Helicopter blade flapping with and without small angle assumption in the presence of dynamic stall

The flapping equation for a rotating rigid helicopter blade is typically derived by considering (1)small flap angle, (2) small induced angle of attack and (3) linear aerodynamics. However, the use of nonlinear aerodynamics such as dynamic stall can make the assumptions of small angles suspect as shown in this paper. A general equation describing helicopter blade flap dynamics for large flap angle and large induced inflow angle of attack is derived. A semi-empirical dynamic stall aerodynamics model (ONERA model) is used. Numerical simulations are performed by solving the nonlinear flapping ordinary differential equation for steady state conditions and the validity of the small angle approximations are examined. It is shown that the small flapping assumption, and to a lesser extent, the small induced angle ofattack assumption, can lead to inaccurate predictions of the blade flap response in certain flight conditions for some rotors when nonlinear aerodynamics is considered. (C) 2010 Elsevier Inc. All rights reserved.

Missile battery placement for air defense: A dynamic programming approach

A procedure to evaluate surface-to-air missile battery placement patterns for air defense is presented. A measure of defense effectiveness is defined as a function of kill probability of the defense missiles and the nature of the surrounding terrain features. The concept of cumulative danger index is used to select the best path for a penetrating hostile aircraft for any given pattern of placement. The aircraft is assumed to be intelligent and well-informed. The path is generated using a dynamic programming methodology. The software package so developed can be used off-line to choose the best among a number of possible battery placement patterns.

Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

J. B. S. Haldane, Ernst Mayr and the Beanbag Genetics Dispute

Starting from the early decades of the twentieth century, evolutionary biology began to acquire mathematical overtones. This took place via the development of a set of models in which the Darwinian picture of evolution was shown to be consistent with the laws of heredity discovered by Mendel. The models, which came to be elaborated over the years, define a field of study known as population genetics. Population genetics is generally looked upon as an essential component of modern evolutionary theory. This article deals with a famous dispute between J. B. S. Haldane, one of the founders of population genetics, and Ernst Mayr, a major contributor to the way we understand evolution. The philosophical undercurrents of the dispute remain relevant today. Mayr and Haldane agreed that genetics provided a broad explanatory framework for explaining how evolution took place but differed over the relevance of the mathematical models that sought to underpin that framework. The dispute began with a fundamental issue raised by Mayr in 1959: in terms of understanding evolution, did population genetics contribute anything beyond the obvious? Haldane's response came just before his death in 1964. It contained a spirited defense, not just of population genetics, but also of the motivations that lie behind mathematical modelling in biology. While the difference of opinion persisted and was not glossed over, the two continued to maintain cordial personal relations.

Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernoulli beam theory

In the present work, the effect of longitudinal magnetic field on wave dispersion characteristics of equivalent continuum structure (ECS) of single-walled carbon nanotubes (SWCNT) embedded in elastic medium is studied. The ECS is modelled as an Euler-Bernoulli beam. The chemical bonds between a SWCNT and the elastic medium are assumed to be formed. The elastic matrix is described by Pasternak foundation model, which accounts for both normal pressure and the transverse shear deformation. The governing equations of motion for the ECS of SWCNT under a longitudinal magnetic field are derived by considering the Lorentz magnetic force obtained from Maxwell's relations within the frame work of nonlocal elasticity theory. The wave propagation analysis is performed using spectral analysis. The results obtained show that the velocity of flexural waves in SWCNTs increases with the increase of longitudinal magnetic field exerted on it in the frequency range: 0-20 THz. The present analysis also shows that the flexural wave dispersion in the ECS of SWCNT obtained by local and nonlocal elasticity theories differ. It is found that the nonlocality reduces the wave velocity irrespective of the presence of the magnetic field and does not influences it in the higher frequency region. Further it is found that the presence of elastic matrix introduces the frequency band gap in flexural wave mode. The band gap in the flexural wave is found to independent of strength of the longitudinal magnetic field. (C) 2011 Elsevier Inc. All rights reserved.

