Analysis of multi-stage running-in process of Sn-11Sb-6Cu alloy and AISI 1045 with phase trajectory plot

Running-in of the main bearings of diesel engine is a crucial process before service. Multi-stage running-in is a better way to enhance running-in quality and efficiency. In order to reveal the evolution of phase trajectory and compare the running-in quality, the running-in tests were performed with the material of bearing bush (Sn-11Sb-6Cu) and shaft (AISI 1045). The running-in quality was comprehensively evaluated via friction coefficient, phase trajectory and surface topography. Results indicate that the phase trajectories show a trend of stage-by-stage convergence. The multi-stage running-in can achieve a more stable attractor, lower friction coefficient and smoother surface, that is, a better running-in quality than the constant running-in scheme. This study provides a reference for formulating running-in specifications for sliding bearings.

Stability of a Viable Non-Minimal Bounce

The main difficulties in constructing a viable early Universe bouncing model are: to bypass the observational and theoretical no-go theorem, to construct a stable non-singular bouncing phase, and perhaps, the major concern of it is to construct a stable attractor solution which can evade the Belinsky–Khalatnikov–Lifshitz (BKL) instability as well. In this article, in the homogeneous and isotropic background, we extensively study the stability analysis of the recently proposed viable non-minimal bouncing theory in the presence of an additional barotropic fluid and show that, the bouncing solution remains stable and can evade BKL instability for a wide range of the model parameter. We provide the expressions that explain the behavior of the Universe in the vicinity of the required fixed point i.e., the bouncing solution and compare our results with the minimal theory and show that ekpyrosis is the most stable solution in any scenario.

Transition and identification of pathological states in p53 dynamics for therapeutic intervention

We study a minimal model of the stress-driven p53 regulatory network that includes competition between active and mutant forms of the tumor-suppressor gene p53. Depending on the nature and level of the external stress signal, four distinct dynamical states of p53 are observed. These states can be distinguished by different dynamical properties which associate to active, apoptotic, pre-malignant and cancer states. Transitions between any two states, active, apoptotic, and cancer, are found to be unidirectional and irreversible if the stress signal is either oscillatory or constant. When the signal decays exponentially, the apoptotic state vanishes, and for low stress the pre-malignant state is bounded by two critical points, allowing the system to transition reversibly from the active to the pre-malignant state. For significantly large stress, the range of the pre-malignant state expands, and the system moves to irreversible cancerous state, which is a stable attractor. This suggests that identification of the pre-malignant state may be important both for therapeutic intervention as well as for drug delivery.

Analysis of Coexistence and Extinction in a Two-Species Competition Model

We study a competition model of two competing species in population biology having exponential and rational growth functions described by Alexander et al. [1992]. They observed that, for some choice of parameters, the competition model has a chaotic attractor [Formula: see text] for which the basin of attraction is riddled. Here, we give a detailed analysis to illustrate what happens when the normal parameter in this model changes. In fact, by varying the normal parameter, we discuss how the geometry of the basin of attraction of [Formula: see text], the region of coexistence or extinction, changes and illustrate the transitions between the set [Formula: see text] being an asymptotically stable attractor (extinction of rational species), a locally riddled basin attractor and a normally repelling chaotic saddle (extinction of exponential species). Additionally, we show that the riddling and the blowout bifurcation occur. Numerical simulations are presented graphically to confirm the validity of our results. In particular, we verify the occurrence of synchronization for some values of parameters. Finally, we apply the uncertainty exponent and the stability index to quantify the degree of riddling basin. Our observation indicates that the stability index is positive for Lebesgue for almost all points whenever the riddling occurs.

A Brief Theory of Epidemic Kinetics

In the context of the COVID-19 epidemic, and on the basis of the Theory of Dynamical Systems, we propose a simple theoretical approach for the expansion of contagious diseases, with a particular focus on viral respiratory tracts. The infection develops through contacts between contagious and exposed people, with a rate proportional to the number of contagious and of non-immune individuals, to contact duration and turnover, inversely proportional to the efficiency of protection measures, and balanced by the average individual recovery response. The obvious initial exponential increase is readily hindered by the growing recovery rate, and also by the size reduction of the exposed population. The system converges towards a stable attractor whose value is expressed in terms of the “reproductive rate” R0, depending on contamination and recovery factors. Various properties of the attractor are examined, and particularly its relations with R0. Decreasing this ratio below a critical value leads to a tipping threshold beyond which the epidemic is over. By contrast, significant values of the above ratio may bring the system through a bifurcating hierarchy of stable cycles up to a chaotic behaviour.

