Efficient solution of multiple cracks in great number using eigen COD boundary integral equations with iteration procedure

A newly developed computational approach is proposed in the paper for the analysis of multiple crack problems based on the eigen crack opening displacement (COD) boundary integral equations. The eigen COD particularly refers to a crack in an infinite domain under fictitious traction acting on the crack surface. With the concept of eigen COD, the multiple cracks in great number can be solved by using the conventional displacement discontinuity boundary integral equations in an iterative fashion with a small size of system matrix to determine all the unknown CODs step by step. To deal with the interactions among cracks for multiple crack problems, all cracks in the problem are divided into two groups, namely the adjacent group and the far-field group, according to the distance to the current crack in consideration. The adjacent group contains cracks with relatively small distances but strong effects to the current crack, while the others, the cracks of far-field group are composed of those with relatively large distances. Correspondingly, the eigen COD of the current crack is computed in two parts. The first part is computed by using the fictitious tractions of adjacent cracks via the local Eshelby matrix derived from the traction boundary integral equations in discretized form, while the second part is computed by using those of far-field cracks so that the high computational efficiency can be achieved in the proposed approach. The numerical results of the proposed approach are compared not only with those using the dual boundary integral equations (D-BIE) and the BIE with numerical Green's functions (NGF) but also with those of the analytical solutions in literature. The effectiveness and the efficiency of the proposed approach is verified. Numerical examples are provided for the stress intensity factors of cracks, up to several thousands in number, in both the finite and infinite plates.

Efficient solution of two-sided nonlinear space-fractional diffusion equations using fast Poisson preconditioners

We develop a fast Poisson preconditioner for the efficient numerical solution of a class of two-sided nonlinear space fractional diffusion equations in one and two dimensions using the method of lines. Using the shifted Gr¨unwald finite difference formulas to approximate the two-sided(i.e. the left and right Riemann-Liouville) fractional derivatives, the resulting semi-discrete nonlinear systems have dense Jacobian matrices owing to the non-local property of fractional derivatives. We employ a modern initial value problem solver utilising backward differentiation formulas and Jacobian-free Newton-Krylov methods to solve these systems. For efficient performance of the Jacobianfree Newton-Krylov method it is essential to apply an effective preconditioner to accelerate the convergence of the linear iterative solver. The key contribution of our work is to generalise the fast Poisson preconditioner, widely used for integer-order diffusion equations, so that it applies to the two-sided space fractional diffusion equation. A number of numerical experiments are presented to demonstrate the effectiveness of the preconditioner and the overall solution strategy.

