Surfactant-induced migration of a spherical drop in Stokes flow

In Stokes flows, symmetry considerations dictate that a neutrally-buoyant spherical particle will not migrate laterally with respect to the local flow direction. We show that a loss of symmetry due to flow-induced surfactant redistribution leads to cross-stream drift of a spherical drop in Poiseuille flow. We derive analytical expressions for the migration velocity in the limit of small non-uniformities in the surfactant distribution, corresponding to weak-flow conditions or a high-viscosity drop. The analysis predicts that the direction of migration is always towards the flow centerline.Comment: Significant extension with additional text, figures, equations, et

Proton emission induced by polarized photons

The proton emission induced by polarized photons is studied in the energy range above the giant resonance region and below the pion emission threshold. Results for the 12C, 16O and 40Ca nuclei are presented. The sensitivity of various observables to final state interaction, meson exchange currents and short range correlations is analyzed. We found relevant effects due to the virtual excitation of the $\Delta$ resonance.Comment: 12 pages, 11 figures, 1 tabl

The no-core shell model with general radial bases

Calculations in the ab initio no-core shell model (NCSM) have conventionally been carried out using the harmonic-oscillator many-body basis. However, the rapid falloff (Gaussian asymptotics) of the oscillator functions at large radius makes them poorly suited for the description of the asymptotic properties of the nuclear wavefunction. We establish the foundations for carrying out no-core configuration interaction (NCCI) calculations using a basis built from general radial functions and discuss some of the considerations which enter into using such a basis. In particular, we consider the Coulomb-Sturmian basis, which provides a complete set of functions with a realistic (exponential) radial falloff.Comment: 7 pages, 3 figures; presented at Horizons on Innovative Theories, Experiments, and Supercomputing in Nuclear Physics 2012, New Orleans, Louisiana, June 4-7, 2012; submitted to J. Phys. Conf. Se

Rotational States of Magnetic Molecules

We study a magnetic molecule that exhibits spin tunneling and is free to rotate about its anisotropy axis. Exact low-energy eigenstates of the molecule that are superpositions of spin and rotational states are obtained. We show that parameter $\alpha = 2(\hbar S)^2/(I\Delta)$ determines the ground state of the molecule. Here $\hbar S$ is the spin, $I$ is the moment of inertia, and $\Delta$ is the tunnel splitting. The magnetic moment of the molecule is zero at $\alpha \alpha_c$. At $\alpha \to \infty$ the spin of the molecule localizes in one of the directions along the anisotropy axis.Comment: 4 pages, 3 figure

Hypergraphic LP Relaxations for Steiner Trees

We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Koenemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this LP, and studying its relation to other linear relaxations. Our results are the following. Structural results: We extend the technique of uncrossing, usually applied to families of sets, to families of partitions. As a consequence we show that any basic feasible solution to the partition LP formulation has sparse support. Although the number of variables could be exponential, the number of positive variables is at most the number of terminals. Relations with other relaxations: We show the equivalence of the partition LP relaxation with other known hypergraphic relaxations. We also show that these hypergraphic relaxations are equivalent to the well studied bidirected cut relaxation, if the instance is quasibipartite. Integrality gap upper bounds: We show an upper bound of sqrt(3) ~ 1.729 on the integrality gap of these hypergraph relaxations in general graphs. In the special case of uniformly quasibipartite instances, we show an improved upper bound of 73/60 ~ 1.216. By our equivalence theorem, the latter result implies an improved upper bound for the bidirected cut relaxation as well.Comment: Revised full version; a shorter version will appear at IPCO 2010

An exactly solvable limit of low energy QCD

Starting from the QCD Hamiltonian, we derive a schematic Hamiltonian for low energy quark dynamics with quarks restricted to the lowest s-level. The resulting eigenvalue problem can be solved analytically. Even though the Hamiltonian exhibits explicit chiral symmetry the severe restriction of the number of degrees of freedom breaks the pattern of chiral symmetry breaking for finite quark masses.Comment: 7 page

Capillary interactions in Pickering emulsions

The effective capillary interaction potentials for small colloidal particles trapped at the surface of liquid droplets are calculated analytically. Pair potentials between capillary monopoles and dipoles, corresponding to particles floating on a droplet with a fixed center of mass and subjected to external forces and torques, respectively, exhibit a repulsion at large angular separations and an attraction at smaller separations, with the latter resembling the typical behavior for flat interfaces. This change of character is not observed for quadrupoles, corresponding to free particles on a mechanically isolated droplet. The analytical results for quadrupoles are compared with the numerical minimization of the surface free energy of the droplet in the presence of ellipsoidal particles.Comment: twocolumn, 8 pages, 3 figures, submitted to Phys. Rev.

Theory of Optical Tweezers

We derive a partial-wave (Mie) expansion of the axial force exerted on a transparent sphere by a laser beam focused through a high numerical aperture objective. The results hold throughout the range of interest for practical applications. The ray optics limit is shown to follow from the Mie expansion by size averaging. Numerical plots show large deviations from ray optics near the focal region and oscillatory behavior (explained in terms of a simple interferometer picture) of the force as a function of the size parameter. Available experimental data favor the present model over previous ones.Comment: 4 pages, 3 figure

Exact diagonalization of the Bohr Hamiltonian for rotational nuclei: Dynamical gamma softness and triaxiality

Detailed quantitative predictions are obtained for phonon and multiphonon excitations in well-deformed rotor nuclei within the geometric framework, by exact numerical diagonalization of the Bohr Hamiltonian in an SO(5) basis. Dynamical gamma deformation is found to significantly influence the predictions through its coupling to the rotational motion. Basic signatures for the onset of rigid triaxial deformation are also obtained.Comment: 17 pages, 10 figures; to be published Phys. Rev.

Magnetic excitations in nuclei with neutron excess

The excitation of the $1^+$, $2^-$ and $3^+$ modes in $^{16}$O, $^{22}$O, $^{24}$O, $^{28}$O, $^{40}$Ca, $^{48}$Ca, $^{52}$Ca and $^{60}$Ca nuclei is studied with self-consistent random phase approximation calculations. Finite-range interactions of Gogny type, containing also tensor-isospin terms, are used. We analyze the evolution of the magnetic resonances with the increasing number of neutrons, the relevance of collective effects, the need of a correct treatment of the continuum and the role of the tensor force.Comment: 18 pages, 12 figures, 2 tables, accepted for publication in Physical Review