Emergence of steady and oscillatory localized structures in a phytoplankton-nutrient model

Co-limitation of marine phytoplankton growth by light and nutrient, both of which are essential for phytoplankton, leads to complex dynamic behavior and a wide array of coherent patterns. The building blocks of this array can be considered to be deep chlorophyll maxima, or DCMs, which are structures localized in a finite depth interior to the water column. From an ecological point of view, DCMs are evocative of a balance between the inflow of light from the water surface and of nutrients from the sediment. From a (linear) bifurcational point of view, they appear through a transcritical bifurcation in which the trivial, no-plankton steady state is destabilized. This article is devoted to the analytic investigation of the weakly nonlinear dynamics of these DCM patterns, and it has two overarching themes. The first of these concerns the fate of the destabilizing stationary DCM mode beyond the center manifold regime. Exploiting the natural singularly perturbed nature of the model, we derive an explicit reduced model of asymptotically high dimension which fully captures these dynamics. Our subsequent and fully detailed study of this model - which involves a subtle asymptotic analysis necessarily transgressing the boundaries of a local center manifold reduction - establishes that a stable DCM pattern indeed appears from a transcritical bifurcation. However, we also deduce that asymptotically close to the original destabilization, the DCM looses its stability in a secondary bifurcation of Hopf type. This is in agreement with indications from numerical simulations available in the literature. Employing the same methods, we also identify a much larger DCM pattern. The development of the method underpinning this work - which, we expect, shall prove useful for a larger class of models - forms the second theme of this article

A finite element based formulation for sensitivity studies of piezoelectric systems

Sensitivity Analysis is a branch of numerical analysis which aims to quantify the affects that variability in the parameters of a numerical model have on the model output. A finite element based sensitivity analysis formulation for piezoelectric media is developed here and implemented to simulate the operational and sensitivity characteristics of a piezoelectric based distributed mode actuator (DMA). The work acts as a starting point for robustness analysis in the DMA technology

Insight into Resonant Activation in Discrete Systems

The resonant activation phenomenon (RAP) in a discrete system is studied using the master equation formalism. We show that the RAP corresponds to a non-monotonic behavior of the frequency dependent first passage time probability density function (pdf). An analytical expression for the resonant frequency is introduced, which, together with numerical results, helps understand the RAP behavior in the space spanned by the transition rates for the case of reflecting and absorbing boundary conditions. The limited range of system parameters for which the RAP occurs is discussed. We show that a minimum and a maximum in the mean first passage time (MFPT) can be obtained when both boundaries are absorbing. Relationships to some biological systems are suggested.Comment: 5 pages, 5 figures, Phys. Rev. E., in pres

Numerical algebraic geometry for model selection and its application to the life sciences

Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to non-linearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data is available. Here, we consider polynomial models (e.g., mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometric structures relating models and data, and we demonstrate its utility on examples from cell signaling, synthetic biology, and epidemiology.Comment: References added, additional clarification

Probing a non-biaxial behavior of infinitely thin hard platelets

We give a criterion to test a non-biaxial behavior of infinitely thin hard platelets of $D_{2h}$ symmetry based upon the components of three order parameter tensors. We investigated the nematic behavior of monodisperse infinitely thin rectangular hard platelet systems by using the criterion. Starting with a square platelet system, and we compared it with rectangular platelet systems of various aspect ratios. For each system, we performed equilibration runs by using isobaric Monte Carlo simulations. Each system did not show a biaxial nematic behavior but a uniaxial nematic one, despite of the shape anisotropy of those platelets. The relationship between effective diameters by simulations and theoretical effective diameters of the above systems was also determined.Comment: Submitted to JPS

A review of human factors principles for the design and implementation of medication safety alerts in clinical information systems.

The objective of this review is to describe the implementation of human factors principles for the design of alerts in clinical information systems. First, we conduct a review of alarm systems to identify human factors principles that are employed in the design and implementation of alerts. Second, we review the medical informatics literature to provide examples of the implementation of human factors principles in current clinical information systems using alerts to provide medication decision support. Last, we suggest actionable recommendations for delivering effective clinical decision support using alerts. A review of studies from the medical informatics literature suggests that many basic human factors principles are not followed, possibly contributing to the lack of acceptance of alerts in clinical information systems. We evaluate the limitations of current alerting philosophies and provide recommendations for improving acceptance of alerts by incorporating human factors principles in their design