Equilibrium Limit Research Articles

Equilibrium shift, poisoning prevention, and selectivity enhancement in catalysis via dehydration of polymeric membranes

Generation of water as a byproduct in chemical reactions is often detrimental because it lowers the yield of the target product. Although several water removal methods, using absorbents, inorganic membranes, and additional dehydration reactions, have been proposed, there is an increasing demand for a stable and simple system that can selectively remove water over a wide range of reaction temperatures. Herein we report a thermally rearranged polybenzoxazole hollow fiber membrane with good water permselectivity and stability at reaction temperatures of up to 400 °C. Common reaction engineering challenges, such as those due to equilibrium limits, catalyst deactivation, and water-based side reactions, have been addressed using this membrane in a reactor.

Research Progress of Carbon Deposition on Ni-Based Catalyst for CO2-CH4 Reforming

As we all know, the massive emission of carbon dioxide has become a huge ecological and environmental problem. The extensive exploration, exploitation, transportation, storage, and use of natural gas resources will result in the emittance of a large amount of the greenhouse gas CH4. Therefore, the treatment and utilization of the main greenhouse gases, CO2 and CH4, are extremely urgent. The CH4 + CO2 reaction is usually called the dry methane reforming reaction (CRM/DRM), which can realize the direct conversion and utilization of CH4 and CO2, and it is of great significance for carbon emission reduction and the resource utilization of CO2-rich natural gas. In order to improve the activity, selectivity, and stability of the CO2-CH4 reforming catalyst, the highly active and relatively cheap metal Ni is usually used as the active component of the catalyst. In the CO2-CH4 reforming process, the widely studied Ni-based catalysts are prone to inactivation due to carbon deposition, which limits their large-scale industrial application. Due to the limitation of thermodynamic equilibrium, the CRM reaction needs to obtain high conversion and selectivity at a high temperature. Therefore, how to improve the anti-carbon deposition ability of the Ni-based catalyst, how to improve its stability, and how to eliminate carbon deposition are the main difficulties faced at present.

Influence of the Au–Ti Active Site of the Titanosilicate MWW Zeolite on the Catalytic Activity of Ethane Dehydrogenation in the Presence of O2

The titanosilicate zeolite with a MWW topology structure was synthesized by the atom-planting method through the dehydrochlorination of the hydroxyl group in the deboronated ERB-1 zeolite (D-ERB-1) and TiCl4, and Au was further loaded with the deposition precipitation method to apply for the ethane direct dehydrogenation (DH) and dehydrogenation of ethane in the presence of O2 (O2-DH). It was found that Au nanoparticles (NPs) below 5 nm exhibited good activity for ethane direct dehydrogenation and O2-DH. The addition of titanium can not only anchor more Au but also make Au have a more dispersed homogeneous distribution. The ethane O2-DH catalytic performances of Au-loaded Ti-incorporated D-ERB-1 (Ti-D-ERB-1) were compared to those of Au-loaded ZnO-D-ERB-1 and pure silicate D-ERB-1. The results confirm that ethane O2-DH catalyzed by Au-Ti paired active sites is a tandem reaction of catalytic ethane DH and selective H2 combustion (SHC) of generated H2. According to the experimental results and calculated kinetic parameters, such as the activation energy of DH and SHC reaction heat of O2-DH, SHC catalyzed by the Au/Ti-D-ERB-1 catalyst containing the Au-Ti active site can not only break the ethane dehydrogenation thermodynamic equilibrium limitation to improve the ethylene yield but also suppress the CO2 and CO selectivity.

