Pinched flow coupled shear-modulated inertial microfluidics for high-throughput rare blood cell separation

Blood is a highly complex bio-fluid with cellular components making up >40% of the total volume, thus making its analysis challenging and time-consuming. In this work, we introduce a high-throughput size-based separation method for processing diluted blood using inertial microfluidics. The technique takes advantage of the preferential cell focusing in high aspect-ratio microchannels coupled with pinched flow dynamics for isolating low abundance cells from blood. As an application of the developed technique, we demonstrate the isolation of cancer cells (circulating tumor cells (CTCs)) spiked in blood by exploiting the difference in size between CTCs and hematologic cells. The microchannel dimensions and processing parameters were optimized to enable high throughput and high resolution separation, comparable to existing CTC isolation technologies. Results from experiments conducted with MCF-7 cells spiked into whole blood indicate >80% cell recovery with an impressive 3.25 × 10(5) fold enrichment over red blood cells (RBCs) and 1.2 × 10(4) fold enrichment over peripheral blood leukocytes (PBL). In spite of a 20× sample dilution, the fast operating flow rate allows the processing of ～10(8) cells min(-1) through a single microfluidic device. The device design can be easily customized for isolating other rare cells from blood including peripheral blood leukocytes and fetal nucleated red blood cells by simply varying the 'pinching' width. The advantage of simple label-free separation, combined with the ability to retrieve viable cells post enrichment and minimal sample pre-processing presents numerous applications for use in clinical diagnosis and conducting fundamental studies.     

Right orders and amalgamation for lattice-ordered groups

Let H _i be a sublattice subgroup of a lattice-ordered group G _i (i = 1, 2). Suppose that H ₁ and H ₂ are isomorphic as lattice-ordered groups, say by φ. In general, there is no lattice-ordered group in which G ₁ and G ₂ can be embedded (as lattice-ordered groups) so that the embeddings agree on the images of H ₁ and H ₁ ^φ . In this article we prove that the group free product of G ₁ and G ₂ amalgamating H ₁ and H ₁ ^φ is right orderable and so embeddable (as a group) in a lattice-orderable group. To obtain this, we use our necessary and sufficient conditions for the free product of right-ordered groups with amalgamated subgroup to be right orderable [BLUDOV, V. V.—GLASS, A. M. W.: Word problems, embeddings, and free products of right-ordered groups with amalgamated subgroup, Proc. London Math. Soc. (3) 99 (2009), 585–608]. We also provide new limiting examples to show that amalgamation can fail in the category of lattice-ordered groups even when the amalgamating sublattice subgroups are convex and normal (?-ideals) and solve of Problem 1.42 from [KOPYTOV, V. M.—MEDVEDEV, N. YA.: Ordered groups. In: Selected Problems in Algebra. Collection of Works Dedicated to the Memory of N. Ya. Medvedev, Altaii State University, Barnaul, 2007, pp. 15–112 (Russian)].     

The scalar Nevanlinna-Pick interpolation problem with boundary conditions

We show that if the Nevanlinna-Pick interpolation problem is solvable by a function mapping into a compact subset of the unit disc, then the problem remains solvable with the addition of any number of boundary interpolation conditions, provided the boundary interpolation values have modulus less than unity. We give new, inductive proofs of the Nevanlinna-Pick interpolation problem with any finite number of interpolation points in the interior and on the boundary of the domain of interpolation (the right half plane or unit disc), with function values and any finite number of derivatives specified. Our solutions are analytic on the closure of the domain of interpolation. Our proofs only require a minimum of matrix theory and operator theory. We also give new, straightforward algorithms for obtaining minimal H_∞ norm solutions. Finally, some numerical examples are given.     

