A Finite Element Approach to Modelling Fractal Ultrasonic Transducers

Piezoelectric ultrasonic transducers usually employ composite structures to improve their transmission and reception sensitivities. The geometry of the composite is regular with one dominant length scale and, since these are resonant devices, this dictates the central operating frequency of the device. In order to construct a wide bandwith device it would seem natural therefore to utilize resonators that span a range of length scales. In this article we derive a mathematical model to predict the dynamics of a fractal ultrasound transducer; the fractal in this case being the Sierpinski gasket. Expressions for the electrical and mechanical fields that are contained within this structure are expressed in terms of a finite element basis. The propagation of an ultrasonic wave in this transducer is then analyzed and used to derive expressions for the non-dimensionalised electrical impedance and the transmission and reception sensitivities as a function of the driving frequency. Comparing these key performance measures to an equivalent standard (Euclidean) design shows some benefits of these fractal designs

Equation of State of H2O Ice Using Melt-Recrystallization

The recent surge in exoplanet discoveries due to advancements in astrophysical technology and analysis has brought the reliability of early equation of state measurements into question as they are the limiting factor when modeling composition of these planets. H2O content is among the most important for the search of habitable planets as well as in understanding planetary dynamics and atmosphere formation. Over the last three decades the equation of state of H2O has been investigated with various techniques but, has suffered from anisotropic strain and poor powder statistics resulting in a large discrepancy in equation of state fits. At pressures within the interior of many planets, the hydrogen bonds in H2O gradually weaken and are replaced by ionic bonds in ice-X. By melt-recrystallization of ice via laser heating as it is compressed, we observe the transition from ice-VII to ice X at a pressure of 30.9 ± 2.9 GPa, evidenced by an abrupt 2.5-fold increase in bulk modulus, implying an increase in bond strength. This transition is preceded by a modified ice structure of tetragonal symmetry, ice-VIIt

Self-similar Properties of the Proton Structure at low x

Self-similar properties of proton structure in the kinematic region of low Bjorken x are introduced and studied numerically. A description of the proton structure function F2(x,Q2) reflecting self-similarity is proposed with a few parameters which are fitted to recent HERA data. The specific parameterisation provides an excellent description of the data which cover a region of four momentum transfer squared, 0.045 < Q2 < 120 GeV2, and of Bjorken x, 6.2E-7 < x < 0.01.Comment: 9 pages (Latex), 5 figures (EPS). Submitted to Eur. Phys.

High-Pressure High-Temperature Exploration of Phase Boundaries Using Raman Spectroscopy

Metastability of states can provide interesting properties that may not be readily accessible in a material’s ground state. Many materials show high levels of polymorphism, indicating a rich energy landscape and a potential for metastable states. Melt crystallization techniques provide a potential route to these states. We use a resistively heated diamond anvil cell (DAC) with fine control of a system’s pressure and temperature to explore these systems. Raman spectroscopy is used to track subtle structural changes across phase boundaries. Organic systems, such as glycine and aspirin, were our initial interest due to their high polymorphism and reported low melting temperatures; however, complications with these systems ultimately showed that they are not ideal candidates for this technique. Metallic systems with allowed Raman modes are better samples for this method. We successfully map the phase stability of β-tin under high pressure and temperature conditions using Raman spectroscopy