Status of Pacific mackerel spawning population, 1975

Three methods were used to determine the Pacific mackerel population. The tag and recovery method estimated the population at 620 short tons. The other two estimates were based on regression techniques of partyboat catches and these results yielded 2,921 tons and 1,385 tons, respectively. All three estimates were below the 10,000 tons prescribed for a fishery and thus no harvest could be allowed. (14pp.

Elastic Foundations as Heterogeneous Adventitial Boundary Condition for the Assessment of Aortic Wall and Peri-Aortic Stiffness from Dense-MRI Data Using Inverse FEM Approach

Background: The establishment of in vivo, patient-specific, and regionally resolved techniques to quantify aortic properties is key for improving risk assessment in clinical practice and scientific understanding of cardiovascular growth and remodeling. Many in vivo studies quantify vascular stiffness using Pulse Wave Velocity. This method provides an averaged measure of stiffness for the entire aorta, ignoring variations in wall stiffness and boundary conditions. Previous studies using Displacement Encoding with Stimulated Echoes Magnetic Resonance Imaging (DENSE-MRI) suggested that the infrarenal abdominal aorta (IAA) deforms heterogeneously throughout the cardiac cycle. Method: Herein, we hypothesize that the aortic wall strain heterogeneity is driven in healthy aortas by adventitial tethering to perivascular tissues that can be modeled with elastic foundation boundary conditions (EFBC) using a collection of linear-springs with a circumferential distribution of stiffness. Nine healthy-human IAAs were modeled using patient-specific imaging and displacement fields from SSFP and DENSE MRI, followed by assessment of aortic wall properties and heterogeneous EFBC parameters using inverse Finite Element Method (FEM). Results: In contrast to traction-free boundary condition, prescription of EFBC reduced the nodal displacement error by 60% and reproduced the DENSE-derived strain distribution. Estimated aortic stiffness was in agreement with previously reported experimental test data. The distribution of normalized EFBC stiffness was consistent among all patients and spatially correlated to standard peri-aortic anatomical features. Conclusion: Results suggest that EFBCs can be generalized for human adults with normal anatomy. This approach is computationally inexpensive, making it ideal for large-population clinical research and incorporation into computational cardiovascular fluid-structure analyses.https://scholarscompass.vcu.edu/gradposters/1113/thumbnail.jp

Turing pattern outside of the Turing domain

There are two simple solutions to reaction-diffusion systems with limit-cycle reaction kinetics, producing oscillatory behaviour. The reaction parameter $\mu$ gives rise to a ‘space-invariant’ solution, and $\mu$ versus the ratio of the diffusion coefficients gives rise to a ‘time-invariant’ solution. We consider the case where both solution types may be possible. This leads to a refinement of the Turing model of pattern formation. We add convection to the system and investigate its effect. More complex solutions arise that appear to combine the two simple solutions. The convective system sheds light on the underlying behaviour of the diffusive system

Limit cycles in the presence of convection, a first order analysis

We consider a diffusion model with limit cycle reaction functions. In an unbounded domain, diffusion spreads pattern outwards from the source. Convection adds instability to the reaction-diffusion system. We see the result of the instability in a readiness to create pattern. In the case of strong convection, we consider that the first-order approximation may be valid for some aspects of the solution behaviour. We employ the method of Riemann invariants and rescaling to transform the reduced system into one invariant under parameter change. We carry out numerical experiments to test our analysis. We find that most aspects of the solution do not comply with this, but we find one significant characteristic which is approximately first order. We consider the correspondence of the Partial Differential Equation with the Ordinary Differential Equation along rays from the initiation point in the transformed system. This yields an understanding of the behaviour

An acceleration simulation method for power law priority traffic

A method for accelerated simulation for simulated self-similar processes is proposed. This technique simplifies the simulation model and improves the efficiency by using excess packets instead of packet-by-packet source traffic for a FIFO and non-FIFO buffer scheduler. In this research is focusing on developing an equivalent model of the conventional packet buffer that can produce an output analysis (which in this case will be the steady state probability) much faster. This acceleration simulation method is a further development of the Traffic Aggregation technique, which had previously been applied to FIFO buffers only and applies the Generalized Ballot Theorem to calculate the waiting time for the low priority traffic (combined with prior work on traffic aggregation). This hybrid method is shown to provide a significant reduction in the process time, while maintaining queuing behavior in the buffer that is highly accurate when compared to results from a conventional simulatio

A parabolic free boundary problem with Bernoulli type condition on the free boundary

Consider the parabolic free boundary problem $$\Delta u - \partial_t u = 0 \textrm{in} \{u>0\}, |\nabla u|=1 \textrm{on} \partial\{u>0\} .$$ For a realistic class of solutions, containing for example {\em all} limits of the singular perturbation problem $$\Delta u_\epsilon - \partial_t u_\epsilon = \beta_\epsilon(u_\epsilon) \textrm{as} \epsilon\to 0,$$ we prove that one-sided flatness of the free boundary implies regularity. In particular, we show that the topological free boundary $\partial\{u>0\}$ can be decomposed into an {\em open} regular set (relative to $\partial\{u>0\}$) which is locally a surface with H\"older-continuous space normal, and a closed singular set. Our result extends the main theorem in the paper by H.W. Alt-L.A. Caffarelli (1981) to more general solutions as well as the time-dependent case. Our proof uses methods developed in H.W. Alt-L.A. Caffarelli (1981), however we replace the core of that paper, which relies on non-positive mean curvature at singular points, by an argument based on scaling discrepancies, which promises to be applicable to more general free boundary or free discontinuity problems