Label-free isolation of a prostate cancer cell among blood cells and the single-cell measurement of drug accumulation using an integrated microfluidic chip

Circulating tumor cells (CTCs) are found in the blood of patients with cancer. Although these cells are rare, they can provide useful information for chemotherapy. However, isolation of these rare cells from blood is technically challenging because they are small in numbers. An integrated microfluidic chip, dubbed as CTC chip, was designed and fabricated for conducting tumor cell isolation. As CTCs usually show multidrug resistance (MDR), the effect of MDR inhibitors on chemotherapeutic drug accumulation in the isolated single tumor cell is measured. As a model of CTC isolation, human prostate tumor cells were mixed with mouse blood cells and the labelfree isolation of the tumor cells was conducted based on cell size difference. The major advantages of the CTC chip are the ability for fast cell isolation, followed by multiple rounds of single-cell measurements, suggesting a potential assay for detecting the drug responses based on the liquid biopsy of cancer patients.

Unsteady free convection flow in the stagnation-point region of a rotating sphere

The unsteady free convection boundary-layer flow in the forward stagnation-point region of a sphere, which is rotating with time-dependent angular velocity in an ambient fluid, has been studied. Both constant wall temperature and constant hear flux conditions have been considered. The non-linear coupled parabolic partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The skin friction and the heat transfer are enhanced by the buoyancy force. The effect of the buoyancy force is found to be more pronounced for smaller Prandtl numbers than for larger Prandtl numbers. For a given buoyancy force, the heat transfer increases with an increase in Prandtl number, but the skin friction decreases.

Unsteady free convection flow in the stagnation-point region of a three-dimensional body

The unsteady free convection flow in the stagnation-point region of a heated three-dimensional body placed in an ambient fluid is studied under boundary layer approximations. We have considered the case where there is an initial steady state that is perturbed by a step-change in the wall temperature. The non-linear coupled partial differential equations governing the free convection flow are solved numerically using a finite difference scheme. The presented results show the temporal development of the momentum and thermal boundary layer characteristics.

Free Energy Gap Dependence of the Electron-Transfer Rate from the Inverted to the Normal Region

numerical study of the free energy gap (FEG) dependence of the electron-transfer rate in polar solvents is presented. This study is based on the generalized multidimensional hybrid model, which not only includes the solvent polarization and the molecular vibration modes, but also the biphasic polar response of the solvent. The free energy gap dependence is found to be sensitive to several factors, including the solvent relaxation rate, the electronic coupling between the surfaces, the frequency of the high-frequency quantum vibrational mode, and the magnitude of the solvent reorganization energy. It is shown that in some cases solvent relaxation can play an important role even in the Marcus normal regime. The minimal hybrid model involves a large number of parameters, giving rise to a diverse non-Marcus FEG behavior which is often determined collectively by these parameters. The model gives the linear free energy gap dependence of the logarithmic rate over a substantial range of FEG, spanning from the normal to the inverted regime. However, even for favorable values of the relevant parameters, a linear free energy gap dependence of the rate could be obtained only over a range of 5000-6000 cm(-1) (compared to the experimentally observed range of 10000 cm(-1) reported by Benniston et al.). The present work suggests several extensions/generalizations of the hybrid model which might be necessary to fully understand the observed free energy gap dependence.

Free energy landscape of a dense hard-sphere system

The topography of the free energy landscape in phase space of a dense hard-sphere system characterized by a discretized free energy functional of the Ramakishnan-Yussouff form is investigated numerically using a specially devised Monte Carlo procedure. We locate a considerable number of glassy local minima of the free energy and analyze the distributions of the free energy at a minimum and an appropriately defined phase-space "distance" between different minima. We find evidence for the existence of pairs of closely related glassy minima("two-level systems"). We also investigate the way the system makes transitions as it moves from the basin of attraction of a minimum to that of another one after a start under nonequilibrium conditions. This allows us to determine the effective height of free energy barriers that separate a glassy minimum from the others. The dependence of the height of free energy barriers on the density is investigated in detail. The general appearance of the free energy landscape resembles that of a putting green: relatively deep minima separated by a fairly flat structure. We discuss the connection of our results with the Vogel-Fulcher law and relate our observations to other work on the glass transition.

