Inertial particle focusing dynamics in a trapezoidal straight microchannel: application to particle filtration

Inertial microfluidics has emerged recently as a promising tool for high-throughput manipulation of particles and cells for a wide range of flow cytometric tasks including cell separation/filtration, cell counting, and mechanical phenotyping. Inertial focusing is profoundly reliant on the cross-sectional shape of channel and its impacts on not only the shear field but also the wall-effect lift force near the wall region. In this study, particle focusing dynamics inside trapezoidal straight microchannels was first studied systematically for a broad range of channel Re number (20 < Re < 800). The altered axial velocity profile and consequently new shear force arrangement led to a cross-lateral movement of equilibration toward the longer side wall when the rectangular straight channel was changed to a trapezoid; however, the lateral focusing started to move backward toward the middle and the shorter side wall, depending on particle clogging ratio, channel aspect ratio, and slope of slanted wall, as the channel Reynolds number further increased (Re > 50). Remarkably, an almost complete transition of major focusing from the longer side wall to the shorter side wall was found for large-sized particles of clogging ratio K ~ 0.9 (K = a/H_min) when Re increased noticeably to ~ 650. Finally, based on our findings, a trapezoidal straight channel along with a bifurcation was designed and applied for continuous filtration of a broad range of particle size (0.3 < K < 1) exiting through the longer wall outlet with ~ 99% efficiency (Re < 100).     

Star reduction among minimal length addition chains

An addition chain for a natural number n is a sequence \({1=a_0 < a_1 < \cdots < a_r=n}\) of numbers such that for each 0 < i ≤ r, a _i  = a _j  + a _k for some 0 ≤ k ≤ j < i. The minimal length of an addition chain for n is denoted by ?(n). If j = i ? 1, then step i is called a star step. We show that there is a minimal length addition chain for n such that the last four steps are stars. Then we conjecture that there is a minimal length addition chain for n such that the last \({\lfloor\frac{\ell(n)}{2}\rfloor}\)-steps are stars. We verify that the conjecture is true for all numbers up to 2¹⁸. An application of the result and the conjecture to generate a minimal length addition chain reduce the average CPU time by 23–29% and 38–58% respectively, and memory storage by 16–18% and 26–45% respectively for m-bit numbers with 14 ≤ m ≤ 22.     

<Emphasis Type="Italic">α</Emphasis>-Systems of differential inclusions and their unification

This paper introduces α-systems of differential inclusions on a bounded time interval [t₀, ?] and defines α-weakly invariant sets in [t₀, ?] × ?_n, where ?_n is a phase space of the differential inclusions. We study the problems connected with bringing the motions (trajectories) of the differential inclusions from an α-system to a given compact set M ? ?_n at the moment ? (the approach problems). The issues of extracting the solvability set W ? [t₀, ?] × ?ⁿ in the problem of bringing the motions of an α-system to M and the issues of calculating the maximal α-weakly invariant set W^c ? [t₀, ?] × ?ⁿ are also discussed. The notion of the quasi-Hamiltonian of an α-system (α-Hamiltonian) is proposed, which seems important for the problems of bringing the motions of the α-system to M.     

Negation-Limited Complexity of Parity and Inverters

In negation-limited complexity, one considers circuits with a limited number of NOT gates, being motivated by the gap in our understanding of monotone versus general circuit complexity, and hoping to better understand the power of NOT gates. We give improved lower bounds for the size (the number of AND/OR/NOT) of negation-limited circuits computing Parity and for the size of negation-limited inverters. An inverter is a circuit with inputs x ₁,…,x _n and outputs ¬ x ₁,…,¬ x _n . We show that: (a) for n=2 ^r ?1, circuits computing Parity with r?1 NOT gates have size at least 6n?log?₂(n+1)?O(1), and (b) for n=2 ^r ?1, inverters with r NOT gates have size at least 8n?log?₂(n+1)?O(1). We derive our bounds above by considering the minimum size of a circuit with at most r NOT gates that computes Parity for sorted inputs x ₁≥???≥x _n . For an arbitrary r, we completely determine the minimum size. It is 2n?r?2 for odd n and 2n?r?1 for even n for ?log?₂(n+1)??1≤r≤n/2, and it is ?3n/2??1 for r≥n/2. We also determine the minimum size of an inverter for sorted inputs with at most r NOT gates. It is 4n?3r for ?log?₂(n+1)?≤r≤n. In particular, the negation-limited inverter for sorted inputs due to Fischer, which is a core component in all the known constructions of negation-limited inverters, is shown to have the minimum possible size. Our fairly simple lower bound proofs use gate elimination arguments in a somewhat novel way.     

