Abstract:
Understanding of magnetic domain wall dynamic behavior is one of the important issues in the realization of spintronic device based on domain wall motion. We investigate the dynamic behaviors of the magnetic domain wall propagation in L-shaped ferromagnetic nanowires under external magnetic driving fields. By micromagnetic simulation, we observe a dynamic characteristic of the magnetic domain wall in a ferromagnetic nanowire with varying the external field. By changing the nanowire thickness, we examine the influence of the demagnetizing field from the nanowire surface on the domain wall dynamics under a magnetic driving field after Walker breakdown field. Using an auxilliary magnetic field perpendicular to the nanowires, we analyze the effect of the demagnetizing field on the domain wall dynamic behaviors. The results show that the stronger external field or the thicker nanowire can enhance the generation of the demagnetizing field on the nanowire surface, leading to the occurrence of the Walker breakdown phenomenon with the periodic change of the inner spin structure of the domain wall during the domain wall propagation in the nanowires. By using an auxilliary magnetic field perpendicular to the nanowires, we find that the strength and the direction of the demagnetizing field can be modulated. It implies that the dynamic behavior of domain wall propagation in the nanowire is controllable.

Abstract:
We compute the purely gluonic contribution to the static QCD potential at three--loop order. This completes the computation of the static potential at this order.

Abstract:
Electro-static potentials for samples with the topology of a ring and penetrated by an Aharonov-Bohm flux are discussed. The sensitivity of the electron-density distribution to small variations in the flux generates an effective electro-static potential which is itself a periodic function of flux. We investigate a simple model in which the flux sensitive potential leads to a persistent current which is enhanced compared to that of a loop of non-interacting electrons. For sample geometries with contacts the sensitivity of the electro-static potential to flux leads to a flux-induced capacitance. This capacitance gives the variation in charge due to an increment in flux. The flux-induced capacitance is contrasted with the electro-chemical capacitance which gives the variation in charge due to an increment in an electro-chemical potential. The discussion is formulated in terms of characteristic functions which give the variation of the electro-static potential in the interior of the conductor due to an increment in the external control parameters (flux, electro-chemical potentials). Paper submitted to the 16th Nordic Semiconductor Meeting, Laugarvatan, Iceland, June 12-15, 1994. The proceedings will be published in Physica Scripta.

Abstract:
In quantum chromodynamics (QCD), the binding energy of an infinitely heavy quark--antiquark pair in a color singlet state can be calculated as a function of the distance. We investigate this static potential of QCD perturbatively and calculate the full two-loop coefficient, correcting an earlier result. Beyond this order, the perturbative expansion breaks down.

Abstract:
We consider the three-loop corrections to the static potential which are induced by a closed fermion loop. For the reduction of the occurring integrals a combination of the Gr\"obner and Laporta algorithm has been used and the evaluation of the master integrals has been performed with the help of the Mellin-Barnes technique. The fermionic three-loop corrections amount to 2% of the tree-level result for top quarks, 8% for bottom quarks and 27% for the charm quark system.

Abstract:
We obtain refined generating series formulae for equivariant characteristic classes of external and symmetric products of singular complex quasi-projective varieties. More concretely, we study equivariant versions of Todd, Chern and Hirzebruch classes for singular spaces, with values in delocalized Borel-Moore homology of external and symmetric products. As a byproduct, we recover our previous characteristic class formulae for symmetric products, and obtain new equivariant generalizations of these results.

Abstract:
Loop Quantum Cosmology strongly modifies the high-energy dynamics of Friedman-Robertson-Walker models and removes the big-bang singularity. We investigate how LQC corrections affect the stability properties of the Einstein static universe. In General Relativity, the Einstein static model with positive cosmological constant Lambda is unstable to homogeneous perturbations. We show that LQC modifications can lead to a centre of stability for a large enough positive value of Lambda.

Abstract:
Cerebellar anatomy is known for its crystal like structure, where neurons and connections are precisely and repeatedly organized with minor variations across the Cerebellar Cortex. The olivo-cerebellar loop, denoting the connections between the Cerebellar cortex, Inferior Olive and Cerebellar Nuclei (CN), is also modularly organized to form what is known as the cerebellar module. In contrast to the relatively organized and static anatomy, the cerebellum is innervated by a wide variety of neuromodulator carrying axons that are heterogeneously distributed along the olivo-cerebellar loop, providing heterogeneity to the static structure. In this manuscript we review modulatory processes in the olivo-cerebellar loop. We start by discussing the relationship between neuromodulators and the animal behavioral states. This is followed with an overview of the cerebellar neuromodulatory signals and a short discussion of why and when the cerebellar activity should be modulated. We then devote a section for three types of neurons where we briefly review its properties and propose possible neuromodulation scenarios.

Abstract:
A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. The connection and curvature forms of these metrics take values in pseudodifferential operators. We develop a theory of Wodzicki-Chern-Simons classes using the s=0, 1 connections and the Wodzicki residue. These classes distinguish the smooth homotopy type of some circle actions on M = S^2 x S^3, and imply that the fundamental group of Diff(M) is infinite.

Abstract:
This is a status report of the evaluation of the three-loop corrections to the static QCD potential of a heavy quark and an antiquark. The families of Feynman integrals that appear in the evaluation are described. To reduce any integral of the families to master integrals we solve integration-by-parts relations by the algorithm called FIRE. To evaluate the corresponding master integrals we apply the Mellin-Barnes technique. First results are presented: the coefficients of n_l^3 and n_l^2, where n_l is the number of light quarks.