Finding the optimal design of a passive microfluidic mixer.

The ability to thoroughly mix two fluids is a fundamental need in microfluidics. While a variety of different microfluidic mixers have been designed by researchers, it remains unknown which (if any) of these mixers are optimal (that is, which designs provide the most thorough mixing with the smallest possible fluidic resistance across the mixer). In this work, we automatically designed and rationally optimized a microfluidic mixer. We accomplished this by first generating a library of thousands of different randomly designed mixers, then using the non-dominated sorting genetic algorithm II (NSGA-II) to optimize the random chips in order to achieve Pareto efficiency. Pareto efficiency is a state of allocation of resources (e.g. driving force) from which it is impossible to reallocate so as to make any one individual criterion better off (e.g. pressure drop) without making at least one individual criterion (e.g. mixing performance) worse off. After 200 generations of evolution, Pareto efficiency was achieved and the Pareto-optimal front was found. We examined designs at the Pareto-optimal front and found several design criteria that enhance the mixing performance of a mixer while minimizing its fluidic resistance; these observations provide new criteria on how to design optimal microfluidic mixers. Additionally, we compared the designs from NSGA-II with some popular microfluidic mixer designs from the literature and found that designs from NSGA-II have lower fluidic resistance with similar mixing performance. As a proof of concept, we fabricated three mixer designs from 200 generations of evolution and one conventional popular mixer design and tested the performance of these four mixers. Using this approach, an optimal design of a passive microfluidic mixer is found and the criteria of designing a passive microfluidic mixer are established

Gradient-based estimation of Manning's friction coefficient from noisy data

We study the numerical recovery of Manning's roughness coefficient for the diffusive wave approximation of the shallow water equation. We describe a conjugate gradient method for the numerical inversion. Numerical results for one-dimensional model are presented to illustrate the feasibility of the approach. Also we provide a proof of the differentiability of the weak form with respect to the coefficient as well as the continuity and boundedness of the linearized operator under reasonable assumptions using the maximal parabolic regularity theory.Comment: 19 pages, 3 figure

The Importance of Ambient Temperature to Growth and the Induction of Flowering

Plant development is exquisitely sensitive to the environment. Light quantity, quality, and duration (photoperiod) have profound effects on vegetative morphology and flowering time. Recent studies have demonstrated that ambient temperature is a similarly potent stimulus influencing morphology and flowering. In Arabidopsis, ambient temperatures that are high, but not so high as to induce a heat stress response, confer morphological changes that resemble the shade avoidance syndrome. Similarly, these high but not stressful temperatures can accelerate flowering under short day conditions as effectively as exposure to long days. Photoperiodic flowering entails a series of external coincidences, in which environmental cycles of light and dark must coincide with an internal cycle in gene expression established by the endogenous circadian clock. It is evident that a similar model of external coincidence applies to the effects of elevated ambient temperature on both vegetative morphology and the vegetative to reproductive transition. Further study is imperative, because global warming is predicted to have major effects on the performance and distribution of wild species and strong adverse effects on crop yields. It is critical to understand temperature perception and response at a mechanistic level and to integrate this knowledge with our understanding of other environmental responses, including biotic and abiotic stresses, in order to improve crop production sufficiently to sustainably feed an expanding world population

On the convergence of chemical reaction optimization for combinatorial optimization

A novel general-purpose optimization method, chemical reaction optimization (CRO), is a population-based metaheuristic inspired by the phenomenon of interactions between molecules in a chemical reaction process. CRO has demonstrated its competitive edge over existing methods in solving many real-world problems. However, all studies concerning CRO have been empirical in nature and no theoretical analysis has been conducted to study its convergence properties. In this paper, we present some convergence results for several generic versions of CRO, each of which adopts different combinations of elementary reactions. We investigate the limiting behavior of CRO. By modeling CRO as a finite absorbing Markov chain, we show that CRO converges to a global optimum solution with a probability arbitrarily close to one when time tends to infinity. Our results also show that the convergence of CRO is determined by both the elementary reactions and the total energy of the system. Moreover, we also study and discuss the finite time behavior of CRO. © 1997-2012 IEEE.published_or_final_versio