all the existing models in literature as special cases. The two-dimensional (2D) unsteady model for suspended concentration distribution contains the effect of hindered settling and the bottom boundary condition considers deposition velocity together with equilibrium bottom concentration. OpenFOAM, an open-source Finite Volume (FV) method based framework, has been used for the numerical approximation of the model. The proposed model addresses the non-linearity in the governing equation as well as the non-linearity in boundary conditions. Picard iteration approach has been utilized to ensure the convergence of the numerical solution. With different physical parameters and conditions, concentration profiles of suspended sediment particles have been analysed theoretically and graphically. It greatly extends the domain of the numerical solutions for determining sediment distribution in suspension through an open channel turbulent flow in a non-equilibrium state.

Uncertainties in multi-temperature nonequilibrium partition functions and application to CO2

Multi-temperature models are often used as a simplified way to describe nonequilibrium gases. These models assume Boltzmann distributions within each energy mode, which is useful for reducing the number of parameters in computations. This assumption requires that the energy modes are properly separated (which is valid, for instance, for vibration and rotation in low-lying rovibrational levels of diatomic molecules). For polyatomic molecules, several limitations arise. First, certain energy modes are often grouped together to further reduce the number of parameters, which requires additional hypotheses, and sometimes arbitrary grouping schemes. Moreover, the rovibrational levels of polyatomic molecules are often strongly coupled, and the assignment of the coupling terms to one or another energy mode is arbitrary. In this work, we present a method to quantify the influence of assignment or grouping schemes on nonequilibrium spectral models by comparing their impact on nonequilibrium partition functions, and we apply it to the CO2 molecule. We show that significant differences arise when reducing the nonequilibrium model to two temperatures only, as often done in CFD or spectroscopy applications. In particular, one should carefully justify whether the vibrational bending mode is in equilibrium with the rotational mode or with the other vibrational modes. We then determine the nonequilibrium range where a simple Uncoupled Vibrating Rotor model is sufficient, where the coupling term assignment scheme becomes important, and where the uncertainty induced by the assignment of the coupling terms can no longer be neglected. This approach can be extended to other molecules.