A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

Analysis of nonlinear sequences and streamciphers

Streamciphers are common cryptographic algorithms used to protect the confidentiality of frame-based communications like mobile phone conversations and Internet traffic. Streamciphers are ideal cryptographic algorithms to encrypt these types of traffic as they have the potential to encrypt them quickly and securely, and have low error propagation. The main objective of this thesis is to determine whether structural features of keystream generators affect the security provided by stream ciphers.These structural features pertain to the state-update and output functions used in keystream generators. Using linear sequences as keystream to encrypt messages is known to be insecure. Modern keystream generators use nonlinear sequences as keystream.The nonlinearity can be introduced through a keystream generator's state-update function, output function, or both. The first contribution of this thesis relates to nonlinear sequences produced by the well-known Trivium stream cipher. Trivium is one of the stream ciphers selected in a final portfolio resulting from a multi-year project in Europe called the ecrypt project. Trivium's structural simplicity makes it a popular cipher to cryptanalyse, but to date, there are no attacks in the public literature which are faster than exhaustive keysearch. Algebraic analyses are performed on the Trivium stream cipher, which uses a nonlinear state-update and linear output function to produce keystream. Two algebraic investigations are performed: an examination of the sliding property in the initialisation process and algebraic analyses of Trivium-like streamciphers using a combination of the algebraic techniques previously applied separately by Berbain et al. and Raddum. For certain iterations of Trivium's state-update function, we examine the sets of slid pairs, looking particularly to form chains of slid pairs. No chains exist for a small number of iterations.This has implications for the period of keystreams produced by Trivium. Secondly, using our combination of the methods of Berbain et al. and Raddum, we analysed Trivium-like ciphers and improved on previous on previous analysis with regards to forming systems of equations on these ciphers. Using these new systems of equations, we were able to successfully recover the initial state of Bivium-A.The attack complexity for Bivium-B and Trivium were, however, worse than exhaustive keysearch. We also show that the selection of stages which are used as input to the output function and the size of registers which are used in the construction of the system of equations affect the success of the attack. The second contribution of this thesis is the examination of state convergence. State convergence is an undesirable characteristic in keystream generators for stream ciphers, as it implies that the effective session key size of the stream cipher is smaller than the designers intended. We identify methods which can be used to detect state convergence. As a case study, theMixer streamcipher, which uses nonlinear state-update and output functions to produce keystream, is analysed. Mixer is found to suffer from state convergence as the state-update function used in its initialisation process is not one-to-one. A discussion of several other streamciphers which are known to suffer from state convergence is given. From our analysis of these stream ciphers, three mechanisms which can cause state convergence are identified.The effect state convergence can have on stream cipher cryptanalysis is examined. We show that state convergence can have a positive effect if the goal of the attacker is to recover the initial state of the keystream generator. The third contribution of this thesis is the examination of the distributions of bit patterns in the sequences produced by nonlinear filter generators (NLFGs) and linearly filtered nonlinear feedback shift registers. We show that the selection of stages used as input to a keystream generator's output function can affect the distribution of bit patterns in sequences produced by these keystreamgenerators, and that the effect differs for nonlinear filter generators and linearly filtered nonlinear feedback shift registers. In the case of NLFGs, the keystream sequences produced when the output functions take inputs from consecutive register stages are less uniform than sequences produced by NLFGs whose output functions take inputs from unevenly spaced register stages. The opposite is true for keystream sequences produced by linearly filtered nonlinear feedback shift registers.

A simplified approach for calculating the moments of action for linear reaction-diffusion equations

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time under-approximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the nth moment of action require the solution of n nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the nth moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.

Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise

There has been considerable recent work on the development of energy conserving one-step methods that are not symplectic. Here we extend these ideas to stochastic Hamiltonian problems with additive noise and show that there are classes of Runge-Kutta methods that are very effective in preserving the expectation of the Hamiltonian, but care has to be taken in how the Wiener increments are sampled at each timestep. Some numerical simulations illustrate the performance of these methods.

Development and validation of anthropometric prediction equations for estimation of lean body mass and appendicular lean soft tissue in Indian men and women

Lean body mass (LBM) and muscle mass remains difficult to quantify in large epidemiological studies due to non-availability of inexpensive methods. We therefore developed anthropometric prediction equations to estimate the LBM and appendicular lean soft tissue (ALST) using dual energy X-ray absorptiometry (DXA) as a reference method. Healthy volunteers (n= 2220; 36% females; age 18-79 y) representing a wide range of body mass index (14-44 kg/m2) participated in this study. Their LBM including ALST was assessed by DXA along with anthropometric measurements. The sample was divided into prediction (60%) and validation (40%) sets. In the prediction set, a number of prediction models were constructed using DXA measured LBM and ALST estimates as dependent variables and a combination of anthropometric indices as independent variables. These equations were cross-validated in the validation set. Simple equations using age, height and weight explained > 90% variation in the LBM and ALST in both men and women. Additional variables (hip and limb circumferences and sum of SFTs) increased the explained variation by 5-8% in the fully adjusted models predicting LBM and ALST. More complex equations using all the above anthropometric variables could predict the DXA measured LBM and ALST accurately as indicated by low standard error of the estimate (LBM: 1.47 kg and 1.63 kg for men and women, respectively) as well as good agreement by Bland Altman analyses. These equations could be a valuable tool in large epidemiological studies assessing these body compartments in Indians and other population groups with similar body composition.

