Variability of complex oscillatory regimes in the stochastic model of cold-flame combustion of a hydrocarbon mixture

Processes of the cold-flame combustion of a mixture of two hydrocarbons are studied on the base of a three-dimensional nonlinear dynamical model. Bifurcation analysis of the deterministic model reveals mono- and bistability parameter zones with equilibrium and oscillatory attractors. For this model, effects of random disturbances in the bistability parameter zone are studied. We show that random forcing causes transitions between coexisting stable equilibria and limit cycles with the formation of complex stochastic mixed-mode oscillations. Properties of these oscillatory regimes are studied by means of statistics of interspike intervals. A phenomenon of anti-coherence resonance is discussed. This article is part of the theme issue ‘Transport phenomena in complex systems (part 2)’.

Resource allocation procedures for unknown sales response functions with additive disturbances

We develop a modified exploration–exploitation algorithm which allocates a fixed resource (e.g., a fixed budget) to several units with the objective to attain maximum sales. This algorithm does not require knowledge of the form and the parameters of sales response functions and is able to cope with additive random disturbances. Note that additive random disturbances, as a rule, are a component of sales response functions estimated by econometric methods. We compare the developed algorithm to three rules of thumb which in practice are often used to solve this allocation problem. The comparison is based on a Monte Carlo simulation for 384 experimental constellations, which are obtained from four function types, four procedures (including our algorithm), similar/varied elasticities, similar/varied saturations, high/low budgets, and three disturbance levels. A statistical analysis of the simulation results shows that across a multi-period planning horizon the algorithm performs better than the rules of thumb considered with respect to two sales-related criteria.

Randomized Estimation of the Net Present Value of a Residential Housing Development

Randomized estimation of the net present value of a housing development allows for the assessment of the efficiency of projects in random implementation conditions. The efficiency of a project is estimated on the basis of primary input data, usually used in project planning. For this purpose, random disturbances are identified that may randomly affect the course and results of the project. The probability and severity of disturbances are determined. The primary initial data is then randomized, and a randomized probabilistic index of the project’s net present value is calculated, the value of which indicates whether the project is profitable or whether implementation should be stopped. Based on this data, the expected total revenue, the expected total cost, the expected gross profit, and the net present value of the randomized performance of the project are calculated. The values of these are estimated for expected, favorable, and unfavorable conditions of implementation. Finally, the risks for the total revenue and total cost of the project are calculated and plotted for comparative revenue values in the range [1, 0] and cost in the range [0, 1]. Their analysis makes it possible to make the right investment decisions before starting the investment at the preparation stage.

Interrogating the Lead-up to a Critical Speed in Rotordynamics

This paper presents a new approach to predicting an incipient critical speed in a rotating shaft. Based on the classical governing equations of motion for an eccentric mass on a flexible shaft (the Jeffcott rotor model), the approach is centered on examining the behavior of small perturbations or random disturbances to infer the approach of a critical speed (resonance). Such disturbances, that may be based on intentional probing, or simply the result of naturally occurring fluctuations, cause small transients. It is the changing nature of these transients (as characterized by their associated eigenvalues) that is used to assess the proximity to a critical speed. In this paper the material developed is based on analysis, but generating the data from simulations or experiments will be the next step. The approach is a kind of stress-test, conceptually not dissimilar to structural health monitoring and damage detection, but here directed toward the lead-up to resonance.

Formalization of target invariants and designing an adaptive control system for the model of anaerobic biological wastewater treatment

A model of a two-step anaerobic fermentation in a bioreactor-mixer, whose mathematical description is a system of nonlinear mathematical equations, is discussed. The purpose is to design an algorithm of an energy-saving control relying on the principles of nonlinear adaptation on target manifolds with an attractive property, which are referred to as invariants or invariable laws of the target system behavior for the object under study. A necessary preliminary step is the formalization of possible target invariants in the form of prescribed (desired) laws of the controlled object behavior. An example is given of designing a vector regulator with a compensation of random disturbances over the control channel in a system of anaerobic biological waste water treatment.

A Robustness Evaluation Method of Natural Gas Pipeline Network Based on Topological Structure Analysis

As the total mileage of natural gas pipeline network continues to increase, the topological structure of natural gas pipeline network will become more and more complex. The complicated topological structure of natural gas pipeline network is likely to cause inherent structural defects, which have serious impacts on the safe operation of natural gas pipeline network. At present, related researches mainly focused on the safe and reliable operation of natural gas pipeline network, which has become a research hotspot, but few of them considered the complexity of natural gas pipeline network and its potential impacts. In order to understand the complexity of natural gas pipeline network and its behaviors when facing structural changes, this paper studied the robustness of natural gas pipeline network based on complex network theory. This paper drew on the methods and experience of robustness researches in other related fields, and proposed a robustness evaluation method for natural gas pipeline network which is combined with its operation characteristics. The robustness evaluation method of natural gas pipeline network is helpful to identify the key components of the pipeline network and understand the response of the pipeline network to structural changes. Furthermore, it can provide a theoretical reference for the safe and stable operation of natural gas pipeline network. The evaluation results show that natural gas pipeline network shows strong robustness when faced with random disturbances represented by pipeline accidents or component failures caused by natural disasters, and when faced with targeted disturbances represented by terrorist disturbances, the robustness of natural gas pipeline network is very weak. Natural gas pipeline network behaves differently in the face of different types of random disturbances. Natural gas pipeline network is more robust when faced with component failures than pipeline accidents caused by natural disasters.