Filtration of aerosol particles by cylindrical fibers within a parallel and staggered array

The World Health Organization (WHO) in 2013 reported that more than seven million unexpected losses every year are credited to air contamination. Because of incredible adaptability and expense viability of fibrous filters, they are broadly used for removing particulates from gasses. The influence of appropriate parameters, e.g., the fiber arrangement, solid volume fraction (SVF or α), fluid flow face velocity (mean inlet velocity), and filter thickness (I _x ), on pressure drop and deposition efficiency are researched. Furthermore, to study the effects of variation of the laminar flow regime and fiber’s cross-sectional shape on the deposition of particles, only a single square fiber has been placed in a channel. By means of finite volume method (FVM), the 2-D motion of 100–1000 nm particles was investigated numerically. The Lagrangian method has been employed and the Saffman’s lift, Drag, and Brownian forces have been considered to affect this motion. Contribution of increasing the Reynolds number to filtration performance increased with smaller fine aerosols to a level of 59.72 %. However, for over 500 nm, the Re = 100 has more efficient results up to 26.97 %. Remarkably, the single square fiber in Re = 200 regime performs similarly to the optimum choice of multi-fibrous filters. It was portrayed the parallel circular multi-fibrous filter with a ratio of horizontal-to-vertical distances between fibers, l/h = 1.143; α = 0.687, I _x  = 116.572, and h/d _f  = 1.0 is the most efficient filter’s structure. The increase in the ratio of vertical distances between fibers-to-fiber’s diameter (h/d _f ) and decrease in SVF or α, results in a drastically decrement of the filtration performance of both parallel and staggered structures. The obtained results have been validated with previous research findings.     

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.     

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.     

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 horizons and wormholes in k-essence theories

We study the properties of possible static, spherically symmetric configurations in k-essence theories with the Lagrangian functions of the form F(X), X ≡ ?,_α ?,^α. A no-go theorem has been proved, claiming that a possible black-hole-like Killing horizon of finite radius cannot exist if the function F(X) is required to have a finite derivative dF/dX. Two exact solutions are obtained for special cases of kessence: one for F(X) = F ₀ X ^1/3, another for F(X) = F ₀|X|^1/2 ? 2Λ, where F ₀ and Λ are constants. Both solutions contain horizons, are not asymptotically flat, and provide illustrations for the obtained nogo theorem. The first solution may be interpreted as describing a black hole in an asymptotically singular space-time, while in the second solution two horizons of infinite area are connected by a wormhole.     

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.     

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.     

<Emphasis Type="Italic">k</Emphasis>-Nearest neighbors tracking in wireless sensor networks with coverage holes

Target tracking is one of the important applications of wireless sensor networks (WSNs). Most of the existing approaches assume that the nodes are dense enough and ignore the coverage holes which are very common in WSNs because of random deployment of the sensor nodes, block of obstacles, etc. Besides, predicting the target’s location of the next time instance is unwise because of the quite a lot random factors. In this paper, we propose a novel target tracking approach without any predicting, called k-nearest neighbors tracking (k-NNT), to tackle the problems of energy efficiency, continuity and coverage holes. In k-NNT, only the k-nearest neighbors keep active and track the target when more than k nodes can sense the target; the k′-nearest neighbors work when there are only k′ nodes (k′ < k) can sense the target. A sophisticated rotation mechanism is designed to improve the continuity of the tracking process. In the worst case, none of the nodes can sense the target, i.e., the target enters into the coverage holes, and then k-NNT recovers by the Round Up mode (RU mode). The nodes on the perimeter of the coverage hole always keep active for a time threshold t and sense the around environment to find the target in time. Once a node finds the target, the RU mode is over and the irrelevant nodes turn into inactive mode. A series of simulation show that k-NNT performs superiorly compared with several existing approaches in terms of tracking accuracy, continuity and energy efficiency.     

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.     

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.     

A novel weighting scheme for random k-SAT关于随机 k-SAT 的新加权方法

Consider a random k-conjunctive normal form F_k(n, rn) with n variables and rn clauses. We prove that if the probability that the formula F_k(n, rn) is satisfiable tends to 0 as n→∞, then r ? 2.83, 8.09, 18.91, 40.81, and 84.87, for k = 3, 4, 5, 6, and 7, respectively.     

A new strategy for generating shortest addition sequences

An addition sequence problem is given a set of numbers X = {n ₁, n ₂, . . . , n _m }, what is the minimal number of additions needed to compute all m numbers starting from 1? This problem is NP-complete. In this paper, we present a branch and bound algorithm to generate an addition sequence with a minimal number of elements for a set X by using a new strategy. Then we improve the generation by generalizing some results on addition chains (m = 1) to addition sequences and finding what we will call a presumed upper bound for each n _j , 1 ≤ j ≤ m, in the search tree.     

