MRT Lattice Boltzmann schemes for confined suspension flows

We introduce a novel multiple-relaxation time (modified MRT) Lattice Boltzmann scheme for simulation of confined suspension flow. Via careful tuning of the free eigenvalues of the collision operator we can substantially reduce the error in the so-called hydrodynamic radius. Its performance has been compared to that of the TRT scheme for several benchmark problems. We have found that the optimal value of the free eigenvalue depends on the curvature of the solid-fluid interfaces. Hence, we have investigated suspension flow problems, with confining boundaries of different curvatures. We have found that the modified MRT scheme is better suited for suspension flow in curved confining walls, while the TRT scheme is better for suspension flow confined between planar walls.With both schemes we have investigated problems for confined suspension flows, namely 1) drag forces experienced by spheres flowing in confining flow channels of different cross sections, and 2) the lubrication force between a sedimenting sphere and the end cap of a confining cylindrical capillary.     

Phase diagrams of confined solutions of dimyristoylphosphatidylcholine (DMPC) lipid and cholesterol in nanotubes

We have studied equilibrium morphologies of dimyristoylphosphatidylcholine lipid solution and cholesterol solution confined to nanotubes using dissipative particle dynamics (DPD) simulations. Phase diagrams regarding monomer concentration c versus radius of nanotube r for both solutions are attained. Three types of the inner surface of nanotubes, namely hydrophobic, hydrophilic, and hydroneutral are considered in the DPD simulations. A number of phases and molecular assemblies for the confined solutions are revealed, among others, such as the spiral wetting and bilayer helix. Several phases and assemblies have not been reported in the literature, and some are non-existence in bulk solutions. The ability to control the morphologies and self-assemblies within nanoscale confinement can be exploited for patterning interior surface of nanochannels for application in nanofluidics and nanomedical devices.     

Faster neighbour list generation using a novel lattice vector representation

In any many-body simulation where particles are coupled using short-range potentials, a key part of the simulation is to find which particles {j} interact with particle i. The set of such particles is known as the neighbour list of particle i. A novel algorithm is developed here which efficiently returns a neighbour list. A partially occupied reference lattice may be constructed for any simulation, with the position of particles defined as being a short vector separation from a node. A lattice vector which preserves translational symmetry in a periodic supercell under addition and subtraction operations can then be constructed from a single 32-bit integer number. A novel neighbour list algorithm is then developed which uses a single set of lattice vectors to return all nodes, and therefore all particles associated with the nodes, within a fixed radius sphere of particle i. This new algorithm preserves translational symmetry in a periodic supercell, requires a small memory overhead, and is shown to be faster than the well-known Linked-Cell method in all cases considered here.     

Switching to Directional Antennas with Constant Increase in Radius and Hop Distance

For any angle α<2π, we show that any connected communication graph that is induced by a set P of n transceivers using omni-directional antennas of radius 1, can be replaced by a strongly connected communication graph, in which each transceiver in P is equipped with a directional antenna of angle α and radius r _dir, for some constant r _dir=r _dir(α). Moreover, the new communication graph is a c-spanner of the original graph, for some constant c=c(α), with respect to number of hops.     

On the Functionality and Usefulness of Quadraginta Octants of Naive Sphere

This paper presents a novel study on the functional gradation of coordinate planes in connection with the thinnest and tunnel-free (i.e., naive) discretization of sphere in the integer space. For each of the 48-symmetric quadraginta octants of naive sphere with integer radius and integer center, we show that the corresponding voxel set forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as its functional plane. We use this fundamental property to prove several other theoretical results for naive sphere. First, the quadraginta octants form symmetry groups and subgroups with certain equivalent topological properties. Second, a naive sphere is always unique and consists of fewest voxels. Third, it is efficiently constructible from its functional-plane projection. And finally, a special class of 4-symmetric discrete 3D circles can be constructed on a naive sphere based on back projection from the functional plane.     

Relativistic modelling of a superdense star containing a charged perfect fluid

The paper presents a variety of classes of interior solutions of the Einstein-Maxwell field equations for a static, spherically symmetric distribution of a charged fluid of well-behaved nature. They describe perfect fluid balls with positive finite central pressure and density; their ratio is less than one (c = 1), and the causality condition is obeyed at the center. The outmarch of pressure, density, pressuredensity ratio and the adiabatic speed of sound is a monotonic decrease, in a physically appealing manner. A certain class of these well-behaved solutions is studied extensively. For this class, the mass of the configuration is maximized. In particular, for a surface density ?? _b = 2×10¹⁴ g/cm³ we obtain a star with a maximummass of 3.47M _??, a radius of 15.21 km and the central redshift 1.014385.     