An orthogonal analysis method for decoupling the nozzle geometrical parameters of microthrusters

This paper proposes an orthogonal analysis method for decoupling the multiple nozzle geometrical parameters of microthrusters, thus an reconfigured design can be implemented to generate a proper thrust. In this method, the effects of various nozzle geometrical parameters, including throat width W _t , half convergence angle θ _in , half divergence angle θ _out , exit-to-throat section ratio W _e /W _t and throat radius of the curvature R _t /W _t , on the performance of microthrusters are sorted by range analysis. Analysis results show that throat width seriously affects thrust because range value of 67.53 mN is extremely larger than the range value of other geometry parameters. For average specific impulse (ASI), the range value of exit-to-throat section ratio W _e /W _t and half divergence angle θ _out are 4.82 s and 3.72 s, respectively. Half convergence angle with the range value of 0.39 s and throat radius with 0.32 s have less influence on ASI compared with exit-to-throat section ratio and half divergence angle. When increasing the half convergence angle from 10° to 40° and throat radius of the curvature from 3 to 9, average specific impulse initially decreases and then increases. A MEMS solid propellant thruster (MSPT) with the reconfigured geometrical parameters of nozzle is fabricated to verify the feasibility of the proposed method. The thrust of the microthruster can reach 25 mN. Power is estimated to be 0.84 W. This work provides design guideline to reasonably configure geometry parameters of microthruster.     

Error bounds for complementarity problems with tridiagonal nonlinear functions

In this paper we consider the complementarity problem NCP(f) with f(x) = Mx + φ(x), where M ∈ R ^n×n is a real matrix and φ is a so-called tridiagonal (nonlinear) mapping. This problem occurs, for example, if certain classes of free boundary problems are discretized. We compute error bounds for approximations \({\hat x}\) to a solution x* of the discretized problems. The error bounds are improved by an iterative method and can be made arbitrarily small. The ideas are illustrated by numerical experiments.     

Effects of topological changes in microchannel geometries on the asymmetric breakup of a droplet

Passive asymmetric breakups of a droplet could be done in many microchannels of various geometries. In order to study the effects of different geometries on the asymmetric breakup of a droplet, four types of asymmetric microchannels with the topological equivalence of geometry are designed, which are T-90, Y-120, Y-150, and I-180 microchannels. A three-dimensional volume of fluid multiphase model is employed to investigate the asymmetric rheological behaviors of a droplet numerically. Three regimes of rheological behaviors as a function of the capillary numbers Ca and the asymmetries As defined by As = (b1 ? b2)/(b1 + b2) (where b1 and b2 are the widths of two asymmetric sidearms) have been observed. A power law model based on three major factors (Ca, As and the initial volume ratio r ₀) is employed to describe the volume ratio of two daughter droplets. The analysis of pressure fields shows that the pressure gradient inside the droplet is one of the major factors causing the droplet translation during its asymmetric breakup. Besides the above similarities among various microchannels, the asymmetric breakup in them also have some slight differences as various geometries have different enhancement or constraint effects on the translation of the droplet and the cutting action of flows. It is disclosed that I-180 microchannel has the smallest critical capillary number, the shortest splitting time, and is hardest to generate satellite droplets.     

Role of interface shape on the laminar flow through an array of superhydrophobic pillars

