Long-Range Coherence and Multiple Steady States in a Lossy Qubit Array.

Chemical reaction network structure and the stability of complex isothermal reactors—II. Multiple steady states for networks of deficiency one

Previous zero-dimensional photochemical calculations indicate that multiple tropospheric steady states may exist, in which different NO x (≡NO+NO2) levels could be supported by the same source of NO x . To investigate this possibility more closely, a one-dimensional photochemical model has been used to estimate the rate of removal of atmospheric NO x compounds at different NO x levels. At low NO x levels NO x is photochemically converted to HNO3, which is removed by either wet or dry deposition. At high NO x levels formation of HNO3 is inhibited, and NO x is removed by a variety of other processes, including rainout of N2O4 and N2O5, surface deposition of NO and NO2, and direct dissolution of NO and NO2 in rainwater. Multiple steady states are possible if surface deposition of NO x is relatively inefficient. The NO x source required to trigger high atmospheric NO x levels is approximately 10 to 15 times the present global emission rate-less than half the source strength predicted by the zero-dimensional model. NO x mixing ratios in excess of 10-7 would cause severe damage to the ozone layer and could result in either a climatic warming or cooling, depending upon the amount of NO2 present.

Simulation Of Robust Stabilization Of A Chemical Reactor

Multiple steady states in combined buoyancy and wind driven natural ventilation: The conditions for multiple solutions and the critical point for initial conditions

Both multiple steady states and dark states have potential applications in the quantum information processing in the presence of dissipation. Here, we propose to implement multiple steady states and dark states in a double quantum dot (DQD) system using quantum reservoir engineering. By coupling the DQD to shared reservoirs, multiple steady states of both four- and two-fold degeneracy can be achieved for specific parameters. It is proved that the occurrence of such multiple steady states is attributed to the strong symmetry of the Lindblad master equation. The multiple steady states can be well revealed by the occupation number of the DQD, which exhibits a discontinuity at the strong-symmetric points and changes drastically in the vicinities of these points. In the regime of unique steady state, the system can be stabilized to a pure state, dubbed dark state, with intact coherence in spite of the dissipation. Our work shows that a variety of novel steady states can be implemented in the DQD system, which paves the way for engineering multiple steady states and dark states in the DQD system.

Steady state multiplicity in an UOP FCC unit with high-efficiency regenerator

Reducing income inequality is a crucial goal of sustainable development as income inequality often viewed as harmful to economic growth. The main aim of this paper was to empirically assess the macroeconomic and institutional drivers of income inequality in Africa. We use a Kuznets curve framework, which emphasises the role of income per capita in explaining the time path of inequality. In contrast to much of the literature, we explicitly examine the possibility of the existence of multiple income steady states. Using the concept of clubs of convergence, we show that per capita income is divergent and identify four steady states to which groups of economies converge (i.e., high-income to low-income economies). Using panel data models and a data set encompassing 52 African countries spanning the years 1980–2017, we show that once these multiple steady states are accounted for, the Kuznets curve relationship becomes unstable. Our findings suggest that inequality may be increasing in high-income countries in Africa, while decreasing in low-income or the least developed economies. In addition, the role of macroeconomic and institutional factors in explaining income inequality is limited and differ across convergence clubs. Evidence suggests the importance of fiscal, employment and monetary policies and the rule of law to tackle inequality in high-income economies, while they have no statistically significant role in low-income economies’ income inequality.

This study analyses the dynamics of an economy with overlapping generations, endogenous population (fertility and adult mortality), logarithmic preferences and Cobb–Douglas technology. We show that the public provision of health investments and the existence of a private system of old-age insurance (i.e., transfers from children to parents) may cause the birth and death of multiple (three) steady states, deterministic chaos and bubbling phenomena when individuals have perfect foresight. Interestingly, however, we show that periodic dynamics (cycles) or complex dynamics (chaos) and global stability of the economy can endogenously be reconciled in the model, because the rise either in public health investments or transfers from young to old people can have the potential to smooth and ultimately suppress endogenous fluctuations in the cases of existence of both a single steady state or multiple steady states.

We examine an otherwise standard model of capital accumulation to which spatial separation and limited communication create a role for money and shocks to portfolio needs create a role for banks. In this context we examine the existence, multiplicity, and dynamical properties of monetary equilibria with positive nominal interest rates. Moderate levels of risk aversion can lead to the existence of multiple monetary steady states, all of which can be approached from a given set of initial conditions. In addition, even if there is a unique monetary steady state, monetary equilibria can be indeterminate, and oscillatory equilibrium paths can be observed. Thus financial market frictions are a potential source of both indeterminacies and endogenously arising economic volatility. ; We also consider the consequences of monetary policy actions that rearrange the composition of government liabilities. Contractionary monetary policy activities can have complicated consequences, depending especially on the nature of the steady state equilibrium that obtains when there are multiple steady states. Under plausible conditions, however, a permanent contractionary change in monetary policy raises both the nominal rate of interest and the rate of inflation, and reduces long-run output levels. Thus liquidity provision by a central bank - just as by the banking system as a whole - can be growth promoting. Loose monetary policy also is conducive to avoiding development trap phenomena.