Development of empirical equations for irradiance profile of a standard parabolic trough collector using Monte Carlo ray tracing technique

Irradiance profile around the receiver tube (RT) of a parabolic trough collector (PTC) is a key effect of optical performance that affects the overall energy performance of the collector. Thermal performance evaluation of the RT relies on the appropriate determination of the irradiance profile. This article explains a technique in which empirical equations were developed to calculate the local irradiance as a function of angular location of the RT of a standard PTC using a vigorously verified Monte Carlo ray tracing model. A large range of test conditions including daily normal insolation, spectral selective coatings and glass envelop conditions were selected from the published data by Dudley et al. [1] for the job. The R2 values of the equations are excellent that vary in between 0.9857 and 0.9999. Therefore, these equations can be used confidently to produce realistic non-uniform boundary heat flux profile around the RT at normal incidence for conjugate heat transfer analyses of the collector. Required values in the equations are daily normal insolation, and the spectral selective properties of the collector components. Since the equations are polynomial functions, data processing software can be employed to calculate the flux profile very easily and quickly. The ultimate goal of this research is to make the concentrating solar power technology cost competitive with conventional energy technology facilitating its ongoing research.

Development and validation of anthropometric prediction equations for estimation of body fat in Indonesian men

Body composition of 292 males aged between 18 and 65 years was measured using the deuterium oxide dilution technique. Participants were divided into development (n=146) and cross-validation (n=146) groups. Stature, body weight, skinfold thickness at eight sites, girth at five sites, and bone breadth at four sites were measured and body mass index (BMI), waist-to-hip ratio (WHR), and waist-to-stature ratio (WSR) calculated. Equations were developed using multiple regression analyses with skinfolds, breadth and girth measures, BMI, and other indices as independent variables and percentage body fat (%BF) determined from deuterium dilution technique as the reference. All equations were then tested in the cross-validation group. Results from the reference method were also compared with existing prediction equations by Durnin and Womersley (1974), Davidson et al (2011), and Gurrici et al (1998). The proposed prediction equations were valid in our cross-validation samples with r=0.77- 0.86, bias 0.2-0.5%, and pure error 2.8-3.6%. The strongest was generated from skinfolds with r=0.83, SEE 3.7%, and AIC 377.2. The Durnin and Womersley (1974) and Davidson et al (2011) equations significantly (p<0.001) underestimated %BF by 1.0 and 6.9% respectively, whereas the Gurrici et al (1998) equation significantly (p<0.001) overestimated %BF by 3.3% in our cross-validation samples compared to the reference. Results suggest that the proposed prediction equations are useful in the estimation of %BF in Indonesian men.

Ozone-induced dissociation of conjugated lipids reveals significant reaction rate enhancements and characteristic odd-electron product ions

Ozone-induced dissociation (OzID) is an alternative ion activation method that relies on the gas phase ion-molecule reaction between a mass-selected target ion and ozone in an ion trap mass spectrometer. Herein, we evaluated the performance of OzID for both the structural elucidation and selective detection of conjugated carbon-carbon double bond motifs within lipids. The relative reactivity trends for \[M + X](+) ions (where X = Li, Na, K) formed via electrospray ionization (ESI) of conjugated versus nonconjugated fatty acid methyl esters (FAMEs) were examined using two different OzID-enabled linear ion-trap mass spectrometers. Compared with nonconjugated analogues, FAMEs derived from conjugated linoleic acids were found to react up to 200 times faster and to yield characteristic radical cations. The significantly enhanced reactivity of conjugated isomers means that OzID product ions can be observed without invoking a reaction delay in the experimental sequence (i.e., trapping of ions in the presence of ozone is not required). This possibility has been exploited to undertake neutral-loss scans on a triple quadrupole mass spectrometer targeting characteristic OzID transitions. Such analyses reveal the presence of conjugated double bonds in lipids extracted from selected foodstuffs. Finally, by benchmarking of the absolute ozone concentration inside the ion trap, second order rate constants for the gas phase reactions between unsaturated organic ions and ozone were obtained. These results demonstrate a significant influence of the adducting metal on reaction rate constants in the fashion Li > Na > K.

Eigenstrain boundary integral equations with local Eshelby matrix for stress analysis of ellipsoidal particles

Aiming at the large scale numerical simulation of particle reinforced materials, the concept of local Eshelby matrix has been introduced into the computational model of the eigenstrain boundary integral equation (BIE) to solve the problem of interactions among particles. The local Eshelby matrix can be considered as an extension of the concepts of Eshelby tensor and the equivalent inclusion in numerical form. Taking the subdomain boundary element method as the control, three-dimensional stress analyses are carried out for some ellipsoidal particles in full space with the proposed computational model. Through the numerical examples, it is verified not only the correctness and feasibility but also the high efficiency of the present model with the corresponding solution procedure, showing the potential of solving the problem of large scale numerical simulation of particle reinforced materials.