In this study, measurements of the pressure drop and the velocity vector fields through a regular array of superhydrophobic pillars were systematically taken to investigate the role of air–water interface shape on laminar drag reduction. A polydimethylsiloxane microfluidic channel was created with a regular array of apple-core-shaped and circular pillars bridging across the entire channel. Due to the shape and hydrophobicity of the apple-core-shaped pillars, air was trapped on the side of the pillars after filling the microchannel with water. The measurements were taken at a capillary number of Ca = 6.6 × 10^?5. The shape of the air–water interface trapped within the superhydrophobic apple-core-shaped pillars was systematically modified from concave to convex by changing the static pressure within the microchannel. The pressure drop through the microchannel containing the superhydrophobic apple-core-shaped pillars was found to be sensitive to the shape of the air–water interface. For static pressures which resulted in the apple-core-shaped superhydrophobic pillars having a circular cross section, D/D ₀ = 1, a drag reduction of 7% was measured as a result of slip along the air–water interface. At large static pressures, the interface was driven into the apple-core-shaped pillars, resulting in decrease in the effective size of the pillars and an increase in the effective spacing between pillars. When combined with a slip velocity measured to be 10% of the average velocity between the pillars, the result was a pressure drop reduction of 18% compared to the circular pillars at a non-dimensional interface diameter of D/D ₀ = 0.8. At low static pressures, the pressure drop increased significantly as the expanded air–water interface constricted flow through the array of pillars even as large interfacial slip velocity was maintained. At D/D ₀ = 1.1, for example, the pressure drop increased by 17% compared to the circular pillar. This drag increase was the result of an increased form drag due to a decrease in porosity and permeability of the pillar array and a decrease in the skin friction drag due to the presence of the air–water interface. For D/D ₀ = 1.1, the slip velocity was measured to be 45% of the average streamwise velocity between the pillars. When compared to no-slip pillars of similar shape, the drag reduction was found to increase from 6 to 9% with increasing convex curvature of the air–water interface.     

Fabrication of piezoelectric multilayer thin-film actuators

In this study, we fabricated multilayer ceramics (MLCs) composed of multilayered Pb(Zr,Ti)O₃ (PZT) piezoelectric thin films with internal electrodes and evaluated their dielectric and piezoelectric properties. The stack of PZT ferroelectric layers (550 nm) and SrRuO₃ (SRO, 80 nm) electrodes were alternatively deposited on Pt/Ti-coated silicon-on-insulator substrates by radio-frequency magnetron sputtering. The MLCs composed of one, three, and five PZT layers were fabricated by the alternate sputtering deposition of PZT ferroelectric layers and SRO electrodes through the movable shadow mask. The capacitances of MLCs were proportionally increased with the number of PZT layers, while their relative dielectric constants were almost same among the each MLC. The MLCs exhibited symmetric and saturated P–E hysteresis loops similar to the conventional PZT thin films. We estimated that the piezoelectric properties of MLCs by FEM simulation, and confirmed that the effective transverse piezoelectric coefficients (d _31,eff ) increased with the number of PZT layers. The piezoelectric coefficients calculated to be d _31,eff  = ?2964 pC/N at 25 PZT layers, which is much higher than those of conventional single-layer piezoelectric thin films.     

Virtual reality software package for implementing motor learning and rehabilitation experiments

Virtual reality games for rehabilitation are attracting increasing growth. In particular, there is a demand for games that allow therapists to identify an individual’s difficulties and customize the control of variables, such as speed, size, distance, as well as visual and auditory feedback. This study presents and describes a virtual reality software package (Bridge Games) to promote rehabilitation of individuals living with disabilities and highlights preliminary researches of its use for implementing motor learning and rehabilitation. First, the study presents seven games in the software package that can be chosen by the rehabilitation team, considering the patient’s needs. All game characteristics are described including name, function presentation, objective and valuable measurements for rehabilitation. Second, preliminary results illustrate some applications of two games, considering 343 people with various disabilities and health status. Based on the results, in the Coincident Timing game, there was a main effect of movement sensor type (in this instance the most functional device was the keyboard when compared with Kinect and touch screen) on average time reached by sample analyzed, F(2, 225) = 4.42, p < 0.05. Similarly, in the Challenge! game, a main effect was found for movement sensor type. However, in this case, touch screen provided better performance than Kinect and Leap Motion, F(2, 709) = 5.90, p < 0.01. Thus, Bridge Games is a possible software game to quantify motor learning. Moreover, the findings suggest that motor skills might be practiced differently depending on the environmental interface in which the game may be used.     

On the <Emphasis Type="Italic">k</Emphasis>-accessibility of cores of <Emphasis Type="Italic">TU</Emphasis>-cooperative games

This paper proposes a strengthening of the author’s core-accessibility theorem for balanced TU-cooperative games. The obtained strengthening relaxes the influence of the nontransitivity of classical domination αv on the quality of the sequential improvement of dominated imputations in a game v. More specifically, we establish the k-accessibility of the core C(α _v ) of any balanced TU-cooperative game v for all natural numbers k: for each dominated imputation x, there exists a converging sequence of imputations x₀, x₁,..., such that x₀ = x, lim x _r ∈ C(α _v ) and x_r?m is dominated by any successive imputation x _r with m ∈ [1, k] and r ≥ m. For showing that the TU-property is essential to provide the k-accessibility of the core, we give an example of an NTU-cooperative game G with a ”black hole” representing a nonempty closed subset B ? G(N) of dominated imputations that contains all the α _G -monotonic sequential improvement trajectories originating at any point x ∈ B.     