The hub number of a graph

A hub set in a graph G is a set U⊆V(G) such that any two vertices outside U are connected by a path whose internal vertices lie in U. We prove that h(G)?hc(G)?γc(G)?h(G)+1, where h(G), hc(G), and γc(G), respectively, are the minimum sizes of a hub set in G, a hub set inducing a connected subgraph, and a connected dominating set. Furthermore, all graphs with γc(G)>hc(G)?4 are obtained by substituting graphs into three consecutive vertices of a cycle; this yields a polynomial-time algorithm to check whether hc(G)=γc(G).     

Optimal algorithms for some intersection radius problems

The intersection radius of a set ofn geometrical objects in ad-dimensional Euclidean space,E ^d , is the radius of the smallest closed hypersphere that intersects all the objects of the set. In this paper, we describe optimal algorithms for some intersection radius problems. We first present a linear-time algorithm to determine the smallest closed hypersphere that intersects a set of hyperplanes inE ^d , assumingd to be a fixed parameter. This is done by reducing the problem to a linear programming problem in a (d+1)-dimensional space, involving 2n linear constraints. We also show how the prune-and-search technique, coupled with the strategy of replacing a ray by a point or a line can be used to solve, in linear time, the intersection radius problem for a set ofn line segments in the plane. Currently, no algorithms are known that solve these intersection radius problems within the same time bounds.     

Parameterized complexity and improved inapproximability for computing the largest j-simplex in a V-polytope

We consider the problem of computing the squared volume of the largest j-simplex contained in an n-dimensional polytope presented by its vertices (a V-polytope). We show that the related decision problem is W[1]-complete, with respect to the parameter j. We also improve the constant inapproximability factor given in [A. Packer, Polynomial-time approximation of largest simplices in V-polytopes, Discrete Appl. Math. 134 (1-3) (2004) 213-237], by showing that there are constants μ<1,c>1 such that it is NP-hard to approximate within a factor of cμn the volume of the largest ⌊μn⌋-simplex contained in an n-dimensional polytope with O(n) vertices.     

Numerical simulations of the generation of Taylor-Görtler vortices during spin-down to rest in finite-length cylinders

Numerical simulations based on the unsteady Navier-Stokes equations are computed to study confined rotating flows during impulsive spin-down to rest. The focus is on the onset of Taylor-Görtler (TG) vortices generated in the sidewall boundary layer. A stability coefficient S_c is introduced to follow the instant action between centrifugal force and pressure gradient. A new criterion for the prediction of the onset and the onset time of TG vortices is suggested. It is based on the sidewall stability coefficient S_blc, which is an integral of S_c over the region of the sidewall boundary layer. According to this criterion, the TG vortices occur when there is a temporally local increase in S_blc history. The numerical tests show that this criterion is more reliable and accurate than the criterion based on the history of the sidewall torque T_s. It is also shown that the increase in S_blc is particularly sensitive to the dramatic increase in the radial velocity gradient with respect to the axial direction near the midplane where the TG vortices appear first.     

Cops and Robbers from a distance

Cops and Robbers is a pursuit and evasion game played on graphs that has received much attention. We consider an extension of Cops and Robbers, distance k Cops and Robbers, where the cops win if at least one of them is of distance at most k from the robber in G. The cop number of a graph G is the minimum number of cops needed to capture the robber in G. The distance k analogue of the cop number, written c_k(G), equals the minimum number of cops needed to win at a given distance k. We study the parameter c_k from algorithmic, structural, and probabilistic perspectives. We supply a classification result for graphs with bounded c_k(G) values and develop an O(n^2s+3) algorithm for determining if c_k(G)≤s for s fixed. We prove that if s is not fixed, then computing c_k(G) is NP-hard. Upper and lower bounds are found for c_k(G) in terms of the order of G. We prove that

     

The complexity of determining the rainbow vertex-connection of a graph

A vertex-colored graph is rainbow vertex-connected if any two vertices are connected by a path whose internal vertices have distinct colors, which was introduced by Krivelevich and Yuster. The rainbow vertex-connection of a connected graph G, denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertex-connected. In this paper, we study the complexity of determining the rainbow vertex-connection of a graph and prove that computing rvc(G) is NP-Hard. Moreover, we show that it is already NP-Complete to decide whether rvc(G)=2. We also prove that the following problem is NP-Complete: given a vertex-colored graph G, check whether the given coloring makes G rainbow vertex-connected.     

M/G/c/c state dependent queuing model for a road traffic system of two sections in tandem

We propose in this article a M/G/c/c state dependent queuing model for road traffic flow. The model is based on finite capacity queuing theory which captures the stationary density-flow relationships. It is also inspired from the deterministic Godunov scheme for the road traffic simulation. We first present a reformulation of the existing linear case of M/G/c/c state dependent model, in order to use flow rather than speed variables. We then extend this model in order to consider upstream traffic demand and downstream traffic supply. After that, we propose the model for two road sections in tandem where both sections influence each other. In order to deal with this mutual dependence, we solve an implicit system given by an algebraic equation. Finally, we derive some performance measures (throughput and expected travel time). A comparison with results predicted by the M/G/c/c state dependent queuing networks shows that the model we propose here captures really the dynamics of the road traffic.     

