Growth and decay of localized disturbances on a surfactant-coated spreading film

If the surface of a quiescent thin liquid film is suddenly coated by a patch of surface active material like a surfactant monolayer, the film is set in motion and begins spreading. An insoluble surfactant will rapidly attempt to coat the entire surface of the film thereby minimizing the liquid's surface tension. The shear stress that develops during the spreading process produces a maximum in surface velocity in the region where the moving film meets the quiescent layer. This region is characterized by a shock front with large interfacial curvature and a corresponding local buildup of surfactant which creates a spike in the concentration gradient. In this paper, we investigate the sensitivity of this region to infinitesimal disturbances. Accordingly, we introduce a measure of disturbance amplification and transient growth analogous to a kinetic energy that couples variations in film thickness to the surfactant concentration. These variables undergo significant amplification during the brief period in which they are convected past the downstream tip of the monolayer, where the variation in concentration gradient and surface curvature are largest. Once they migrate past this sensitive area, the perturbations weaken considerably and the system approaches a stable configuration. It appears that the localized disturbances of the type we consider here, cannot sustain asymptotic instability. Nonetheless, our study of the dynamics leading to the large transient growth clearly illustrates how the coupling of Marangoni and capillary forces work in unison to stabilize the spreading process against localized perturbations

INLA or MCMC? A Tutorial and Comparative Evaluation for Spatial Prediction in log-Gaussian Cox Processes

We investigate two options for performing Bayesian inference on spatial log-Gaussian Cox processes assuming a spatially continuous latent field: Markov chain Monte Carlo (MCMC) and the integrated nested Laplace approximation (INLA). We first describe the device of approximating a spatially continuous Gaussian field by a Gaussian Markov random field on a discrete lattice, and present a simulation study showing that, with careful choice of parameter values, small neighbourhood sizes can give excellent approximations. We then introduce the spatial log-Gaussian Cox process and describe MCMC and INLA methods for spatial prediction within this model class. We report the results of a simulation study in which we compare MALA and the technique of approximating the continuous latent field by a discrete one, followed by approximate Bayesian inference via INLA over a selection of 18 simulated scenarios. The results question the notion that the latter technique is both significantly faster and more robust than MCMC in this setting; 100,000 iterations of the MALA algorithm running in 20 minutes on a desktop PC delivered greater predictive accuracy than the default \verb=INLA= strategy, which ran in 4 minutes and gave comparative performance to the full Laplace approximation which ran in 39 minutes.Comment: This replaces the previous version of the report. The new version includes results from an additional simulation study, and corrects an error in the implementation of the INLA-based method

The effects of temperature on hatching and survival of northern rock sole larvae (Lepidopsetta polyxystra)

Northern rock sole (Lepidopsetta polyxystra) is a commercially important flatfish in Alaska and was recently classified as a distinct species from southern rock sole (L. bilineata). Taxonomic and vital rate data for northern rock sole are still not fully described, notably at early egg and larval stages. In this study, we provide new taxonomic descriptions of late-stage eggs and newly hatched larvae, as well as temperature-response models of hatching (timing, duration, success), and larval size-at-hatch and posthatch survival at four temperatures (2°, 5°, 9°, and 12°C). Time-to-first-hatch, hatch cycle duration, and overall hatching success showed a negative relationship with temperature. Early hatching larvae within each temperature treatment were smaller and had larger yolk sacs, but larvae incubated at higher temperatures (9° and 12°C) had the largest yolk reserves overall. Despite having smaller yolks, size-at-hatch and the maximum size achieved during the hatching cycle was highest for larvae reared at cold temperatures (2° and 5°C), indicating that endogenous reserves are more efficiently used for growth at these temperatures. In addition, larvae reared at high temperatures died more rapidly in the absence of food despite having more yolk reserves than cold-incubated larvae. Overall, northern rock sole eggs and larvae display early life history traits consistent with coldwater adaptation for winter spawning in the North Pacific

Thinning and disturbance growth in liquid films mobilized by continuous surfactant delivery

A generalized linear stability analysis is applied to the case of a thin liquid film propelled to spread by a continuous supply of surfactant. The time-dependent base states for the film thickness and surfactant concentration give rise to a nonautonomous system describing disturbance propagation. As a first approximation, the nonautonomous operator is treated as time independent, thereby reducing the system of equations to a standard eigenvalue problem. For the range of parameters investigated, this modal approximation reveals a band of unstable modes corresponding to the growth of transverse, sinusoidal corrugations. A transient growth analysis of the fully time-dependent system, which requires the solution of an initial value problem, also signals the possibility of large disturbance growth. In both cases, significant amplification of infinitesimal disturbances can be traced to the region of the film most rapidly thinned by Marangoni stresses, which is characterized by large interfacial curvature and a sharp variation in shear stress. In contrast to previous models implementing a finite surfactant source that predict asymptotic stability, large transient growth and asymptotic instability are possible for the case of sustained surfactant release

Parity-expanded variational analysis for non-zero momentum

In recent years, the use of variational analysis techniques in lattice QCD has been demonstrated to be successful in the investigation of the rest-mass spectrum of many hadrons. However, due to parity-mixing, more care must be taken for investigations of boosted states to ensure that the projected correlation functions provided by the variational analysis correspond to the same states at zero momentum. In this paper we present the Parity-Expanded Variational Analysis (PEVA) technique, a novel method for ensuring the successful and consistent isolation of boosted baryons through a parity expansion of the operator basis used to construct the correlation matrix.Comment: 9 pages, 3 figures, 1 tabl

Probing the proton and its excitations in full QCD

We present a first look at the application of variational techniques for the extraction of the electromagnetic properties of an excited nucleon system. In particular, we include preliminary results for charge radii and magnetic moments of the proton, its first even-parity excitation and the $\Delta^{+}$.Comment: 7 pages, 5 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Transition of ρ→πγ\rho \rightarrow \pi \gamma in Lattice QCD

With the ongoing experimental interest in exploring the excited hadron spectrum, evaluations of the matrix elements describing the formation and decay of such states via radiative processes provide us with an important connection between theory and experiment. In particular, determinations obtained via the lattice allow for a direct comparison of QCD-expectation with experimental observation. Here we present the first light quark determination of the $\rho \rightarrow \pi \gamma$ transition form factor from lattice QCD using dynamical quarks. Using the PACS-CS 2+1 flavour QCD ensembles we are able to obtain results across a range of masses, to the near physical value of $m_\pi = 157$ MeV. An important aspect of our approach is the use of variational methods to isolate the desired QCD eigenstate. For low-lying states, such techniques facilitate the removal of excited state contributions. In principle the method enables one to consider arbitrary eigenstates. We find our results are in accord with the non-relativistic quark model for heavy masses. In moving towards the light-quark regime we observe an interesting quark mass dependence, contrary to the quark model expectation. Comparison of our light-quark result with experimental determinations highlights a significant discrepancy suggesting that disconnected sea-quark loop contributions may play a significant role in fully describing this process.Comment: 9 pages, 5 figures and 1 tabl