Emergent behaviors of discrete Lohe aggregation flows

<p style='text-indent:20px;'>The Lohe sphere model and the Lohe matrix model are prototype continuous aggregation models on the unit sphere and the unitary group, respectively. These models have been extensively investigated in recent literature. In this paper, we propose several discrete counterparts for the continuous Lohe type aggregation models and study their emergent behaviors using the Lyapunov function method. For suitable discretization of the Lohe sphere model, we employ a scheme consisting of two steps. In the first step, we solve the first-order forward Euler scheme, and in the second step, we project the intermediate state onto the unit sphere. For this discrete model, we present a sufficient framework leading to the complete state aggregation in terms of system parameters and initial data. For the discretization of the Lohe matrix model, we use the Lie group integrator method, Lie-Trotter splitting method and Strang splitting method to propose three discrete models. For these models, we also provide several analytical frameworks leading to complete state aggregation and asymptotic state-locking.</p>

A Hard Sphere Model for Bimolecular Recombination of Heavy Ions

We propose a hard sphere model of bimolecular recombination RM+ + X– → MX + R, where M+ is an alkali ion, X– is a halide ion, and R is a neutral rare gas or mercury atom. Calculations are carried out for M+ = Cs+, X– = Br–, R = Ar, Kr, Xe, Hg, for collision energies in the range from 1 to 10 eV, and for distributions of the RM+ complex internal energy corresponding to temperatures of 500, 1000, and 2000 K. The excitation functions and opacity functions of bimolecular recombination in the hard sphere approximation are found, and the classification of the collisions according to the sequences of pairwise encounters of the particles is considered. In more than half of all the cases, recombination occurs due to a single impact of the Br– ion with the R atom. For the recombination XeCs+ + Br–, the hard sphere model enables one to reproduce the most important characteristics of the collision energy dependence of the recombination probability obtained within the framework of quasiclassical trajectory calculations.

Reaction Rate Theory-Based Mathematical Approximation For The Amount Of Time It Takes For Cellular Respiration To Occur

The venerable process of cellular respiration is essential for cells to produce energy from glucose molecules, in order to carry out cellular work. The process is responsible for producing molecules of ATP, a molecule which is thermodynamically coupled with other biochemical and biophysical processes in order to provide energy for such processes to occur. While the process of cellular respiration is essential to biology, one cycle of the process occurs only in a matter of milliseconds, and so, it would be impractical to measure the time it takes for the process to occur through conventional means. Therefore, using concepts from reaction rate theory, particularly Marcus Theory of electron transfer, Michaelis-Menten kinetics for enzymatic catalysis, and the hard-sphere model of collision theory, I formulate and propose a mathematical approximation for the amount of time it takes forcellular respiration to occur. Through this heuristic approach, quantitatively knowing the amount of time it takes for one cycle of cellular respiration to occur could potentially have future applications in biological research.

Elastic Scattering of Slow Electrons by Noble Gases—The Effective Range Theory and the Rigid Sphere Model

We report on an extensive semi-empirical analysis of scattering cross-sections for electron elastic collision with noble gases via the Markov Chain Monte Carlo-Modified Effective Range Theory (MCMC−MERT). In this approach, the contribution of the long-range polarization potential (∼r−4) to the scattering phase shifts is precisely expressed, while the effect of the complex short-range interaction is modeled by simple quadratic expression (the so-called effective range expansion with several adjustable parameters). Additionally, we test a simple potential model of a rigid sphere combined with r−4 interaction. Both models, the MERT and the rigid sphere are based on the analytical properties of Mathieu functions, i.e., the solutions of radial Schrödinger equation with pure polarization potential. However, in contrast to MERT, the rigid sphere model depends entirely upon one adjustable parameter—the radius of a hard-core. The model’s validity is assessed by a comparative study against numerous experimental cross-sections and theoretical phase shifts. We show that this simple approach can successfully describe the electron elastic collisions with helium and neon for energies below 1 eV. The purpose of the present analysis is to give insight into the relations between the parameters of both models (that translate into the cross-sections in the very low energy range) and some “macroscopic” features of atoms such as the polarizability and atomic “radii”.

Size and Structure of Empty and Filled Nanocontainer Based on Peptide Dendrimer with Histidine Spacers at Different pH

Novel peptide dendrimer with Lys-2His repeating units was recently synthesized, studied by NMR (Molecules, 2019, 24, 2481) and tested as a nanocontainer for siRNA delivery (Int. J. Mol. Sci., 2020, 21, 3138). Histidine amino acid residues were inserted in the spacers of this dendrimer. Increase of their charge with a pH decrease turns a surface-charged dendrimer into a volume-charged one and should change all properties. In this paper, the molecular dynamics simulation method was applied to compare the properties of the dendrimer in water with explicit counterions at two different pHs (at normal pH with neutral histidines and at low pH with fully protonated histidines) in a wide interval of temperatures. We obtained that the dendrimer at low pH has essentially larger size and size fluctuations. The electrostatic properties of the dendrimers are different but they are in good agreement with the theoretical soft sphere model and practically do not depend on temperature. We have shown that the effect of pairing of side imidazole groups is much stronger in the dendrimer with neutral histidines than in the dendrimer with protonated histidines. We also demonstrated that the capacity of a nanocontainer based on this dendrimer with protonated histidines is significantly larger than that of a nanocontainer with neutral histidines.

Emotional Intelligence, Identification, and Self-Awareness According to the Sphere Model of Consciousness

While emotion and cognition were previously considered separate concepts, current research demonstrates an interplay between them. In the current chapter, we discuss the importance of the body in relation to emotional intelligence (EI) and executive functioning. In particular, we address a specific movement meditation called Quadrato Motor Training (QMT), which has been shown to enhance emotion regulation and neurocognitive functions. We then examine the importance of emotion regulation in the context of the Sphere Model of Consciousness (SMC) and related neurocognitive studies. The SMC is a neuro-phenomenal model of consciousness based on three main axes: Emotion, Time, and Self-Determination. It presents all phenomenal experiences in a sphere-shaped matrix, aiming to account for different interactions among the axes. Through this model, the processes leading to improved EI can be framed in a general theory of consciousness and described in relation to the three axes. We discuss three key concepts in relation to the SMC: (1) EI; (2) identification, namely excessive self-involvement or feeling caught up by experience (3) self-awareness, or awareness and management of ongoing inner processes.