Nonideal Systems Research Articles

An Analytical and Numerical Sensitivity and Robustness Analysis of Wave Energy Control Systems

Considerable effort has been expended on the design of control systems for wave energy converters (WECs) over the past two decades. Working from the fundamental requirement of impedance matching, a variety of conceptual and practical algorithms have emerged, which bring various levels of realism to the original complex conjugate ideal, facilitating maximum power transfer. Simplifications can be introduced, such as passive control and causal control, while some enhanced algorithms allow physical constraints to be observed, nonlinear model dynamics to be articulated, or nonideal power takeoff systems to be recognized. However, in general, model-based WEC control systems are evaluated in tandem with identical simulation models, while the sensitivity of controller performance to modeling errors is ignored. In addition, the WEC model utilized by the controller rarely, if ever, fully represents the nonlinear nature of the true WEC dynamics. This paper articulates this model sensitivity issue for different WEC control system architectures and shows that it is of potentially greater impact than for traditional regulation/servomechanism control problems. Recommendations are given on the best WEC control architecture to adopt from a sensitivity/robustness perspective.

Crystalline order and disorder in dusty plasmas investigated by nonequilibrium molecular dynamics simulations**Project supported by the National Natural Science Foundation of China (Grant Nos. 11505286 and 11805272).

The particle structure of a complex system has been explored through a unique Evans's homogenous nonequilibrium molecular dynamics (HNEMD) simulation technique. The crystalline order–disorder structures (OD-structures) and the corresponding energies of three-dimensional (3D) nonideal complex systems (NICSs) have been measured over a wide range of plasma states (Γ, κ) for a body-centered cubic (BCC) structure. The projected technique provides accurate OD-structures with fast convergence and applicable to very small size effect for different temperatures ( 1 / and constant force field ( values. The OD-structure obtained through HNEMD approach is found to be reasonable agreement and more reliable than those earlier identified by simulation approaches and experimental data of NICSs. New simulations of OD-structures show that dusty plasma remains in crystalline (strongly coupled) state at lower temperature and constant values, for the whole simulation runs. Our investigations show that the crystalline structure is changed and the particle structure switches from intermediate to disorder (nonideal gaseous) state with an increase of the system's temperature. It has been shown that the long range order shifts toward lower temperature with increasing *. The presented technique exhibits that the potential energy has a maximum value when the dusty plasma remains in crystalline states (low temperatures), which confirms earlier 3D simulation results.

Quasi-Invariants of Chemical Reactions with Nonideal Kinetics

A method is developed to determine approximate dynamic kinetic invariants (quasi-invariants) of complex chemical reactions with nonideal general-form kinetic laws. The quasi-invariants are expressions relating nonequilibrium reactant concentrations and temperatures, measured in two or more experiments under different initial conditions (multiexperiments) that remain almost constant throughout the reaction. The number of quasi-invariants is determined by the number of independent reactants. The application of the method was illustrated by the example of a two-step reaction in an open system with the Marcelin- de Donder kinetics. The quasi-invariant curves obtained for this reaction were compared with the concentration curves for the entire reaction time. It was shown that the quasi-invariants vary over a narrower range than their corresponding concentrations and temperature in various temperatures; i.e., the quasi-invariants remain nearly constant over time. The method expands the range of tools for the solution of inverse problems of unsteady-state kinetics of chemical reactions in nonideal systems.

Design and control of pressure‐swing distillation for separating ternary systems with three binary minimum azeotropes

The separation of ternary nonideal systems with multi‐azeotrope is very important because they are often found in the waste of chemical and pharmaceutical industries, which is much more difficult due to the formation of multi‐azeotrope and distillation boundary. We propose a systematic procedure for design and control of a triple‐column pressure‐swing distillation for separating ternary systems with three binary minimum azeotropes. This procedure involves thermodynamic insights, a two‐step optimization method, and effective control strategy. The separation of tetrahydrofuran (THF)/ethanol/water is used to illustrate the capability of the proposed procedure. It is found that the pressure limits in columns can be determined through the analysis of residue curve maps, distillation boundary, and isovolatility curves. The optimal triple‐column pressure‐swing distillation is generated with the minimum total annual cost (TAC) of $2.181 × 106 in sequence A. The operating conditions are well controlled approaching their desired specifications in an acceptable time when disturbances occur. © 2019 American Institute of Chemical Engineers AIChE J, 65: 1281–1293, 2019

The phase space exchange pseudopotential for fermions and bosons

Effects of the Bose–Einstein statistics and the Fermi–Dirac one in the phase space quantum thermodynamics are considered. The Wigner function of ideal gases of fermions and bosons is calculated explicitly in pair approximation. It is shown that exchange effects can be taken into account using pseudopotential in the phase space, attractive for bosons and repulsive for fermions. This result is generalized to non-ideal systems.

