Conformation dependence of DNA electrophoretic mobility in a converging channel

The electrophoresis of λ‐DNA is observed in a microscale converging channel where the center‐of‐masses trajectories of DNA molecules are tracked to measure instantaneous electrophoretic (EP) mobilities of DNA molecules of various stretch lengths and conformations. Contrary to the usual assumption that DNA mobility is a constant, independent of field and DNA length in free solution, we find DNA EP mobility varies along the axis in the contracting geometry. We correlate this mobility variation with the local stretch and conformational changes of the DNA, which are induced by the electric field gradient produced by the contraction. A “shish‐kebab” model of a rigid polymer segment is developed, which consists of aligned spheres acting as charge and drag centers. The EP mobility of the shish‐kebab is obtained by determining the electrohydrodynamic interactions of aligned spheres driven by the electric field. Multiple shish‐kebabs are then connected end‐to‐end to form a freely jointed chain model for a flexible DNA chain. DNA EP mobility is finally obtained as an ensemble average over the shish‐kebab orientations that are biased to match the overall stretch of the DNA chain. Using physically reasonable parameters, the model agrees well with experimental results for the dependence of EP mobility on stretch and conformation. We find that the magnitude of the EP mobility increases with DNA stretch, and that this increase is more pronounced for folded conformations.     

Modeling texture evolution in equal channel angular extrusion using crystal plasticity finite element models

A new approach to modeling crystallographic texture evolution in Equal Channel Angular Extrusion (ECAE) is presented in this paper. The proposed approach utilizes an elastic–viscoplastic single crystal constitutive model implemented in a finite element framework. A representative volume element of the polycrystal is subjected to boundary conditions that simulate the approximate deformation history experienced by different regions of the sample (at different through-thickness depths) in both Route A and Route C processing. The proposed approach aims to capture the influence of the complex interactions that ensue among the constituent individual crystals of a polycrystal in controlling the texture evolution in the sample, while capturing the boundary conditions inherent to ECAE deformation. The predictions from the proposed approach are compared against previously reported experimental measurements in ECAE of copper. It is observed that the proposed approach provides significantly better agreement with the measurements when compared against previously reported model predictions.     

Quantum Computation in a Ising Spin Chain Taking into Account Second Neighbor Couplings

We consider the realization of a quantum computer in a chain of nuclear spins coupled by an Ising interaction. Quantum algorithms can be performed with the help of appropriate radio-frequency pulses. In addition to the standard nearest-neighbor Ising coupling, we also allow for a second neighbor coupling. It is shown, how to apply the 2π k method in this more general setting, where the additional coupling eventually allows to save a few pulses. We illustrate our results with two numerical simulations: the Shor prime factorization of the number 4 and the teleportation of a qubit along a chain of 3 qubits. In both cases, the optimal Rabi frequency (to suppress non-resonant effects) depends primarily on the strength of the second neighbor interaction.     

Regularity for solutions of nonlinear second order evolution equations

This paper deals with the existence of solutions for the class of nonlinear second order evolution equations. The regularity and a variation of solutions of the given equations are also given. As particular cases of our general formulation, some results for Volterra integrodifferential equations of the hyperbolic type are given.     

Analysis of polymer drag reduction mechanisms from energy budgets

The transfer of energy in drag reducing viscoelastic flows is analyzed through a sequence of energetic budgets that include the mean and turbulent kinetic energy, and the mean polymeric energy and mean elastic potential energy. Within the context of single-point statistics, this provides a complete picture of the energy exchange between the mean, turbulent and polymeric fields. The analysis utilizes direct simulation data of a fully developed channel flow at a moderately high friction Reynolds number of 1000 and at medium (30%) and high (58%) drag reduction levels using a FENE-P polymeric model.Results show that the primary effect of the interaction between the turbulent and polymeric fields is to transfer energy from the turbulence to the polymer, and that the magnitude of this transfer does not change between the low and high drag reduction flows. This one-way transfer, with an amplitude independent of the drag reduction regime, comes in contradiction with the purely elastic coupling which is implicit within the elastic theory of the polymer drag reduction phenomenon by Tabor and De Gennes (Europhys. Lett. 2, pp. 519–522, 1986).     

