Polynomial profits in renewable resources management

A system of renewal equations on a graph provides a framework to describe the exploitation of a biological resource. In this context, we formulate an optimal control problem, prove the existence of an optimal control and ensure that the target cost function is polynomial in the control. In specific situations, further information about the form of this dependence is obtained. As a consequence, in some cases the optimal control is proved to be necessarily bang–bang, in other cases the computations necessary to find the optimal control are significantly reduced.     

大初值的抛物型守恒律方程解的大时间性态(英文)

In this paper,we study the large-time behavior of periodic solutions for parabolic conservation laws.There is no smallness assumption on the initial data.We firstly get the local existence of the solution by the iterative scheme,then we get the exponential decay estimates for the solution by energy method and maximum principle,and obtain the global solution in the same time.     

机械能守恒定律及动量守恒定律演示仪器的制作

制作一种可以同时验证机械能守恒和动量守恒的实验装置,并通过这两个实验现象的对比更显著地体现了两个实验的物理现象与原理,有利于学生对机械能守恒与动量守恒原理的理解与认知。     

利用机械能守恒求解非惯性系单摆的振动周期

由于不同的非惯性系具有不同的加速度,导致单摆在不同的非惯性系中具有不同的振动周期,所以有必要掌握非惯性系下单摆振动周期的计算.基本的计算方法是利用非惯性系动力学方程,结合受力分析求解,但这种方法既要考虑惯性力,又需要进行力的分解,比较麻烦.本文通过引入惯性力势能,给出非惯性系机械能守恒定律,并利用机械能守恒定律对处于特定非惯性系中的单摆周期进行分析计算,得出非惯性系中单摆的振动周期不仅与单摆自身属性有关,而且与非惯性系的运动加速度或角速度有关的结论.     

Entropy is conserved in Hawking radiation as tunneling: A revisit of the black hole information loss paradox

We revisit in detail the paradox of black hole information loss due to Hawking radiation as tunneling. We compute the amount of information encoded in correlations among Hawking radiations for a variety of black holes, including the Schwarzchild black hole, the Reissner–Nordström black hole, the Kerr black hole, and the Kerr–Newman black hole. The special case of tunneling through a quantum horizon is also considered. Within a phenomenological treatment based on the accepted emission probability spectrum from a black hole, we find that information is leaked out hidden in the correlations of Hawking radiation. The recovery of this previously unaccounted for information helps to conserve the total entropy of a system composed of a black hole plus its radiations. We thus conclude, irrespective of the microscopic picture for black hole collapsing, the associated radiation process: Hawking radiation as tunneling, is consistent with unitarity as required by quantum mechanics.     

Weyl-gauge symmetry of graphene

The conformal invariance of the low energy limit theory governing the electronic properties of graphene is explored. In particular, it is noted that the massless Dirac theory in point enjoys local Weyl symmetry, a very large symmetry. Exploiting this symmetry in the two spatial dimensions and in the associated three dimensional spacetime, we find the geometric constraints that correspond to specific shapes of the graphene sheet for which the electronic density of states is the same as that for planar graphene, provided the measurements are made in accordance to the inner reference frame of the electronic system. These results rely on the (surprising) general relativistic-like behavior of the graphene system arising from the combination of its well known special relativistic-like behavior with the less explored Weyl symmetry. Mathematical structures, such as the Virasoro algebra and the Liouville equation, naturally arise in this three-dimensional context and can be related to specific profiles of the graphene sheet. Speculations on possible applications of three-dimensional gravity are also proposed.     

A conservative level set method suitable for variable-order approximations and unstructured meshes

This paper presents a formulation for free-surface computations capable of handling complex phenomena, such as wave breaking, without excessive mass loss or smearing of the interface. The formulation is suitable for discretizations using finite elements of any topology and order, or other approaches such as isogeometric and finite volume methods. Furthermore, the approach builds on standard level set tools and can therefore be used to augment existing implementations of level set methods with discrete conservation properties. Implementations of the method are tested on several difficult two- and three-dimensional problems, including two incompressible air/water flow problems with available experimental results. Linear and quadratic approximations on unstructured tetrahedral and trilinear approximations on hexahedral meshes were tested. Global conservation and agreement with experiments as well as computations by other researchers are obtained.     

What does Finite Volume-based implicit filtering really resolve in Large-Eddy Simulations?

The study illustrated in this paper completes the topics initially investigated in Ref. [42], the aim being here to analyze the role of the integral-based Finite Volume (FV) discretizations in Large Eddy Simulations that exploit the implicit filtering approach. Specifically, a theoretical study on the effective shape and length of three-dimensional filters induced by some FV-based flux reconstructions is the object of this paper. For any integral-based flux reconstruction, one gets always an approximation of the top-hat filter kernel. This is not the case of the filters induced by the differential-based Finite Difference operators, such as those reported and analyzed in Refs.  and . Considering the sub-filter resolution parameter Q = Δ_eff/h, being Δ_eff the effective filter width and h the computational grid size, allows us discerning the effective measure of the approximate built-in top-hat filter. The induced shape and width is analyzed by means of a modified wavenumber-like analysis that is developed in the 3D Fourier space. Several evaluation criteria applied on different schemes are considered and the differences in terms of either velocity or flux interpolations on staggered or non-staggered grids are analyzed. Conclusions are reported that, depending on the using of either the integral or the differential form of the filtered equations, the induced numerical filter is or is not a congruent approximation of the exact top-hat transfer function for some value Q. The need of a suitable estimation of the sub-filter parameter Q is assessed from several real LES computations, that make use of the new integral-based version of the eddy-viscosity dynamic modeling presented in Ref. [42]. In fact, it is shown that the test-filtering length has to be carefully chosen as a function of the FV-based induced filter.