Threshold quantum secret sharing based on single qubit

Based on unitary phase shift operation on single qubit in association with Shamir’s (t, n) secret sharing, a (t, n) threshold quantum secret sharing scheme (or (t, n)-QSS) is proposed to share both classical information and quantum states. The scheme uses decoy photons to prevent eavesdropping and employs the secret in Shamir’s scheme as the private value to guarantee the correctness of secret reconstruction. Analyses show it is resistant to typical intercept-and-resend attack, entangle-and-measure attack and participant attacks such as entanglement swapping attack. Moreover, it is easier to realize in physic and more practical in applications when compared with related ones. By the method in our scheme, new (t, n)-QSS schemes can be easily constructed using other classical (t, n) secret sharing.     

Generation and distillation of non-Gaussian entanglement from nonclassical photon statistics

With a product state of the form \({{\rho}_{\rm in} = {\rho}_{a} \otimes |0 \rangle_b {_b} \langle 0|}\) as input to a beam splitter, the output two-mode state ρ _out is shown to be negative under partial transpose (NPT) whenever the photon number distribution (PND) statistics { p(n _a ) } associated with the possibly mixed state ρ _a of the input a-mode is antibunched or otherwise nonclassical, i.e., whenever { p(n _a ) } fails to respect any one of an infinite sequence of necessary and sufficient classicality conditions. Negativity under partial transpose turns out to be a necessary and sufficient test for entanglement of ρ _out which is generically non-Gaussian. The output of a PND distribution is further shown to be distillable if any one of an infinite sequence of three term classicality conditions is violated.     

Study on microchannel flows with a sudden contraction–expansion at a wide range of Knudsen number using lattice Boltzmann method

Numerical simulations have been performed on the pressure-driven rarefied flow through channels with a sudden contraction–expansion of 2:1:2 using isothermal two and three-dimensional lattice Boltzmann method (LBM). In the LBM, a Bosanquet-type effective viscosity and a modified second-order slip boundary condition are used to account for the rarefaction effect on gas viscosity to cover the slip and transition flow regimes, that is, a wider range of Knudsen number. Firstly, the in-house LBM code is verified by comparing the computed pressure distribution and flow pattern with experimental ones measured by others. The verified code is then used to study the effects of the outlet Knudsen number Kn _o , driving pressure ratio P _i /P _o , and Reynolds number Re, respectively, varied in the ranges of 0.001–1.0, 1.15–5.0, and 0.02–120, on the pressure distributions and flow patterns as well as to document the differences between continuum and rarefied flows. Results are discussed in terms of the distributions of local pressure, Knudsen number, centerline velocity, and Mach number. The variations of flow patterns and vortex length with Kn _o and Re are also documented. Moreover, a critical Knudsen number is identified to be Kn _oc  = 0.1 below and above which the behaviors of nonlinear pressure profile and velocity distribution and the variations of vortex length with Re upstream and downstream of constriction are different from those of continuum flows.     

Quartic B-spline collocation method for fifth order boundary value problems

Given two sorted arrays \({A=(a_1,a_2,\ldots ,a_{n_1})}\) and \({B=(b_1,b_2,\ldots ,b_{n_2})}\), where their elements are drawn from a linear range in n and n = Max(n ₁, n ₂). The merging of two sorted arrays is one of the fundamental problems in computer science. The main contribution of this work is to give a new merging algorithm on a EREW PRAM. The algorithm is cost optimal, deterministic and simple. The algorithm uses \({\frac{n}{\log{n}}}\) processors and O(n) storage. We also give the conditions that make the algorithm run in a constant time on a EREW PRAM.     

On the Price of Heterogeneity in Parallel Systems

Suppose we have a parallel or distributed system whose nodes have limited capacities, such as processing speed, bandwidth, memory, or disk space. How does the performance of the system depend on the amount of heterogeneity of its capacity distribution? We propose a general framework to quantify the worst-case effect of increasing heterogeneity in models of parallel systems. Given a cost function g(C,W) representing the system’s performance as a function of its nodes’ capacities C and workload W (such as the makespan of an optimum schedule of jobs W on machines C), we say that g has price of heterogeneity α when for any workload, cost cannot increase by more than a factor α if node capacities become arbitrarily more heterogeneous. The price of heterogeneity also upper bounds the “value of parallelism”: the maximum benefit obtained by increasing parallelism at the expense of decreasing processor speed. We give constant or logarithmic bounds on the price of heterogeneity of several well-known job scheduling and graph degree/diameter problems, indicating that in many cases, increasing heterogeneity can never be much of a disadvantage.     