Modeling hydrocarbon droplet dissolution in near-critical or supercritical water using GCA-EOS and non-ideal diffusional driving force in binary mixtures

In this work, the mixing of a hydrocarbon droplet in near- and super-critical water (NCW/SCW) is mathematically modeled, coupling thermodynamic properties calculation with transport processes. In non-ideal systems, mass transfer is captured using the generalized Maxwell-Stefan equations with the driving force expressed in terms of the fugacity gradients. The GCA-EOS is used to predict the thermodynamic properties and phase equilibrium compositions. We select n-decane, n-triacontane, benzene, naphthalene and 1-decylnaphthalene as representative hydrocarbons. Our simulations show delayed mixing processes as the temperature approaches the upper critical solution temperature (UCST) of the mixture, consistent with the impact of non-ideal diffusional driving forces evaluated from pure thermodynamic calculations. Results also show that the phase behavior notably affects the non-ideal driving forces near the UCST, which confirms the importance of coupling accurate thermodynamic models in predictive mixing studies.

Low‐power non‐ideal pulse‐width modulated DC–DC buck–boost converter: design, analysis and experimentation

In this study, parasitic elements (non-idealities) effect on a low-power DC-DC buck-boost converter design is analysed and investigation is carried out by both large (i.e. steady-state) and small signal analysis. The large signal analysis of non-ideal buck-boost converter explored the significant information such as nearly accurate duty cycle, maximum allowable duty cycle and maximum possible output voltage. Further, accurate mathematical design formulae are derived of inductor and capacitor for specified inductor current ripple and output voltage ripple (OVR), respectively. Moreover, consequences of different equivalent series resistance of capacitor on OVR is examined. Subsequently, the exact model of buck-boost converter is procured from the small signal analysis, which is almost analogous to practical system. In order to show the impact of non-idealities on controller design, an internal model control PID controller is designed for ideal, semi-non-ideal and complete non-ideal systems based on their respective models, which shows the controller based on non-ideal model provides very close results to practical system. Conclusively, the complete theoretical explorations are justified by simulations and substantiated by experimental results.

Constant-pattern design method for the separation of ternary mixtures of rare earth elements using ligand-assisted displacement chromatography

A constant-pattern design method for separating ternary mixtures using ligand-assisted displacement chromatography was developed for non-ideal systems. The general correlation for the minimum column length required to achieve the constant–pattern state for binary separations from our previous study was extended to ternary separations. Additionally, an equation for the yield of a target component as a function of key dimensionless groups was derived based on the constant-pattern mass transfer zone lengths. The column length and operating velocity solved from the two equations ensured the yields and the constant–pattern state for the target components. A selectivity weighted composition factor was developed to allow the design method to specify a minimum target yield for one or multiple components. The design method was verified using simulations and experiments for different targeted yields (70–95%), ligand concentrations (0.03–0.06 M), and feed compositions (1/12–5/6). The targeted yields were achieved or exceeded in all cases tested. The minimum column length required to achieve a constant pattern-state and the productivity of LAD are limited by the lowest selectivity or by a minority component with a low concentration in the feed, even when it does not have the lowest selectivity. Sacrificing the yields of minor components can increase the total productivity significantly. The productivities achieved using this design method are 839 times higher than literature results for ternary separations with the same purity and similar yields.

Improving yields of deuterated, methyl labeled protein by growing in H2O.

Solution NMR continues to make strides in addressing protein systems of significant size and complexity. A fundamental requirement to fully exploit the 15N-1H TROSY and 13C-1H3 methyl TROSY effects is highly deuterated protein. Unfortunately, traditional overexpression in Escherichia coli (E. coli) during growth on media prepared in D2O leads to many difficulties and limitations, such as cell toxicity, decreased yield, and the need to unfold or destabilize proteins for back exchange of amide protons. These issues are exacerbated for non-ideal systems such as membrane proteins. Expression of protein during growth in H2O, with the addition of 2H-labeled amino acids derived from algal extract, can potentially avoid these issues. We demonstrate a novel fermentation methodology for high-density bacterial growth in H2O M9 medium that allows for appropriate isotopic labeling and deuteration. Yields are significantly higher than those achieved in D2O M9 for a variety of protein targets while still achieving 75-80% deuteration. Because the procedure does not require bulk D2O or deuterated glucose, the cost per liter of growth medium is significantly decreased; taking into account improvements in yield, these savings can be quite dramatic. Triple-labeled protein is also efficiently produced including specific 13CH3 labeling of isoleucine, leucine, and valine using the traditional ILV precursors in combination with an ILV-depleted mix of 2H/15N amino acids. These results are demonstrated for the membrane protein sensory rhodopsin II and the soluble proteins human aldoketoreductase AKR1c3, human ubiquitin, and bacterial flavodoxin. Limitations of the approach in the context of very large molecular weight proteins are illustrated using the bacterial Lac repressor transcription factor.

