Impact of delay on HIV-1 dynamics of fighting a virus with another virus

In this paper, we propose a mathematical model for HIV-1 infection with intracellular delay. The model examines a viral-therapy for controlling infections through recombining HIV-1 virus with a genetically modified virus. For this model, the basic reproduction number $\mathcal{R}_0$ are identified and its threshold properties are discussed. When $\mathcal{R}_0 < 1$, the infection-free equilibrium $E_0$ is globally asymptotically stable. When $\mathcal{R}_0 > 1$, $E_0$ becomes unstable and there occurs the single-infection equilibrium $E_s$, and $E_0$ and $E_s$ exchange their stability at the transcritical point $\mathcal{R}_0 =1$. If $1< \mathcal{R}_0 < R_1$, where $R_1$ is a positive constant explicitly depending on the model parameters, $E_s$ is globally asymptotically stable, while when $\mathcal{R}_0 > R_1$, $E_s$ loses its stability to the double-infection equilibrium $E_d$. There exist a constant $R_2$ such that $E_d$ is asymptotically stable if $R_1<\mathcal R_0 < R_2$, and $E_s$ and $E_d$ exchange their stability at the transcritical point $\mathcal{R}_0 =R_1$. We use one numerical example to determine the largest range of $\mathcal R_0$ for the local stability of $E_d$ and existence of Hopf bifurcation. Some simulations are performed to support the theoretical results. These results show that the delay plays an important role in determining the dynamic behaviour of the system. In the normal range of values, the delay may change the dynamic behaviour quantitatively, such as greatly reducing the amplitudes of oscillations, or even qualitatively changes the dynamical behaviour such as revoking oscillating solutions to equilibrium solutions. This suggests that the delay is a very important fact which should not be missed in HIV-1 modelling

On the turbulent flow models in modelling of omni-flow wind turbine

Yong Chen, Pei Ying, Yigeng Xu, Yuan Tian, 'On the turbulent flow models in modelling of omni-flow wind turbine', paper presented at The International Conference on Next Generation Wind Energy (ICNGWE2014), the Universidad Europa de Madrid, Madrid, Spain, 7th-10th October 2014.The computational fluid dynamics (CFD) has a wide application in the wind energy industry. In CFD simulations, a turbulence model plays a significantly important role in accuracy and resource cost. In this paper, a novel wind turbine, omni-flow wind turbine, was investigated with different turbulence models. Four turbulence models, standard k-ε, realizable k-ε, standard k-ω and SST k-ω models, were employed for this wind turbine in order to assess the best numerical configuration. The performance of these four turbulence models was validated with wind tunnel tests. It is evident that the realizable k-ε turbulence model is most suitable to simulate this novel wind turbine

UV-finite scalar field theory with unitarity

In this paper we show how to define the UV completion of a scalar field theory such that it is both UV-finite and perturbatively unitary. In the UV completed theory, the propagator is an infinite sum of ordinary propagators. To eliminate the UV divergences, we choose the coefficients and masses in the propagator to satisfy certain algebraic relations, and define the infinite sums involved in Feynman diagram calculation by analytic continuation. Unitarity can be proved relatively easily by Cutkosky's rules. The theory is equivalent to infinitely many particles with specific masses and interactions. We take the $\phi^4$ theory as an example and demonstrate our idea through explicit Feynman diagram computation.Comment: 14 pages, references adde

Thermodynamics of percolation in interacting systems

Interacting systems can be studied as the networks where nodes are system units and edges denote correlated interactions. Although percolation on network is a unified way to model the emergence and propagation of correlated behaviours, it remains unknown how the dynamics characterized by percolation is related to the thermodynamics of phase transitions. It is non-trivial to formalize thermodynamics for most complex systems, not to mention calculating thermodynamic quantities and verifying scaling relations during percolation. In this work, we develop a formalism to quantify the thermodynamics of percolation in interacting systems, which is rooted in a discovery that percolation transition is a process for the system to lose the freedom degrees associated with ground state configurations. We derive asymptotic formulas to accurately calculate entropy and specific heat under our framework, which enables us to detect phase transitions and demonstrate the Rushbrooke equality (i.e., $\alpha+2\beta+\gamma=2$) in six representative complex systems (e.g., Bernoulli and bootstrap percolation, classical and quantum synchronization, non-linear oscillations with damping, and cellular morphogenesis). These results suggest the general applicability of our framework in analyzing diverse interacting systems and percolation processes

High-contrast coronagraph for ground-based imaging of Jupiter-like planets

We propose a high-contrast coronagraph for direct imaging of young Jupiter-like planets orbiting nearby bright stars. The coronagraph employs a step-transmission filter in which the intensity is apodized with a finite number of steps of identical transmission in each step. It should be installed on a large ground-based telescope equipped with state-of-the-art adaptive optics systems. In that case, contrast ratios around 10^-6 should be accessible within 0.1 arc seconds of the central star. In recent progress, a coronagraph with circular apodizing filter has been developing, which can be used for a ground-based telescope with central obstruction and spider structure. It is shown that ground-based direct imaging of Jupiter-like planets is promising with current technology

Computational and Experimental Investigations of an Omni-Flow Wind Turbine

This document is the Accepted Manuscript version, made available under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License CC BY NC-ND 4.0 (http://creativecommons.org/licenses/by-nc-nd/4.0/ ). The final, definitive version of this paper is available online at doi: https://doi.org/10.1016/j.apenergy.2015.01.067.Both numerical and experimental studies were conducted to evaluate the performance of an omni-flow wind turbine designed to provide renewable electricity on the top of urban buildings like skyscrapers. The numerical approach was based on Finite Volume Method (FVM) and the turbulence flow was studied with several commonly used Reynolds-averaged Navier–Stokes turbulence models. The results of the study were evaluated with the wind tunnel test results over a range of tip speed ratios. The numerical results showed the effect of blade number on both power output and starting capability. Although both the power and torque coefficient were improved significantly by the optimisation of the blade number, there was only a slight change when the blade number was greater than twenty. The results from wind tunnel testing also showed excellent starting capability with a starting wind velocity as low as 1.6 m/s. A numerical simulation was also conducted for the wind turbine working under non-uniform flow conditions. The numerical results have shown that the peak power coefficient of such a wind turbine under non-uniform flow, was lower than that under the uniform flow. Additionally, the applied thrust on a blade was subject to frequent and periodical changes. However, the effect of the change of thrust in magnitude and frequency was not significant. Therefore the omni-flow wind turbine has the potential to meet the challenge of unpredictable wind velocity and direction as a consequence of the urban environment.Peer reviewedFinal Accepted Versio