Numerical simulation on fluid mixing by effects of geometry in staggered oriented ridges micromixers

Owing to the enhancement of surface effects at the micro-scale, patterned grooves on a microchannel remain a powerful method to induce chaotic advection within a pressure driven system. Since the staggered oriented ridges static micromixers are presented, there are few results in the literature about the geometric effects of such micromixer on the fluid mixing. This paper presents simulations within the micromixer and identifies geometric factors that affect the generation of advection flow over staggered oriented ridges. By varying the inflow directions, the ridge height ratio and the ridge asymmetry index, the modes of fluid motion and the pressure drops are studied respectively. Furthermore, through a set of numerical simulations, the relation expression between a mixing index to evaluate the mixing performance and the mentioned geometric parameters is obtained and the value of this mixing index could be calculated continuously. It indicates that the mixing performance of every staggered oriented ridges static micromixer could be estimated.     

Analysis and measurements of mixing in pressure-driven microchannel flow

The mixing phenomena for two fluid streams in pressure-driven rectangular microchannels are analyzed and directly compared with the measurements of mixing intensity for a wide range of aspect ratio (width/depth = 1–20). In the analysis, the three-dimensional transport equation for species mixing was solved using the spectral method in a dimensionless fashion covering a large regime of the normalized downstream distance. The analysis reveals the details of non-uniform mixing process, which originates from the top and bottom walls of the channel and stretches out toward the center of the channel, and its transition to uniformity. Employing different length scales for the non-uniform and uniform mixing regimes, the growth of mixing intensity can be expressed in a simple relationship for various aspect ratios in the large range. The mixing experiments were carried out on silicon- and poly(methyl methacrylate) (PMMA)-based T-type micromixers utilizing fluids of pH indicator (in silicon channel) and fluorescent dye (in PMMA channel) to evaluate the mixing intensity based on flow visualization images. Using conventional microscopes, the experiments demonstrate the mixing intensity as a power law of the stream velocity for all the microfluidic channels tested. The variations of measured mixing intensity with the normalized downstream distance are found in favorable agreement with the numerical simulations. The comparison between the experiments and simulations tells the capabilities and limitations on the use of conventional microscopes to measure the mixing performance.     

Theoretical and experimental characterization of a low-Reynolds number split-and-recombine mixer

A mixing device based on the split-and-recombine (SAR) principle is characterized using both theoretical and experimental methods. The theoretical model relies on solving a 1D diffusion equation in a frame of reference comoving with the flow, thus avoiding the usual numerical artefacts related to the prediction of high-Péclet number mixing. It accounts both for the hydrodynamic focusing of the flow inside the mixing channel and the nontrivial flow topology. The experimental technique used for quantifying the degree of mixing utilizes two initially transparent salt solutions that form a colored compound in a fast chemical reaction. The degree of mixing is derived from the average color saturation found at specific positions along the mixing channel. The data obtained from the theoretical model are in reasonable agreement with the experiments and underline the excellent performance of the SAR mixer, with a mixing length growing only logarithmically as a function of Péclet number.     

Numerical simulation of the MHD equations by a kinetic-type method

We introduce a flux-splitting formula for the approximation of the ideal MHD equations in conservative form. The Faraday equation is considered as the average of an abstract kinetic equation, giving a flux-splitting formula. For the other part of the equations, we generalize formally the classical half-Maxwellian flux-splitting of the Euler equations. Numerical results on MHD shock tube problems are displayed.     

A polynomial characterization of hypergraphs using the Ihara zeta function

The aim of this paper is to seek a compact characterization of irregular unweighted hypergraphs for the purposes of clustering. To this end, we develop a polynomial characterization for hypergraphs based on the Ihara zeta function. We investigate the flexibility of the polynomial coefficients for learning relational structures with different relational orders. Furthermore, we develop an efficient method for computing the coefficient set. Our representation for hypergraphs takes into account not only the vertex connections but also the hyperedge cardinalities, and thus can distinguish different relational orders, which is prone to ambiguity if the hypergraph Laplacian is used. In our experimental evaluation, we demonstrate the effectiveness of the proposed characterization for clustering irregular unweighted hypergraphs and its advantages over the spectral characterization of the hypergraph Laplacian.     

Spectral characterization and ASTER-based lithological mapping of an ophiolite complex: A case study from Neyriz ophiolite, SW Iran

The Neyriz ophiolite occurs along the Zagros suture zone in SW Iran, and is part of a 3000-km obduction belt thrusting over the edge of the Arabian continent during the late Cretaceous. This complex typically consists of altered dunites and peridotites, layered and massive gabbros, sheeted dykes and pillow lavas, and a thick sequence of radiolarites. Reflectance and emittance spectra of Neyriz ophiolite rock samples were measured in the laboratory and their spectra were used as endmembers in a spectral feature fitting (SFF) algorithm. Laboratory spectral reflectance measurements of field samples showed that in the visible through shortwave infrared (VNIR-SWIR) wavelength region the ultramafic and gabbroic rocks are characterized by ferrous-iron and Fe, MgOH spectral features, and the pillow lavas and radiolarites are characterized by spectral features of ferric-iron and AlOH. The laboratory spectral emittance spectra also revealed a wide wavelength range of SiO spectral features for the ophiolite rock units. After continuum removal of the spectra, the SFF classification method was applied to the VNIR + SWIR 9-band stack, and to the 11-band data set of SWIR and TIR data sets of the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) sensor, using field spectra as training sets for evaluating the potential of these data sets in discriminating ophiolite rock units. Output results were compared with the geological map of the area and field observations, and were assessed by the use of confusion matrices. The assessment showed, in terms of kappa coefficient, that the SFF classification method with continuum removal applied to the SWIR data achieved excellent results, which were distinctively better than those obtained using VNIR + SWIR data and TIR data alone.     