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.

Multiple parents crossover operators: A new approach removes the overlapping solutions for sequencing problems

Maintaining population diversity throughout generations of Genetic Algorithms (GAs) is key to avoid premature convergence. Redundant solutions is one cause for the decreasing population diversity. To prevent the negative effect of redundant solutions, we propose a framework that is based on the multi-parents crossover (MPX) operator embedded in GAs. Because MPX generates diversified chromosomes with good solution quality, when a pair of redundant solutions is found, we would generate a new offspring by using the MPX to replace the redundant chromosome. Three schemes of MPX will be examined and will be compared against some algorithms in literature when we solve the permutation flowshop scheduling problems, which is a strong NP-Hard sequencing problem. The results indicate that our approach significantly improves the solution quality. This study is useful for researchers who are trying to avoid premature convergence of evolutionary algorithms by solving the sequencing problems.

Analysis of grating inscribed micro-cantilever for high resolution AFM probe

We present a mathematical modelling and analysis of reflection grating etched Si AFM cantilever deflections under different loading conditions. A simple analysis of the effect of grating structures on cantilever deflection is carried out with emphasis on optimizing the beam and gratings such that maximum amount of diffracted light remains within the detector area.

Analytical solutions for movement of cold water thermal front in a heterogeneous geothermal reservoir

In the present study an analytical model has been presented to describe the transient temperature distribution and advancement of the thermal front generated due to the reinjection of heat depleted water in a heterogeneous geothermal reservoir. One dimensional heat transport equation in porous media with advection and longitudinal heat conduction has been solved analytically using Laplace transform technique in a semi infinite medium. The heterogeneity of the porous medium is expressed by the spatial variation of the flow velocity and the longitudinal effective thermal conductivity of the medium. A simpler solution is also derived afterwards neglecting the longitudinal conduction depending on the situation where the contribution to the transient heat transport phenomenon in the porous media is negligible. Solution for a homogeneous aquifer with constant values of the rock and fluid parameters is also derived with an aim to compare the results with that of the heterogeneous one. The effect of some of the parameters involved, on the transient heat transport phenomenon is assessed by observing the variation of the results with different magnitudes of those parameters. Results prove the heterogeneity of the medium, the flow velocity and the longitudinal conductivity to have great influence and porosity to have negligible effect on the transient temperature distribution. (C) 2013 Elsevier Inc. All rights reserved.

CONVERGENCE ANALYSIS OF THE LOWEST ORDER WEAKLY PENALIZED ADAPTIVE DISCONTINUOUS GALERKIN METHODS

In this article, we prove convergence of the weakly penalized adaptive discontinuous Galerkin methods. Unlike other works, we derive the contraction property for various discontinuous Galerkin methods only assuming the stabilizing parameters are large enough to stabilize the method. A central idea in the analysis is to construct an auxiliary solution from the discontinuous Galerkin solution by a simple post processing. Based on the auxiliary solution, we define the adaptive algorithm which guides to the convergence of adaptive discontinuous Galerkin methods.

Emergent properties of the interferon-signalling network may underlie the success of hepatitis C treatment

Current interferon alpha-based treatment of hepatitis C virus (HCV) infection fails to cure a sizeable fraction of patients treated. The cause of this treatment failure remains unknown. Here using mathematical modelling, we predict treatment failure to be a consequence of the emergent properties of the interferon-signalling network. HCV induces bistability in the network, creating a new steady state where it can persist. Cells that admit the new steady state alone are refractory to interferon. Using a model of viral kinetics, we show that when the fraction of cells refractory to interferon in a patient exceeds a critical value, treatment fails. Direct-acting antivirals that suppress HCV replication can eliminate the new steady state, restoring interferon sensitivity and improving treatment response. Our study thus presents a new conceptual basis of HCV persistence and treatment response, elucidates the origin of the synergy between interferon and direct-acting antivirals, and facilitates rational treatment optimization.

