Trifluoromethyl group disorder in crystalline 2,8-bis(trifluoromethyl)-4-hydroxymethylquinoline

The title compound crystallized in space groupPna2₁ with lattice constantsa=13.406(1),b=18.799 (4), andc=4.785(1). The molecule is essentially flat with only fluorine atoms, methylene hydrogen atoms, and the hydroxyl hydrogen atom out of the plane of the quinoline ring. Only one of the trifluoromethyl groups of the title compound is disordered following a pattern observed in other crystal structures. Quantum chemical calculations at the AM1 level are consistent with this phenomenon. Although the carbon atom of the fixed trifluoromethyl group is further from the quinoline nitrogen atom than the carbon atom of the disordered trifluoromethyl group, the fluorine atoms of the fixed trifluoromethyl group more closely approach the quinoline nitrogen atom by 0.3 Å if the C(8)–C(10) bond in the crystal structure is freely rotated.National Research Council Associate     

Statistical characterization of the pore space of random systems of hard spheres

An improved statistical characterization of disordered structures such as metallic glasses, random porous media, or granular matter is presented. Suitable structure models follow the idea of dense random packed spheres, where the spheres represent atoms and particles in the case of metallic glasses and porous or granular matter, respectively. The geometry of the empty space between the atoms or particles is described by means of the already otherwise successful concept of so-called contact distributions. Their exact mathematical forms are unknown for hard sphere systems. Knowledge on these is obtained by means of Monte Carlo simulations of the structure models. The numerical results are approximated by simple and general mathematical expressions, with parameters that can be easily determined. These may serve as additional tools for the structural characterization of disordered matter, including systems of partly penetrable spheres.     

Efficient algebraic multigrid for migration–diffusion–convection–reaction systems arising in electrochemical simulations

The article discusses components and performance of an algebraic multigrid (AMG) preconditioner for the fully coupled multi-ion transport and reaction model (MITReM) with nonlinear boundary conditions, important for electrochemical modeling. The governing partial differential equations (PDEs) are discretized in space by a combined finite element and residual distribution method. Solution of the discrete system is obtained by means of a Newton-based nonlinear solver, and an AMG-preconditioned BICGSTAB Krylov linear solver. The presented AMG preconditioner is based on so-called point-based classical AMG. The linear solver is compared to a standard direct and several one-level iterative solvers for a range of geometries and chemical systems with scientific and industrial relevance. The results indicate that point-based AMG methods, carefully designed, are an attractive alternative to more commonly employed numerical methods for the simulation of complex electrochemical processes.     

α-三Ⅰ约束问题的形式解

提出了α-三Ⅰ约束问题,并在逻辑系统L~*和Luk中给出了这些问题的形式解,建立了这两个逻辑系统中三Ⅰ约束算法的形式推理机制,为α-三Ⅰ约束算法建立了严格的理论基础。     

“Product Partition” and related problems of scheduling and systems reliability: Computational complexity and approximation

Problem Product Partition differs from the NP-complete problem Partition in that the addition operation is replaced by the multiplication operation. Furthermore it differs from the NP-complete problem Subset Product in that it does not contain the product value B in its input. We prove that problem Product Partition and several of its modifications are NP-complete in the strong sense. Our results imply the strong NP-hardness of a number of scheduling problems with start-time-dependent job processing times and a problem of designing a reliable system with a series–parallel structure. It should be noticed that the strong NP-hardness of the considered optimization problems does not preclude the existence of a fully polynomial time approximation scheme (FPTAS) for them. We present a simple FPTAS for one of these problems.     

新型傅里叶变换光谱仪反射镜倾斜容限分析及实验

采用微机电系统微镜阵列和倾斜反射镜替代传统傅里叶变换光谱仪的动镜系统,提出一种基于微机电系统微镜阵列的新型傅里叶变换光谱仪.介绍了该光谱仪的工作原理,分析了倾斜反射镜倾斜角度的容限范围,并搭建了实验系统,进行了实验验证.理论推导表明:在近红外区域,反射镜倾角理论最大值为0.52°,光谱分辨率达到8 nm;在可见光区域,反射镜倾角理论最大值0.183°,光谱分辨率达到3 nm.选取可见光源488 nm激光器进行的实验验证结果表明:在倾角容限范围之内,光谱能准确还原;反之,光谱严重失真.最终,采用复色光源进一步实验验证了理论分析的正确性.     

Localization of disordered bosons and magnets in random fields

We study localization properties of disordered bosons and spins in random fields at zero temperature. We focus on two representatives of different symmetry classes, hard-core bosons (XY magnets) and Ising magnets in random transverse fields, and contrast their physical properties. We describe localization properties using a locator expansion on general lattices. For 1d Ising chains, we find non-analytic behavior of the localization length as a function of energy at ω=0$\omega =0$, ξ⁻¹(ω)=ξ⁻¹(0)+A|ω|^α${\xi }^{-1}\left(\omega \right)={\xi }^{-1}\left(0\right)+A{\left|\omega \right|}^{\alpha }$, with α$\alpha$ vanishing at criticality. This contrasts with the much smoother behavior predicted for XY magnets. We use these results to approach the ordering transition on Bethe lattices of large connectivity K$K$, which mimic the limit of high dimensionality. In both models, in the paramagnetic phase with uniform disorder, the localization length is found to have a local maximum at ω=0$\omega =0$. For the Ising model, we find activated scaling at the phase transition, in agreement with infinite randomness studies. In the Ising model long range order is found to arise due to a delocalization and condensation initiated at ω=0$\omega =0$, without a closing mobility gap. We find that Ising systems establish order on much sparser (fractal) subgraphs than XY models. Possible implications of these results for finite-dimensional systems are discussed.     

Superinsulator–superconductor duality in two dimensions

For nearly a half century the dominant orthodoxy has been that the only effect of the Cooper pairing is the state with zero resistivity at finite temperatures, superconductivity. In this work we demonstrate that by the symmetry of the Heisenberg uncertainty principle relating the amplitude and phase of the superconducting order parameter, Cooper pairing can generate the dual state with zero conductivity in the finite temperature range, superinsulation. We show that this duality realizes in the planar Josephson junction arrays (JJA) via the duality between the Berezinskii–Kosterlitz–Thouless (BKT) transition in the vortex–antivortex plasma, resulting in phase-coherent superconductivity below the transition temperature, and the charge-BKT transition occurring in the insulating state of JJA and marking formation of the low-temperature charge-BKT state, superinsulation. We find that in disordered superconducting films that are on the brink of superconductor–insulator transition the Coulomb forces between the charges acquire two-dimensional character, i.e. the corresponding interaction energy depends logarithmically upon charge separation, bringing the same vortex-charge-BKT transition duality, and realization of superinsulation in disordered films as the low-temperature charge-BKT state. Finally, we discuss possible applications and utilizations of superconductivity–superinsulation duality.     

Analysis of the Solvability of Linear Vibration Models

In this article we consider a general linear vibration problem in variational form. Models for the vibration of systems of elastic bodies can be written in this form. We show how properties of the damping term determines the time differentiability of the solution and establish classes of permissible initial conditions. The proofs are based on a direct link between the variational form and an abstract differential equation.