Calibration of the biotrainer pro activity monitor in children

The unique physical and movement characteristics of children necessitate the development of accelerometer equations and cut points that are population specific. The purpose of this study is to develop an ecologically valid cut point for the Biotrainer Pro monitor that reflects a threshold for moderate-intensity physical activity in elementary school children. A sample of 30 children (ages 8-12) wore a Biotrainer monitor while completing a series of 7 movement tasks (calibration phase) and while participating in an organized group activity (cross-validation phase). Videotapes from each session were processed using a computerized direct-observation technique to provide a criterion measure of physical activity. Analyses involved the use of mixed-model regression and receiver operator characteristic (ROC) curves. The results indicated that a cut point of 4 counts/min provides the optimal balance between the related needs for sensitivity (accurately detecting activity) and specificity (limiting misclassification of activity as inactivity). Results with the cross-validation data demonstrated that this value yielded the best overall kappa (.58) and a high classification agreement (84%) for activity determination. The specificity of 93% demonstrates that the proposed cut point can accurately detect activity; however, the lower sensitivity value of 61% suggests that some minutes of activity might be incorrectly classified as inactivity. The cut point of 4 counts/min provides an ecologically valid cut point to capture physical activity in children using the Biotrainer Pro activity monitor.

Predictive validity of accelerometer prediction equations for energy expenditure (EE) during overland walking and running in children and adolescents

Purpose The aim of this study was to assess the predictive validity of three accelerometer prediction equations (Freedson et aL, 1997; Trost et aL, 1998; Puyau et al., 2002) for energy expenditure (EE) during overland walking and running in children and adolescents. Methods 45 healthy children and adolescents aged 10-18 completed the following protocol, each task 5-mins in duration, with a 5-min rest period in between; walking normally; walking briskly; running easily and running fast. During each task participants wore MTI (WAM 7164) Actigraphs on the left and right hips. VO2 was monitored breath by breath using the Cosmed K4b2 portable indirect calorimetry system. For each prediction equation, difference scores were calculated as EE measured minus EE predicted. The percentage of 1-min epochs correctly categorized as light (<3 METs), moderate (3-5.9 METs), and vigorous (≥6 METS) was also calculated. Results The Freedson and Trost equations consistently overestimated MET level. The level of overestimation was statistically significant across all tasks for the Freedson equation, and was significant for only the walking tasks for the Trost equation. The Puyau equation consistently underestimated AEE with the exception of the walking normally task. In terms of categorisation, the Freedson equation (72.8% agreement) demonstrated better agreement than the Puyau (60.6%). Conclusions These data suggest that the three accelerometer prediction equations do not accurately predict EE on a minute-by-minute basis in children and adolescents during overland walking and running. However, the cut points generated by these equations maybe useful for classifying activity as either, light, moderate, or vigorous.

A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction–diffusion equations

Fractional differential equations have been increasingly used as a powerful tool to model the non-locality and spatial heterogeneity inherent in many real-world problems. However, a constant challenge faced by researchers in this area is the high computational expense of obtaining numerical solutions of these fractional models, owing to the non-local nature of fractional derivatives. In this paper, we introduce a finite volume scheme with preconditioned Lanczos method as an attractive and high-efficiency approach for solving two-dimensional space-fractional reaction–diffusion equations. The computational heart of this approach is the efficient computation of a matrix-function-vector product f(A)bf(A)b, where A A is the matrix representation of the Laplacian obtained from the finite volume method and is non-symmetric. A key aspect of our proposed approach is that the popular Lanczos method for symmetric matrices is applied to this non-symmetric problem, after a suitable transformation. Furthermore, the convergence of the Lanczos method is greatly improved by incorporating a preconditioner. Our approach is show-cased by solving the fractional Fisher equation including a validation of the solution and an analysis of the behaviour of the model.