Fermat’s principle and the effect of jerk on light motion near the Sun

In classical mechanics, in the case of gravitational and electromagnetic interactions, the force on a particle is usually proportional to its acceleration: The force acts locally on the particle. However, there are situations possible-if the particle moves through a suitable medium, for example, in which the force depends also on the first-time derivative of its acceleration, the jerk, and on its second-time derivative, the snap, and possibly also on higher-time derivatives. Such forces are called nonlocal, and this work investigates such nonlocal forces, mainly those depending on the jerk. In particular, we implement jerk and acceleration in geodesics by means of the nonlocal-in-time kinetic energy approach to spacetime physics. We describe a framework that can be used to estimate the quantum nonlocal time parameter by studying the deflection of light around the Sun. Comparing our results with long baseline interferometry (VLBI) observations, we concluded that the nonlocal time parameter [Formula: see text] s.

On global trajectory tracking control of robot manipulators with a delayed feedback

In this paper, the trajectory tracking control problem of a robot manipulator with cylindrical joints is considered by means of a nonlinear PD controller taking into account the delayed feedback structure. The conclusion about stability of a closed-loop system is obtained on the basis of the development of the direct Lyapunov method in the study of the stability property for a non-autonomous functional differential equation by constructing a Lyapunov functional with a semi-definite time derivative.

An External Circular Crack in an Infinite Solid Under Axisymmetric Heat Flux Loading in the Framework of Fractional Thermoelasticity

In a real solid there are different types of defects. During sudden cooling, near cracks, there can appear high thermal stresses. In this paper, the time-fractional heat conduction equation is studied in an infinite space with an external circular crack with the interior radius R in the case of axial symmetry. The surfaces of a crack are exposed to the constant heat flux loading in a circular ring R<r<ρ. The stress intensity factor is calculated as a function of the order of time-derivative, time, and the size of a circular ring and is presented graphically.

COVID-19 Pandemic: How Effective Are Preventive Control Measures and Is a Complete Lockdown Justified? A Comparison of Countries and States

For fighting the COVID-19 pandemic, countries used control measures of different severity, from “relaxed” to lockdown. Drastic lockdown measures are considered more effective but also have a negative impact on the economy. When comparing the financial value of lost lives to the losses of an economic disaster, the better option seems to be lockdown measures. We developed a new parameter, the effectiveness of control measures, calculated from the 2nd time derivative of daily case data, for 92 countries, states and provinces. We compared this parameter, and also the mortality during and after the effective phase, for countries with and without lockdowns measures by means of the Mann–Whitney test. We did not find any statistically significant difference in the effectiveness between countries with and without lockdowns (p > 0.76). There was also no significant difference in mortality during the effective phase (p > 0.1); however, a significant difference after the effective phase, with higher mortality for lockdown countries, was identified. The effectiveness correlated well with a parameter derived from the reproductive number (R2 = 0.9480). The average duration of the effective phase was 17.3 ± 10.5 days. The results indicated that lockdown measures are not necessarily superior to relaxed measures, which in turn are not necessarily a recipe for failure. Relaxed measures are, however, more economy-friendly.

Adaptive finite-time tracking control for full state constrained nonlinear systems with time-varying delays and input saturation

This paper investigates the adaptive finite-time tracking control problem for a class of nonlinear full state constrained systems with time-varying delays and input saturation. Compared with the previously published work, the considered system involves unknown time-varying delays, asymmetric input saturation, and time-varying asymmetric full state constraints. To ensure the state constraint satisfaction, the appropriate time-varying asymmetric Barrier Lyapunov Functions and the backstepping technique are utilized. Meanwhile, the finite covering lemma and the radial basis function neural networks are employed to solve the unknown time-varying delays. The assumption that the time derivative of time-varying delay functions is required to be less than one in traditional Lyapunov–Krasovskii functionals is removed by the proposed method. Moreover, the asymmetric input saturation is handled by an auxiliary design system. Taking the norm of the neural network weight vector as an adaptive parameter, a novel adaptive finite-time tracking controller with minimal learning parameters is constructed. It is proved that the proposed controller can guarantee that all signals in the closed-loop system are bounded, all states are constrained within the predefined sets, and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, a comparison study simulation is given to demonstrate the effectiveness of our proposed strategy. The simulation results show that our proposed strategy has good advantages of high tracking precision and disturbance rejection.

