Theoretical modeling of photo-induced wave propagation in liquid-crystalline Langmuir monolayers

A phenomenological model of wave propagation in photo-excited liquid-crystalline Langmuir monolayers is constructed. The spontaneous splay deformation of the liquid-crystalline order and the anisotropy of photo-excitation of molecules are taken into account in this model. Numerical simulations of the model well reproduce qualitative features of the wave propagation phenomenon observed in recent experiments. A linear stability analysis of the model equations reveals that an interplay between the spontaneous splay deformation and the anisotropy of the photo-excitation can lead to the wave propagation.     

Traveling Waves in Degenerate Diffusion Equations

In this survey, we present a literature review on the study of traveling waves in degenerate diffusion equations by illustrating the interesting and singular wave behavior caused by degeneracy. The main results on wave existence and stability are presented for the typical degenerate equations, including porous medium equations, flux limited diffusion equations, delayed degenerate diffusion equations, and other strong degenerate diffusion equations.     

An improved approximation algorithm for the asymmetric TSP with strengthened triangle inequality

We consider the asymmetric traveling salesperson problem with γ-parameterized triangle inequality for γ[1/2,1). That means, the edge weights fulfill w(u,v)γ(w(u,x)+w(x,v)) for all nodes u,v,x. Chandran and Ram [L.S. Chandran, L.S. Ram, Approximations for ATSP with parametrized triangle inequality, in: Proc. 19th Int. Symp. on Theoret. Aspects of Comput. Sci. (STACS), in: Lecture Notes in Comput. Sci., vol. 2285, Springer, Berlin, 2002, pp. 227–237] gave the first constant factor approximation algorithm with polynomial running time for this problem. They achieve performance ratio γ/(1−γ). We devise an approximation algorithm with performance ratio (1+γ)/(2−γ−γ³), which is better for γ[0.5437,1), that is, for the particularly interesting large values of γ.     

毫米波行波管电子光学系统的设计

 利用基于虚边界元法的VBGUN程序和基于边界元法的MOM程序,对一折叠波导毫米波行波管的电子光学系统进行了设计。设计过程中使用计算相关性系数的方法调节参数,通过计算敏感性系数以考察加工误差带来的影响。设计过程显示：低导流系数、小束腰、高压缩比的毫米波电子枪的层流性与电极尺寸相关性很大,易受到加工误差的影响;聚束系统的设计难点在于轴上峰值磁感应强度要受到漂移管半径的限制,这一点可以通过提高工作电压和降低电流来平衡,因此它的设计必须与慢波结构的设计同时进行。     

Influence of atmosphere on lunar rover performance analysis based on soil parameter identification

This paper outlines an analysis of the traveling performance of a lunar rover. The analysis is in the form of numerical simulations and it uses soil properties, identified in vacuum, and mechanics of wheel-based travel. The wheel-to-ground contact model and soil parameters are determined first so they could be used in the numerical simulation. A soil test device is introduced and the soil parameters are identified from plate-pressing and shear tests. Finally, numerical simulations are conducted using the parameters identified and their results are discussed along with those of the traveling tests conducted in vacuum. The soil tests indicated that the wheel sinkage into the ground can increase in vacuum and that the shear stress acting beneath the wheel in vacuum is almost the same as that in the atmosphere. Because of these trends, the simulations and traveling tests showed that the traveling performance of the wheel can decrease in vacuum. Although it has been widely considered that the vacuum environments enhance the traveling performance of the wheel, this study confirmed that it is not always the case.     

Pareto memetic algorithm with path relinking for bi-objective traveling salesperson problem

The paper presents an effective version of the Pareto memetic algorithm with path relinking and efficient local search for multiple objective traveling salesperson problem. In multiple objective Traveling salesperson problem (TSP), multiple costs are associated with each arc (link). The multiple costs may for example correspond to the financial cost of travel along a link, time of travel, or risk in the case of hazardous materials. The algorithm searches for new good solutions along paths in the decision space linking two other good solutions selected for recombination. Instead of a simple local search it uses short runs of tabu search based on the steepest version of the Lin–Kernighan algorithm. The efficiency of local search is further improved by the techniques of candidate moves and locked arcs. In the final step of the algorithm the neighborhood of each potentially Pareto-optimal solution is searched for new solutions that could be added to this set. The algorithm is compared experimentally to the state-of-the-art algorithms for multiple objective TSP.     

Resolvent Estimates for Boundary Value Problems on Large Intervals Via the Theory of Discrete Approximations

In many applications such as the stability analysis of traveling waves, it is important to know the spectral properties of a linear differential operator on the whole real line. We investigate the approximation of this operator and its spectrum by finite interval boundary value problems from an abstract point of view. Under suitable assumptions on the boundary operators, we prove that the approximations converge regularly (in the sense of discrete approximations) to the all line problem, which has strong implications for the behavior of resolvents and spectra. As an application, we obtain resolvent estimates for abstract coupled hyperbolic–parabolic equations. Furthermore, we show that our results apply to the FitzHugh–Nagumo system.     

Study on probability distributions for evolution in modified extremal optimization

It is widely believed that the power-law is a proper probability distribution being effectively applied for evolution in τ-EO (extremal optimization), a general-purpose stochastic local-search approach inspired by self-organized criticality, and its applications in some NP-hard problems, e.g., graph partitioning, graph coloring, spin glass, etc. In this study, we discover that the exponential distributions or hybrid ones (e.g., power-laws with exponential cutoff) being popularly used in the research of network sciences may replace the original power-laws in a modified τ-EO method called self-organized algorithm (SOA), and provide better performances than other statistical physics oriented methods, such as simulated annealing, τ-EO and SOA etc., from the experimental results on random Euclidean traveling salesman problems (TSP) and non-uniform instances. From the perspective of optimization, our results appear to demonstrate that the power-law is not the only proper probability distribution for evolution in EO-similar methods at least for TSP, the exponential and hybrid distributions may be other choices.     

Asymptotic stability of traveling wave fronts in nonlocal reaction–diffusion equations with delay

This paper is concerned with the asymptotic stability of traveling wave fronts of a class of nonlocal reaction–diffusion equations with delay. Under monostable assumption, we prove that the traveling wave front is exponentially stable by means of the (technical) weighted energy method, when the initial perturbation around the wave is suitable small in a weighted norm. The exponential convergent rate is also obtained. Finally, we apply our results to some population models and obtain some new results, which recover, complement and/or improve a number of existing ones.     

Existence of traveling wavefronts in a cooperative systems with discrete delays

In this paper, we consider an important Lotka-Volterra model describing a two-species cooperative system with diffusive and discrete delays, and investigate the existence of traveling wavefronts by some mathematics tools including the monotone iteration technique as well as the upper and lower solution method. The results obtained can be seen as a generalization of previous results.