Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

Nanopatterning by solid-state dewetting on reconstructed ceramic surfaces

We demonstrate ordered array formation of Au nanoparticles by controlled solid-state dewetting of a metal film on stepped alumina substrates. In situ transmission electron microscopy studies reveal that the dewetting process starts with nucleation of ordered dry regions on the substrate. The chemical potential difference between concave and convex surface regions induces anisotropic metal diffusion leading to the formation of nanowires in the valleys. The nanowires fragment due to Rayleigh instability forming arrays of metal nanoparticles on the substrate. The length scale of reconstruction relative to the starting film thickness is an important parameter in controlling the spatial order of the nanoparticles.

Changes in depression during and following pregnancy

Rates of depression were studied in a sample of over 9000 women who were participants in the Avon Longitudinal Study of Pregnancy and Childhood. Assessments of depression were made at 18 and 32 weeks gestation, and at 8 and 32 weeks postpartum. Changes in depressive status across time were modelled using latent Markov modelling methods. This analysis showed that when classification errors were taken into account there was relatively high stability in diagnostic status during pregnancy and after pregnancy. However, the transition from late pregnancy to the early postnatal period showed evidence of increased instability and remission of depression. The net effects of this were that rates of depression tended to decline following childbirth. The implications of these results for a series of issues including measurement errors in depression reports and the prevalence of depression before and after childbirth are discussed.

Introducing a new limit states design concept to railway concrete sleepers: An Australian experience

Over 50 years, a large number of research and development projects with respect to the use of cementitious and concrete materials for manufacturing railway sleepers have been significantly progressed in Australia, Europe, and Japan (Wang, 1996; Murray and Cai, 1998; Wakui and Okuda, 1999; Esveld, 2001; Freudenstein and Haban, 2006; Remennikov and Kaewunruen, 2008). Traditional sleeper materials are timber, steel, and concrete. Cost-efficiency, superior durability, and improved track stability are the main factors toward significant adoption of concrete materials for railway sleepers. The sleepers in a track system, as shown in Figure 1, are subjected to harsh and aggressive external forces and natural environments across a distance. Many systemic problems and technical issues associated with concrete sleepers have been tackled over decades. These include pre-mature failures of sleepers, concrete cancer or ettringite, abrasion of railseats and soffits, impact damages by rail machinery, bond-slip damage, longitudinal and lateral instability of track system, dimensional instability of sleepers, nuisance noise and vibration, and so on (Pfeil, 1997; Gustavson, 2002; Kaewunruen and Remennikov, 2008a,b, 2013). These issues are, however, becoming an emerging risk for many countries (in North and South Americas, Asia, and the Middle East) that have recently installed large volumes of concrete sleepers in their railway networks (Federal Railroad Administration, 2013). As a result, it is vital to researchers and practitioners to critically review and learn from previous experience and lessons around the world.

Non-linear resonance in strings under narrow band random excitation, part I: Planar response and stability

Non-linear planar response of a string to planar narrow band random excitation is investigated in this paper. A response equation for the mean square deflection σ2 is obtained under a single mode approximation by using the equivalent linearization technique. It is shown that the response is triple valued, as in the case of harmonic excitation, if the centre frequency of excitation Ω lies in a certain specified range. The triple valued response occurs only if the excitation bandwidth β is smaller than a critical value βcrit which is a monotonically increasing function of the intensity of excitation. An approximate method of investigating the almost sure asymptotic stability of the solution is presented and regions of instability in the Ω-σ2 plane have been charted. It is shown that planar response can become unstable either due to an unbounded growth of the in-plane component of motion or due to a spontaneous appearance of an out-of-plane component.

A fluctuation-based probe to athermal phase transitions

We focus on athermal phase transitions where in discrete and dissipative avalanches are observed in physical observables as the system jumps from one metastable state to another, when driven by an external field. Using higher order statistics of time dependent avalanches, or noise, in electrical resistivity during temperature-driven martensite transformation in thin nickel-titanium films, we demonstrate evidence suggesting the existence of a singular `global instability' or divergence of the correlation length as a function of temperature at the transition. These results not only establish a mapping of non-equilibrium first order phase transition and equilibrium critical phenomena, but perhaps also call for a re-evaluation of many existing experimental claims of self-organized criticality.