Competing constraints shape the nonequilibrium limits of cellular decision-making

Gene regulation is central to cellular function. Yet, despite decades of work, we lack quantitative models that can predict how transcriptional control emerges from molecular interactions at the gene locus. Thermodynamic models of transcription, which assume that gene circuits operate at equilibrium, have previously been employed with considerable success in the context of bacterial systems. However, the presence of ATP-dependent processes within the eukaryotic transcriptional cycle suggests that equilibrium models may be insufficient to capture how eukaryotic gene circuits sense and respond to input transcription factor concentrations. Here, we employ simple kinetic models of transcription to investigate how energy dissipation within the transcriptional cycle impacts the rate at which genes transmit information and drive cellular decisions. We find that biologically plausible levels of energy input can lead to significant gains in how rapidly gene loci transmit information but discover that the regulatory mechanisms underlying these gains change depending on the level of interference from noncognate activator binding. When interference is low, information is maximized by harnessing energy to push the sensitivity of the transcriptional response to input transcription factors beyond its equilibrium limits. Conversely, when interference is high, conditions favor genes that harness energy to increase transcriptional specificity by proofreading activator identity. Our analysis further reveals that equilibrium gene regulatory mechanisms break down as transcriptional interference increases, suggesting that energy dissipation may be indispensable in systems where noncognate factor interference is sufficiently large.

Mach reflection of detonation wave on porous wall

This study reports the Mach reflection of gaseous detonation on porous wedges experimentally, in which the porous wall is consisted of equidistant inline square columns. The smoked foil technique was utilized to monitor the evolution of the triple-point trajectory and detonation cells in the Mach stem region. In addition to the wedge angle and initial pressure of gaseous mixture, this paper also focuses on the effect of porosity and pore size on the Mach reflection and its mechanism. The results show that the strength of the Mach stem is significantly weakened by the porous media compared with that on the smooth wedge, which is ascribed to the diffraction and reflection waves generated by the interaction of the Mach stem front with the pore. Furthermore, the onset of the triple-point trajectory is delayed, the angle of which is decreased. The porosity and pore size present distinct influence on the Mach stem height. With the increase in the porosity and the decrease in the pore size, the Mach stem region is attenuated more dramatically and the Mach stem is harder to be formed or even could not be observed. Furthermore, the triple-point trajectory on the porous wall exhibits local self-similarity and satisfies the frozen limit in the near field and the equilibrium limit in the far field. However, the lengths of the existence of the frozen limit and the transition to the equilibrium limit on the porous wall are found to be much shorter than the hydrodynamic thickness, and the recovery of the self-similarity depends largely on the porosity and pore size.

A New Hydrodynamic Spherical Accretion Exact Solution and Its Quasi-spherical Perturbations

We present an exact γ = 5/3 spherical accretion solution that modifies the Bondi boundary condition of as r → ∞ to ρ → 0 as r → ∞. This change allows for simple power-law solutions on the density and infall velocity fields, ranging from a cold empty freefall condition where pressure tends to zero, to a hot hydrostatic equilibrium limit with no infall velocity. As in the case of the Bondi solution, a maximum accretion rate appears. As in the γ = 5/3 case of the Bondi solution, no sonic radius appears, this time however, because the flow is always characterized by a constant Mach number. This number equals 1 for the case of the maximum accretion rate, diverges toward the cold empty state, and becomes subsonic toward the hydrostatic equilibrium limit. It can be shown that in the limit r → 0, the Bondi solution tends to the new solution presented, extending the validity of the Bondi accretion value to cases where the accretion density profile does not remain at a fixed constant value out to infinity. We then explore small deviations from sphericity and the presence of angular momentum through an analytic perturbative analysis. Such perturbed solutions yield a rich phenomenology through density and velocity fields in terms of Legendre polynomials, which we begin to explore for simple angular velocity boundary conditions having zeros on the plane and pole. The new solution presented provides complementary physical insight into accretion problems in general.