Key parameters controlling the development of constant-pattern isotachic trains of two rare earth elements in ligand-assisted displacement chromatography

Ligand-assisted displacement chromatography (LAD) has been developed for separating rare earth elements since the 1950’s. Isotachic displacement trains, which are similar to those in conventional displacement chromatography, were reported previously. However, there has been no general theory delineating the conditions required to form constant-pattern displacement trains for non-ideal systems (or systems with significant mass transfer resistance). The constant-pattern state is critical for obtaining pure products with high yield and high productivity. Without theoretical guidance, all the previous studies found the constant–pattern state by experimental trial and error, which was time consuming and costly.In this study, an efficient rate model and simulations of LAD were developed and verified with experimental data for non-ideal systems. Verified simulations were used to understand the mechanisms of separations and the transition from the transient state to the constant-pattern state. The key dimensionless factors affecting the transition for binary non-ideal systems were identified. Dimensionless groups were developed to reduce the number of variables. Simulations were used to find the transition points fromthe transient state to the constant-pattern state, which indicates the minimum dimensionless column lengths in the multi-parameter space. Strategic combination of the key dimensionless groups allows the minimum dimensionless column lengths to correlate with the combined groups in a two-dimensional diagram (or a map). The correlation curve divides the multi-dimensional space into the transient region and the constant-pattern region. The correlation was further verified with five sets of experiments. It can be used to find, without process simulations or experiments, the minimum column lengths for developing constant-pattern isotachic trains for non-ideal systems, which is useful for designing efficient ligand-assisted displacement chromatography at any scale.

Self-Consistency of the Theory of Elementary Stage Rates of Reversible Processes and the Equilibrium Distribution of Reaction Mixture Components

An analysis is presented of one of the key concepts of physical chemistry of condensed phases: the theory self-consistency in describing the rates of elementary stages of reversible processes and the equilibrium distribution of components in a reaction mixture. It posits that by equating the rates of forward and backward reactions, we must obtain the same equation for the equilibrium distribution of reaction mixture components, which follows directly from deducing the equation in equilibrium theory. Ideal reaction systems always have this property, since the theory is of a one-particle character. Problems arise in considering interparticle interactions responsible for the nonideal behavior of real systems. The Eyring and Temkin approaches to describing nonideal reaction systems are compared. Conditions for the self-consistency of the theory for mono- and bimolecular processes in different types of interparticle potentials, the degree of deviation from the equilibrium state, allowing for the internal motions of molecules in condensed phases, and the electronic polarization of the reagent environment are considered within the lattice gas model. The inapplicability of the concept of an activated complex coefficient for reaching self-consistency is demonstrated. It is also shown that one-particle approximations for considering intermolecular interactions do not provide a theory of self-consistency for condensed phases. We must at a minimum consider short-range order correlations.

An analytical approximated solution and numerical simulations of a non-ideal system with saturation phenomenon

Nowadays, researches about non-ideal problems have been increased considerably in technical-scientific community. Nonlinear problems have been widely studied due to their particularities in real problems, mainly when these nonlinearities induce interactions between a dynamical system with its excitation source, these kind of systems are called non-ideal systems. One of the excitation sources, which is of non-ideal kind, is an unbalanced DC motor with limited power supply. When it is coupled to a dynamical system, this system is subjected to Sommerfeld effect, where jump phenomena may occur. However, when the same dynamical system is of two-degrees-of-freedom and possesses 2:1 internal resonance, saturation phenomenon occurs. Therefore, in this work, the dynamical behavior of a non-ideal three-degrees-of-freedom weakly coupled system associated with quadratic nonlinearities in the equations of motion is investigated. The full system consists of two nonlinear mechanical oscillators coupled through quadratic nonlinearities and which produces a 2:1 internal resonance between their translational movements. In the bigger oscillator, an unbalanced DC motor is used as an excitation source. Under these conditions, equations of motion of the system were obtained using Lagrange’s method, and the method of multiple scales was applied to find an analytical approximated solution of the equations of motion. In addition, numerical simulations of the equations of motion were carried out to analyze the response of the non-ideal system by varying the torque of the motor. It is shown that when the excitation frequency is near to second natural frequency of the main system, saturation and jump phenomena occur. Furthermore, this work investigates the ranges of some torques of the motor, which causes the phenomena, and explores the possibility to harvest energy from high-amplitudes of vibration in a future work.