Design,optimization and simulation of a low-voltage shunt capacitive RF-MEMS switch

This paper presents the design, optimization and simulation of a radio frequency (RF) micro-electromechanical system (MEMS) switch. The capacitive RF-MEMS switch is electrostatically actuated. The structure contains a coplanar waveguide, a big suspended membrane, four folded beams to support the membrane and four straight beams to provide the bias voltage. The switch is designed in standard 0.35 µm complementary metal oxide semiconductor process and has a very low pull-in voltage of 3.04 V. Taguchi method and weighted principal component analysis is employed to optimize the geometric parameters of the beams, in order to obtain a low spring constant, low pull-in voltage, and a robust design. The optimized parameters were obtained as w = 2.5 µm, L1 = 30 µm, L2 = 30 µm and L3 = 65 µm. The mechanical and electrical behaviours of the RF-MEMS switch were simulated by the finite element modeling in software of COMSOL Multiphysics 4.3^® and IntelliSuite v8.7^®. RF performance of the switch was obtained by simulation results, which are insertion loss of ?5.65 dB and isolation of ?24.38 dB at 40 GHz.     

<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.     

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.     

Mathematical models and routing algorithms for CAD technological preparation of cutting processes

Resource-conscious technologies for cutting sheet material include the ICP and ECP technologies that allow for aligning fragments of the contours of cutouts. In this work, we show the mathematical model for the problem of cutting out parts with these technologies and algorithms for finding cutting tool routes that satisfy technological constraints. We give a solution for the problem of representing a cutting plan as a plane graph G = (V,F,E), which is a homeomorphic image of the cutting plan. This has let us formalize technological constraints on the trajectory of cutting the parts according to the cutting plan and propose a series of algorithms for constructing a route in the graph G = (V,F,E), which is an image of an admissible trajectory. Using known coordinates of the preimages of vertices of graph G = (V,F,E) and the locations of fragments of the cutting plan that are preimages of edges of graph G = (V,F,E), the resulting route in the graph G = (V,E) can be interpreted as the cutting tool’s trajectory.The proposed algorithms for finding routes in a connected graph G have polynomial computational complexity. To find the optimal route in an unconnected graph G, we need to solve, for every dividing face f of graph G, a travelling salesman problem on the set of faces incident to f.     

Greatest Lower Bound of System Failure Probability on a Special Time Interval Under Incomplete Information About the Distribution Function of the Time to Failure of the System

The author solves the problem of finding greatest lower bounds for the probability F (??) – F (u),0 < u <, ?? < ∞, where \( u= m-{\upsigma}_{\mu}3\sqrt{3},\kern0.5em \upupsilon = m+{\upsigma}_{\mu}3\sqrt{3},\kern0.5em \mathrm{and}\kern0.5em {\upsigma}_{\mu} \) is a fixed dispersion in the set of distribution functions F (x) of non-negative random variables with unimodal differentiable density with mode m and two first fixed moments μ ₁ and μ ₂. The case is considered where the mode coincides with the first moment: m = μ ₁. The greatest lower bound of all possible greatest lower bounds for this problem is obtained and it is nearly one, namely, 0.98430.     

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.     

Occurrence indices of elements in linear recurrence sequences over primary residue rings

We study distances to the first occurrence (occurrence indices) of a given element in a linear recurrence sequence over a primary residue ring \(\mathbb{Z}_{p^n } \). We give conditions on the characteristic polynomial F(x) of a linear recurrence sequence u which guarantee that all elements of the ring occur in u. For the case where F(x) is a reversible Galois polynomial over \(\mathbb{Z}_{p^n } \), we give upper bounds for occurrence indices of elements in a linear recurrence sequence u. A situation where the characteristic polynomial F(x) of a linear recurrence sequence u is a trinomial of a special form over ?₄ is considered separately. In this case we give tight upper bounds for occurrence indices of elements of u.     

Guaranteed strategies for escaping encirclement

This paper considers a conflict situation on the plane as follows. A fast evader E has to break out the encirclement of slow pursuers P _{j1,...,j n} = {P _j1,..., P _jn }, n ≥ 3, with a miss distance not smaller than r ≥ 0. First, we estimate the minimum guaranteed miss distance from E to a pursuer P _a , a ∈ {j ₁,..., j _n }, when the former moves along a given straight line. Then the obtained results are used to calculate the guaranteed estimates to a group of two pursuers P _b,c = {P _b , P _c }, b, c ∈ {j ₁,..., j _n }, b ≠ c, when E maneuvers by crossing the rectilinear segment P _b P _c , and the state passes to the domain of the game space where E applies a strategy under which the miss distance to any of the pursuers is not decreased. In addition, we describe an approach to the games with a group of pursuers P _{j1,... jn} , n ≥ 3, in which E seeks to break out the encirclement by passing between two pursuers P _b and P _c , entering the domain of the game space where E can increase the miss distance to all pursuers by straight motion. By comparing the guaranteed miss distances with r for all alternatives b, c ∈ {j ₁,..., j _n }, b ≠ c, and a ? {b, c}, it is possible to choose the best alternative and also to extract the histories of the game in which the designed evasion strategies guarantee a safe break out from the encirclement.