Triazoles and tetrazoles: Prime ligands to generate remarkable coordination materials

The current great interest in preparing functional metal-organic materials is inevitably associated with tremendous research efforts dedicated to the design and synthesis of new families of sophisticated multi-nucleating ligands. In this context, the N-donor triazole and tetrazole rings represent two categories of ligands that are increasingly used, most likely as the result of the recent dramatic development of “click chemistry” and Zeolitic Imidazolate Frameworks (ZIFs). Thus, azole-based complexes have found numerous applications in coordination chemistry.In the present review, we focus on the utilization of 1,2,3-triazole, 1,2,4-triazole and tetrazole ligands to create coordination polymers, metal complexes and spin-crossover compounds, reported to the end of 2009. In the first instance, we present a compendium of all the relevant ligands that have been employed to generate coordination polymers and Metal-Organic Frameworks (MOFs). Due to the huge amount of reported MOFs and coordination polymers bearing these azole rings, three representative examples for each category (therefore nine in total) are described in detail. The second section is devoted to the use of the bridging abilities of these azole ligands to prepare metal complexes (containing at least two metal centers). Given the large number and the great structural diversity of the polynuclear compounds found in the literature, these have been grouped according to their nuclearity. Finally, in the last section, the triazole- and tetrazole-containing coordination compounds exhibiting spin-crossover properties are presented.     

Local virial and tensor theorems

We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem.     

Size-selective molecular transport through silica colloidal nanopores

Diffusion rate of dye-labelled PAMAM dendrimers through free-standing silica colloidal crystals was studied as a function of the dendrimer generation and nanopore size to determine the transport selectivity.     

Adaptive panel representation for oblique collision of two vortex rings

In this article, we use a hierarchical panel method for representing vortex sheet surface motion in 3D flow to investigate the oblique collision of two vortex rings. The particles representing the sheet are advected by a regularized Biot-Savart integral with smoothed Rosenhead-Moore kernel. The particle velocities are evaluated by an adaptive treecode algorithm based on Taylor expansions in Cartesian coordinates. The method allowed us to consider late stages of a vortex rings collision, producing a funnel region. Vorticity iso-surfaces evolution is also investigated.     

The Assignment of the 1600 cm−1 Mystery Band of Carbons

Abstract

The assignment of a band near 1600 cm^?1 in IR spectra of carbons has been controversial for four decades. However, many different carbons have been studied: effectively, a single band assignment was sought for an absorption appearing with three different classes of carbon. As these differ in over-all structure, not one but three explanations are needed. These are discussed. However, undue emphasis has been placed on a single absorption; attention should also be paid to other absorptions accompanying the 1600 cm^?1 band.     

Thermal fluctuations in pinned elastic systems: field theory of rare events and droplets

Using the functional renormalization group (FRG) we study the thermal fluctuations of elastic objects (displacement field u, internal dimension d) pinned by a random potential at low temperature T, as prototypes for glasses. A challenge is how the field theory can describe both typical (minimum energy T = 0) configurations, as well as thermal averages which, at any non-zero T as in the phenomenological droplet picture, are dominated by rare degeneracies between low lying minima. We show that this occurs through an essentially non-perturbative thermal boundary layer (TBL) in the (running) effective action Γ [u] at T > 0 for which we find a consistent scaling ansatz to all orders. The TBL describes how temperature smoothes the singularities of the T = 0 theory and contains the physics of rare thermal excitations (droplets). The formal structure of this TBL, which involves all cumulants of the coarse grained disorder, is first explored around d = 4 using a one-loop Wilson RG. Next, a more systematic exact RG (ERG) method is employed, and first tested on d = 0 models where it can be pushed quite far. There we obtain precise relations between TBL quantities and droplet probabilities (those are constrained by exact identities which are then checked against recent exact results). Our analysis is then extended to higher d, where we illustrate how the TBL scaling remains consistent to all orders in the ERG and how droplet picture results can be retrieved. Since correlations are determined deep in the TBL (by derivatives of Γ [u] at u = 0), it remains to be understood (in any d) how they can be retrieved (as u = 0⁺ limits in the non-analytic T = 0 effective action), i.e., how to recover a T = 0 critical theory. This formidable “matching problem” is solved in detail for d = 0, N = 1 by studying the (partial) TBL structure of higher cumulants when points are brought together. We thereby obtain the β-function at T = 0, all ambiguities removed, displayed here up to four loops. A discussion of the d > 4 case and an exact solution at large d are also provided.