Effect of Varying Bulk Viscosity on Generalized Chaplygin Gas

In this paper, viscous generalized Chaplygin gas as a model of dark energy considered. We assume non-constant bulk viscous coefficient and study dark energy density. We consider several cases of density-dependent viscosities. We find that, in the special case, the viscous generalized Chaplygin gas is corresponding to modified Chaplygin gas.Comment: 7 pages, 2 figures, references adde

Quantum gravity effects on Ho\v{r}ava-Lifshitz black hole

In this paper, we would like to obtain quantum gravity effects by using Ho\v{r}ava-Lifshitz black hole. We consider logarithmic corrected thermodynamics quantities and investigate the effects of logarithmic correction term. Logarithmic correction comes from thermal fluctuation and may be interpreted as quantum loop corrections. As black hole is a gravitational system, hence we can investigate quantum gravity effect. We find such effects on the black hole stability and obtain domain of correction coefficient.Comment: 22 pages, Accepted for publication in NP

Encouraging better evaluation in digital health: guidance, training and community development

Abstract Digital health have the potential to deliver effective interventions on a wide scale. However, digital health products and services need better evaluations. There are significant barriers to this. Public Health England wanted to understand and tackle pragmatically the problem of evaluating digital health. This is particularly important in the time of COVID-19, when a large number of digital interventions are being developed and introduced at pace. It assembled a multidisciplinary team including service designers, academics, and public health professionals. They employed user-centred design methods, including qualitative research, and engagement with end-users and stakeholders. They used the findings to identify opportunity areas, develop concepts, test prototypes, and plan service implementation. This work led to the Evaluating Digital Health Products resource on GOV.UK which includes practical guidance, a methods library with digital case studies, and workshop templates for teams. It is intended to help anyone developing or running a digital health intervention. This resource launched to the public in 2020 but the service is still being improved and developed. The aim of this presentation is to introduce the online resource, describe its comprehensive iterative development, and present the evaluation training models. We will also describe the immediate next steps, which include development of an evaluation community, user testing of new content, and plans for developing a sustainable workshop model. Funding: This project is funded by Public Health England

Neural tangent kernel analysis of PINN for advection-diffusion equation

Physics-informed neural networks (PINNs) numerically approximate the solution of a partial differential equation (PDE) by incorporating the residual of the PDE along with its initial/boundary conditions into the loss function. In spite of their partial success, PINNs are known to struggle even in simple cases where the closed-form analytical solution is available. In order to better understand the learning mechanism of PINNs, this work focuses on a systematic analysis of PINNs for the linear advection-diffusion equation (LAD) using the Neural Tangent Kernel (NTK) theory. Thanks to the NTK analysis, the effects of the advection speed/diffusion parameter on the training dynamics of PINNs are studied and clarified. We show that the training difficulty of PINNs is a result of 1) the so-called spectral bias, which leads to difficulty in learning high-frequency behaviours; and 2) convergence rate disparity between different loss components that results in training failure. The latter occurs even in the cases where the solution of the underlying PDE does not exhibit high-frequency behaviour. Furthermore, we observe that this training difficulty manifests itself, to some extent, differently in advection-dominated and diffusion-dominated regimes. Different strategies to address these issues are also discussed. In particular, it is demonstrated that periodic activation functions can be used to partly resolve the spectral bias issue

ON THE INVESTIGATION OF MACHINE TOOL CHATTER IN THE MILLING PROCESS

ABSTRACT In this paper, the chatter phenomenon is investigated through a single degree of freedom model of the milling process. In this regard, the non-linear equation of motion obtained from modeling of the milling process, which is a time-periodic delay differential equation, is simulated, and by changing the parameters: spindle speed and depth of cut, and assuming constant quantities for other parameters of the system the stable and instable points for the system are gained according to these two parameters by numerical method. In the end, the stability chart for this system is plotted and the approximate boundaries between the stability and instability regions are obtained numerically

On the rules for aquatic locomotion

We present unifying rules governing the efficient locomotion of swimming fish and marine mammals. Using scaling and dimensional analysis, supported by new experimental data, we show that efficient locomotion occurs when the values of the Strouhal (St) number St(=f A/U) and A∗(=A/L), two nondimensional numbers that relate forward speed U, tail-beat amplitude A, tail-beat frequency f , and the length of the swimmer L are bound to the tight ranges of 0.2–0.4 and 0.1–0.3, respectively. The tight range of 0.2–0.4 for the St number has previously been associated with optimal thrust generation. We show that the St number alone is insufficient to achieve optimal aquatic locomotion, and an additional condition on A∗ is needed. More importantly, we show that when swimming at minimal power consumption, the Strouhal number of a cruising swimmer is predetermined solely by the shape and drag characteristics of the swimmer. We show that diverse species of fish and cetaceans cruise indeed with the St number and A∗ predicted by our theory. Our findings provide a physical explanation as to why fast aquatic swimmers cruise with a relatively constant tail-beat amplitude of approximately 20% of the body length, and their swimming speed is nearly proportional to their tail-beat frequenc