Weighted averaged equations for modeling velocity profiles of 1D steady open channel flows

A new mathematical algorithm is proposed to address the essential details of vertical distributions of horizontal velocity for one‐dimensional steady open‐channel flow. This new algorithm comprises a system of weighted averaged equations developed from corresponding Reynolds equations by performing weighted average operations instead of conventional depth average operations. It is the system of weighted averaged equations, instead of the vertical grids, that allows for more hydraulic coefficients identifiable. It can be thought of as an extension of the St. Venant equations to address the vertical distributions of horizontal velocities, as well as the water surface profiles. To avoid the difficult expansion of governing partial differential equations in high order, an indirect scheme is proposed to solve hydraulic variables through their weighted average values. The governing partial differential equations are generated by using a variety of weight functions, and the weighted averages of relevant hydraulic variables are taken as the unknown independent variables to be solved first. Then, on the basis of the values and polynomial expansions of these weighted averaged velocities, a system of linear algebraic equations is generated and the unknown hydraulic variables or their coefficients are easily solved. Note that the new model is not proposed to compete with any three‐dimensional models in modeling accuracy or accommodation ability to all conditions. It just provides a valuable option to study the vertical structure of flow in open channels where only essential detail and reasonable accuracy of vertical distributions are required, and the data availability and other conditions limit the application of fully three‐dimensional models. The performance of the model is evaluated with experimental data of flows in two different flumes. It is shown that the model well predicted the velocity profiles of sections along the centerlines of these flumes with reasonable accuracy and essential details of vertical distributions of horizontal velocity. Copyright © 2013 John Wiley & Sons, Ltd.     

A hybrid algorithm for nonlinear minimax problems

In this paper, a hybrid algorithm for solving finite minimax problem is presented. In the algorithm, we combine the trust-region methods with the line-search methods and curve-search methods. By means of this hybrid technique, the algorithm, according to the specific situation at each iteration, can adaptively performs the trust-region step, line-search step or curve-search step, so as to avoid possibly solving the trust-region subproblems many times, and make better use of the advantages of different methods. Moreover, we use second-order correction step to circumvent the difficulties of the Maratos effect occurred in the nonsmooth optimization. Under mild conditions, we prove that the new algorithm is of global convergence and locally superlinear convergence. The preliminary experiments show that the new algorithm performs efficiently.     

Oscillation Theorems of the Second Order Linear Matrix Differential System with Damping

By using the Riccati technique and the technique, new oscillation criteria are obtained for the second order matrix differential system(P(t)Y′(t))′ r(t)P(t)Y′(t) Q(t)Y(t) = 0, t≥t0.These results in the present paper generalize and improve many known conclusions. Furthermore, some results are different from the most known ones in the sense that they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. In particular, our results complement a number of existing results and handle the ease that is not covered by the known criteria.     

Computer Simulations on the Channel Membrane Formation by Nonsolvent Induced Phase Separation

The formation of channel membrane of polystyrene‐block‐poly(4‐vinyl pyridine) block copolymer is studied by computer simulations with the nonsolvent induced phase separation (SNIPS) method. Dissipative particle dynamics is employed to study the microphase separation process and the SNIPS mechanism. Simulation results indicate that polymer concentration has a significant effect on the membrane structure. Channel membranes form in the copolymer concentration range of 44–58%. Block ratio plays an important role in shaping the membrane structure. Solvent exchange rate also affects the degree of microphase separation at each evolution stage of simulation. The time evolution of morphologies shows that the microphase separation processes happen with the following sequences: the polymer self‐assembled and many small pores appear, then they form irregular cavities and cross‐link gradually, finally the channel membrane forms. These results throw light on the formation mechanism of polymer membranes and provide insightful guidance for future membrane design and preparation.