Semicanonical bases and preprojective algebras

We study the multiplicative properties of the dual of Lusztig's semicanonical basis. The elements of this basis are naturally indexed by the irreducible components of Lusztig's nilpotent varieties, which can be interpreted as varieties of modules over preprojective algebras. We prove that the product of two dual semicanonical basis vectors ρZ^′ and ρZ^″ is again a dual semicanonical basis vector provided the closure of the direct sum of the corresponding two irreducible components Z^′ and Z^″ is again an irreducible component. It follows that the semicanonical basis and the canonical basis coincide if and only if we are in Dynkin type An with n?4. Finally, we provide a detailed study of the varieties of modules over the preprojective algebra of type A₅. We show that in this case the multiplicative properties of the dual semicanonical basis are controlled by the Ringel form of a certain tubular algebra of type (6,3,2) and by the corresponding elliptic root system of type .     

Localized subharmonic waves in a circularly vibrated granular bed

Localized period-doubling waves arise in circularly shaken granular beds contained in an annular channel. These solitary wave packets are accompanied by a locally increased particle density. The width and velocity of the granular wave pulse are measured as a function of the bed height. A continuum model for the material distribution, based on the measured granular transport velocity as a function of the bed thickness, captures the essence of the experimental findings.     

Distributed memory parallel implementation of energies and gradients for second-order Møller-Plesset perturbation theory with the resolution-of-the-identity approximation

We present a parallel implementation of second-order M?ller-Plesset perturbation theory with the resolution-of-the-identity approximation (RI-MP2). The implementation is based on a recent improved sequential implementation of RI-MP2 within the Turbomole program package and employs the message passing interface (MPI) standard for communication between distributed memory nodes. The parallel implementation extends the applicability of canonical MP2 to considerably larger systems. Examples are presented for full geometry optimizations with up to 60 atoms and 3300 basis functions and MP2 energy calculations with more than 200 atoms and 7000 basis functions.     

Assignment and extraction of dynamics of a small molecule with a complex vibrational spectrum: thiophosgene

The dispersed fluorescence spectrum of the ground electronic state of thiophosgene, SCCl2, is analyzed in a very complex region of vibrational excitation, 7000-9000 cm(-1). The final result is that most of the inferred excited vibrational levels are assigned in terms of approximate constants of the motion. Furthermore, each level is associated with a rung on a ladder of quantum states on the basis of common reduced dimension fundamental motions. The resulting ladders cannot be identified by any experimental means, and it is the interspersing in energy of their rungs that makes the spectrum complex even after the process of level separation into polyads. Van Vleck perturbation theory is used to create polyad constants of the motion and a spectroscopic Hamiltonian from a potential fitted to experimental data. The eigen functions of this spectroscopic Hamiltonian are rewritten as semiclassical wave functions and transformed to a representation that allows us to analyze and assign the spectra with no other work other than to utilize concepts from nonlinear dynamics.     

Structural evolution of anionic silicon clusters SiN (20 <or= N <or= 45)

Results of a combined photoelectron spectroscopy and first-principles density-functional study of SiN- clusters in the size range 20 or= 20. For 28 相似文献   

Mechanical Properties of Bacterially Synthesized Nanocellulose Hydrogels

The mechanical characteristics of bacterially synthesized nano-cellulose (BNC) were studied with uniaxial compression and tensile tests. Compressive loads result in a release of water and the deformation of the water-saturated network corresponds approximately to the volume of released water. The BNC hydrogel exhibits a mainly viscous response under compression. The strain response under tensile loads has an elastic and a viscous component. This can be described with a Maxwell model, where the viscosity is strain rate-dependent. When the aqueous phase of the BNC hydrogel is stabilized with an additional alginate hydrogel matrix, the system exhibits an elastic response under compressive loads. The analysis of the ‘alginated’ BNC network with the Maxwell model shows that the alginate matrix increases the viscosity of the composite system. The results of the mechanical tests show that the water absorbed in the BNC hydrogel strongly influences its mechanical behavior.     

Linking confinement to spectral properties of the dirac operator

We represent Polyakov loops and their correlators as spectral sums of eigenvalues and eigenmodes of the lattice Dirac operator. The deconfinement transition of pure gauge theory is characterized as a change in the response of moments of eigenvalues to varying the boundary conditions of the Dirac operator. We argue that the potential between static quarks is linked to spatial correlations of Dirac eigenvectors.