Observer-based event-triggered tracking consensus of non-ideal general linear multi-agent systems

In this paper, the leader-following consensus problem of general linear multi-agent systems without direct access to real-time state is investigated. A novel observer-based event-triggered tracking consensus control scheme is proposed. In the control scheme, a distributed observer is designed to estimate the relative full states, which are used in tracking consensus protocol to achieve overall consensus. And an event-triggered mechanism with estimated state-dependent event condition is adopted to update the control signals so as to reduce unnecessary data communication. Based on the Lyapunov theorem and graph theory, the proposed event-triggered control scheme is proved to implement the tracking consensus when real-time state cannot direct obtain. Moreover, such scheme can exclude Zeno-behavior. Finally, numerical simulations illustrate the effectiveness of the theoretical results.

Measurement and Modeling of Isobaric Vapor–Liquid Equilibrium of Water + Glycols

We present new experimental data on the isobaric vapor–liquid equilibria (VLE) of four binary mixtures of water with ethylene glycol, diethylene glycol, triethylene glycol, or tetraethylene glycol, measured at three different system pressures (0.05, 0.07, and 0.1 MPa). Water activity coefficients were estimated from the mixtures boiling temperatures and used to rationalize the effect of the increasing glycols chain length on the molecular interactions with water. The soft statistical associating fluid theory (SAFT) equation of state was used to describe the experimental VLE data of these highly nonideal systems, providing insights into the molecular interactions leading the macroscopic behavior of the mixtures. Glycols and water were both modeled as associating molecules, with models and parameters from previous works, in a transferable manner. Soft-SAFT accurately reproduces the experimental data using one single, state independent, binary interaction parameter to correct the mixtures dispersive energy. It is further shown that the parametrization obtained from the pure glycols can be used to provide accurate predictions of the water activities in aqueous solutions of PEGs of higher molecular weight (600–6000 g/mol) highlighting the soft-SAFT robustness and the soundness of the parametrization used.

Unsupervised Screening of Vibrational Spectra by Principal Component Analysis for Identifying Molecular Clusters

Vibrational spectra are commonly used to study molecular interactions in solutions. However, the data analysis is often demanding and requires significant experience in order to obtain meaningful results. This study demonstrates that principal component analysis (PCA) can serve as an unsupervised tool for initial screening of non-ideal mixture systems. Taking the aqueous solutions of dimethyl sulfoxide (DMSO) as an example, PCA reveals-easily and fast-the two prominent stoichiometries at 1:2 and 1:1 molar DMSO:water ratio and significantly outperforms elaborate spectral profile analysis or common algorithms as indirect hard modeling (IHM) or multivariate curve resolution (MCR). The corresponding molecular 1:1 and 1:2 clusters are known to be dominating configurations in the solutions.

Energy from Negentropy of Non-Cahotic Systems.

Negative contribution of entropy (negentropy) of a non-cahotic system, representing the potential of work, is a source of energy that can be transferred to an internal or inserted subsystem. In this case, the system loses order and its entropy increases. The subsystem increases its energy and can perform processes that otherwise would not happen, like, for instance, the nuclear fusion of inserted deuterons in liquid metal matrix, among many others. The role of positive and negative contributions of free energy and entropy are explored with their constraints. The energy available to an inserted subsystem during a transition from a non-equilibrium to the equilibrium chaotic state, when particle interaction (element of the system) is switched off, is evaluated. A few examples are given concerning some non-ideal systems and a possible application to the nuclear reaction screening problem is mentioned.

Quantum tails in the momentum distribution functions of non‐ideal Fermi systems

In classical statistics, the momentum distribution functions are Maxwellian in the state of thermodynamic equilibrium. However, quantum effects can change it to non‐Maxwellian through two mechanisms. The first mechanism is an exchange interaction between identical particles, leading to the Fermi distribution. The second mechanism is the Heisenberg's principle: an interaction of a particle with others reduces the volume available to it, which leads to uncertainty in the momentum and results in an increased probability of having a higher momentum. In this paper, the momentum distribution functions of a two‐component Coulomb system are computed using the Monte Carlo method. It is shown that the momentum distribution functions have high‐momentum “tails” in the regime of strong coupling.

A predictive model for the diffusion of a highly non-ideal ternary system.