Free vibration of a kinked cantilever with attached masses

In this paper free vibration characteristics of a centrally kinked cantilever beam of unit mass carrying masses at the kink (m(k)) and at the tip (m(t)) are analyzed. Frequency factors are presented for the first two modes for different combinations of m(k),m(t) and the kink angle delta. A relationship of the form f(m(k),m(t), delta) = m(k) + m(t)(4 + 10/3 cos delta+ 2/3 cos(2) delta)=const appears to give the same fundamental frequency for a given delta and different combinations of [m(k), m(t)]. Mode shapes as well as bending moments at the support and at the kink are also discussed. The utility of a discrete beam model in understanding the free vibration characteristics is also highlighted.

Extended Kalman filters using explicit and derivative-free local linearizations

We propose three variants of the extended Kalman filter (EKF) especially suited for parameter estimations in mechanical oscillators under Gaussian white noises. These filters are based on three versions of explicit and derivative-free local linearizations (DLL) of the non-linear drift terms in the governing stochastic differential equations (SDE-s). Besides a basic linearization of the non-linear drift functions via one-term replacements, linearizations using replacements through explicit Euler and Newmark expansions are also attempted in order to ensure higher closeness of true solutions with the linearized ones. Thus, unlike the conventional EKF, the proposed filters do not need computing derivatives (tangent matrices) at any stage. The measurements are synthetically generated by corrupting with noise the numerical solutions of the SDE-s through implicit versions of these linearizations. In order to demonstrate the effectiveness and accuracy of the proposed methods vis-à-vis the conventional EKF, numerical illustrations are provided for a few single degree-of-freedom (DOF) oscillators and a three-DOF shear frame with constant parameters.

Metal-free graphitic carbon nitride as mechano-catalyst for hydrogen evolution reaction

Graphitic carbon nitride (g-C3N4), as a promising metal-free catalyst for photo-catalytic and electrochemical water splitting, has recently attracted tremendous research interest. However, the underlying catalytic mechanism for the hydrogen evolution reaction (HER) is not fully understood. By using density functional theory calculations, here we have established that the binding free energy of hydrogen atom (ΔGH∗0) on g-C3N4 is very sensitive to mechanical strain, leading to substantial tuning of the HER performance of g-C3N4 at different coverages. The experimentally-observed high HER activity in N-doped graphene supported g-C3N4 (Zheng et al., 2014) is actually attributed to electron-transfer induced strain. A more practical strategy to induce mechanical strain in g-C3N4 is also proposed by doping a bridge carbon atom in g-C3N4 with an isoelectronic silicon atom. The calculated ΔGH∗0 on the Si-doped g-C3N4 is ideal for HER. Our results indicate that g-C3N4 would be an excellent metal-free mechano-catalyst for HER and this finding is expected to guide future experiments to efficiently split water into hydrogen based on the g-C3N4 materials.

Controversy on the Free Energy of Formation of CaO Additional Evidence in Support of Thermochemical Data

The standard free energies of formation of CaO derived from a variety of high-temperature equilibrium measurements made by seven groups of experimentalists are significantly different from those given in the standard compilations of thermodynamic data. Indirect support for the validity of the compiled data comes from new solid-state electrochemical measurements using single-crystal CaF2 and SrF2 as electrolytes. The change in free energy for the following reactions are obtained: CaO + MgF2 --> MgO + CaF2 Delta G degrees = -68,050 -2.47 T(+/-100) J mol(-1) SrO + CaF2 --> SrF2 + CaO Delta G degrees = -35,010 + 6.39 T (+/-80) J mol(-1) The standard free energy changes associated with cell reactions agree with data in standard compilations within +/- 4 kJ mol(-1). The results of this study do not support recent suggestions for a major revision in thermodynamic data for CaO.

Unsteady Free-Convection Flow on a Rotating flat-Plate Under Nonuniform Gravity

The free convection problem with nonuniform gravity finds applications in several fields. For example, centrifugal gravity fieldsarisein many rotating machinery applications. A gravity field is also created artificially in an orbital space station by rotation. The effect of nonuniform gravity due to the rotation of isothermal or nonisothermal plates has been studied by several authors [l-5] using various mathematical techniques.

Algebraic and geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups Coincides With the geometric intersection number for the sphere complex of the connected sum of copies of S-2 x S-1. (C) 2009 Elsevier B.V. All rights reserved.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.