Antibandwidth and cyclic antibandwidth of meshes and hypercubes

The antibandwidth problem consists of placing the vertices of a graph on a line in consecutive integer points in such a way that the minimum difference of adjacent vertices is maximised. The problem was originally introduced in [J.Y.-T. Leung, O. Vornberger, J.D. Witthoff, On some variants of the bandwidth minimisation problem, SIAM Journal of Computing 13 (1984) 650-667] in connection with the multiprocessor scheduling problems and can also be understood as a dual problem to the well-known bandwidth problem, as a special radiocolouring problem or as a variant of obnoxious facility location problems. The antibandwidth problem is NP-hard, there are a few classes of graphs with polynomial time complexities. Exact results for nontrivial graphs are very rare. Miller and Pritikin [Z. Miller, D. Pritikin, On the separation number of a graph, Networks 19 (1989) 651-666] showed tight bounds for the two-dimensional meshes and hypercubes. We solve the antibandwidth problem precisely for two-dimensional meshes, tori and estimate the antibandwidth value for hypercubes up to the third-order term. The cyclic antibandwidth problem is to embed an n-vertex graph into the cycle C_n, such that the minimum distance (measured in the cycle) of adjacent vertices is maximised. This is a natural extension of the antibandwidth problem or a dual problem to the cyclic bandwidth problem. We start investigating this invariant for typical graphs and prove basic facts and exact results for the same product graphs as for the antibandwidth.     

A characteristic finite element method with local mesh refinements for the Lamm equation in analytical ultracentrifugation

The Lamm equation is a fundamental differential equation in analytical ultracentrifugation, for describing the transport of solutes in an ultracentrifuge cell. In this article, we present a characteristic finite element method with local mesh refinements for solving the Lamm equation. The numerical method is mass‐conservative by design and allows relatively large time steps to be used. Numerical experiments indicate that the numerical solutions are oscillation‐free in the region near the cell bottom, where mass build up and large concentration gradients occur. Positivity of solutions is also well kept. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

RNA unrestrained molecular dynamics ensemble improves agreement with experimental NMR data compared to single static structure: a test case

Nuclear magnetic resonance (NMR) provides structural and dynamic information reflecting an average, often non-linear, of multiple solution-state conformations. Therefore, a single optimized structure derived from NMR refinement may be misleading if the NMR data actually result from averaging of distinct conformers. It is hypothesized that a conformational ensemble generated by a valid molecular dynamics (MD) simulation should be able to improve agreement with the NMR data set compared with the single optimized starting structure. Using a model system consisting of two sequence-related self-complementary ribonucleotide octamers for which NMR data was available, 0.3 ns particle mesh Ewald MD simulations were performed in the AMBER force field in the presence of explicit water and counterions. Agreement of the averaged properties of the molecular dynamics ensembles with NMR data such as homonuclear proton nuclear Overhauser effect (NOE)-based distance constraints, homonuclear proton and heteronuclear ¹H–³¹P coupling constant (J) data, and qualitative NMR information on hydrogen bond occupancy, was systematically assessed. Despite the short length of the simulation, the ensemble generated from it agreed with the NMR experimental constraints more completely than the single optimized NMR structure. This suggests that short unrestrained MD simulations may be of utility in interpreting NMR results. As expected, a 0.5 ns simulation utilizing a distance dependent dielectric did not improve agreement with the NMR data, consistent with its inferior exploration of conformational space as assessed by 2-D RMSD plots. Thus, ability to rapidly improve agreement with NMR constraints may be a sensitive diagnostic of the MD methods themselves.     

Valence Tautomerism in Octahedral and Square‐Planar Phenoxyl–Nickel(II) Complexes: Are Imino Nitrogen Atoms Good Friends?

The two tetradentate ligands H(2)L and H(2)L(Me) afford the slightly distorted square-planar low-spin Ni(II) complexes 1 and 2, which comprise two coordinated phenolate groups. Complex 1 has been electrochemically oxidized into 1(+), which contains a coordinated phenoxyl radical, with a contribution from the nickel orbital. In the presence of pyridine, 1(+) is converted into 1(Py) (+), an octahedral phenolate nickel(III) complex with two pyridines axially coordinated: An intramolecular electron transfer (valence tautomerism) is promoted by the geometrical changes, from square planar to octahedral, around the metal center. The tetradentate ligand H(2)L(Me), in the presence of pyridine, and the hexadentate ligand H(2)L(Py) in CH(2)Cl(2) afford, respectively, the octahedral high-spin Ni(II) complexes 2(Py) and 3, which involve two equatorial phenolates and two axially coordinated pyridines. At 100 K, the one-electron-oxidized product 2(Py) (+) comprises a phenoxyl radical ferromagnetically coupled to the high-spin Ni(II) ion, with large zero-field splitting parameters, while 3(+) involves a phenoxyl radical antiferromagnetically coupled to the high-spin Ni(II) ion.     