Automatic finite element formulation and assembly of hyperelastic higher order structural models

The formulation of higher order structural models and their discretization using the finite element method is difficult owing to their complexity, especially in the presence of non-linearities. In this work a new algorithm for automating the formulation and assembly of hyperelastic higher-order structural finite elements is developed. A hierarchic series of kinematic models is proposed for modeling structures with special geometries and the algorithm is formulated to automate the study of this class of higher order structural models. The algorithm developed in this work sidesteps the need for an explicit derivation of the governing equations for the individual kinematic modes. Using a novel procedure involving a nodal degree-of-freedom based automatic assembly algorithm, automatic differentiation and higher dimensional quadrature, the relevant finite element matrices are directly computed from the variational statement of elasticity and the higher order kinematic model. Another significant feature of the proposed algorithm is that natural boundary conditions are implicitly handled for arbitrary higher order kinematic models. The validity algorithm is illustrated with examples involving linear elasticity and hyperelasticity. (C) 2013 Elsevier Inc. All rights reserved.

A Generalist Predator Regulating Spread of a Wildlife Disease: Exploring Two Infection Transmission Scenarios

Ecoepidemiology is a well-developed branch of theoretical ecology, which explores interplay between the trophic interactions and the disease spread. In most ecoepidemiological models, however, the authors assume the predator to be a specialist, which consumes only a single prey species. In few existing papers, in which the predator was suggested to be a generalist, the alternative food supply was always considered to be constant. This is obviously a simplification of reality, since predators can often choose between a number of different prey. Consumption of these alternative prey can dramatically change their densities and strongly influence the model predictions. In this paper, we try to bridge the gap and explore a generic ecoepidemiological system with a generalist predator, where the densities of all prey are dynamical variables. The model consists of two prey species, one of which is subject to an infectious disease, and a predator, which consumes both prey species. We investigate two main scenarios of infection transmission mode: (i) the disease transmission rate is predator independent and (ii) the transmission rate is a function of predator density. For both scenarios we fulfil an extensive bifurcation analysis. We show that including a second dynamical prey in the system can drastically change the dynamics of the single prey case. In particular, the presence of a second prey impedes disease spread by decreasing the basic reproduction number and can result in a substantial drop of the disease prevalence. We demonstrate that with efficient consumption of the second prey species by the predator, the predator-dependent disease transmission can not destabilize interactions, as in the case with a specialist predator. Interestingly, even if the population of the second prey eventually vanishes and only one prey species finally remains, the system with two prey species may exhibit different properties to those of the single prey system.

The two-component signalling networks of Mycobacterium tuberculosis display extensive cross-talk in vitro

Two-component systems (TCSs), which contain paired sensor kinase and response regulator proteins, form the primary apparatus for sensing and responding to environmental cues in bacteria. TCSs are thought to be highly specific, displaying minimal cross-talk, primarily due to the co-evolution of the participating proteins. To assess the level of cross-talk between the TCSs of Mycobacterium tuberculosis, we mapped the complete interactome of the M. tuberculosis TCSs using phosphotransfer profiling. Surprisingly, we found extensive crosstalk among the M. tuberculosis TCSs, significantly more than that in the TCSs in Escherichia coli or Caulobacter crescentus, thereby offering an alternate to specificity paradigm in TCS signalling. Nearly half of the interactions we detected were significant novel cross-interactions, unravelling a potentially complex signalling landscape. We classified the TCSs into specific `one-to-one' and promiscuous `one-to-many' and `many-to-one' circuits. Using mathematical modelling, we deduced that the promiscuous signalling observed can explain several currently confounding observations about M. tuberculosis TCSs. Our findings suggest an alternative paradigm of bacterial signalling with significant cross-talk between TCSs yielding potentially complex signalling landscapes.