Synchronization of Chaotic Systems: A Generic Nonlinear Integrated Observer-Based Approach

The purpose of this research is to study the synchronization of two integrated nonlinear systems with time delay and disturbances. A nonlinear system is a system in which the difference in output is not relative to the difference in input. A new control methodology for synchronization of the two chaotic systems master and slave is recognized by means of the unique integrated chaotic synchronous observer and the integrated chaotic adaptive synchronous observer. The instantaneous approximation states of the master and slave systems are accomplished by means of methods for suggesting observers for every one of the master and slave systems and by the production of error signals between these approximated states. This approximated synchronization error signal and state approximation errors meet at the origin by means of methods involving a particular observer-based feedback control signal to ensure synchronization and state approximation. Using Lyapunov stability theory, adaptive and nonadaptive laws for control systems, and nonlinear properties, the intermingling conditions for state approximation errors and approximated synchronization errors are established as nonlinear matrix inequalities. A solution to the resulting inequality constraints using a two-step linear matrix inequality (LMI)-based approach is introduced, giving essential and adequate conditions to extract values from the controller gain and observer gain matrices. Simulation of the suggested synchronization procedure for FitzHugh–Nagumo neuronal systems is demonstrated to expand the viability of the suggested observer-based control techniques.

Interpretation of NO₃–N₂O₅ observation via steady state in high aerosol air mass: The impact of equilibrium coefficient in ambient conditions

Steady state approximation for interpreting NO3 and N2O5 has large uncertainty under complicated ambient conditions and could even produces incorrect results unconsciously. To provide an assessment and solution to the dilemma, we formulate data sets based on in-situ observations to reassess the applicability of the method. In most of steady state cases, we find a prominent discrepancy between Keq (equilibrium coefficient for reversible reactions of NO3 and N2O5) and correspondingly simulated [N2O5]/([NO2]×[NO3]), especially in wintertime high aerosol conditions. This gap reveals the accuracy of Keq has a critical impact on the steady state analysis in polluted region. In addition, the accuracy of γ(N2O5) derived by steady state fit depends closely on the reactivity of NO3 (kNO3) and N2O5 (kN2O5). Based on a complete set of simulations, air mass of kNO3 less than 0.01 s−1 with high aerosol and temperature higher than 10 °C is suggested to be the best suited for steady state analysis of NO3–N2O5 chemistry. Instead of confirming the validity of steady state by numerical modeling for every case, this work directly provides concentration ranges appropriate for accurate steady state approximation, with implications for choosing suited methods to interpret nighttime chemistry in high aerosol air mass.

The response of a metapopulation to a changing environment

A species distributed across heterogeneous environments may adapt to local conditions. Szep et al. (2021, Evolution) modelled this process in the infinite island model, finding the stationary distribution of allele frequencies and deme sizes. We extend this to ask how a metapopulation responds to changes in carrying capacity, selection strength, or migration rate, restricting attention to fixed deme size ("soft selection"). We develop a "fixed-state" approximation (accurate when migration is rare) which assumes that the loci are near fixation. Under this approximation, polymorphism is only possible for a narrow range of habitat proportions when selection is weak compared to drift, but for a much wider range otherwise. When local conditions (Ns or Nm) change in a single deme, it takes a time of ~1/m to reach the new equilibrium. However, even withmany loci, there can be substantial fluctuations in net adaptation, due to the bimodal allele frequency distributions at each locus. Thus, in a finite metapopulation, variation may gradually be lost by chance, even if it would persist with infinitely many demes. When conditions change across the whole metapopulation, there can be rapid response, accurately predicted by the fixed-state approximation when Nm <<1.

The Double Phospho/Dephosphorylation Cycle as a Benchmark to Validate an Effective Taylor Series Method to Integrate Ordinary Differential Equations

The double phosphorylation/dephosphorylation cycle consists of a symmetric network of biochemical reactions of paramount importance in many intracellular mechanisms. From a network perspective, they consist of four enzymatic reactions interconnected in a specular way. The general approach to model enzymatic reactions in a deterministic fashion is by means of stiff Ordinary Differential Equations (ODEs) that are usually hard to integrate according to biologically meaningful parameter settings. Indeed, the quest for model simplification started more than one century ago with the seminal works by Michaelis and Menten, and their Quasi Steady-State Approximation methods are still matter of investigation nowadays. This work proposes an effective algorithm based on Taylor series methods that manages to overcome the problems arising in the integration of stiff ODEs, without settling for model approximations. The double phosphorylation/dephosphorylation cycle is exploited as a benchmark to validate the methodology from a numerical viewpoint.

