On Growth Rate of Wind Waves: Impact of Short-Scale Breaking Modulations

The wave generation model based on the rapid distortion concept significantly underestimates empirical values of the wave growth rate. As suggested before, inclusion of the aerodynamic roughness modulations effect on the amplitude of the slope-correlated surface pressure could potentially reconcile this model approach with observations. This study explores the role of short-scale breaking modulations to amplify the growth rate of modulating longer waves. As developed, airflow separations from modulated breaking waves result in strong modulations of the turbulent stress in the inner region of the modulating waves. In turn, this leads to amplifying the slope-correlated surface pressure anomalies. As evaluated, such a mechanism can be very efficient for enhancing the wind-wave growth rate by a factor of 2-3.

Ocean bottom pressure records from the Cascadia array and short surface gravity waves

The ocean bottom pressure records from eight stations of the Cascadia array are used to investigate the properties of short surface gravity waves with frequencies ranging from 0.2 to 5 Hz. It is found that the pressure spectrum at all sites is a well-defined function of the wind speed U10 and frequency f, with only a minor shift of a few dB from one site to another that can be attributed to variations in bottom properties. This observation can be combined with the theoretical prediction that the ocean bottom pressure spectrum is proportional to the surface gravity wave spectrum E(f) squared, times the overlap integral I(f) which is given by the directional wave spectrum at each frequency. This combination, using E(f) estimated from modeled spectra or parametric spectra, yields an overlap integral I(f) that is a function of the local wave age inline image. This function is maximum for f∕fPM = 8 and decreases by 10 dB for f∕fPM = 2 and f∕fPM = 30. This shape of I(f) can be interpreted as a maximum width of the directional wave spectrum at f∕fPM = 8, possibly equivalent to an isotropic directional spectrum, and a narrower directional distribution toward both the dominant low frequencies and the higher capillary-gravity wave frequencies.

A bidomain threshold model of propagating calcium waves

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travelling wave solutions to probe the dependence of Ca wave speed on physiologically important parameters such as the threshold for Ca release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca resequestration from the cytosol to the ER, and the total [Ca] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called "tango waves" and the dependence of Ca wave speed on the total [Ca]. The original publication is available at www.springerlink.com (Journal of Mathematical Biology)

Ocean waves across the Arctic: attenuation due to dissipation dominates over scattering for periods longer than 19 s

The poorly understood attenuation of surface waves in sea ice is generally attributed to the combination of scattering and dissipation. Scattering and dissipation have very different effects on the directional and temporal distribution of wave energy, making it possible to better understand their relative importance by analysis of swell directional spreading and arrival times. Here we compare results of a spectral wave model – using adjustable scattering and dissipation attenuation formulations – with wave measurements far inside the ice pack. In this case, scattering plays a negligible role in the attenuation of long swells. Specifically, scattering-dominated attenuation would produce directional wave spectra much broader than the ones recorded, and swell events arriving later and lasting much longer than observed. Details of the dissipation process remain uncertain. Average dissipation rates are consistent with creep effects but are 12 times those expected for a laminar boundary layer under a smooth solid ice plate.

Interaction of Acoustic Waves with a Laminar Line-Flame

A systematic study was conducted to elucidate the effects of acoustic perturbations on laminar diffusion line-flames and the conditions required to cause acoustically-driven extinction. Flames were produced from the fuels n-pentane, n-hexane, n-heptane, n-octane, and JP-8, using fuel-laden wicks. The wicks were housed inside of a burner whose geometry produced flames that approximated a two dimensional flame sheet. The acoustics utilized ranged in frequency between 30-50 Hz and acoustic pressures between 5-50 Pa. The unperturbed mass loss rate and flame height of the alkanes were studied, and they were found to scale in a linear manner consistent with Burke-Schumann. The mass loss rate of hexane-fueled flames experiencing acoustic perturbations was then studied. It was found that the strongest influence on the mass loss rate was the magnitude of oscillatory air movement experienced by the flame. Finally, acoustic perturbations were imposed on flames using all fuels to determine acoustic extinction criterion. Using the data collected, a model was developed which characterized the acoustic conditions required to cause flame extinction. The model was based on the ratio of an acoustic Nusselt Number to the Spalding B Number of the fuel, and it was found that at the minimum speaker power required to cause extinction this ratio was a constant. Furthermore, it was found that at conditions where the ratio was below this constant, a flame could still exist; at conditions where the ratio was greater than or equal to this constant, flame extinction always occurred.

