Chanharrell9634

Extreme multistability with coexisting infinite orbits has been reported in many continuous memristor-based dynamical circuits and systems, but rarely in discrete dynamical systems. This paper reports the finding of initial values-related coexisting infinite orbits in an area-preserving Lozi map under specific parameter settings. We use the bifurcation diagram and phase orbit diagram to disclose the coexisting infinite orbits that include period, quasi-period and chaos with different types and topologies, and we employ the spectral entropy and sample entropy to depict the initial values-related complexity. Finally, a microprocessor-based hardware platform is developed to acquire four sets of four-channel voltage sequences by switching the initial values. The results show that the area-preserving Lozi map displays coexisting infinite orbits with complicated complexity distributions, which heavily rely on its initial values.Due to the principle of minimal information gain, the measurement of points in an affine space V determines a Legendrian submanifold of V×V*×R. Such Legendrian submanifolds are equipped with additional geometric structures that come from the central moments of the underlying probability distributions and are invariant under the action of the group of affine transformations on V. We investigate the action of this group of affine transformations on Legendrian submanifolds of V×V*×R by giving a detailed overview of the structure of the algebra of scalar differential invariants, and we show how the scalar differential invariants can be constructed from the central moments. In the end, we view the results in the context of equilibrium thermodynamics of gases, and notice that the heat capacity is one of the differential invariants.Background Electrical impedance spectroscopy (EIS) is a fast, non-invasive, and safe approach for electrical impedance measurement of biomedical tissues. Applied to dental research, EIS has been used to detect tooth cracks and caries with higher accuracy than visual or radiographic methods. Recent studies have reported age-related differences in human dental tissue impedance and utilized fractional-order equivalent circuit model parameters to represent these measurements. Objective We aimed to highlight that fractional-order equivalent circuit models with different topologies (but same number of components) can equally well model the electrical impedance of dental tissues. Diphenhydramine cost Additionally, this work presents an equivalent circuit network that can be realized using Electronic Industries Alliance (EIA) standard compliant RC component values to emulate the electrical impedance characteristics of dental tissues. Results To validate the results, the goodness of fits of electrical impedance models were evaluated visua different topologies to represent biological tissue impedance and their interpretation.We analyze the efficiency in terms of a thermoelectric system of a one-dimensional Silicon-Germanium alloy. The dependency of thermal conductivity on the stoichiometry is pointed out, and the best fit of the experimental data is determined by a nonlinear regression method (NLRM). The thermoelectric efficiency of that system as function of the composition and of the effective temperature gradient is calculated as well. For three different temperatures (T=300K, T=400K, T=500K), we determine the values of composition and thermal conductivity corresponding to the optimal thermoelectric energy conversion. The relationship of our approach with Finite-Time Thermodynamics is pointed out.Non-extensive statistical mechanics (NESM), which is a generalization of the traditional Boltzmann-Gibbs statistics, constitutes a theoretical and analytical tool for investigating the irreversible damage evolution processes and fracture mechanisms occurring when materials are subjected to mechanical loading. In this study, NESM is used for the analysis of the acoustic emission (AE) events recorded when marble and cement mortar specimens were subjected to mechanical loading until fracture. In total, AE data originating from four distinct loading protocols are presented. The cumulative distribution of inter-event times (time interval between two consecutive AE events) and the inter-event distances (three-dimensional Euclidian distance between the centers of successive AE events) were examined under the above concept and it was found that NESM is suitable to detect criticality under the terms of mechanical status of a material. This was conducted by evaluating the fitting results of the q-exponential function and the corresponding q-indices of Tsallis entropy qδτ and qδr, along with the parameters τδτ and dδr. Results support that qδτ+qδr≈2 for AE data recorded from marble and cement mortar specimens of this work, which is in good agreement with the conjecture previously found in seismological data and AE data recorded from Basalt specimens.In this article, using numerical simulations we investigate the self-assembly of rod-like particles in suspension due to depletion forces which naturally emerge due to the presence of smaller spherical depletant particles. We characterize the type of clusters that are formed and the evolution of aggregation departing from a random initial configuration. We show that eventually the system reaches a thermodynamic equilibrium state in which the aggregates break and reform dynamically. We investigate the equilibrium state of aggregation, which exhibits a strong dependence on depletant concentration. In addition, we provide a simple thermodynamic model inspired on the theory of self-assembly of amphiphilic molecules which allows us to understand qualitatively the equilibrium aggregate size distributions that we obtain in simulation.In this contribution, we carry on with the research program initiated in J. Math. Chem., 58(6), 2020. Using the methods from geometric thermodynamics, we formally derive and analyze different conditions for thermodynamic stability and determine the limits of their use. In particular, we study, in detail, several versions of the Le Chatelier-Brown principle and demonstrate their application to the analysis of thermodynamic stability.