Inelastic rate coefficients for collisions of C4H− with H2

Carbon-chain anions were recently detected in the interstellar medium. These very reactive species are used as tracers of the physical and chemical conditions in a variety of astrophysical environments. However, the Local Thermodynamical Equilibrium conditions are generally not fulfilled in these environments. Therefore, collisional as well as radiative rates are needed to accurately model the observed emission lines. We determine in this work the state-to-state rate coefficients of C4H− in collision with both ortho- and para-H2. A new ab initio 4D potential energy surface was computed using explicitly-correlated coupled cluster procedures. This surface was then employed to determine rotational excitation and de-excitation cross sections and rate coefficients for the first 21 rotational levels (up to rotational level j1 = 20) using the close-coupling method, while the coupled-state approximation was used to extend the calculations up to j1 = 30. State-to-state rate coefficients were obtained for the temperature range 2–100 K. The differences between the ortho- and para-H2 rate coefficients are found to be small.

Density Functional Theory Study of Substitution Effects on the Second-Order Nonlinear Optical Properties of Lindquist-Type Organo-Imido Polyoxometalates

Density functional theory and time-dependent density functional theory have been enacted to investigate the effects of donor and acceptor on the first hyperpolarizability of Lindquist-type organo-imido polyoxometalates (POMs). These calculations employ a range-separated hybrid exchange-correlation functional (ωB97X-D), account for solvent effects using the implicit polarizable continuum model, and analyze the first hyperpolarizabilities by using the two-state approximation. They highlight the beneficial role of strong donors as well as of π-conjugated spacers (CH=CH rather than C≡C) on the first hyperpolarizabilities. Analysis based on the unit sphere representation confirms the one-dimensional push-pull π-conjugated character of the POMs substituted by donor groups and the corresponding value of the depolarization ratios close to 5. Furthermore, the use of the two-state approximation is demonstrated to be suitable for explaining the origin of the variations of the first hyperpolarizabilities as a function of the characteristics of a unique low-energy charge-transfer excited state and to attribute most of the first hyperpolarizability changes to the difference of dipole moment between the ground and that charge-transfer excited state.

Evaluation of a Quasi-steady state approximation of the cloud Droplet Growth Equation (QDGE) scheme for aerosol activation in global models using multiple aircraft data over both continental and marine environments

This research introduces a numerically efficient aerosol activation scheme and evaluates it by using stratus and stratocumulus cloud data sampled during multiple aircraft campaigns in Canada, Chile, Brazil, and China. The scheme employs a Quasi-steady state approximation of the cloud Droplet Growth Equation (QDGE) to efficiently simulate aerosol activation, the vertical profile of supersaturation, and the activated cloud droplet number concentration (CDNC) near the cloud base. We evaluate the QDGE scheme by specifying observed environmental thermodynamic variables and aerosol information from 31 cloud cases as input and comparing the simulated CDNC with cloud observations. The average of mean relative error of the simulated CDNC for cloud cases in each campaign ranges from 17.30 % in Brazil to 25.90 % in China, indicating that the QDGE scheme successfully reproduces observed variations in CDNC over a wide range of different meteorological conditions and aerosol regimes. Additionally, we carried out an error analysis by calculating the Maximum Information Coefficient (MIC) between the mean relative error (MRE) and input variables for the individual campaigns and all cloud cases. MIC values are then sorted by aerosol properties, pollution level, environmental humidity, and dynamic condition according to their relative importance to MRE . Based on the error analysis we found that the magnitude of MRE is more relevant to the specification of input aerosol pollution level in marine regions and aerosol hygroscopicity in continental regions than to other variables in the simulation.

Reversible enzyme-catalysed reactions: the quasi steady state as a a quasi-equilibrium, and a correction to Haldane's kinetic constants and to secondary relationships involving kinetic constants.

For reversible enzyme-catalysed reactions obeying Henri-Michaelis-Menten kinetics, theoretical solution of the rate equations for the enzyme-substrate intermediate are generally incorrect when the quasi-steady state approximation, equating the rate of change of the concentration of the enzyme-substrate intermediate to zero, is used. For the simplest kinetic model used by Haldane, such a procedure does not reveal that in one direction, that starting with the reactant having the lower binding constant, the quasi-steady state is one of quasi-equilibrium, and Haldane’s structure of the Km written in terms of rate constants is incorrect. This is probably also true of more complex mechanisms in which the structure of kcat may also be in error. Modern methods of numerical integration for the solution of rate equations, if applied to reversible reactions to obtain rate constants from measured catalytic constants, will require the correct expressions for kcat and Km. Furthermore, the (now called) Haldane relationship, relating the kinetic constants kcat and Km for the forward and reverse reactions to the equilibrium constant of a reaction, is now seen to be generally incorrect, and in addition another exception for a the theoretical validation of kcat /Km as a specificity constant arises.