Percolation theory approach to transport phenomena in porous media

The percolation theory approach to static and dynamic properties of the single- and two-phase fluid flow in porous media is described. Using percolation cluster scaling laws, one can obtain functional relations between the saturation fraction of a given phase and the capillary pressure, the relative permeability, and the dispersion coefficient, in drainage and imbibition processes. In addition, the scale dependency of the transport coefficient is shown to be an outcome of the fractal nature of pore space and of the random flow pattern of the fluids or contaminant.     

Triply bridged (1,3,5) cyclophanes from cystine and lanthionine linkers—a comparison

The condensation of benzene 1,3,5-tricarbonylchloride with cystine-di-Me [H₂N-CH(COOMe)-CH₂-S-S-CH₂-CH(COOMe)-NH₂] yielded triply bridged (1,3,5) cyclophane 1, which was shown by detailed spectral studies and molecular orbital calculations to have a D₃ symmetry with conformationally identical linkers and a spherical topology. In sharp contrast, the (1,3,5) cyclophane 2 from the rarely studied lanthionine di-Me [H₂N-CH(COOMe)-CH₂-S-CH₂-CH(COOMe)-NH₂], showed only a equatorial twofold symmetry. This work highlights the special properties of the -S-S- bridge in cystine, which makes it an exceptional synthon in nature and organic synthesis.     

An unexpected coupling reaction between isocyanides and carboxylic acids: a method for the synthesis of highly stable symmetrical and unsymmetrical alkylamidine and arylamidine carbocations

An unexpected coupling reaction between isocyanides and carboxylic acids which led to the synthesis of highly stable symmetrical and unsymmetrical alkylamidine and arylamidine carbocations under mild reaction conditions is described. The structures of these compounds were confirmed by IR, mass, ¹H NMR, ¹³C NMR, and single-crystal X-ray diffraction studies and a plausible mechanism is proposed.     

Features of stable radical generation in lignin on exposure to nitrogen dioxide

The mechanism of stable radical generation in lignin under the action of nitrogen dioxide and NO₂ - air mixture is considered. The formation of phenoxyl, iminoxyl and acylaminoxyl radicals has been detected by EPR. The proposed mechanism involves a primary oxidative reaction of phenol groups with dimers of NO₂ (nitrosyl nitrate) resulting in the formation of phenoxyl radicals and nitric oxide. In the subsequent recombination of phenoxyl radicals and nitric oxide, nitroso compounds and oximes are formed. By reaction of oximes with radicals NO₂, stable iminoxyl radicals are formed. This mechanism is confirmed by kinetic dependencies obtained over a wide range of NO₂ concentrations. From IR spectroscopy measurements it follows that hydroxyl groups of non-phenolic structures of lignin are oxidised to aldehydes producing acylaminoxyl radicals by reaction with NO₂. The kinetic data show that the adsorption of NO₂ on the lignin surface is the rate-determining factor in stable radical formation.     

Point-wise hierarchical reconstruction for discontinuous Galerkin and finite volume methods for solving conservation laws

We develop a new hierarchical reconstruction (HR) method  and  for limiting solutions of the discontinuous Galerkin and finite volume methods up to fourth order of accuracy without local characteristic decomposition for solving hyperbolic nonlinear conservation laws on triangular meshes. The new HR utilizes a set of point values when evaluating polynomials and remainders on neighboring cells, extending the technique introduced in Hu, Li and Tang [9]. The point-wise HR simplifies the implementation of the previous HR method which requires integration over neighboring cells and makes HR easier to extend to arbitrary meshes. We prove that the new point-wise HR method keeps the order of accuracy of the approximation polynomials. Numerical computations for scalar and system of nonlinear hyperbolic equations are performed on two-dimensional triangular meshes. We demonstrate that the new hierarchical reconstruction generates essentially non-oscillatory solutions for schemes up to fourth order on triangular meshes.     

Modeling,simulation and validation of material flow on conveyor belts

In this paper a model comparison approach based on material flow systems is investigated that is divided into a microscopic and a macroscopic model scale. On the microscopic model scale particles are simulated using a model based on Newton dynamics borrowed from the engineering literature. Phenomenological observations lead to a hyperbolic partial differential equation on the macroscopic model scale. Suitable numerical algorithms are presented and both models are compared numerically and validated against real-data test settings.     

Lifespan of classical discontinuous solutions to general quasilinear hyperbolic systems of conservation laws with small BV initial data: Rarefaction waves

In the present paper the author investigates the global structure stability of Riemann solutions for general quasilinear hyperbolic systems of conservation laws under small BV perturbations of the initial data, where the Riemann solution contains rarefaction waves, while the perturbations are in BV but they are assumed to be C¹$C^1$-smooth, with bounded and possibly large C¹$C^1$-norms. Combining the techniques employed by Li–Kong with the modified Glimm’s functional, the author obtains a lower bound of the lifespan of the piecewise C¹$C^1$ solution to a class of generalized Riemann problems, which can be regarded as a small BV perturbation of the corresponding Riemann problem. This result is also applied to the system of traffic flow on a road network using the Aw–Rascle model.     

An extension of the Noether theorem: Accompanying equations possessing conservation laws

It is shown that the Noether theorem can be extended for some equations associated (accompanying) with Euler–Lagrange equation. Each symmetry of Lagrangian yields a class of accompanying equations possessing conservation law (first integral).The generalization is done for canonical Hamiltonian equations as well.     

时滞系统在博弈中的应用研究

演化博弈理论解决策略均衡问题是目前比较认可的好方法.对于博弈方的经验行为,还未曾研究.本文以非对称2×2的博弈问题为研究对象,建立起带有时滞的博弈系统,通过动力学相关知识,分别研究了两类系统下博弈参与者策略的稳定状态.数值模拟分析了延时给决策带来的影响.实验表明,时滞作用不改变策略的稳定状态,改变的仅是达到稳态的速率.