Optimal L∞(L2)L^\infty(L^2) and L1(L2)L^1(L^2) a posteriori error estimates for the fully discrete approximations of time fractional parabolic differential equations

We derive optimal order a posteriori error estimates in the $L^\infty(L^2)$ and $L^1(L^2)$-norms for the fully discrete approximations of time fractional parabolic differential equations. For the discretization in time, we use the $L1$ methods, while for the spatial discretization, we use standard conforming finite element methods. The linear and quadratic space-time reconstructions are introduced, which are generalizations of the elliptic space reconstruction. Then the related a posteriori error estimates for the linear and quadratic space-time reconstructions play key roles in deriving global and pointwise final error estimates. Numerical experiments verify and complement our theoretical results.Comment: 22 page

Convergence of the variational iteration method for solving multi-order fractional differential equations

AbstractIn this paper, the variational iteration method (VIM) is applied to obtain approximate solutions of multi-order fractional differential equations (M-FDEs). We can easily obtain the satisfying solution just by using a few simple transformations and applying the VIM. A theorem for convergence and error estimates of the VIM for solving M-FDEs is given. Moreover, numerical results show that our theoretical analysis are accurate and the VIM is a powerful method for solving M-FDEs

Propagation Path Loss Models in Forest Scenario at 605 MHz

When signals propagate through forest areas, they will be affected by environmental factors such as vegetation. Different types of environments have different influences on signal attenuation. This paper analyzes the existing classical propagation path loss models and the model with excess loss caused by forest areas and then proposes a new short-range wireless channel propagation model, which can be applied to different types of forest environments. We conducted continuous-wave measurements at a center frequency of 605 MHz on predetermined routes in distinct types of forest areas and recorded the reference signal received power. Then, we use various path loss models to fit the measured data based on different vegetation types and distributions. Simulation results show that the proposed model has substantially smaller fitting errors with reasonable computational complexity, as compared with representative traditional counterparts

Finite Difference and Sinc-Collocation Approximations to a Class of Fractional Diffusion-Wave Equations

We propose an efficient numerical method for a class of fractional diffusion-wave equations with the Caputo fractional derivative of order α. This approach is based on the finite difference in time and the global sinc collocation in space. By utilizing the collocation technique and some properties of the sinc functions, the problem is reduced to the solution of a system of linear algebraic equations at each time step. Stability and convergence of the proposed method are rigorously analyzed. The numerical solution is of 3-α order accuracy in time and exponential rate of convergence in space. Numerical experiments demonstrate the validity of the obtained method and support the obtained theoretical results

Plasma kinetics: Discrete Boltzmann modelling and Richtmyer-Meshkov instability

A discrete Boltzmann model (DBM) for plasma kinetics is proposed. The constructing of DBM mainly considers two aspects. The first is to build a physical model with sufficient physical functions before simulation. The second is to present schemes for extracting more valuable information from massive data after simulation. For the first aspect, the model is equivalent to a magnetohydrodynamic model plus a coarse-grained model for the most relevant TNE behaviors including the entropy production rate. A number of typical benchmark problems including Orszag-Tang (OT) vortex problem are used to verify the physical functions of DBM. For the second aspect, the DBM use non-conserved kinetic moments of (f-feq) to describe non-equilibrium state and behaviours of complex system. The OT vortex problem and the Richtmyer-Meshkov instability (RMI) are practical applications of the second aspect. For RMI with interface inverse and re-shock process, it is found that, in the case without magnetic field, the non-organized momentum flux shows the most pronounced effects near shock front, while the non-organized energy flux shows the most pronounced behaviors near perturbed interface. The influence of magnetic field on TNE effects shows stages: before the interface inverse, the TNE strength is enhanced by reducing the interface inverse speed; while after the interface inverse, the TNE strength is significantly reduced. Both the global average TNE strength and entropy production rate contributed by non-organized energy flux can be used as physical criteria to identify whether or not the magnetic field is sufficient to prevent the interface inverse.Comment: 20 pages, 15 figure

Emission reduction and cost-benefit analysis of the use of ammonia and green hydrogen as fuel for marine applications

Increasingly stringent emission standards have led shippers and port operators to consider alternative energy sources which can reduce emissions while minimizing capital investment. It is essential to understand whether there is a certain economic investment gap for alternative energy. The present work mainly focuses on the simulation study of ships using ammonia and hydrogen fuels arriving at Guangzhou Port to investigate the emission advantages and cost-benefit analysis of ammonia and hydrogen as alternative fuels. By collecting actual data and fuel consumption emissions of ships arriving at Guangzhou Port, the present study calculated the pollutant emissions and cost of ammonia and hydrogen fuels substitution. As expected, it is shown that with the increase of NH3 in fuel, mixed fuels will effectively reduce CO and CO2 emissions. Compared to conventional fuel, the injection of NH3 increases the NOx emission. However, the cost savings of ammonia fuel for CO2, SOx and PM10 reduction are higher than that for NOx. In terms of pollutants, ammonia is less expensive than conventional fuels when applied to the Guangzhou Port. However, the cost of fuel supply is still higher than conventional energy as ammonia has not yet formed a complete fuel supply and storage system for ships. On the other hand, hydrogen is quite expensive to store and transport, resulting in higher overall costs than ammonia and conventional fuels, even if no pollutants are produced. At present, conventional fuels still have advantage in terms of cost. With the promotion of ammonia fuel technology and application, the cost of supply will be reduced. It is predicted that by 2035 ammonia will not only have emission reduction benefits, but also will have a lower overall economic cost than conventional fuels. Hydrogen energy will need longer development and technological breakthroughs due to the limitation of storage conditions