Numerical investigation of fractional model of Phytoplankton–Toxic Phytoplankton–Zooplankton system with convergence analysis

In this paper, a fractional order model of the phytoplankton–toxic phytoplankton–zooplankton system with Caputo fractional derivative is investigated via three computational methods, namely, residual power series method (RPSM), homotopy perturbation Sumudu transform method (HPSTM) and the homotopy analysis Sumudu transform method (HASTM). This model is constituted by three components: phytoplankton, toxic phytoplankton and zooplankton. Phytoplankton species are self-feeding members of the plankton community and play a very significant role in ecosystems. A wide range of sea creatures get food through phytoplankton. This paper focuses on the implementation of the three above-mentioned computational methods for a nonlinear time-fractional phytoplankton–toxic phytoplankton–zooplankton (PTPZ) model with a perception to study the dynamics of a model. This study shows that the solutions obtained by employing the suggested computational methods are in good agreement with each other. The computational procedures reveal that the HASTM solution generates a more general solution as compared to RPSM and HPSTM and incorporates their results as a special case. The numerical results presented in the form of graphs authenticate the accuracy of computational schemes. Hence, the implemented methods are very appropriate and relevant to handle nonlinear fractional models. In addition, the effect of variation of fractional order of a time derivative and time [Formula: see text] on populations of phytoplankton, toxic–phytoplankton and zooplankton has also been studied through graphical presentations. Moreover, the uniqueness and convergence analyses of HASTM solution have also been discussed in view of the Banach fixed-point theory.

Parametric and V&V study in a fundamental CFD process: revisiting the lid-driven cavity flow

Purpose The openings on aircraft structures can be modeled from an aerodynamical point of view as lid-driven cavities (LDC). This paper aims to show the primary verification and validation (V&V) process in computational fluid dynamics (CFD, and to investigate the influences of numerical settings on the efficiency and accuracy for solving the LDC problem. Design/methodology/approach To dig into the details of CFD approaches, this paper outlines the design, implementation, V&V and results of an efficient explicit algorithm. The parametric study is performed thoroughly focusing on various iteration methods, grid density discretization terms and Reynolds number effects. Findings This study parameterized the numerical implementation which provides empirical insights into how computational accuracy and efficiency are affected by changing numerical settings. At a low Reynolds number (not over 1,000), the time-derivative preconditioning is necessary, and k = 0.1 can be the optimal value to guarantee the efficiency, as well as the stability. A larger artificial viscosity (c = 1/16) would relieve the calculating oscillation issue but proportionally increase the discretization error. Furthermore, the iteration method and the mesh quality are two key factors that affect the convergence efficiency, thus need to be selected “wisely”. Practical implications The study shows how numerical implementation can enhance an accurate and efficient solution. This workflow can be used to determine the best parameter settings whenever CFD researchers applying this LDC problem as a complementary design tool for testing newly developed solvers. Originality/value The studied LDC problem is representative of CFD analysis in real aircraft structures. These numerical simulations provide a cost-effective and convenient tool to understand the parameter sensitivity, solution receptivity and physics of the CFD process.

A guide to trajectory inference and RNA velocity

Technological developments have led to an explosion of high-throughput single cell data, which are revealing unprecedented perspectives on cell identity. Recently, significant attention has focused on investigating, from single-cell RNA-sequencing (scRNA-seq) data, cellular dynamic processes, such as cell differentiation, cell cycle and cell (de)activation. Trajectory inference methods estimate a trajectory, a collection of differentiation paths of a dynamic system, by ordering cells along the paths of such a dynamic process. While trajectory inference tools typically work with gene expression levels, common scRNA-seq protocols allow the identification and quantification of unspliced pre-mRNAs and mature spliced mRNAs, for each gene. By exploiting the abundance of unspliced and spliced mRNA, one can infer the RNA velocity of individual cells, i.e., the time derivative of the gene expression state of cells. Whereas traditional trajectory inference methods reconstruct cellular dynamics given a population of cells of varying maturity, RNA velocity relies on a dynamical model describing splicing dynamics. Here, we initially discuss conceptual and theoretical aspects of both approaches, then illustrate how they can be combined together, and finally present an example use-case on real data.

On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system

Consider an inverse problem of determining two stochastic source functions and the initial status simultaneously in a stochastic thermoelastic system, which is constituted of two stochastic equations of different types, namely a parabolic equation and a hyperbolic equation. To establish the conditional stability for such a coupling system in terms of some suitable norms revealing the stochastic property of the governed system, we first establish two Carleman estimates with regular weight function and two large parameters for stochastic parabolic equation and stochastic hyperbolic equation, respectively. By means of these two Carleman estimates, we finally prove the conditional stability for our inverse problem, provided the source in the elastic equation be known near the boundary and the solution be in a prior bound set. Due to the lack of information about the time derivative of wave field at final moment, the stability index with respect to the wave field at final time is found to be halved, which reveals the special characteristic of our inverse problem for the coupling system.

Energetic Particle Superdiffusion in Solar System Plasmas: Which Fractional Transport Equation?

Superdiffusive transport of energetic particles in the solar system and in other plasma environments is often inferred; while this can be described in terms of Lévy walks, a corresponding transport differential equation still calls for investigation. Here, we propose that superdiffusive transport can be described by means of a transport equation for pitch-angle scattering where the time derivative is fractional rather than integer. We show that this simply leads to superdiffusion in the direction parallel to the magnetic field, and we discuss some advantages with respect to approaches based on transport equations with symmetric spatial fractional derivates.