The stability of predator-prey systems subject to the Allee effects

In recent years, many theoreticians and experimentalists have concentrated on the processes that affect the stability of predator-prey systems. But few papers have addressed the Allee effect with focus on the their stability. In this paper, we select two classical models describing predator-prey systems and introduce the Allee effects into the dynamics of both the predator and prey populations in these models, respectively. By combining mathematical analysis with numerical simulation, we have shown that the Allee effect may be a destabilizing force in predator-prey systems: the equilibrium point of the system could be changed from stable to unstable or otherwise, the system, even when it is stable, will take much longer time to reach the stable state. We also conclude that the equilibrium of the prey population will be enlarged due to the Allee effect of the predator, but the Allee effects of the prey may decrease the equilibrium value of the predator, or that of both the predator and prey. It should also be pointed out that the impact of the Allee effects of predator and prey due to different mechanisms on different predator-prey systems could also vary.     

Numerical simulation of selective freezing of target biological tissues following injection of solutions with specific thermal properties

Recently, we proposed a method for controlling the extent of freezing during cryosurgery by percutaneously injecting some solutions with particular thermal properties into the target tissues. In order to better understand the mechanism of the enhancement of freezing by these injections, a new numerical algorithm was developed to simulate the corresponding heat transfer process that is involved. The three-dimensional phase change processes in biological tissues subjected to cryoprobe freezing, with or without injection, were compared numerically. Two specific cases were investigated to illustrate the selective freezing method: the injection of solutions with high thermal conductivity; the injection of solutions with low latent heat. It was found that the localized injection of such solutions could significantly enhance the freezing effect and decrease the lowest temperature in the target tissues. The result also suggests that the injection of these solutions may be a feasible and flexible way to control the size of the ice ball and its direction of growth during cryosurgery, which will help to optimize the treatment process.     

Numerical study of size-structured population models: a case of Gambussia affinis

We study, from a numerical point of view, some properties of a model which describes the evolution of a population of Gambussia affinis. Our model includes sufficiently smooth vital functions. First we select, among four numerical methods of second order, the most appropriate in terms of adaptation to the problem. The most efficient method also reveals new properties of the model for long times, such as the tendency to periodicity, obtained with different initial conditions. We also discuss some advantages and deficiencies of the model.     

Using numerical approximation as an intermediate step in analytical derivations: some observations from biomechanics

We present four examples to illustrate the use of a type of numerical approximation as an intermediate step in analytical derivation of seemingly complicated biomechanical equations. The method involves examination of curve shapes to elucidate useful underlying trends, which may otherwise be overlooked through consideration of only the equations themselves. Two examples of the method's use are drawn from recently published results in the area of experimental methods in biomechanics of very soft tissues, and two others are taken from our current work on cartilage tissue mechanics. We think that such observations provide a useful means of circumventing complexity issues when deriving models for biomechanical analysis, and further that the method, while simple in concept, could be effective in a range of biomechanics applications.     

A novel numerical optimization algorithm inspired from weed colonization

This paper introduces a novel numerical stochastic optimization algorithm inspired from colonizing weeds. Weeds are plants whose vigorous, invasive habits of growth pose a serious threat to desirable, cultivated plants making them a threat for agriculture. Weeds have shown to be very robust and adaptive to change in environment. Thus, capturing their properties would lead to a powerful optimization algorithm. It is tried to mimic robustness, adaptation and randomness of colonizing weeds in a simple but effective optimizing algorithm designated as Invasive Weed Optimization (IWO). The feasibility, the efficiency and the effectiveness of IWO are tested in details through a set of benchmark multi-dimensional functions, of which global and local minima are known. The reported results are compared with other recent evolutionary-based algorithms: genetic algorithms, memetic algorithms, particle swarm optimization, and shuffled frog leaping. The results are also compared with different versions of simulated annealing — a generic probabilistic meta-algorithm for the global optimization problem — which are simplex simulated annealing, and direct search simulated annealing. Additionally, IWO is employed for finding a solution for an engineering problem, which is optimization and tuning of a robust controller. The experimental results suggest that results from IWO are better than results from other methods. In conclusion, the performance of IWO has a reasonable performance for all the test functions.     

Spatial heterogeneity of wind forcing: application to artificial reef functioning influenced by the circulation in the Bay of Marseilles, France

In the frame of the largest French project of artificial production reefs, initiated by the city of Marseilles in 2001, the present study aimed at describing the hydrodynamic pattern of the coastal area considered, by the use of a 3D numerical modelling. Results were local wind statistics, bottom current fields and drifting particle maps. The knowledge of the hydrodynamic connexions between particle (such as larvae) sources or targeted areas linked to the reefs, allows us to explain the success or failure of the reefs' colonizing. Moreover, the study confirms the wind spatial variability and demonstrates the error resulting from the use of an average but locally absent wind direction.     

DNA数进制与酶催化的信息传递

通过对DNA中四种碱基进行排列组合的计算,发现DNA是一个多种的数进制系统;20进制信息约占全部数进制信息的4.515%;每种数进制信息由它的产生方式而表现出不同的调控功能;相同的DNA片段用不同的读取方式,可以得到不同的数进制信息.从能量守恒定理和小分子RNA具有酶催化功能推断,酶的催化机制是一个信息传递的过程.     

Numerical simulation of trace element transport on subsurface environment pollution in coal mine spoil

An understanding of the dynamic behavior of trace elements leaching from coal mine spoil is important in predicting the groundwater quality. The relationship between trace element concentrations and leaching times, pH values of the media is studied. Column leaching tests conducted in the laboratory showed that there was a close correlation between pH value and trace element concentrations. The longer the leaching time, the higher the trace element concentrations. Different trace elements are differently affected by pH values of leaching media. A numerical model for water flow and trace element transport has been developed based on analyzing the characteristics of migration and transformation of trace elements leached from coal mine spoil. Solutions to the coupled model are accomplished by Eulerian-Lagrangian localized adjoint method. Numerical simulation shows that rainfall intensity determined maximum leaching depth. As rainfall intensity is 3.6ml/s, the outflow concentrations indicate a breakthrough of trace elements beyond the column base, with peak concentration at 90cm depth. And the subsurface pollution range has a trend of increase with time. The model simulations are compared to experimental results of trace element concentrations, with reasonable agreement between them. The analysis and modeling of trace elements suggested that the infiltration of rainwater through the mine spoil might lead to potential groundwater pollution. It provides theoretical evidence for quantitative assessment soil-water quality of trace element transport on environment pollution.     

Improved methods for fitting sedimentation coefficient distributions derived by time-derivative techniques

Time-derivative approaches to analyzing sedimentation velocity data have proven to be highly successful and have now been used routinely for more than a decade. For samples containing a small number of noninteracting species, the sedimentation coefficient distribution function, g(s *), traditionally has been fitted by Gaussian functions to derive the concentration, sedimentation coefficient, and diffusion coefficient of each species. However, the accuracy obtained by that approach is limited, even for noise-free data, and becomes even more compromised as more scans are included in the analysis to improve the signal/noise ratio (because the time span of the data becomes too large). Two new methods are described to correct for the effects of long time spans: one approach that uses a Taylor series expansion to correct the theoretical function and a second approach that creates theoretical g(s *) curves from Lamm equation models of the boundaries. With this second approach, the accuracy of the fitted parameters is approximately 0.1% and becomes essentially independent of the time span; therefore, it is possible to obtain much higher signal/noise when needed. This second approach is also compared with other current methods of analyzing sedimentation velocity data.