Analysis of drop formation at conical tips : 1. Theory

The phenomenon of drop formation at conical tips under near zero flow conditions has been investigated using a theoretical approach. The analysis permits the prediction of drop profile and drop volume, until the onset of instability. A semiempirical approach based on the similarity of drop shapes has been adopted to predict the detaching drop volumes at conical tips. The effects of base diameter of the cone, cone angle, interfacial tension, and the densities of the drop and the surrounding fluid on the maximum and detached drop volumes are predicted.

Note On The Stability Of Parallel Magnetic-Fields - Comment

It is shown that the conclusions arrived at regarding the instability of an incompressible fluid cylinder in the presence of the magnetic field and the streaming velocity in a recent communication easily follow from the study of propagation characteristics of Alfvén surface waves along cylindrical plasma columns made earlier.

A mechanism for the west-north-west movement of monsoon depressions

The monsoon depressions intensify over the Bay of Bengal, move in a west-north-west (WNW) direction and dissipate over the Indian continent. No convincing physical explanation for their observed movement has so far been arrived at, but here, I suggest why the maximum precipitation occurs in the western sector of the depression and propose a feedback mechanism for the WNW movement of the depressions. We assume that a heat source is created over the Bay of Bengal due to organization of cumulus convection by the initial instability. In a linear sense, heating at this latitude (20° N), produces an atmospheric response mainly in the form of a stationary Rossby–gravity wave to the west of the heat source. The low-level vorticity (hence the frictional convergence) and the vertical velocity associated with the steady-state response is such that the maximum moisture convergence (and precipitation) is expected to occur in the WNW sector at a later time. Thus, the heat source moves to the WNW sector at a later time and the feedback continues resulting in the WNW movement of the depressions.

Mathematical modelling of the impaction and spreading of spray droplets on leaves

This thesis concerns the development of mathematical models to describe the interactions that occur between spray droplets and leaves. Models are presented that not only provide a contribution to mathematical knowledge in the field of fluid dynamics, but are also of utility within the agrichemical industry. The thesis is presented in two parts. First, thin film models are implemented with efficient numerical schemes in order to simulate droplets on virtual leaf surfaces. Then the interception event is considered, whereby energy balance techniques are employed to instantaneously predict whether an impacting droplet will bounce, splash, or adhere to a leaf.

A simulation study of the mixing, atomic flow and velocity profiles of crystalline materials during sliding

Self-contained Non-Equilibrium Molecular Dynamics (NEMD) simulations using Lennard-Jones potentials were performed to identify the origin and mechanisms of atomic scale interfacial behavior between sliding metals. The mixing sequence and velocity profiles were compared via MD simulations for three cases, viz.: sell-mated, similar and hard-softvcrystal pairs. The results showed shear instability, atomic scale mixing, and generation of eddies at the sliding interface. Vorticity at the interface suggests that atomic flow during sliding is similar to fluid flow under Kelvin-Helmholtz instability and this is supported by velocity profiles from the simulations. The initial step-function velocity profile spreads during sliding. However the velocity profile does not change much at later stages of the simulation and it eventually stops spreading. The steady state friction coefficient during simulation was monitored as a function of sliding velocity. Frictional behavior can be explained on the basis of plastic deformation and adiabatic effects. The mixing layer growth kinetics was also investigated.

Radish sprouts versus broccoli sprouts: a comparison of anti-cancer potential based on glucosinolate breakdown products.

Radish sprouts and broccoli sprouts have been implicated in having a potential chemoprotective effect against certain types of cancer. Each contains a glucosinolate that can be broken down to an isothiocyanate capable of inducing chemoprotective factors known as phase 2 enzymes. In the case of broccoli, the glucosinolate, glucoraphanin, is converted to an isothiocyanate, sulforaphane, while in radish a similar glucosinolate, glucoraphenin, is broken down to form the isothiocyanate, sulforaphene. When sprouts are consumed fresh (uncooked), however, the principal degradation product of broccoli is not the isothiocyanate sulforaphane, but a nitrile, a compound with little anti-cancer potential. By contrast, radish sprouts produce largely the anti-cancer isothiocyanate, sulforaphene. The reason for this difference is likely to be due to the presence in broccoli (and absence in radish) of the enzyme cofactor, epithiospecifier protein (ESP). In vitro induction of the phase 2 enzyme, quinone reductase (QR), was significantly greater for radish sprouts than broccoli sprouts when extracts were self-hydrolysed. By contrast, boiled radish sprout extracts (deactivating ESP) to which myrosinase was subsequently added, induced similar QR activity to broccoli sprouts. The implication is that radish sprouts have potentially greater chemoprotective action against carcinogens than broccoli sprouts when hydrolysed under conditions similar to that during human consumption.