Diffusion plays a central part in many unit operations. The Maxwell-Stefan model is the dominant model for both gaseous and liquid diffusion. However, it was developed from the kinetic theory of gases, raising the question of whether it can be extended to non-ideal liquid systems. The dynamic fluctuation model is an alternative model based on the Cussler theory and predicts a smaller thermodynamic influence relative to the linear influence of the Maxwell-Stefan model due to dynamic concentration fluctuations. Since the dynamic fluctuation model, which uses the scaling factor α, had improved performance relative to the Maxwell-Stefan model for a wide range of binary systems, it is postulated that this improved performance should also be observed for a ternary system. In this work, the dynamic molecular fluctuation model was extended to a highly non-ideal ternary system, using the same scaling factor α, through matrix manipulation. Using self-diffusion data measured by NMR, mutual diffusion predictions of the developed model and the Maxwell-Stefan model were compared to experimental mutual diffusion data of the partially miscible system ethanol/toluene/n-decane. It is demonstrated that the dynamic fluctuation model gives improved predictions relative to the Maxwell-Stefan approach, consistent with previous observations on binary systems, showing that the reduced thermodynamic influence of the dynamic fluctuation model is an improvement. In addition, we show that the use of local mole fractions, to account for molecular association, in both the dynamic fluctuation and Maxwell-Stefan models, results in improved diffusion predictions for the ternary system. The results confirm that the dynamic fluctuation model improves predictions of mutual diffusion in liquid mixtures, suggesting a non-linear correction to the thermodynamic correction factor. The results also suggest that that the key assumptions in the Maxwell-Stefan model and its derivation, rooted in the kinetic theory of gases, are not entirely accurate for highly non-ideal liquid systems. The optimum α for the ternary system studied here is approximately 0.45, similarly to the optimum α of 0.40 to 0.80 for a range of binary systems previously studied, suggesting that the use of the α scaling factor, which is grounded in scaling laws theory, is of general validity.

Emerging investigator series: exploring the surface properties of aqueous aerosols coated with mixed surfactants.

Mixed Langmuir monolayers of cholesterol with both saturated and unsaturated fatty acids, stearic acid (SA), and oleic acid (OA) spread at the air-seawater surface were studied. The phase behavior, molecular interaction, and conformational order of the monolayers were investigated by surface pressure-area (π-A) isotherms and infrared reflection-absorption spectroscopy (IRRAS) measurements. The thermodynamic parameters of the mixed films, including excess molecular area and excess Gibbs free energy were calculated by using the isotherm data. The interaction between SA (or OA) and cholesterol varied with the molar fraction of the fatty acids and surface pressure. OA/chol monolayers showed the characteristics of miscibility, but they acted as nonideal systems. Cholesterol has been observed to have a stabilizing effect on OA monolayers. The negative values of the excess Gibbs free energy in the entire composition range demonstrated that mixed OA/chol monolayers were thermodynamically stable. IRRAS spectra showed that mixing with cholesterol changes the ordering of fatty acid monolayers at the air-seawater surface. The findings provide general information regarding the structural changes in the monolayer induced by lateral packing. These results help in the understanding of the mixing behavior of fatty acids and cholesterol and provide insights into the fate of the mixed-monolayer-coated sea salt aerosol in the ocean environment.

Kinetics pathway of precipitation in model Co-Al-W superalloy

The early stages of precipitation of the γ′ phase in a model Co based superalloy (Co-9.1Al-7W (at.%)) have been investigated at 900 °C using electron microscopy and atom probe tomography. Nucleation, growth and coarsening stages have been studied with a focus on the temporal evolution of the precipitate composition in the light of recent theoretical developments on phase separation in multicomponent alloys. The experimental data have been confronted to the theories of nucleation and coarsening recently developed for such alloys, which are valid for non-ideal and non-dilute systems, and predict the temporal evolution of both the matrix and precipitate compositions. The rate constant for the mean size evolution of the particles, as derived from experiments, has been compared to the one predicted by the mentioned coarsening theory that accounts for a more accurate description of the thermodynamics of the phases, as compared with more classical approaches. From this comparison the γ/γ′ interfacial energy was derived and found equal to ∼48 mJ/m2 The exponents for the temporal evolution of average particles size, number of particles per unit volume were found identical to those for binary alloys during the coarsening regime, as expected, and the temporal evolutions of compositions in both γ and γ′ phases were found to evolve as predicted by theory. Indeed, the W content in the particles, measured from atom probe tomography (APT) experiments, was found to significantly decrease with time and the observed evolution is remarkably well described by the theory and therefore is shown to originate from the competition between diffusion and capillarity.