Asymptotic approximations for vibrational modes of helices

The free vibrations in the plane normal to the helical axis are studied under the assumption that the helical pitch is small. Asymptotic approximations for eigenvalues and eigenfunctions are derived for both small and large numbers of helical turns. The analytic approximations reveal interesting features of helix vibrations and the connection between the vibrational modes of a helix and the flexural modes of a curved beam. Comparison with numerical calculations shows that the approximations derived cover with sufficient accuracy a wide range of number of helical turns

Wave Propagation on Helices and Hyperhelices: A Fractal Regression

A hyperhelix of order N is defined to be a self-similar object consisting of a thin elastic rod wound into a helix, which is itself wound into a larger helix, until this process has been repeated N times. Wave propagation on such a structure can be discussed in a hierarchical manner, ultimately in terms of the wavenumber κ defining propagation on the elementary rod. It is found that the dispersion curve expressing the wave frequency ω as a function of the elementary wavenumber κ on the rod making up the initial helix is also a fractal object, with all the macroscopically observable wave phenomena for a hyperhelix of arbitrarily large order being compressed into a small wavenumber range of width about 2R2-1α centred on the value κ = R1-1, where R1 is the radius, α is the helical pitch angle of the smallest helix in the progression, and R2 is the radius of the next-larger helix

A comparison of adaptive management and real options approaches for environmental decisions under uncertainty

Two approaches to sequential decisions under uncertainty in the environmental management adaptive management and real options analysis -have evolved independently over the last decades

A comparison of adaptive management and real options approaches for environmental decisions under uncertainty

Two approaches to sequential decisions under uncertainty in the environmental management - adaptive management and real options analysis – have evolved independently over the last decades. Adaptive management, or learning by doing, originated from adaptive control. Adaptive management is acknowledged as one of the best-practice methods to manage biological systems under structural uncertainty. Adaptive management has been used for the management of renewable natural resources (such as fisheries and waterfowl) and the conservation of species (such as assisted colonization, restoration and threatened species management). In this context, stochastic dynamic models and historical data would be valuable for describing and predicting responses of management decisions, but these are either non-existent or severely limited in their scope. Real options analysis originated from mathematical finance and is based on financial options pricing theory. The real options analysis can be viewed as both sequential decision-making and project valuation in a highly uncertain environment with non-stationary dynamics. Real options analysis has most often been used for industrial applications (such as mining, asset management, infrastructure, energy, defence, and agriculture). In this context, reasonably good stochastic dynamic models and historical data exist for describing and forecasting the behaviour of risk factors. In mathematical terms, both adaptive management and real options approaches are based on stochastic optimal control and Markov decision processes. In environmental decision-making both enable practitioners and managers to make optimal decisions under uncertainty. However, the numerical methods of solving adaptive management versus real options problems are different, as their development has been motivated by the different needs of respective application areas. An important feature of adaptive management is the presence of and need to account for a small number of hidden variables. In contrast, real options focus on the development of techniques capable of dealing with high-dimensional problems with multiple stochastic risk factors. Limited for a long time by the inefficiency of the solution methods, recent advances in both adaptive management and real options now allow us to solve more realistic environmental decision problems under uncertainty, widening the scope of their applications. Growing availability of data in the environmental management arena and an emerging need to conduct industrial operations in the proximity of conservation areas will require new decision-making approaches that can combine recent advances in adaptive management and real options. This paper reviews recent advances in both adaptive management and real options methodologies, and compares methods for solving decisions under uncertainty problems based on the type of uncertainty they are addressing, the type of decision-making approach, important assumptions, and the size of the problems they are capable of dealing with. This paper proposes new areas of development that could inspire future research and better-informed environmental decisions under uncertainty

Asymptotic Analysis of The Free In-Plane Vibrations of Beams With Arbitrarily Varying Curvature And Cross-Section

An asymptotic analysis is carried out for the equations of free vibrations of a beam having varying curvature and cross!section[ The effect of splitting the asymptotic limit for eigenvalues into two families is revealed and its connection with boundary conditions is discussed[ The analysis of the properties of the asymptotic solution explains the phenomenon of transformation of mode shape with change in curvature and provides a method for predicting the spectrum of curved beams[ The asymptotic solution obtained also gives a simple approximation for high mode number extensional vibrations of curved beams which are dif_cult to analyse by other means[ The asymptotic behaviour of the solution is illustrated numerically for different types of curvature including antisymmetric curvature[ An experimental veri_cation of the asymptotic behaviour of mode frequencies is presente

Instability in lateral dynamics of a metal strip in cold rolling

Consider the lateral dynamics of a strip between the uncoiler and the first stand of a cold rolling mill: operational problems are experienced in the metal rolling industry. Here we introduce a physically based model for the buckling of the strip between the uncoiler and the reduction mill. The model reveals, for the first time, that there exists a critical level of asymmetry in rolling conditions above which the strip motion becomes unstable. Below this level, two solutions of the steady-state model exist. Whereas one of these solutions represents a stable equilibrium, the other exhibits the features of unstable equilibrium. The motion of the strip is sensitive to the initial lateral deviation of the strip. For a given level of asymmetry, a sudden transition to unstable motion occurs if a critical lateral deviation is reached. The model can be used as a basis for development of a multi-stand model of lateral dynamics

The epidemiology of the primary brain tumors in Rostov region in 2010-2015

The dynamics of the prevalence, incidence, and clinical and statistical characteristics of primary and metastatic brain tumors (BT) with regard to their histological types in the Rostov region, depending on the environmental conditions of life, different age and gender and social groups who were treated in specialized and non-specialized hospitals of Rostov-on-Don for the period from 1 january 2010 to 2015 is a proven result. A further increase in the level of incidence of malignant brain tumors, both due to the improved diagnostics of tumor diseases of the brain, and the influence of climatic, demographic, environmental and medico-social characteristics of the study region were showed. However, many epidemiological aspects of neoplastic diseases of the brain remains poorly understood, requires the continuation of this study