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Furthermore, the slope of the regression line between ⟨b⟩ and ⟨K-M slope⟩ in the range of ⟨b⟩ between 1 and 2 changes with the definition of magnitude and the length of the earthquake sequence.Szilard’s now-famous single-molecule engine was only the first of three constructions he introduced in 1929 to resolve several challenges arising from Maxwell’s demon paradox. Given that it has been thoroughly analyzed, we analyze Szilard’s remaining two demon models. We show that the second one, though a markedly different implementation employing a population of distinct molecular species and semipermeable membranes, is informationally and thermodynamically equivalent to an ideal gas of the single-molecule engines. One concludes that (i) it reduces to a chaotic dynamical system-called the Szilard Map, a composite of three piecewise linear maps and associated thermodynamic transformations that implement measurement, control, and erasure; (ii) its transitory functioning as an engine that converts disorganized heat energy to work is governed by the Kolmogorov-Sinai entropy rate; (iii) the demon’s minimum necessary “intelligence” for optimal functioning is given by the engine’s statistical complexity; and (iv) its functioning saturates thermodynamic bounds and so it is a minimal, optimal implementation. We show that Szilard’s third construction is rather different and addresses the fundamental issue raised by the first two the link between entropy production and the measurement task required to implement either of his engines. The analysis gives insight into designing and implementing novel nanoscale information engines by investigating the relationships between the demon’s memory, the nature of the “working fluid,” and the thermodynamic costs of erasure and measurement.To address the issue of whether there exists determinism in a two-phase flow system, we first conduct a gas-liquid two-phase flow experiment to collect the flow pattern fluctuation signals. Then, we investigate the determinism in the dynamics of different gas-liquid flow patterns by calculating the number of missing ordinal patterns associated with the partitioning of the phase space. In addition, we use the recently proposed stretched exponential model to reveal the flow pattern transition behavior. With the joint distribution of two fitted parameters, which are the decay rate of the missing ordinal patterns and the stretching exponent, we systematically analyze the flow pattern evolutional dynamics associated with the flow deterministic characteristics. This research provides a new understanding of the two-phase flow pattern evolutional dynamics, and broader applications in more complex fluid systems are suggested.We consider the Yamada model for an excitable or self-pulsating laser with saturable absorber and study the effects of delayed optical self-feedback in the excitable case. More specifically, we are concerned with the generation of stable periodic pulse trains via repeated self-excitation after passage through the delayed feedback loop and their bifurcations. We show that onset and termination of such pulse trains correspond to the simultaneous bifurcation of countably many fold periodic orbits with infinite period in this delay differential equation. We employ numerical continuation and the concept of reappearance of periodic solutions to show that these bifurcations coincide with codimension-two points along families of connecting orbits and fold periodic orbits in a related advanced differential equation. These points include heteroclinic connections between steady states and homoclinic bifurcations with non-hyperbolic equilibria. Tracking these codimension-two points in parameter space reveals the critical parameter values for the existence of periodic pulse trains. We use the recently developed theory of temporal dissipative solitons to infer necessary conditions for the stability of such pulse trains.The position and motion of localized states of light in propagative geometries can be controlled via an adequate parameter modulation. click here Here, we show theoretically and experimentally that this process can be accurately described as the phase locking of oscillators to an external forcing and that non-reciprocal interactions between light bits can drastically modify this picture. Interactions lead to the convective motion of defects and to an unlocking as a collective emerging phenomenon.The low-density lipoprotein (LDL)/high-density lipoprotein (HDL)-cholesterol ratio has been shown to have a high correlation with the cardiovascular risk assessment. Is it possible to quantify the correlation mathematically? In this paper, we develop a bifurcation analysis for a mathematical model of the plaque formation with a free boundary in the early stage of atherosclerosis. This bifurcation analysis, to the ratio of LDL/HDL, is based on explicit formulations of radially symmetric steady-state solutions. By performing the perturbation analysis to these solutions, we establish the existence of bifurcation branches and derive a theoretical condition that a bifurcation occurs for different modes. We also analyze the stability of radially symmetric steady-state solutions and conduct numerical simulations to verify all theoretical results.The effect of levodopa in alleviating the symptoms of Parkinson’s disease is altered in a highly nonlinear manner as the disease progresses. This can be attributed to different compensation mechanisms taking place in the basal ganglia where the dopaminergic neurons are progressively lost. This alteration in the effect of levodopa complicates the optimization of a drug regimen. The present work aims at investigating the nonlinear dynamics of Parkinson’s disease and its therapy through mechanistic mathematical modeling. Using a holistic approach, a pharmacokinetic model of levodopa was combined to a dopamine dynamics and a neurocomputational model of basal ganglia. The influence of neuronal death on these different mechanisms was also integrated. Using this model, we were able to investigate the nonlinear relationships between the levodopa plasma concentration, the dopamine brain concentration, and a response to a motor task. Variations in dopamine concentrations in the brain for different levodopa doses were also studied.