An interactive analysis of harmonic and diffusion equations on discrete 3D shapes

Recent results in geometry processing have shown that shape segmentation, comparison, and analysis can be successfully addressed through the spectral properties of the Laplace–Beltrami operator, which is involved in the harmonic equation, the Laplacian eigenproblem, the heat diffusion equation, and the definition of spectral distances, such as the bi-harmonic, commute time, and diffusion distances. In this paper, we study the discretization and the main properties of the solutions to these equations on 3D surfaces and their applications to shape analysis. Among the main factors that influence their computation, as well as the corresponding distances, we focus our attention on the choice of different Laplacian matrices, initial boundary conditions, and input shapes. These degrees of freedom motivate our choice to address this study through the executable paper, which allows the user to perform a large set of experiments and select his/her own parameters. Finally, we represent these distances in a unified way and provide a simple procedure to generate new distances on 3D shapes.     

Spectral properties of infinite-dimensional closed-loop systems

We consider feedback systems obtained from infinite-dimensional well-posed linear systems by output feedback. Thus, our framework allows for unbounded control and observation operators. Our aim is to investigate the relationship between the open-loop system, the feedback operator K and the spectrum (in particular, the eigenvalues and eigenvectors) of the closed-loop generator A^K. We give a useful characterization of that part of the spectrum σ(A^K) which lies in the resolvent set of A, the open-loop generator, via the “characteristic equation” involving the open-loop transfer function. We show that certain points of σ(A) cannot be eigenvalues of A^K if the input and output are scalar (so that K is a number) and K≠0. We devote special attention to the case when the output feedback operator K is compact. It is relatively easy to prove that in this case, σ_e(A), the essential spectrum of A, is invariant, that is, it is equal to σ_e(A^K). A related but much harder problem is to determine the largest subset of σ(A) which remains invariant under compact output feedback. This set, which we call the immovable spectrum of A, strictly contains σ_e(A). We give an explicit characterization of the immovable spectrum and we investigate the consequences of our results for a certain class of well-posed systems obtained by interconnecting an infinite chain of identical systems.     

Spectral regularization methods for solving a sideways parabolic equation within the framework of regularization theory

We introduce three spectral regularization methods for solving a general sideways parabolic equation. For these three spectral regularization methods, we give some stability error estimates with optimal order under a-priori and a-posteriori regularization parameter choice rules. Numerical results show that these spectral methods are effective.     

On The Eigenvalues of the Spectral Second Order Differentiation Operator and Application to the Boundary Observability of the Wave Equation

The behaviour of the eigenvalues of the spectral second-order differentiation operator is studied and the results are used to investigate the boundary observability of the one dimensional wave equation approximated with a spectral Galerkin method. New explicit estimates of the discrete eigenvalues are given. These estimates improve the previous results on the subject especially for the portion of eigenvalues converging exponentially to those of the continuous problem. Although the boundary observability property of the discretized wave equation is not uniform with respect to the discretization parameter, we show that a uniform observability estimate can be obtained by filtering out the highest eigenmodes.      

Spectral characterization of periglacial surfaces and geomorphological units in the Arctic Lena Delta using field spectrometry and remote sensing

Important environmental parameters in arctic periglacial landscapes (i.e. permafrost temperature, active-layer depth, soil moisture, precipitation, vegetation cover) will very likely change in a warming climate. The thawing of permafrost, especially, might cause massive landscape changes due to thermokarst and an enhanced release of greenhouse gasses from the large amounts of carbon stored in frozen deposits, resulting in positive climate-warming feedback. For the identification, mapping, and quantification of such changes on various scales up to the entire circum-Arctic, remote sensing and spatial data analysis are essential tools. In this study an extensive field-work dataset including spectral surface properties, vegetation, soils, and geomorphology was acquired in the largest Arctic delta formed by a single river, the Siberian Lena River Delta. A portable field spectrometer (ASD FieldSpec Pro FR®) was used for spectral surveys of terrain surfaces, and optical satellite data (Landsat Enhanced Thematic Mapper (ETM+), CHRIS-Proba) were used for the characterization, manual mapping, and automatic classification of typical periglacial land-cover units in the Lena Delta. Qualitative data from soils, vegetation, soil moisture, and relief units were correlated with the field-spectral data and catalogued for a wide variety of surface types. The wide range of micro- and meso-scale variations of periglacial surface features in the delta results in distinctive spectral characteristics for different land-cover units. The three main delta terraces could also be spectrally separated and characterized. The present dataset provides a basis for further spectral data acquisitions in the Lena Delta and for comparisons with periglacial surfaces from other regions.