MgB2 under pressure and plane strain: a DFT study

Full potential density functional theory (DFT) calculations have been performed for the MgB₂ superconductor. Results show that applying positive (negative) pressure leads to a decrement (increment) in the DOS at the Fermi level that this calculations suggest a decrement in Tc under application of positive pressure. In the Γ-A path of momentum space, the band which has the dominant role in conduction properties, moves upward when c increases or a decreases, and moves downward when c decreases or a increases. By relaxation of the system under the plane strain, we have studied the behavior of axial lattice parameter c. Our results show that changes in the axial lattice constant c is one third of the changes of planar lattice constant a. It has been seen that by applying small in-plane strain (tensile), DOS at the Fermi level increases, but it decreases for higher applied strain. For the negative in-plane strain (compression), DOS decreases monotonically at the Fermi level. It can be seen that tension makes the electronic bands to move downward in the Γ-A direction of the reciprocal lattice, but by compression, they move upward. Based on these results, it can be concluded that by applying small tension, one can enhance Tc in MgB₂ compound.     

Phase diagram of a two-dimensional large-Q Potts model in an external field

We use a two-dimensional Wang-Landau sampling algorithm to map out the phase diagram of a Q-state Potts model with Q?10 in an external field H that couples to one state. Finite-size scaling analyses show that for large Q the first-order phase transition point at H=0 is in fact a triple point at which three first-order phase transition lines meet. One such line is restricted to H=0; another line has H?0. The third line, which starts at the H=0 triple point, ends at a critical point (Tc,Hc) which needs to be located in a two-dimensional parameter space. The critical field Hc(Q) is positive and decreases with decreasing Q, which is in qualitative agreement with previous predictions.     

An example for the switching delay feedback stabilization of an infinite dimensional system: The boundary stabilization of a string

For vibrating systems, a delay in the application of a feedback control may destroy the stabilizing effect of the control. In this paper we consider a vibrating string that is fixed at one end and stabilized with a boundary feedback with delay at the other end.We show that certain delays in the boundary feedback preserve the exponential stability of the system. In particular, we show that the system is exponentially stable with delays freely switching between the values 4L/c and 8L/c, where L is the length of the string and c is the wave speed.     

A technique for decomposing algorithms which use a single shared variable

A general theorem is proved which shows how a system of contending asynchronous processes with a special auxiliary supervisor process can be simulated by a system of contending processes without such a supervisor, with only a small increase in the shared space needed for communication. Two applications are presented, synchronization algorithms with different fairness properties requiring N + c and [N/2] + c (c a constant) shared values to synchronize N processes, respectively.     

Exponential Inapproximability of Selecting a Maximum Volume Sub-matrix

Given a matrix A∈? ^m×n (n vectors in m dimensions), and a positive integer k<n, we consider the problem of selecting k column vectors from A such that the volume of the parallelepiped they define is maximum over all possible choices. We prove that there exists δ<1 and c>0 such that this problem is not approximable within 2^?ck for k=δn, unless P=NP.     

Sparse Covers for Planar Graphs and Graphs that Exclude a Fixed Minor

We consider the construction of sparse covers for planar graphs and other graphs that exclude a fixed minor. We present an algorithm that gives a cover for the γ-neighborhood of each node. For planar graphs, the cover has radius less than 16γ and degree no more than 18. For every n node graph that excludes a minor of a fixed size, we present an algorithm that yields a cover with radius no more than 4γ and degree O(logn). This is a significant improvement over previous results for planar graphs and for graphs excluding a fixed minor; in order to obtain clusters with radius O(γ), it was required to have the degree polynomial in n. Our algorithms are based on a recursive application of a basic routine called shortest-path clustering, which seems to be a novel approach to the construction of sparse covers. Since sparse covers have many applications in distributed computing, including compact routing, distributed directories, synchronizers, and Universal TSP, our improved cover construction results in improved algorithms for all these problems, for the class of graphs that exclude a fixed minor.     

Rainbow graph splitting

Given an integer c, an edge colored graph G is said to be rainbow c-splittable if it can be decomposed into at most c vertex-disjoint monochromatic induced subgraphs of distinct colors. We provide a polynomial-time algorithm for deciding whether an edge-colored complete graph is rainbow c-splittable. For not necessarily complete graphs, we show that the problem is polynomial if c=2, whereas for c≥3 it is NP-complete even if the graph has maximum degree 2c−1. Finally, it remains NP-complete even for 2-edge colored graphs of maximum degree 7c−14.