Internet Traffic Characterization
Internet traffic resulting from world-wide-web access is increasing at exponential rates and resulting in congested networks. At the same time, Internet voice and video applications are being seen as a cost-effective means of communication for both residential and corporate users. The end- to-end delay, delay variation and packet losses are traffic impairments that influence the audio and visual quality of packet voice and video applications. The characterization of Internet traffic and traffic impairments is therefore an important problem for the testing and implementation of protocols that support real-time applications. This research is focused on developing probabilistic models that can predict the delay and loss experienced by packet streams arising from real-time applications. These models are based on the analysis of measurements of delay and packet loss experienced by probe packets sent out at periodic intervals over the Internet. These measurements provide the seasonal time-of-day patterns of delay and delay variation. The figure depicts the time-of-day variation of the average round-trip delay experienced by a fifteen-minute constant bit rate packet stream when traversing a sequence of fourteen hops between the source and destination on the Internet. The maximum delay typically occur during peak occurs of 10-12 am and 2-5 PM. Predictive models of such patterns comprising of a deterministic cyclic behavior superimposed by stochastic disturbances are being investigated
Chaotic Motion in Oscillatory Flows
Over the last 150 years, the problem of oscillatory motion of fluids has been examined by numerous investigators. However, only recently have some of the causes for instability and chaotic motion in such flows been uncovered. Chaotic oscillations in wall-bounded oscillatory flows have been linked to the nonlinear growth of vortical disturbances introduced into the viscous boundary layer. The temporal evolution of these disturbances gives rise to the basic features evident in the resulting chaotic fluid motion. Disturbances are generated by the environment and consequently are comprised of numerous modes having a varied spatial wave number and amplitude. Once the fluid motion becomes unstable, according to linear theory, the least linearly stable mode will prevail and chaotic oscillation will ensue at a threshold value of the controlling parameter. Nonlinear amplitude growth can yield alternative solutions, which display chaotic oscillations at lower threshold values. To determine the least stable disturbance, the sensitivity of the fluid motion to the wave number composition and amplitude of an imposed disturbance must be understood. The figure depicts the state space trajectory of the kinetic energy of a chaotic three-dimensional disturbance in an oscillatory boundary layer. The orbits demonstrate an exponential sensitivity to initial conditions. The feature indicates the presence of chaotic oscillations.
Therapeutic Applications of Ultrasound
Shear-Wave Elastography (SWE) imaging is an emerging field of medical imaging for noninvasive evaluation of tissue stiffness. The noninvasive modality is based on the excitation of shear waves in a tissue using acoustic radiation force (‘push’) beams. SWE allows for a reconstructed shear wave speed map. Higher shear wave speeds correlate to higher tissue stiffness. It is known, that tissue stiffness highly correlates with malignancy. In the case of thyroid cancer screening, B-mode ultrasound (US) is the clinical gold standard. Currently, 90% of positive findings in US thyroid cancer screening are negative for cancer when biopsied. In breast cancer screening, 80% of breast tumors positive in mammograms are negative for cancer. The addition of SWE has demonstrated the ability to differentiate benign and malignant tissues, increasing the sensitivity and specificity of the conventional clinical imaging techniques. Therefore, SWE has the potential of reducing the number of biopsies. The Ultrasound Imaging Laboratory at the Mayo Clinic (Rochester, MN) has developed an SWE technique called comb-push ultrasound elastography (CUSE), which uses multiple laterally spaced push beams for shear wave generation. The top figure demonstrates the screening of a thyroid nodule with US and CUSE in concert, the shear wave speed map is overlaid onto the US image. The region of interest (thyroid nodule) has a high shear wave speed, therefore is highly stiff and possibly cancerous. The positive cancer finding was confirmed with biopsy.
