Alternating Current Electrohydrodynamics Induced Nanoshearing and Fluid Micromixing for Specific Capture of Cancer Cells

We report a new tuneable alternating current (ac) electrohydrodynamics (ac‐EHD) force referred to as “nanoshearing” which involves fluid flow generated within a few nanometers of an electrode surface. This force can be externally tuned via manipulating the applied ac‐EHD field strength. The ability to manipulate ac‐EHD induced forces and concomitant fluid micromixing can enhance fluid transport within the capture domain of the channel (e.g., transport of analytes and hence increase target–sensor interactions). This also provides a new capability to preferentially select strongly bound analytes over nonspecifically bound cells and molecules. To demonstrate the utility and versatility of nanoshearing phenomenon to specifically capture cancer cells, we present proof‐of‐concept data in lysed blood using two microfluidic devices containing a long array of asymmetric planar electrode pairs. Under the optimal experimental conditions, we achieved high capture efficiency (e.g., approximately 90 %; % RSD=2, n=3) with a 10‐fold reduction in nonspecific adsorption of non‐target cells for the detection of whole cells expressing Human Epidermal Growth Factor Receptor 2 (HER2). We believe that our ac‐EHD devices and the use of tuneable nanoshearing phenomenon may find relevance in a wide variety of biological and medical applications.     

A New Look at the Ashtekar–Magnon Energy Condition

In 1975, Ashtekar and Magnon showed that anenergy condition selects a unique quantization procedurefor hypersurface orthogonal observers in general, curvedspacetimes. We generalize this result in two important ways, by eliminating the need toassume a particular form for the (quantum) Hamiltonian,and by considering the surprisingly nontrivial extensionto non-minimal coupling, for which the classical Hamiltonian differs from the classical energycalculated from the stress-energy tensor.     

Conserved quantities from piecewise Killing vectors

In the presence of symmetries, conserved quantities can be obtained by contracting the stress-energy tensor with a Killing vector. We generalize this result to piecewise Killing vectors by giving sufficient conditions for the construction of an associated conserved quantity. A typical example, namely, two stationary space-times joined together in such a way that the resulting space-time is not stationary, is treated in detail.     

Distributional Modes for Scalar Field Quantization

We propose a mode-sum formalism for the quantization of the scalar field based on distributional modes, which are naturally associated with a slight modification of the standard plane-wave modes. We show that this formalism leads to the standard Rindler temperature result, and that these modes can be canonically defined on any Cauchy surface.     

Note on Signature Change and Colombeau Theory

Recent work alludes to various 'controversies' associated with signature change in general relativity and claims to resolve them. As we have argued previously, these are in fact disagreements about the (often unstated) assumptions underlying various possible approaches. We demonstrate that the issue has not been resolved and the choice between approaches remains open.     

Particle production from signature change

We consider the (massless) scalar field on 2-dimensional manifolds whose metric changes signature and which admit a spacelike isometry. Choosing the wave equation so that there will be a conserved Klein-Gordon product implicitly determines the junction conditions one needs to impose in order to obtain global solutions. The resulting mix of positive and negative frequencies produced by the presence of Euclidean regions depends only on the total width of the regions, and not on the detailed form of the metric.This essay received honorable mention in the 1991 competition of the Gravity Research Foundation.     

The normal-form (In)dependence of the adiabatic particle definitions

The adiabatic particle definition of Parker [1] has only been discussed for particular choices of the field variable and time coordinate, referred to here as the choice of a normal-form. It seems to have been implicitly assumed that the associated vacuum is independent of the normal-form chosen; we show that this is indeed the case.NATO Postdoctoral Fellow.     

Comment on “smooth and discontinuous signature change in general relativity”

Kossowski and Kriele derived boundary conditions on the metric at a surface of signature change. We point out that their derivation is based not only on certain smoothness assumptions but also on a postulated form of the Einstein field equations. Since there is no canonical form of the field equations at a change of signature, their conclusions are not inescapable. We show here that a weaker formulation is possible, in which less restrictive smoothness assumptions are made, and (a slightly different form of) the Einstein field equations are satisfied. In particular, in this formulation it is possible to have a bounded energy-momentum tensor at a change of signature without satisfying their condition that the extrinsic curvature vanish.     

Slicing,threading and parametric manifolds

We present a unified treatment of theslicing (3+1) andthreading (1+3) decompositions of spacetime in terms of foliations. It is well-known how to decompose the metric and connection in the slicing picture; this is at the heart of any initial-value problem in general relativity. We describe here the analogous problem in the threading picture, recovering the recent results of Perjés onparametric manifolds.     

On the asymptotic flatness of theC metrics at spatial infinity

It is shown that a family of exact, radiating solutions of Einstein's field equations (theC metrics) is asymptotically flat at spatial infinity (in the sense of Ashtekar-Hansen). The ADM and Bondi masses are discussed.