Frequencies and resonances around L4L_4 in the elliptic restricted three-body problem

The stability of the Lagrangian point $L_4$ is investigated in the elliptic restricted three-body problem by using Floquet's theory. Stable and unstable domains are determined in the parameter plane of the mass parameter and the eccentricity by computing the characteristic exponents. Frequencies of motion around $L_4$ have been determined both in the stable and unstable domains and fitting functions for the frequencies are derived depending on the mass parameter and the eccentricity. Resonances between the frequencies are studied in the whole parameter plane. It is shown that the 1:1 resonances are not restricted only to single curves but extend to the whole unstable domain. In the unstable domains longer escape times of the test particle from the neighbourhood of $L_4$ are related to certain resonances, but changing the parameters the same resonances may lead to faster escape

Dipole-dipole instability of atom clouds in a far-detuned optical dipole trap

The effect of the dipole-dipole interaction on the far-off-resonance optical dipole trapping scheme is calculated by a mean-field approach. The trapping laser field polarizes the atoms and the accompanying dipole-dipole energy shift deepens the attractive potential minimum in a pancake-shaped cloud. At high density the thermal motion cannot stabilize the gas against self-contraction and an instability occurs. We calculate the boundary of the stable and unstable equilibrium regions on a two-dimensional phase diagram of the atom number and the ratio of the trap depth to the temperature. We discuss the limitations imposed by the dipole-dipole instability on the parameters needed to reach Bose-Einstein condensation in an optical dipole trap.Comment: 8 pages, 3 figure

Hydrodynamic Trapping of Swimming Bacteria by Convex Walls

Swimming bacteria display a remarkable tendency to move along flat surfaces for prolonged times. This behavior may have a biological importance but can also be exploited by using microfabricated structures to manipulate bacteria. The main physical mechanism behind the surface entrapment of swimming bacteria is, however, still an open question. By studying the swimming motion of Escherichia coli cells near microfabricated pillars of variable size, we show that cell entrapment is also present for convex walls of sufficiently low curvature. Entrapment is, however, markedly reduced below a characteristic radius. Using a simple hydrodynamic model, we predict that trapped cells swim at a finite angle with the wall and a precise relation exists between the swimming angle at a flat wall and the critical radius of curvature for entrapment. Both predictions are quantitatively verified by experimental data. Our results demonstrate that the main mechanism for wall entrapment is hydrodynamic in nature and show the possibility of inhibiting cell adhesion, and thus biofilm formation, using convex features of appropriate curvature

QCD corrections to e+ e- --> 4 jets

We report on the next-to-leading order QCD calculation for e+ e- --> 4 jets. We explain some modern techniques which have been used to calculate the one-loop amplitudes efficiently. We further report on the general purpose numerical program ``Mercutio'', which can be used to calculate any infrared safe four-jet quantity in electron-positron annihilation at next-to-leading order.Comment: 4 pages, talk given at the UK Phenomenology Workshop on Collider Physics, Durham, 19-24 September 199

Tree tensor network state with variable tensor order: an efficient multireference method for strongly correlated systems

We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement

Deformation mechanics of deep surface flaw cracks

A combined analytical and experimental program was conducted to determine the deformation characteristics of deep surface cracks in Mode I loading. An approximate plane finite element analysis was performed to make a parameter study on the influence of crack depth, crack geometry, and stress level on plastic zones, crack opening displacement, and back surface dimpling in Fe-3Si steel and 2219-T87 aluminum. Surface replication and profiling techniques were used to examine back surface dimple configurations in 2219-T87 aluminum. Interferometry and holography were used to evaluate the potential of various optical techniques to detect small surface dimples on large surface areas

Semiclassical model for calculating fully differential ionization cross sections of the H2_2 molecule

Fully differential cross sections are calculated for the ionization of H$_2$ by fast charged projectiles using a semiclassical model developed previously for the ionization of atoms. The method is tested in case of 4 keV electron and 6 MeV proton projectiles. The obtained results show good agreement with the available experimental data. Interference effects due to the two-center character of the target are also observed and analyzed.Comment: 11 pages, 4 figure