Improved Approximation Algorithm for k-level Uncapacitated Facility Location Problem (with Penalties)

We study the k-level uncapacitated facility location problem (k-level UFL) in which clients need to be connected with paths crossing open facilities of k types (levels). In this paper we first propose an approximation algorithm that for any constant k, in polynomial time, delivers solutions of cost at most α _k times OPT, where α _k is an increasing function of k, with \(\lim _{k\to \infty } \alpha _{k} = 3\). Our algorithm rounds a fractional solution to an extended LP formulation of the problem. The rounding builds upon the technique of iteratively rounding fractional solutions on trees (Garg, Konjevod, and Ravi SODA’98) originally used for the group Steiner tree problem. We improve the approximation ratio for k-level UFL for all k ≥ 3, in particular we obtain the ratio equal 2.02, 2.14, and 2.24 for k = 3,4, and 5.     

A Priori knowledge based secure payload estimation

Many contemporary steganographic schemes aim to embed fixed-length secret message in the cover while minimizing the stego distortion. However, in some cases, the secret message sender requires to embed a variable-length secret payload within his expected stego security. This kind of problem is named as secure payload estimation (SPE). In this paper, we propose a practical SPE approach for individual cover. The stego security metric we adopt here is the detection error rate of steganalyzer (P _E ). Our method is based on a priori knowledge functions, which are two kinds of functions to be determined before the estimation. The first function is the relation function of detection error rate and stego distortion (P _E ? D function). The second function reflects the relationship between stego distortion and payload rate (D ? α) of the chosen cover. The P _E ? D is the general knowledge, which is calculated from image library. On the other hand, D ? α is for specific cover, which is needed to be determined on site. The estimating procedure is as follows: firstly, the sender solves the distortion D under his expected P _E via P _E ? D, and then calculates the corresponding secure payload α via D ? α of the cover. For on-site operations, the most time-consuming part is calculating D ? α function for cover image, which costs 1 time of STC coding. Besides this, the rest on-site operations are solving single-variable formulas, which can be easily tackled. Our approach is an efficient and practical solution for SPE problem.     

When LP Is the Cure for Your Matching Woes: Improved Bounds for Stochastic Matchings

Consider a random graph model where each possible edge e is present independently with some probability p _e . Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we can find out whether an edge is present or not is to query it, and if the edge is indeed present in the graph, we are forced to add it to our matching. Further, each vertex i is allowed to be queried at most t _i times. How should we adaptively query the edges to maximize the expected weight of the matching? We consider several matching problems in this general framework (some of which arise in kidney exchanges and online dating, and others arise in modeling online advertisements); we give LP-rounding based constant-factor approximation algorithms for these problems. Our main results are the following:

• We give a 4 approximation for weighted stochastic matching on general graphs, and a 3 approximation on bipartite graphs. This answers an open question from Chen et al. (ICALP’09, LNCS, vol. 5555, pp. 266–278, [2009]).
• We introduce a generalization of the stochastic online matching problem (Feldman et al. in FOCS’09, pp. 117–126, [2009]) that also models preference-uncertainty and timeouts of buyers, and give a constant factor approximation algorithm.

     

An SMVQ-based reversible data hiding technique exploiting side match distortion

Secure online communication is a necessity in today’s digital world. This paper proposes a novel reversible data hiding technique based on side match vector quantization (SMVQ). The proposed scheme classifies SMVQ indices as Case 1 or 2 based on the value of the first state codeword’s side match distortion (SMD) and a predefined threshold t. The proposed scheme uses this classification to switch between compression codes designed for Cases 1 and 2 SMVQ indices. The length of these compression codes is controlled by the parameter ?. Thus, with the selection of appropriate ? and t values, the proposed scheme achieves good compression, creating spaces to embed secret information. The embedding algorithm can embed n secret bits into each SMVQ index, where n = 1, 2, 3, or 4. The experimental results show that the proposed scheme obtains the embedding rates of 1, 2, 3, or 4 bit per index (bpi) at the average bit rates of 0.340, 0.403, 0.465, or 0.528 bit per pixel (bpp) for the codebook size 256. This improves the performance of recent VQ and SMVQ-based data hiding schemes.