Power system stability implications from electromechanical wave propagation

Electromechanical wave propagation characterizes the first-swing dynamic response in a spatially delayed manner. This paper investigates the characteristics of this phenomenon in two-dimensional and one-dimensional power systems. In 2-D systems, the wave front expands as a ripple in a pond. In 1-D systems, the wave front is more concentrated, retains most of its magnitude, and travels like a pulse on a string. This large wave front is more impactful upon any weak link and easily causes transient instability in 1-D systems. The initial disturbance injects both high and low frequency components, but the lumped nature of realistic systems only permits the lower frequency components to propagate through. The kinetic energy split at a junction is equal to the generator inertia ratio in each branch in an idealized continuum system. This prediction is approximately valid in a realistic power system. These insights can enhance understanding and control of the traveling waves.

Genetic and Epigenetic Characterization of Colorectal and Endometrial Cancer

Colorectal cancer is one of the three most common cancers today, for both men and women. Approximately 90% of the cases are sporadic while the remaining 10% is hereditary. Among this 10% is hereditary nonpolyposis colorectal cancer (HNPCC), an autosomal dominant disease, accounting for up to 13% of these cases. HNPCC is associated with germline mutations in four mismatch repair (MMR) genes, MLH1, MSH2, MSH6, and PMS2, and is characterized by a familial accumulation of endometrial, gastric, urological, and ovarian tumors, in addition to colorectal cancer. An important etiological characteristic of HNPCC is the presence of microsatellite instability (MSI), caused by mutations of the MMR genes. Approximately 15% of sporadic cases share the MSI+ trait. Colon cancer is believed to be a consequence of an accumulation of mutations in tumor suppressor genes and oncogenes, eventually resulting in tumor development. This phenomena is accelerated in HNPCC due the presence of an inherited mutation in the MMR genes, accounting for one of the two hits proposed to be needed by Knudson (1971) in order for the manifestation of the MSI phenotype. MMR alterations alone, however, do not occur in the majority of sporadic colon cancers, prompting searches for other mechanisms. One such mechanism found to play a role in colon cancer development was DNA methylation, which is known to play a role in MLH1 inactivation. Our objective was clarification of mechanisms associated with tumor development in both HNPCC and sporadic colorectal cancer in relation to tumorigenic mechanisms. Of particular interest were underlying mechanisms of MSI in sporadic colorectal cancers, with attention to DNA methylation changes and their correlation to MSI. Of additional interest were the genetic and epigenetic events leading to the HNPCC tumor spectrum, chiefly colon and endometrial cancers, in regards to what extent the somatic changes in target tissue explained this phenomenon. We made a number of important findings pertaining to these questions. First, MSI tumor development differs epigenetically from stable tumor development, possibly underlying developmental pathway differences. Additionally, while epigenetic modification, principally DNA methylation, is a major mechanism in sporadic MSI colorectal cancer MLH1 inactivation it does not play a significant role in HNPCC tumors with germline MLH1 mutations. This is possibly an explanation for tumorigenic pathways and clinicopathological characteristic differences between sporadic and hereditary MSI colorectal cancers. Finally, despite indistinguishable genetic predisposition for endometrial and colorectal cancers, instability profiles highlighting organ-specific differences, may be important HNPCC tumor spectrum determinants.

Analysis of EXCOBULLE two-phase expansion tests

analysis of a complex physical problem and the close agreement they achieved with observations. However, the following points need to be clarified. First of all the authors assume that during the initial phases of expansion, the Tayior's instability sets in due to the acceleraacceleration of lighter fluid against the more dense cold water.