A new hydrogenation-coupling approach for supra-equilibrium conversion in a water–gas shift reaction: Simultaneous hydrogen generation and chemical storage

This work reports a practical system of hydrogenation-coupled water–gas shift reaction (HC-WGSR) for simultaneous hydrogen production and storage. The performance of the HC-WGSR system was predicted through thermodynamic simulation. The proof-of-concept tandem water–gas shift and propene hydrogenation strategy was successfully demonstrated using a bifunctional catalyst. The hydrogen produced from the WGSR was successfully stored in propane simultaneously, and the overall CO conversion of nearly 100% overcame the equilibrium limitation of the WGSR over a wide range of space velocities (3000 - 6000 h−1) at 200 °C and 1 bar. This study demonstrated that the in situ removal/storage of H2 using the hydrogenation-coupling approach is promising even in a CO2-rich environment (20% CO2). The new approach shall see a great opportunity in using organic hydrogen carriers, e.g., benzene, toluene, N-ethylcarbazole, to expand the industrial applications, underpinning the global supply chain for hydrogen energy.

Tuning nonequilibrium phase transitions with inertia.

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation-dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.

Analyzing and predicting non-equilibrium many-body dynamics via dynamic mode decomposition

Simulating the dynamics of a nonequilibrium quantum many-body system by computing the two-time Green's function associated with such a system is computationally challenging. However, we are often interested in the time-diagonal of such a Green's function or time-dependent physical observables that are functions of one time. In this paper, we discuss the possibility of using dynamic mode decomposition (DMD), a data-driven model order reduction technique, to characterize one-time observables associated with the nonequilibrium dynamics using snapshots computed within a small time window. The DMD method allows us to efficiently predict long time dynamics from a limited number of trajectory samples. We demonstrate the effectiveness of DMD on a model two-band system. We show that, in the equilibrium limit, the DMD analysis yields results that are consistent with those produced from a linear response analysis. In the nonequilibrium case, the extrapolated dynamics produced by DMD is more accurate than a special Fourier extrapolation scheme presented in this paper. We point out a potential pitfall of the standard DMD method caused by insufficient spatial/momentum resolution of the discretization scheme. We show how this problem can be overcome by using a variant of the DMD method known as higher order DMD.

Stability Analysis of Equilibrium Point and Limit Cycle of Two-Dimensional Nonlinear Dynamical Systems—A Tutorial

The equilibrium state of a dynamical system can be divided into the equilibrium point and limit cycle. In this paper, the stability analysis of the equilibrium point and limit cycle of dynamical systems are presented through different and all possible approaches, and those approaches are compared as well. In particular, the author presented the stability analysis of the equilibrium point through phase plane approach, Lyapunov–LaSalle energy-based approach, and linearization approach, respectively, for two-dimensional nonlinear system, while the stability analysis of the limit cycle is analyzed by using the LaSalle local invariant set theorem and Poincaré–Bendixson theorem, which is only valid in two-dimensional systems. Different case studies are used to demonstrate the stability analysis of equilibrium point and limit cycle.

On the statistics of coherent vortices in incoherent environments

Coherent vortices are important building blocks of complex flows on all scales, governing dynamics in various applications from geophysics over engineering to the coherent-structures’ paradigm of turbulence. As a commonly studied prototype of this configuration, we consider a large-scale, line vortex evolving in a background flow of small-scale, incoherent turbulence, which, nevertheless, naturally occurs in trailing vortices and tornadoes. The main unsteadiness of the large-scale vortex in this configuration is called meandering. Despite a common observation in experiments since the 1970s and a multitude of studies, its origin and physical mechanism remain puzzling as of this writing. Nevertheless, we do have considerable experimental evidence that, in the range of typically assumed parameters, vortex meandering shares four universal characteristics; namely, (i) fluctuations of the vortex-centre position obey a Gaussian distribution with (ii) monotonously growing standard deviation downstream. Besides, (iii) the fluctuation kinetic energy and enstrophy increase downstream, whereas the main contribution comes from a dipolar vorticity fluctuation pattern confined to the vortex core. This corresponds to the (iv) typical spectral signature of power spectra spanning all resolved scales, whereas the variance level increases monotonously towards the low frequencies. We present the first theoretical model to explain all four experimental cornerstones of vortex meandering in one theory. Starting from the definition of the vortex centre, we first show that the meandering motion is linearly proportional to the leading expansion coefficients of a Karhunen–Loève decomposition of the vorticity field. This has been conjectured before but has never been shown. The configuration strongly suggests scale separation between the response times of the vortex and the surrounding turbulence. On this assumption, we derive a Langevin equation for the slow, large scales driven by the fast, small scales, represented as a stochastic forcing. The particular phenomenon of vortex meandering therewith is found to belong to the large class of Gauss–Markov processes. That is, vortex meandering is an (abstract) Brownian motion. From this understanding, we infer immediately that the Gaussian statistics are a consequence of the central limit theorem and that the growing standard deviation follows from a competition between external forcing and intrinsic resistance. In the equilibrium limit, we derive the spectral signature of the large scales as a power law of the frequency, response time and forcing variance. Eventually, comparing our theoretical model with an experimental database gathered at the ONERA, we find good overall agreement.

