Resonances in a spring-pendulum: algorithms for equivariant singularity theory

A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.

Dissipative Boussinesq System of Equations in the B\'enard-Marangoni Phenomenon

By using the long-wave approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a B\'enard-Marangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussinesq system is obtained. Finnaly, some speculations are made on the nature of the physical phenomena described by this system of equations.Comment: 15 Pages, REVTEX (Version 3.0), no figure

GronOR:Massively parallel and GPU-accelerated non-orthogonal configuration interaction for large molecular systems

GronOR is a program package for non-orthogonal configuration interaction calculations for an electronic wave function built in terms of anti-symmetrized products of multi-configuration molecular fragment wave functions. The two-electron integrals that have to be processed may be expressed in terms of atomic orbitals or in terms of an orbital basis determined from the molecular orbitals of the fragments. The code has been specifically designed for execution on distributed memory massively parallel and Graphics Processing Unit (GPU)-accelerated computer architectures, using an MPI+OpenACC/OpenMP programming approach. The task-based execution model used in the implementation allows for linear scaling with the number of nodes on the largest pre-exascale architectures available, provides hardware fault resiliency, and enables effective execution on systems with distinct central processing unit-only and GPU-accelerated partitions. The code interfaces with existing multi-configuration electronic structure codes that provide optimized molecular fragment orbitals, configuration interaction coefficients, and the required integrals. Algorithm and implementation details, parallel and accelerated performance benchmarks, and an analysis of the sensitivity of the accuracy of results and computational performance to thresholds used in the calculations are presented

Geometric Satake, Springer correspondence, and small representations

For a simply-connected simple algebraic group $G$ over \C, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of $G$, generalizing a well-known fact about $GL_n$. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number of known facts (mostly due to Broer and Reeder) about small representations of the dual group.Comment: Version 2: minor revisions, 33 page

Ultrafast X-ray scattering of xenon nanoparticles: imaging transient states of matter

Sem informaçãoFemtosecond x-ray laser flashes with power densities of up to 10(14) W/cm(2) at 13.7 nm wavelength were scattered by single xenon clusters in the gas phase. Similar to light scattering from atmospheric microparticles, the x-ray diffraction patterns carry information about the optical constants of the objects. However, the high flux of the x-ray laser induces severe transient changes of the electronic configuration, resulting in a tenfold increase of absorption in the developing nanoplasma. The modification in opaqueness can be correlated to strong atomic charging of the particle leading to excitation of Xe4+. It is shown that single-shot single-particle scattering on femtosecond time scales yields insight into ultrafast processes in highly excited systems where conventional spectroscopy techniques are inherently blind.Femtosecond x-ray laser flashes with power densities of up to 10(14) W/cm(2) at 13.7 nm wavelength were scattered by single xenon clusters in the gas phase. Similar to light scattering from atmospheric microparticles, the x-ray diffraction patterns carry information about the optical constants of the objects. However, the high flux of the x-ray laser induces severe transient changes of the electronic configuration, resulting in a tenfold increase of absorption in the developing nanoplasma. The modification in opaqueness can be correlated to strong atomic charging of the particle leading to excitation of Xe4+. It is shown that single-shot single-particle scattering on femtosecond time scales yields insight into ultrafast processes in highly excited systems where conventional spectroscopy techniques are inherently blind.108915Sem informaçãoSem informaçãoBMBF [05KS4KT1, 05KS7KT2]HGF Virtuelles Institut [VH-VI-103, VH-VI-302]Sem informaçãoWe would like to thank all staff at FLASH for their outstanding support. Funding is acknowledged from BMBF 05KS4KT1 and 05KS7KT2, as well as HGF Virtuelles Institut VH-VI-103 and VH-VI-302

Modeling the dynamics of glacial cycles

This article is concerned with the dynamics of glacial cycles observed in the geological record of the Pleistocene Epoch. It focuses on a conceptual model proposed by Maasch and Saltzman [J. Geophys. Res.,95, D2 (1990), pp. 1955-1963], which is based on physical arguments and emphasizes the role of atmospheric CO2 in the generation and persistence of periodic orbits (limit cycles). The model consists of three ordinary differential equations with four parameters for the anomalies of the total global ice mass, the atmospheric CO2 concentration, and the volume of the North Atlantic Deep Water (NADW). In this article, it is shown that a simplified two-dimensional symmetric version displays many of the essential features of the full model, including equilibrium states, limit cycles, their basic bifurcations, and a Bogdanov-Takens point that serves as an organizing center for the local and global dynamics. Also, symmetry breaking splits the Bogdanov-Takens point into two, with different local dynamics in their neighborhoods