Self-oscillations in an Alpha Stirling Engine: a bifurcation analysis

We study a thermo-mechanical system comprised of an alpha Stirling engine and a flywheel from the perspective of dynamical systems theory. Thermodynamics establish a static relation between the flywheel's angle and the forces exerted by the two power pistons that constitute the engine. Mechanics, in turn, provide a dynamic relation between the forces and the angle, ultimately leading to a closed dynamical model. We are interested in the different behaviors that the engine displays as parameters are varied. The temperature of the hot piston and the mechanical phase between both pistons constitute our bifurcation parameters. Considering that energy conversion in the engine can only take place through cyclic motions, we are particularly interested in the appearance of limit cycles.Comment: To be submitte

Systematic evaluation of the population-level effects of alternative treatment strategies on the basic reproduction number

An approach to estimate the influence of the treatment-type controls on the basic reproduction number, R 0 , is proposed and elaborated. The presented approach allows one to estimate the effect of a given treatment strategy or to compare a number of different treatment strategies on the basic reproduction number. All our results are valid for sufficiently small values of the control. However, in many cases it is possible to extend this analysis to larger values of the control as was illustrated by examples

Numerical optimal control for HIV prevention with dynamic budget allocation

This paper is about numerical control of HIV propagation. The contribution of the paper is threefold: first, a novel model of HIV propagation is proposed; second, the methods from numerical optimal control are successfully applied to the developed model to compute optimal control profiles; finally, the computed results are applied to the real problem yielding important and practically relevant results.Comment: Submitted pape

A substitute for the classical Neumann--Morgenstern characteristic function in cooperative differential games

In this paper, we present a systematic overview of different endogenous optimization-based characteristic functions and discuss their properties. Furthermore, we define and analyze in detail a new, $\eta$-characteristic function. This characteristic function has a substantial advantage over other characteristic functions in that it can be obtained with a minimal computational effort and has a reasonable economic interpretation. In particular, the new characteristic function can be seen as a reduced version of the classical Neumann-Morgenstern characteristic function, where the players both from the coalition and from the complementary coalition use their previously computed strategies instead of solving respective optimization problems. Our finding are illustrated by a pollution control game with $n$ non-identical players. For the considered game, we compute all characteristic functions and compare their properties. Quite surprisingly, it turns out that both the characteristic functions and the resulting cooperative solutions satisfy some symmetry relations

Optimality and sustainability of hybrid limit cycles in the pollution control problem with regime shifts

In this paper, we consider the problem of pollution control in a system that undergoes regular regime shifts. We first show that the optimal policy of pollution abatement is periodic as well, and is described by the unique hybrid limit cycle. We next introduce the notion of an environmentally sustainable solution, and demonstrate that such a policy is the only one that yields the best possible trade-off between steadily achieving profit and ensuring environmental preservation. In contrast to that, the policy that is not environmentally sustainable eventually enters stagnation. To further illustrate our findings, we compare the optimal periodic solution with a myopic one. Interestingly enough, the myopic solution yields higher overall payoff in the short-run, but completely fails in the long-run, while the environmentally sustainable policy yields maximal payoff and preserves the environment over the infinite time interval

Within-host phenotypic evolution and the population-level control of chronic viral infections by treatment and prophylaxis

Chronic viral infections can persist in an infected person for decades. From the perspective of the virus, a single infection can span thousands of generations, leading to a highly diverse population of viruses with its own complex evolutionary history. We propose a mathematical framework for understanding how the emergence of new viral strains and phenotype within infected persons affects the population-level control of those infections by both non-curative treatment and chemo-prophylactic measures. We consider the within-host emergence of new strains that lack phenotype novelty and also the evolution of variability in contagiousness, resistance to therapy, and efficacy of prophylaxis. Our framework balances the need for verisimilitude with our desire to retain a model that can be approached analytically. We show how to compute the population-level basic reproduction number accounting for the within-host evolutionary process where new phenotypes emerge and are lost in infected persons, which we also extend to include both treatment and prophylactic control efforts. This allows us to make clear statements about both the global and relative efficacy of different control efforts accounting for within-host phenotypic evolution. Finally, we give expressions for the endemic equilibrium of these models for certain constrained versions of the within-host evolutionary model providing a potential method for estimating within-host evolutionary parameters from population-level genetic sequence data

Toward Formal Analysis of Thermodynamic Stability: Le Chatelier—Brown Principle

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.Russian Foundation for Basic Research (project number 19-03-00375