Simulation model for shapiro time delay and light deflection experiments

The time delay experiment proposed by I.I. Shapiro in 1964 and conducted in the seventies was the most precise experiment of general relativity until that time. Further experimentation has improved the accuracy level of both the time delay and the light deflection experiments. A simulation model is proposed that involves only a simple mass and time transformation factor involving velocity of light. The light deflection and the time delay experiments are numerically simulated using this model that does not use the general relativistic equations. The computed values presented in this paper compare well with recent levels of accuracy of their respective experimental results.     

Controlled evaporative self-assembly of polymer nanoribbons using oscillating capillary bridges

Evaporative self-assembly (ESA), based on the “coffee-ring” effect, is a versatile technique for assembling particle solutions into mesoscale patterns and structures on different substrates. ESA works with a wide variety of organic and inorganic materials, where the solution is a combination of volatile solvent and nonvolatile solute. Modified ESA methods, such as “stop-and-go flow coating,” use a programmed meniscus “stick–slip” motion to create mesoscale assemblies with controlled shape, size, and architecture. However, current methods are not scalable for increased production volumes or patterning large surface areas. We demonstrate a new ESA method, where an oscillating blade controls the meniscus depinning and drives the evaporative assembly of solutes at the pinned meniscus. Results show that oscillation frequency and substrate speed control time/distance intervals between successive meniscus depinning, and the assembly dimensions depend on solution concentration, oscillation frequency, substrate speed, and meniscus height. We report the mechanism of the meniscus depinning and the control over assembly cross-sectional dimensions. This advance provides a scalable ESA method with faster processing times and maintained advantages. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1545–1551     

A DFT study on the formation of a phosphohistidine intermediate in prostatic acid phosphatase

Histidine phosphatases are a class of enzymes that are characterized by the presence of a conserved RHGXRXP motif. This motif contains a catalytic histidine that is being phosphorylated in the course of a dephosphorylation reaction catalyzed by these enzymes. Prostatic acid phosphatase (PAP) is one such enzyme. The dephosphorylation of phosphotyrosine by PAP is a two-step process. The first step involves the transfer of a phosphate group from the substrate to the histidine (His12). The present study reports on the details of the first step of this reaction, which was investigated using a series of quantum chemistry calculations. A number of quantum models were constructed containing various residues that were thought to play a role in the mechanism. In all these models, the transition state displayed an associative character. The transition state is stabilized by three active site arginines (Arg11, Arg15, and Arg79), two of which belong to the aforementioned conserved motif. The work also demonstrated that His12 could act as a nucleophile. The enzyme is further characterized by a His257-Asp258 motif. The role of Asp258 has been elusive. In this work, we propose that Asp258 acts as a proton donor which becomes protonated when the substrate enters the binding pocket. Evidence is also obtained that the transfer of a proton from Asp258 to the leaving group is possibly mediated by a water molecule in the active site. The work also underlines the importance of His257 in lowering the energy barrier for the nucleophilic attack.     

Controlled processing of polymer nanoribbons: Enabling microhelix transformations

Flow‐coated, two‐dimensional polymer ribbon structures undergo a shape‐transformation into a three‐dimensional helix upon their release into a solution. Driven by surface forces and due to geometric asymmetry, the helix radius and spring constant depend upon the ribbon cross‐section dimensions, surface energy, and material elastic modulus. Such spring‐like microhelices offer multiple functionalities combined with mechanical stretching and shape recovery. Fabricating such microhelices requires a sequence of processing steps, beginning with flow‐coating of ribbons on a substrate, followed by etching of a “scum layer” to allow for an independent release into a solution, upon which shape‐transformation occurs. During the deposition‐etch‐release sequence, various control parameters influence the nanoribbon size and geometry, hence the helix properties. The experimental study presented here focuses on the influence of meniscus height, substrate velocity, substrate surface energy, and etch time on nanoribbon size (height and width), scum layer thickness, and helix radius. The results show that meniscus height and contact angle dictate flux toward the meniscus edge and volume available for spatial assembly, allowing control over the aspect ratio of ribbons. We vary the aspect ratio by two orders of magnitude, while maintaining geometric asymmetry needed for helix shape‐transformation. We provide robust scaling for the nanoribbon size and geometry and report the advantages and disadvantages of different parameters, in the control of polymer nanoribbon and helix fabrication. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1270–1278     

Schur complement preconditioners for anisotropic problems

We present two new variants of Schur complement domain decompositionpreconditioners suitable for 2D anisotropic problems. Thesevariants are based on adaptations of the probing idea, describedby Chan et al (1992 Fifth Int. Symp. on Domain DecompositionMethods for Partial Differential Equations, Philadelphia: SIAM,pp 236-249), used in conjunction with a coarse grid approximationas introduced by Bramble et al (1986 Math. Comput. 47, 103-134).The new methods are specifically designed for situations wherethe coupling between neighbouring interfaces is stronger thanthe coupling within an interface. Taking into account this strongcoupling, one variant uses a multicolour probing technique toavoid distortion in the probe approximations that appear whenusing the method proposed by Chan et al. The second techniqueuses additional probe matrices to approximate not only the couplingwithin the interfaces but also the coupling between interfacepoints across the subdomains. This latter procedure looks somewhatlike an alternating line relaxation method for anisotropic problems,see Brandt (1977 Math. Comput.. 31, 333-390). To assess therelevance of the new preconditioners, we compare their numericalbehaviour with well known robust preconditioners such as thebalanced Neumann-Neumann method proposed by Mandel (1993 Commun.Numer. Methods Eng.. 9, 233-241).     

评《马氏决策过程》

（《马氏决策过程》,侯振挺、郭先平著,长沙,湖南科技出版社,1997,中文版,386页,定价：28元）马尔可夫决策过程是概率论的运筹学的理论研究和实际应用中极其重要的领域之一．随着中国和国际上对马尔可夫决策过程（MarkovDecisionProcesses,简记为MDP）研究的新进展,许     

Unitary group decomposition of Hamiltonian operators. I. Structure and sizes in the Hartree-Fock basis

The extent to which the Hartree-Fock (HF) procedure converts a two-body interaction into an effective one-body operator has been studied. For this purpose, the nuclear Hamiltonian is classified according to its tensor properties under the unitary group U(N) and its direct-sum subgroup U(m) + U(N ? m) generated by the Hartree-Fock procedure. Here N is the total number of HF single particle states of which m are occupied. The sizes of different tensor parts in m-particle spaces have been determined for both U(N) and U(m) + U(N ? m). In terms of these sizes a ratio is defined which provides a measure of the conversion efficiency of HF and a global measure of the goodness of HF s.p. basis. This ratio is evaluated for N = Z even-even nuclei in 0d-1s shell and 0f-1p shell using realistic Hamiltonian operators.     

Simulation model for anomalous precession of the perihelion of mercury's orbit

The ‘anomalous perihelion precession’ of Mercury, announced by Le Verrier in 1859, was a highly controversial topic for more than half a century and invoked many alternative theories until 1916, when Einstein presented his theory of general relativity as an alternative theory of gravitation and showed perihelion precession to be one of its potential manifestations. As perihelion precession was a directly derived result of the full General Theory and not just the Equivalence Principle, Einstein viewed it as the most critical test of his theory. This paper presents the computed value of the anomalous perihelion precession of Mercury's orbit using a new relativistic simulation model that employs a simple transformation factor for mass and time, proposed in an earlier paper. This computed value compares well with the prediction of general relativity and is, also, in complete agreement with the observed value within its range of uncertainty. No general relativistic equations have been used for computing the results presented in this paper.