Cancer Dynamics: Identification of States for Therapeutic Intervention

We study a minimal model of the stress-driven p53 regulatory network that includes competition between active and mutant forms of the tumor-suppressor gene p53. Depending on the nature of the external stress signal, four distinct dynamical states are observed. These states can be distinguished by dierent dynamical properties and correspond to active, apoptotic, pre-malignant and cancer states. Transitions between any two of these states are found to be unidirectional and irreversible if the stress signal is either oscillatory or constant. When the signal decays exponentially, the apoptotic state vanishes, and for low stress the pre-malignant state is bounded by two critical points, allowing the system to transition reversibly from the active to the pre-malignant state. For signicantly large stress, the range of the pre-malignant state expands and the system moves to the cancerous state which is a stable attractor. This suggests that identification of the pre-malignant state may be important both for therapeutic intervention as well as for drug discovery.

A Brief Theory of Epidemic Kinetics

In the context of the COVID-19 epidemic, and on the basis of the Theory of Dynamical Systems, we propose a simple model for the expansion of contagious diseases, with a particular focus on viral respiratory tracts. The infection develops through contacts between contagious and exposed people, with a rate proportional to contact duration and turnover, inversely proportional to the efficiency of protection measures, and balanced by the average immunological response. The obvious initial exponential increase is readily hindered by the size reduction of the exposed population. The system converges towards a stable attractor whose value is expressed in terms of the ratio C/D of contamination vs decay factors. Decreasing this ratio below a critical value leads to a tipping point beyond which the epidemic is over. By contrast, significant values of C/D may bring the system through a bifurcating hierarchy of stable cycles up to a chaotic behaviour.

Universe with quadratic equation of state: A dynamical systems perspective

This paper deals with the dynamical systems analysis of Friedmann–Robertson–Walker (FRW) model of the Universe in the framework of general relativity with quadratic equation of state and bulk viscosity. The evolution equations are transformed into an autonomous system of differential equations using suitable variables transformation. Stability analysis of cosmological models with quadratic equation of state parameter are discussed in detail in two different scenarios viz, first Universe filled with barotropic fluid and second filled with bulk viscous fluid. The nature of critical points is analyzed for both cases accordance with respective eigenvalues. We have also analyzed the stable attractor for both cases and examined their properties from the point of cosmological view.

An asymptotically optimal heuristic for general nonstationary finite-horizon restless multi-armed, multi-action bandits

We propose an asymptotically optimal heuristic, which we term randomized assignment control (RAC) for a restless multi-armed bandit problem with discrete-time and finite states. It is constructed using a linear programming relaxation of the original stochastic control formulation. In contrast to most of the existing literature, we consider a finite-horizon problem with multiple actions and time-dependent (i.e. nonstationary) upper bound on the number of bandits that can be activated at each time period; indeed, our analysis can also be applied in the setting with nonstationary transition matrix and nonstationary cost function. The asymptotic setting is obtained by letting the number of bandits and other related parameters grow to infinity. Our main contribution is that the asymptotic optimality of RAC in this general setting does not require indexability properties or the usual stability conditions of the underlying Markov chain (e.g. unichain) or fluid approximation (e.g. global stable attractor). Moreover, our multi-action setting is not restricted to the usual dominant action concept. Finally, we show that RAC is also asymptotically optimal for a dynamic population, where bandits can randomly arrive and depart the system.

The chaotic nature of TRAPPIST-1 planetary spin states

ABSTRACT The TRAPPIST-1 system has seven known terrestrial planets arranged compactly in a mean motion resonant chain around an ultracool central star, some within the estimated habitable zone. Given their short orbital periods of just a few days, it is often presumed that the planets are tidally locked such that the spin rate is equal to that of the orbital mean motion. However, the compact, and resonant, nature of the system implies that there can be significant variations in the mean motion of these planets due to their mutual interactions. We show that such fluctuations can then have significant effects on the spin states of these planets. In this paper, we analyse, using detailed numerical simulations, the mean motion histories of the three planets that are thought to lie within or close to the habitable zone of the system: planets d, e, and f. We demonstrate that, depending on the strength of the mutual interactions within the system, these planets can be pushed into spin states which are effectively non-synchronous. We find that it can produce significant libration of the spin state, if not complete circulation in the frame co-rotating with the orbit. We also show that these spin states are likely to be unable to sustain long-term stability, with many of our simulations suggesting that the spin evolves, under the influence of tidal synchronization forces, into quasi-stable attractor states, which last on time-scales of thousands of years.