Preparation of high-quality FeV50 alloy by an improved SHS-EAH multi-stage process

As the most widely used vanadium intermediate alloy, ferrovanadium is mainly prepared by the self-propagating high-temperature synthesis (SHS) process with the advantages of short process and large heat release. However, there is a trade-off between the amount of reduction agent of Al and the product quality of ferrovanadium, which is caused by the thermodynamic equilibrium limitation of the reduction between Al and vanadium oxides. The reasonable adjustment of the trade-off has become an urgent problem to be solved for the preparation of high-quality ferrovanadium. In the present work, the thermodynamic equilibrium for the reduction limitation using Al as reducing agent has been thoroughly analyzed with the reference to the equilibrium phase diagram. It was found that the theoretical reduction limitation of total vanadium (T.V) in slag was decreased from 4.08 wt.% to wt. 0.86 wt.% when the Al content in alloy reached 2.0 wt.% at 1800 °C. The vanadium in slag was mainly presented in the form of MgV3O8 and coexisting with other phases of MgAl2O4, CaAl2O4, CaAl4O7, CaAl12O19. With the purpose of further decrease the high Al concentration in alloy and vanadium loss in slag, an improved SHS-EAH process was implemented by multi-stage gradient aluminum addition coefficient pattern, the average vanadium content in slag was reduced from 1.82 wt.% to 0.83 wt.%, while the aluminum content in FeV50 alloy was decreased from 1.5 wt.% to 0.4 wt.%. The SHS-EAH process was proved to be a better process with improved yield and quality for the preparation of ferrovanadium.

Large population games with interactions through controls and common noise: convergence results and equivalence between open-loop and closed-loop controls

In the presence of a common noise, we study the convergence problems in mean field game (MFG) and mean field control (MFC) problem where the cost function and the state dynamics depend upon the joint conditional distribution of the controlled state and the control process. In the first part, we consider the MFG setting. We start by recalling the notions of measure-valued MFG equilibria and of approximate closed-loop Nash equilibria associated to the corresponding N-player game. Then, we show that all convergent sequences of approximate closed-loop Nash equilibria, when N → ∞, converge to measure-valued MFG equilibria. And conversely, any measure-valued MFG equilibrium is the limit of a sequence of approximate closed-loop Nash equilibria. In other words, measure-valued MFG equilibria are the accumulation points of the approximate closed-loop Nash equilibria. Previous work has shown that measure-valued MFG equilibria are the accumulation points of the approximate openloop Nash equilibria. Therefore, we obtain that the limits of approximate closed-loop Nash equilibria and approximate open-loop Nash equilibria are the same. In the second part, we deal with the MFC setting. After recalling the closed-loop and open-loop formulations of the MFC problem, we prove that they are equivalent. We also provide some convergence results related to approximate closed-loop Pareto equilibria.