Ethylene oligomerisation and polymerisation with nickel phosphanylenolates bearing electron-withdrawing substituents: Structure-reactivity relationships

Three SHOP-type catalysts, in which the C=C(O) double bond was substituted by electron-withdrawing substituents, [Ni{Ph2PC(R1)=C(R2)O}Ph(PPh3)] (2: R1,R2 = -C(Me)=NN(Ph)-; 3: R1 = CO2Et, R2 = Ph; 4: R1 = CO2Et, R2 = CF3), were assessed as ethylene-oligomerisation and -polymerisation catalysts and compared to Keim's complex, [Ni{Ph2PCH=C(Ph)O}Ph(PPh3)] (1). A rationale for the influence of the double-bond substituents of the P,O-chelate unit on the catalytic properties is proposed, on the basis of X-ray diffraction studies, spectroscopic data and DFT-B3 LYP calculations. Whatever their relative electron-withdrawing strength, the R1 and R2 substituents induce an increase in activity with respect to catalyst 1. For those systems in which the basicity of the oxygen atom is decreased relative to that of the phosphorus atom, the chain-propagation rate increases with respect to that for catalyst 1. Reduction of the basicity of the P relative to that of the O, however, induces higher chain-termination rates.     

基于无线Mesh网络的一种信道分配算法及路由协议

提出了在多信道环境下的无线Mesh网络中的一种混合型路由协议TOIRP(tree-based and on-de-mand integrated routing protocol)以及一种分布式的信道分配算法CLBCA(channel load based channel assign-ment).TOIRP协议采用HWMP(hybrid wireless mesh protocol)所提出的混合路由技术,将基于树的路由与传统的AODV(ad hoc on-demand distance vector)路由相结合,减少路由发现的时延,同时采用了一种新的路由判据CETTI(cumulative expected transmission time with interference).该路由判据充分考虑多信道的特性,设计了一种量化通信干扰的方法,将干扰分为外部数据流对路径的干扰以及路径内部数据流的干扰两个方面,并综合考虑了跳数、时延等因素,提高了网络的吞吐量.信道分配算法分为收发器与邻居节点绑定和收发器与信道绑定两个部分,将信道的负载作为选择信道的标准,避免了多信道中常见的信道依赖所造成的影响,并且提高了信道的利用率.模拟结果表明,采用新的路由判据后,网络的吞吐量最优情况下得到提升.     

High-order Lagrangian cell-centered conservative scheme on unstructured meshes

A high-order Lagrangian cell-centered conservative gas dynamics scheme is presented on unstructured meshes. A high-order piecewise pressure of the cell is intro- duced. With the high-order piecewise pressure of the cell, the high-order spatial discretiza- tion fluxes are constructed. The time discretization of the spatial fluxes is performed by means of the Taylor expansions of the spatial discretization fluxes. The vertex velocities are evaluated in a consistent manner due to an original solver located at the nodes by means of momentum conservation. Many numerical tests are presented to demonstrate the robustness and the accuracy of the scheme.     

网格模型PDE曲面重建中的边界曲线构造

利用偏微分方程(PDE)进行曲面拟合是计算机图形学研究领域中的常用方法,该类方法通过选取适当的边界条件来构造PDE,用PDE的解来表示几何曲面.基于网格简化方法和离散曲面测地线计算等技术,提出一种从网格模型提取PDE曲面片边界条件曲线的方法.首先,对复杂模型进行简化并分片处理;通过计算离散曲面的测地线为每个分片定义相应的PDE边界条件曲线,进而构造复杂模型的PDE拟合表面.最后,通过细分方法建立原模型的多分辨率表示.实验表明,该方法可以对具有不同几何复杂度的网格模型进行处理,产生具有细分连通性的多分辨网格模型.     

A Numerical Study of Blowup in the Harmonic Map Heat Flow Using the MMPDE Moving Mesh Method

The numerical solution of the harmonic heat map flow problems with blowup in finite or infinite time is considered using an adaptive moving mesh method. A properly chosen monitor function is derived so that the moving mesh method can be used to simulate blowup and produce accurate blowup profiles which agree with formal asymptotic analysis. Moreover, the moving mesh method has finite time blowup when the underlying continuous problem does. In situations where the continuous problem has infinite time blowup, the moving mesh method exhibits finite time blowup with a blowup time tending to infinity as the number of mesh points increases. The inadequacy of a uniform mesh solution is clearly demonstrated.     

A Pseudo-Stokes Mesh Motion Algorithm

This work presents a moving mesh methodology based on the solution of a pseudo flow problem. The mesh motion is modeled as a pseudo Stokes problem solved by an explicit finite element projection method. The mesh quality requirements are satisfied by employing a null divergent velocity condition. This methodology is applied to triangular unstructured meshes and compared to well known approaches such as the ones based on diffusion and pseudo structural problems. One of the test cases is an airfoil with a fully meshed domain. A specific rotation velocity is imposed as the airfoil boundary condition. The other test is a set of two cylinders that move toward each other. A mesh quality criterion is employed to identify critically distorted elements and to evaluate the performance of each mesh motion approach. The results obtained for each test case show that the pseudo-flow methodology produces satisfactory meshes during the moving process.