44,216 research outputs found
Ab Initio Studies of Cellulose I: Crystal Structure, Intermolecular Forces, and Interactions with Water
We have studied the structural, energetic, and electronic properties of crystalline cellulose I using first-principles density functional theory (DFT) with semiempirical dispersion corrections. The predicted crystal structures of both Iα and Iβ phases agree well with experiments and are greatly improved over those predicted by DFT within the local and semilocal density approximations. The cohesive energy is analyzed in terms of interchain and intersheet interactions, which are calculated to be of similar magnitude. Both hydrogen bonding and van der Waals (vdW) dispersion forces are found to be responsible for binding cellulose chains together. In particular, dispersion corrections prove to be indispensable in reproducing the equilibrium intersheet distance and binding strength; however, they do not improve the underestimated hydrogen bond length from DFT. The computed energy gaps of crystalline cellulose are 5.7 eV (Iα) and 5.4 eV (Iβ), whereas localized surface states appear within the gap for surfaces. The interaction of cellulose with water is studied by investigating the adsorption of a single water molecule on the hydrophobic Iβ(100) surface. The formation of hydrogen bond at the water/cellulose interface is shown to depend sensitively on the adsorption site for example above the equatorial hydroxyls or the CH moieties pointing out of the cellulose sheets. VdW dispersion interactions also contribute significantly to the adsorption energy
Global Gevrey hypoellipticity for the twisted Laplacian on forms
We study in this paper the global hypoellipticity property in the Gevrey
category for the generalized twisted Laplacian on forms. Different from the
0-form case, where the twisted Laplacian is a scalar operator, this is a system
of differential operators when acting on forms, each component operator being
elliptic locally and degenerate globally. We obtain here the global
hypoellipticity in anisotropic Gevrey space
OPE of the stress tensors and surface operators
We demonstrate that the divergent terms in the OPE of a stress tensor and a
surface operator of general shape cannot be constructed only from local
geometric data depending only on the shape of the surface. We verify this
holographically at d=3 for Wilson line operators or equivalently the twist
operator corresponding to computing the entanglement entropy using the
Ryu-Takayanagi formula. We discuss possible implications of this result.Comment: 20 pages, no figur
Arbitrary phase rotation of the marked state can not be used for Grover's quantum search algorithm
A misunderstanding that an arbitrary phase rotation of the marked state
together with the inversion about average operation in Grover's search
algorithm can be used to construct a (less efficient) quantum search algorithm
is cleared. The rotation of the phase of the marked state is not only the
choice for efficiency, but also vital in Grover's quantum search algorithm. The
results also show that Grover's quantum search algorithm is robust.Comment: 5 pages, 5 figure
Fast Proximal Linearized Alternating Direction Method of Multiplier with Parallel Splitting
The Augmented Lagragian Method (ALM) and Alternating Direction Method of
Multiplier (ADMM) have been powerful optimization methods for general convex
programming subject to linear constraint. We consider the convex problem whose
objective consists of a smooth part and a nonsmooth but simple part. We propose
the Fast Proximal Augmented Lagragian Method (Fast PALM) which achieves the
convergence rate , compared with by the traditional PALM. In
order to further reduce the per-iteration complexity and handle the
multi-blocks problem, we propose the Fast Proximal ADMM with Parallel Splitting
(Fast PL-ADMM-PS) method. It also partially improves the rate related to the
smooth part of the objective function. Experimental results on both synthesized
and real world data demonstrate that our fast methods significantly improve the
previous PALM and ADMM.Comment: AAAI 201
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