The Macroeconomic and Institutional Effects on Income Inequality in Africa

The Effects of Open Market Operations a Model of Intermediation and Growth

Coupling between continuous-flow, stirred tank reactors (CSTR’s), each having multiple steady states, can produce new steady states with different concentrations of the chemical species in each of the coupled tanks. In this work, we identify a kinetic potential ψ that governs the deterministic time evolution of coupled tank reactors, when the reaction mechanism permits a single-variable description of the states of the individual tanks; examples include the iodate-arsenous acid reaction, a cubic model suggested by Noyes, and two quintic models. Stable steady states correspond to minima of ψ, and unstable steady states to maxima or saddle points; marginally stable states typically correspond to saddle-node points. We illustrate the variation in ψ due to changes in the rate constant for external material intake (k0) and for exchange between tanks (kx). For fixed k0 values, we analyze the changes in numbers and types of steady states as kx increases from zero. We show that steady states disappear by pairwise coalescence; we also show that new steady states may appear with increasing kx, when the reaction mechanism is sufficiently complex. For fixed initial conditions, the steady state ultimately reached in a mixing experiment may depend on the exchange rate constant as a function of time, kx(t) : Adiabatic mixing is obtained in the limit of slow changes in kx(t) and instantaneous mixing in the limit as kx(t)→∞ while t remains small. Analyses based on the potential ψ predict the outcome of mixing experiments for arbitrary kx(t). We show by explicit counterexamples that a prior theory developed by Noyes does not correctly predict the instability points or the transitions between steady states of coupled tanks, to be expected in mixing experiments. We further show that the outcome of such experiments is not connected to the relative stability of steady states in individual tank reactors. We find that coupling may effectively stabilize the tanks. We provide examples in which coupled CSTR’s can be operated stably with one of the tanks at or beyond the single-tank marginal stability point.

We continue our development of a global thermodynamic and stochastic theory of open chemical systems far from equilibrium with an analysis of a broad class of isothermal, multicomponent reaction mechanisms with multiple steady states, studied under the assumption of local equilibrium. We generalize species-specific affinities of reaction intermediates, obtained in prior work for nonautocatalytic reaction mechanisms, to autocatalytic kinetics and define with these affinities an excess free energy differential Fφ. The quantity Fφ is the difference between the work required to reverse a spontaneous concentration change and the work available when the same concentration change is imposed on a system in a reference steady state. The integral of Fφ is in general not a state function; in contrast, the function φdet obtained by integrating Fφ along deterministic kinetic trajectories is a state function, as well as an identifiable term in the time-integrated dissipation. Unlike the total integrated dissipation, φdet remains finite during the infinite duration of the system’s relaxation to a steady state and hence φdet can be used to characterize that process. The variational relation δφ≥0 is shown to be a necessary and sufficient thermodynamic criterion for a stable steady state in terms of the excess work of displacement of the intermediates and φdet is a Liapunov function in the domain of attraction of such steady states. Based on these results and earlier work with nonautocatalytic and equilibrating systems, we hypothesize that the stationary distribution of the master equation may be obtained in the form Ps=𝒩 exp(−φdet/kT) and provide an analytical argument for this form for macroscopic systems. This generalizes the Einstein fluctuation formula to multivariable systems with multiple steady states, far from equilibrium. In the following article, the utility of the approximation to Ps for systems with single or multiple intermediates, and single or multiple steady states is shown by comparison with numerical solutions of the master equation.

The representation of metabolic network reaction kinetics in a scaled, polynomial form can allow for the prediction of multiple steady states. The polynomial formalism is used to study chemostat-cultured Escherichia coli which has been observed to exhibit two multiple steady states under ammonium ion-limited growth conditions: a high cell density-low ammonium ion concentration steady state and a low cell density-high ammonium ion concentration steady state. Additionally, the low-cell-density steady state has been observed to drift to the high-cell-density steady state. Inspection of the steady-state rate expressions for the ammonium ion transport/assimilation network (in polynomial form) suggests that at low ammonium ion concentrations, two steady states are possible. One corresponds to heavy use of the glutamine synthetase-glutamate synthase (GLNS-GS) branch and the second to heavy use of the glutamate dehydrogenase (GDH) branch. Realization of the predicted intracellular steady states is also found to be dependent on the parameters of the transport process. Moreover, the two steady states differ in where their energy intensity lies. To explain the drift, GLNS, which is inducible under low ammonium ion concentrations, is suggested to be a "memory element." A chemostat-based model is developed to illustrate that perturbations in dilution rate can lead to drift between the two steady states provided that the disturbance in dilution rate is sufficiently large and/or long in duration.

The admissible multiple nonuniform steady states of a model bimolecular autocatalytic reaction–diffusion system with Michaelis–Menten (first-order Hinshelwood–Langmuir) saturation law are constructed in the case of large scale separation in the two diffusion constants. Both the Dirichlet and the Neumann problems are discussed in a one-dimensional geometry, and the corresponding bifurcation pictures are given.