HYDROGEN GENERATION USING LOW CARBON TECHNOLOGIES

Hydrogen is the cleanest fuel as it only emits water when combusted. Furthermore, it has the highest combustion energy as compared to fossil fuels. Steam-methane reforming is the dominant process for hydrogen production, but it is energy intensive and suffers from chemical equilibrium limitation. In this paper, alternative technologies for hydrogen production are discussed. This includes gasification of fossil fuels, electrolysis and biological techniques. Carbon dioxide emissions from these processes are discussed as well. The paper also compares the technologies in terms of technical and economic points of view.

Dynamics of Three Coupled Generators of Quasi-periodic Oscillations

The dynamics of three coupled generators capable of demonstrating autonomous quasi-periodic oscillations is studied. The complex structure of the Lyapunov charts of the system is discussed, which reveals invariant tori of different dimensions, quasi-periodic bifurcations of tori, and Arnold’s resonant web based on tori of different dimensions. Cases of different types of tuning of individual generators (periodic oscillations, quasi-periodic oscillations) are considered. A detailed numerical bifurcation analysis of the equilibrium state and limit cycles, which form a complex picture of dynamic regimes, is carried out.Common features and differences compared to the case of three coupled van der Pol oscillators are discussed.

Charmonium, Bc and X(3872) Transport at the LHC

We deploy a kinetic-rate equation to evaluate the transport of J/ψ, ψ(2S), Bc and X (3872) in ultrarelativistic heavy-ion collisions and compare their production yields to experimental data from the Large Hadron Collider. The rate equation has two main transport parameters: the equilibrium limit and reaction rate for each state. The temperature-dependent equilibrium limits include charm- and bottom-quark fugacities based on their initial production. The reaction rates for charmonia, bottomonia and Bc rely on charm- and bottomquark masses and binding energies from a thermodynamic T-matrix approach. For the X (3872) particle, internal structure information is encoded in reaction rates and initial conditions in the hadronic phase via two different scenarios: a loosely bound hadronic molecule vs. a compact tetraquark.

Optimization Modeling for Advanced Syngas to Olefin Reactive Systems

Reactor designs with mixed catalysts play an important role in transforming a multiple reactor system to single-shot reactors. In addition to savings in capital and ease of implementation, single-shot reactors are useful to break equilibrium limitations, thereby increasing the yield and selectivity of desired product as shown in previous studies. However, the nonlinear and highly exothermic nature of mixed-catalyst systems makes it difficult for commercial process simulation and optimization tools to optimize these systems. This study describes the development and application of optimization strategies for mixed-catalyst, single-shot reactors for syngas to olefin (STO) processes. Finding the optimal catalyst distribution is challenging and requires advanced solution strategies for singular optimal control problems, which are poorly conditioned and often lead to flat response surfaces. The graded bed and partial-moving finite-element approaches are used to find the optimal catalyst distribution that maximizes the olefins yield. A 1.3% increase in the yield is observed from one zone to three zones. The yield further improves from three zones to the exact infinite dimensional solution by 0.2%. This improvement can be realized in practice by changing only the catalyst distribution, without any extra investment. Finally, the results suggest that a mixed-catalyst single shot reactor bed can be applied to other reaction mechanisms to increase reactor performance.

Attapulgite Nanorod-Incorporated Polyimide Membrane for Enhanced Gas Separation Performance.

Polyimide (PI) membrane is an ideal gas separation material due to its advantages of high designability, good mechanical properties and easy processing; however, it has equilibrium limitations in gas selectivity and permeability. Introducing nanoparticles into polymers is an effective method to improve the gas separation performance. In this work, nano-attapulgite (ATP) functionalized with KH-550 silane coupling agent was used to prepare polyimide/ATP composite membranes by in-situ polymerization. A series of characterization and performance tests were carried out on the membranes. The obtained results suggested a significant increase in gas permeability upon increasing the ATP content. When the content of ATP was 50%, the gas permeability of H2, He, N2, O2, CH4, and CO2 reached 11.82, 12.44, 0.13, 0.84, 0.10, and 4.64 barrer, which were 126.87%, 119.40%, 160.00%, 140.00%, 150.00% and 152.17% higher than that of pure polyimide, respectively. No significant change in gas selectivity was observed. The gas permeabilities of membranes at different pressures were also investigated. The inefficient polymer chain stacking and the additional void volume at the interface between the polymer and TiO2 clusters leaded to the increase of the free volume, thus improving the permeability of the polyimide membrane. As a promising separation material, the PI/ATP composite membrane can be widely used in gas separation industry.