Shaping surface acoustic waves for cardiac tissue engineering

The heart is a non-regenerating organ that gradually suffers a loss of cardiac cells and functionality. Given the scarcity of organ donors and complications in existing medical implantation solutions, it is desired to engineer a three-dimensional architecture to successfully control the cardiac cells in vitro and yield true myocardial structures similar to native heart. This thesis investigates the synthesis of a biocompatible gelatin methacrylate hydrogel to promote growth of cardiac cells using biotechnology methodology: surface acoustic waves, to create cell sheets. Firstly, the synthesis of a photo-crosslinkable gelatin methacrylate (GelMA) hydrogel was investigated with different degree of methacrylation concentration. The porous matrix of the hydrogel should be biocompatible, allow cell-cell interaction and promote cell adhesion for growth through the porous network of matrix. The rheological properties, such as polymer concentration, ultraviolet exposure time, viscosity, elasticity and swelling characteristics of the hydrogel were investigated. In tissue engineering hydrogels have been used for embedding cells to mimic native microenvironments while controlling the mechanical properties. Gelatin methacrylate hydrogels have the advantage of allowing such control of mechanical properties in addition to easy compatibility with Lab-on-a-chip methodologies. Secondly in this thesis, standing surface acoustic waves were used to control the degree of movement of cells in the hydrogel and produce three-dimensional engineered scaffolds to investigate in-vitro studies of cardiac muscle electrophysiology and cardiac tissue engineering therapies for myocardial infarction. The acoustic waves were characterized on a piezoelectric substrate, lithium niobate that was micro-fabricated with slanted-finger interdigitated transducers for to generate waves at multiple wavelengths. This characterization successfully created three-dimensional micro-patterning of cells in the constructs through means of one- and two-dimensional non-invasive forces. The micro-patterning was controlled by tuning different input frequencies that allowed manipulation of the cells spatially without any pre- treatment of cells, hydrogel or substrate. This resulted in a synchronous heartbeat being produced in the hydrogel construct. To complement these mechanical forces, work in dielectrophoresis was conducted centred on a method to pattern micro-particles. Although manipulation of particles were shown, difficulties were encountered concerning the close proximity of particles and hydrogel to the microfabricated electrode arrays, dependence on conductivity of hydrogel and difficult manoeuvrability of scaffold from the surface of electrodes precluded measurements on cardiac cells. In addition, COMSOL Multiphysics software was used to investigate the mechanical and electrical forces theoretically acting on the cells. Thirdly, in this thesis the cardiac electrophysiology was investigated using immunostaining techniques to visualize the growth of sarcomeres and gap junctions that promote cell-cell interaction and excitation-contraction of heart muscles. The physiological response of beating of co-cultured cardiomyocytes and cardiac fibroblasts was observed in a synchronous and simultaneous manner closely mimicking the native cardiac impulses. Further investigations were carried out by mechanically stimulating the cells in the three-dimensional hydrogel using standing surface acoustic waves and comparing with traditional two-dimensional flat surface coated with fibronectin. The electrophysiological responses of the cells under the effect of the mechanical stimulations yielded a higher magnitude of contractility, action potential and calcium transient.

Radiation from a D-dimensional collision of shock waves: two-dimensional reduction and Carter–Penrose diagram

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

A Numerical study of fluid flow in peristaltic pumps and polymeric elastic pipes

This thesis work deals with a mathematical description of flow in polymeric pipe and in a specific peristaltic pump. This study involves fluid-structure interaction analysis in presence of complex-turbulent flows treated in an arbitrary Lagrangian-Eulerian (ALE) framework. The flow simulations are performed in COMSOL 4.4, as 2D axial symmetric model, and ABAQUS 6.14.1, as 3D model with symmetric boundary conditions. In COMSOL, the fluid and structure problems are coupled by monolithic algorithm, while ABAQUS code links ABAQUS CFD and ABAQUS Standard solvers with single block-iterative partitioned algorithm. For the turbulent features of the flow, the fluid model in both codes is described by RNG k-ϵ. The structural model is described, on the basis of the pipe material, by Elastic models or Hyperelastic Neo-Hookean models with Rayleigh damping properties. In order to describe the pulsatile fluid flow after the pumping process, the available data are often defective for the fluid problem. Engineering measurements are normally able to provide average pressure or velocity at a cross-section. This problem has been analyzed by McDonald's and Womersley's work for average pressure at fixed cross section by Fourier analysis since '50, while nowadays sophisticated techniques including Finite Elements and Finite Volumes exist to study the flow. Finally, we set up peristaltic pipe simulations in ABAQUS code, by using the same model previously tested for the fl uid and the structure.