Quasiparticle structure and coherent propagation in the t−Jz−J⊥t-J_{z}-J_{\perp} model

Numerical studies, from variational calculation to exact diagonalization, all indicate that the quasiparticle generated by introducing one hole into a two-dimensional quantum antiferromagnet has the same nature as a string state in the $t-J_{z}$ model. Based on this observation, we attempt to visualize the quasiparticle formation and subsequent coherent propagation at low energy by studying the generalized $t-J_{z}-J_{\perp}$ model in which we first diagonalize the $t-J_{z}$ model and then perform a {\em degenerate} perturbation in $J_{\perp}$. We construct the quasiparticle state and derive an effective Hamiltonian describing the coherent propagation of the quasiparticle and its interaction with the spin wave excitations in the presence of the N\'{e}el order. We expect that qualitative properties of the quasiparticle remain intact when analytically continuing $J_{\perp}$ from the anisotropic $J_{\perp} < J_{z}$ to the isotropic $J_{\perp} = J_{z}$ limit, despite the fact that the spin wave excitations change from gapful to gapless. Extrapolating to $J_{\perp}=J_{z}$, our quasiparticle dispersion and spectral weight compare well with the exact numerical results for small clusters.Comment: Revised with minor changes and references updated. To appear in Phys. Rev. B., Jan. 1996. 10 pages, The complete PostScript file including figures can be obtained via ftp at ftp://serval.berkeley.edu/tjzjp.ps . It is also posted in the WEB site of Niels Bohr Institute at http://roemer.fys.ku.dk/recent.ht

Multi-patch discontinuous Galerkin isogeometric analysis for wave propagation: explicit time-stepping and efficient mass matrix inversion

We present a class of spline finite element methods for time-domain wave propagation which are particularly amenable to explicit time-stepping. The proposed methods utilize a discontinuous Galerkin discretization to enforce continuity of the solution field across geometric patches in a multi-patch setting, which yields a mass matrix with convenient block diagonal structure. Over each patch, we show how to accurately and efficiently invert mass matrices in the presence of curved geometries by using a weight-adjusted approximation of the mass matrix inverse. This approximation restores a tensor product structure while retaining provable high order accuracy and semi-discrete energy stability. We also estimate the maximum stable timestep for spline-based finite elements and show that the use of spline spaces result in less stringent CFL restrictions than equivalent piecewise continuous or discontinuous finite element spaces. Finally, we explore the use of optimal knot vectors based on L2 n-widths. We show how the use of optimal knot vectors can improve both approximation properties and the maximum stable timestep, and present a simple heuristic method for approximating optimal knot positions. Numerical experiments confirm the accuracy and stability of the proposed methods

Amidine-Mediated Zwitterionic Ring-Opening Polymerization of N-Alkyl N-Carboxyanhydride: Mechanism, Kinetics, and Architecture Elucidation

© 2016 American Chemical Society. Zwitterionic ring-opening polymerization (ZROP) of N-butyl N-carboxyanhydrides (Bu-NCAs) has been investigated using 1,8-diazabicycloundec-7-ene (DBU), a bicyclic amidine initiator. It was found that poly(N-butylglycine)s (PNBGs) with molecular weight (Mn) in the 3.5-32.4 kg mol-1 range and polydispersity index (PDI) in the 1.02-1.12 range can be readily obtained by systematically varying the initial monomer to initiator feed ratio. The polymerization exhibits characteristics of a controlled polymerization, as evidenced by the linear increase of polymer molecular weight with conversion and the successful enchainment experiments. Kinetic studies revealed that the reaction is first-order dependent on the monomer and the DBU concentration. The rate of initiation is comparable to that of the propagation. Random copolypeptoids of poly[(N-propargylglycine)-r-(N-butylglycine)]s [P(NPgG-r-NBG)s] were also synthesized by DBU-mediated copolymerization of Bu-NCA and N-propargyl N-carboxyanhydride (Pg-NCA). Subsequent grafting with azido-terminated poly(ethylene glycol) (PEG) produces bottlebrush copolymers. Analysis of bottlebrush copolymer samples using atomic force microscopy (AFM) revealed a surface morphology of toroid-shaped nanostructures, consistent with the polypeptoid backbone having cyclic architecture. Small-angle neutron scattering (SANS) characterization of the bottlebrush polymer ensemble in solution also confirms the cyclic architecture of the polypeptoid backbones

New acceleration technique for the backpropagation algorithm

Artificial neural networks have been studied for many years in the hope of achieving human like performance in the area of pattern recognition, speech synthesis and higher level of cognitive process. In the connectionist model there are several interconnected processing elements called the neurons that have limited processing capability. Even though the rate of information transmitted between these elements is limited, the complex interconnection and the cooperative interaction between these elements results in a vastly increased computing power; The neural network models are specified by an organized network topology of interconnected neurons. These networks have to be trained in order them to be used for a specific purpose. Backpropagation is one of the popular methods of training the neural networks. There has been a lot of improvement over the speed of convergence of standard backpropagation algorithm in the recent past. Herein we have presented a new technique for accelerating the existing backpropagation without modifying it. We have used the fourth order interpolation method for the dominant eigen values, by using these we change the slope of the activation function. And by doing so we increase the speed of convergence of the backpropagation algorithm; Our experiments have shown significant improvement in the convergence time for problems widely used in benchmarKing Three to ten fold decrease in convergence time is achieved. Convergence time decreases as the complexity of the problem increases. The technique adjusts the energy state of the system so as to escape from local minima