Non-minimal coupling of scalar and gauge fields with gravity: an entropy current and linearized second law

This work extends the proof of a local version of the linearized second law involving an entropy current with non-negative divergence by including the arbitrary non-minimal coupling of scalar and U(1) gauge fields with gravity. In recent works, the construction of entropy current to prove the linearized second law rested on an important assumption about the possible matter couplings to gravity: the corresponding matter stress tensor was assumed to satisfy the null energy conditions. However, the null energy condition can be violated, even classically, when the non-minimal coupling of matter fields to gravity is considered. Considering small dynamical perturbations around stationary black holes in diffeomorphism invariant theories of gravity with non-minimal coupling to scalar or gauge fields, we prove that an entropy current with non-negative divergence can still be constructed. The additional non-minimal couplings that we have incorporated contribute to the entropy current, which may even survive in the equilibrium limit. We also obtain a spatial current on the horizon apart from the entropy density in out-of-equilibrium situations. We achieve this by using a boost symmetry of the near horizon geometry, which constraints the off-shell structure of a specific component of the equations of motion with newer terms due to the non-minimal couplings. The final expression for the entropy current is U(1) gauge-invariant for gauge fields coupled to gravity. We explicitly check that the entropy current obtained from our abstract arguments is consistent with the expressions already available in the literature for specific model theories involving non-minimal coupling of matter with higher derivative theories of gravity. Finally, we also argue that the physical process version of the first law holds for these theories with arbitrary non-minimal matter couplings.

TEMPORAL LIMITS OF THE REALIZATION OF THE CIVIL RIGHT OF A PERSON

This scientific work is devoted to the study of the topical issue of the temporal limits of subjective civil law. The main thesis is argued that the exercise of the right is possible only during its existence. At the same time, it should be noted that the exercise or non-exercise of one's civil right depends entirely on the will of the authorized person. Such implementation of the powers laid down in the law can take place through the active action of the managed person, or by requiring him to perform an action from the debtor. But the corresponding act should be carried out within the limits of the existence of the right. It is necessary to distinguish between the period of existence of the material right itself and the period of its belonging to a certain person. For example, ownership of a certain thing will exist as long as the thing itself exists. However, during this time, the owner of this property may change several times. But the change of specific owners does not affect the period of existence of civil law. Thus, it is emphasized that the time factor is necessarily part of civil relations. The work analyzes the protection of the interests of legal subjects by establishing certain limits of the exercise of subjective rights and establishing the duty of each authorized person to exercise their rights properly. The determination of the limits of the exercise of subjective rights is not considered as a limitation of these rights, but as a legal expression of the already existing equal position of people in the system of social relations. The article critically evaluates the outdated classic thesis, according to which going beyond the limits of legal equilibrium by carrying out an "untimely" civil action is an abuse of law, a special type of misconduct aimed at the realization by the subject of legal relations of his subjective interest with a negative content, which manifests itself in violation of the subjective rights of other persons. It turns out that in a temporal sense such a qualification is simply impossible. Exercising a subjective right outside the limits of its existence cannot be qualified as an abuse of the right, because the right, in fact, does not yet exist or no longer exists. Actions by a person outside the limits of permitted conduct or the validity period of the right will be considered as the actions of a person to whom the right does not belong at all. Therefore, abusing the right through "untimely" application of it during its validity is impossible, exercising the powers that were part of the right outside its time limits will be a common offense.