Global stability of a three-dimensional bio-reactor with inhibition responses

A three-dimensional bio-reactor model of exploitative competition of two predator organisms with inhibition responses for the same renewable organism with reproductive properties is considered. By constructing a modified Lyapunov function and using LaSalle’s invariant principle, it is shown that the lower “break-even” concentration predator organism survives in the competition.      

p-Median theorems for competitive locations

In competitive location theory, one wishes to optimally choose the locations ofr facilities to compete againstp existing facilities for providing service (or goods) to the customers who are at given discrete points (or nodes). One normally assumes that: (a) the level of demand of each customer is fixed (i.e. this demand is not a function of how far a customer is from a facility), and (b) the customer always uses the closest available facility. In this paper we study competitive locations when one or both of the above assumptions have been relaxed. In particular, we show that for each case and under certain assumptions, there exists a set of optimal locations which consists entirely of nodes.This work was supported by a National Science Foundation Grant ECS-8121741.     

电子商务网站竞争模型分析及其策略

研究电子商务网站竞争模型,分析其平衡点的稳定性,给出数值模拟图,建立一系列电子商务网站获胜的新策略.     

Monotonicity in the stock competition game with consumer search

Anupindi and Bassok investigate the impact of centralizing the stocks in a one-manufacturer-two-retailer supply chain with consumer search. They observed through numerical studies that in the decentralized scenario, the retailers’ order quantities are monotonic in the consumer search probability. This paper provides an analytical justification of this monotonicity.     

Resonant dynamics in a rotordynamic system with nonlinear inertial coupling and shaft anisotropy

The response of a nonlinear, damped Jeffcott rotor with anisotropic stiffness is considered in the presence of an imbalance. For sufficiently small external torque or large imbalance, resonance capture or rotordynamic stall can occur, whereby the rotational velocity of the shaft is unable to increase beyond the fundamental resonance between the rotational and translational motion. This phenomena provides a mechanism for energy transfer from the rotational to the translational mode. Using the method of averaging a reduced-order model is developed, valid near the resonance, that describes this resonant behavior. The equilibrium points of these averaged equations, which correspond to stationary solutions of the original equations and rotordynamic stall, are described as the applied torque, damping, and anisotropy vary. As the anisotropy increases, assumed to arise from increasing shaft cracks, the torque required to eliminate the possibility of stall increases. However, when the system is started with zero initial conditions, the minimum torque required to pass through the resonance is approximately constant as the anisotropy increases. The predictions from the reduced-order model are verified against numerical simulations of the original equations of motion.     

Spatial competition facility location models: Definition,formulation and solution approach

Models are presented for locating a firm's production facilities and determining production levels at these facilities so as to maximize the firm's profit. These models take into account the changes in price at each of the spatially separated markets that would result from the increase in supply provided by the new facilities and also from the response of competing firms. Two different models of spatial competition are presented to represent the competitive market situation in which the firm's production facilities are being located. These models are formulated as variational inequalities; recent sensitivity analysis results for variational inequalities are used to develop derivatives of the prices at each of the spatially separated markets with respect to the production levels at each of the new facilities. These derivatives are used to develop a linear approximation of the implicit function relating prices to productions. A heuristic solution procedure making use of this approximation is proposed.     

Design of Cavities for a Short Pulse Powerful Large Orbit Gyrotron

Designs of cavities for fundamental and high harmonic operation in Large Orbit Gyrotron (LOG) are discussed. The fundamental operation allows one to use beam currents in the range from 200 A to 300 A achieve output power of the order of 9–10 MW at frequency 143.6 GHz. Mode competition calculations show that stable oscillations in the TE^1,4 mode using high beam currents are possible even with the pitch factor 1.3 which is significantly lower than the design value 1.55. For the second harmonic operation, the maximum current used for excitation of the TE^2,4 mode is 60 A and the optimum magnetic field is 7.6 T. A cavity design for fourth harmonic operation using the TE^4,4 mode is also presented.     

Magnitude Estimations for Line Bisection Under Lateral Visuo-Spatial Neglect

Human subjects can bisect a line, with error, even when they have neglect on one side. How this skill, even though inefficient, can be represented in nonlinear psychophysical theory is explored here. A problem for previous theoretical explanations of lateral neglect bisection, where the errors of bisection are reversed in sign for brain-damaged subjects, when very short lines are used as stimuli, is shown not in fact to be a problem for N(onlinear) P(sychophysical) D(ynamics) theory at all, but is exactly what is expected to arise when sensitivities are biassed on one side. It is suggested that an imbalance in channel inputs in a nonlinear system representation has results which do not follow from a more conventional connectionist approach.     

A Kolmogorov-type competition model with multiple coexistence states and its applications to plant competition for sunlight

It is demonstrated that a Kolmogorov-type competition model featuring species allocation and gain functions can possess multiple coexistence states. Two examples are constructed: one in which the two competing species possess rectangular allocation functions but distinct gain functions, and the other in which one species has a rectangular allocation function, the second species has a bi-rectangular allocation function, and the two species share a common gain function. In both examples, it is shown that the species nullclines may intersect multiple times within the interior of the first quadrant, thus creating both locally stable and unstable equilibrium points. These results have important applications in the study of plant competition for sunlight, in which the allocation functions describe the vertical placement of leaves for two competing species, and the gain functions represent rates of photosynthesis performed by leaves at different heights when shaded by overlying leaves belonging to either species.     

高速气流中激光加热平板数值模拟与分析

 采用流固耦合方法,数值模拟了高速流场中激光作用下来流速度对平板温度分布的影响。结果表明:无激光辐照时,高速气流中平板有较高的气动生热平衡温度,且平板-气流之间的换热系数随来流速度增大而增大;在平板前沿换热系数增长最快,沿平板长度方向增速趋于平缓。分析了激光辐照时高速气流中激光加热平板的温度分布情况,考察了来流速度不同时,气动生热、散热和激光辐照对平板温度的影响,给出了激光辐照后的温升情况和温度分布,分析了在不同速度来流下,对流散热、摩擦生热和激光加热之间的竞争关系,结果表明,平板温度具体分布主要是加热过程竞争的结果。