Effective capillary interaction of spherical particles at fluid interfaces

We present a detailed analysis of the effective force between two smooth spherical colloids floating at a fluid interface due to deformations of the interface. The results hold in general and are applicable independently of the source of the deformation provided the capillary deformations are small so that a superposition approximation for the deformations is valid. We conclude that an effective long--ranged attraction is possible if the net force on the system does not vanish. Otherwise, the interaction is short--ranged and cannot be computed reliably based on the superposition approximation. As an application, we consider the case of like--charged, smooth nanoparticles and electrostatically induced capillary deformation. The resulting long--ranged capillary attraction can be easily tuned by a relatively small external electrostatic field, but it cannot explain recent experimental observations of attraction if these experimental systems were indeed isolated.Comment: 23 page

Structure characterization of hard sphere packings in amorphous and crystalline states

The channel size distribution in hard sphere systems, based on the local neighbor correlation of four particle positions, is investigated for all volume fractions up to jamming. For each particle, all three particle combinations of neighbors define channels, which are relevant for the concept of caging. The analysis of the channel size distribution is shown to be very useful in distinguishing between gaseous, liquid, partially and fully crystallized, and glassy (random) jammed states. A common microstructural feature of four coplanar particles is observed in crystalline and glassy jammed states, suggesting the presence of "hidden" two-dimensional order in three-dimensional random close packings.Comment: 5 pages, 5 figure

Oblique ion collection in the drift-approximation: how magnetized Mach-probes really work

The anisotropic fluid equations governing a frictionless obliquely-flowing plasma around an essentially arbitrarily shaped three-dimensional ion-absorbing object in a strong magnetic field are solved analytically in the quasi-neutral drift-approximation, neglecting parallel temperature gradients. The effects of transverse displacements traversing the magnetic presheath are also quantified. It is shown that the parallel collection flux density dependence upon external Mach-number is $n_\infty c_s \exp[-1 -(M_{\parallel\infty}- M_\perp\cot\theta)]$ where $\theta$ is the angle (in the plane of field and drift velocity) of the object-surface to the magnetic-field and $M_{\parallel\infty}$ is the external parallel flow. The perpendicular drift, \M_\perp, appearing here consists of the external \E\wedge\B drift plus a weighted sum of the ion and electron electron diamagnetic drifts that depends upon the total angle of the surface to the magnetic field. It is that somewhat counter-intuitive combination that an oblique (transverse) Mach probe experiment measures.Comment: Revised version following refereeing for Physics of Plasma

Stationary states of a nonlinear Schrödinger lattice with a harmonic trap

We study a discrete nonlinear Schrödinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and numerically investigated. Starting from the linear limit of the problem, we use global bifurcation theory to rigorously prove that – in the discrete regime – all linear states lead to nonlinear generalizations thereof, which assume the form of a chain of discrete dark solitons (as the density increases). The stability of the ensuing nonlinear states is studied and it is found that the ground state is stable, while the excited states feature a chain of stability/instability bands. We illustrate the mechanisms under which discreteness destabilizes the dark-soliton configurations, which become stable only in the continuum regime. Continuation from the anti-continuum limit is also considered, and a rich bifurcation structure is revealed

Topological Field Theories and Geometry of Batalin-Vilkovisky Algebras

The algebraic and geometric structures of deformations are analyzed concerning topological field theories of Schwarz type by means of the Batalin-Vilkovisky formalism. Deformations of the Chern-Simons-BF theory in three dimensions induces the Courant algebroid structure on the target space as a sigma model. Deformations of BF theories in $n$ dimensions are also analyzed. Two dimensional deformed BF theory induces the Poisson structure and three dimensional deformed BF theory induces the Courant algebroid structure on the target space as a sigma model. The deformations of BF theories in $n$ dimensions induce the structures of Batalin-Vilkovisky algebras on the target space.Comment: 25 page

Kinetic theory of point vortex systems from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy

Kinetic equations are derived from the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for point vortex systems in an infinite plane. As the level of approximation for the Landau equation, the collision term of the kinetic equation derived coincides with that by Chavanis ({\it Phys. Rev. E} {\bf 64}, 026309 (2001)). Furthermore, we derive a kinetic equation corresponding to the Balescu-Lenard equation for plasmas, using the theory of the Fredholm integral equation. For large $N$, this kinetic equation is reduced to the Landau equation above.Comment: 10 pages, No figures. To be published in Physical Review E, 76-

QP-Structures of Degree 3 and 4D Topological Field Theory

A A BV algebra and a QP-structure of degree 3 is formulated. A QP-structure of degree 3 gives rise to Lie algebroids up to homotopy and its algebraic and geometric structure is analyzed. A new algebroid is constructed, which derives a new topological field theory in 4 dimensions by the AKSZ construction.Comment: 17 pages, Some errors and typos have been correcte

Pseudopotential in resonant regimes

The zero-range potential approach is extended for the description of situations where two-body scattering is resonant in arbitrary partial waves. The formalism generalizes the Fermi pseudopotential which can be used only for s-wave broad resonances. In a given channel, the interaction is described either in terms of a contact condition on the wave function or with a family of pseudopotentials. We show that it is necessary to introduce a regularized scalar product for wave functions obtained in the zero-range potential formalism (except for the Fermi pseudopotential). This metrics shows that the geometry of these Hilbert spaces depends crucially on the interaction.Comment: 12 pages - 1 figur

Courant-Dorfman algebras and their cohomology

We introduce a new type of algebra, the Courant-Dorfman algebra. These are to Courant algebroids what Lie-Rinehart algebras are to Lie algebroids, or Poisson algebras to Poisson manifolds. We work with arbitrary rings and modules, without any regularity, finiteness or non-degeneracy assumptions. To each Courant-Dorfman algebra (\R,\E) we associate a differential graded algebra \C(\E,\R) in a functorial way by means of explicit formulas. We describe two canonical filtrations on \C(\E,\R), and derive an analogue of the Cartan relations for derivations of \C(\E,\R); we classify central extensions of \E in terms of H^2(\E,\R) and study the canonical cocycle \Theta\in\C^3(\E,\R) whose class $[\Theta]$ obstructs re-scalings of the Courant-Dorfman structure. In the nondegenerate case, we also explicitly describe the Poisson bracket on \C(\E,\R); for Courant-Dorfman algebras associated to Courant algebroids over finite-dimensional smooth manifolds, we prove that the Poisson dg algebra \C(\E,\R) is isomorphic to the one constructed in \cite{Roy4-GrSymp} using graded manifolds.Comment: Corrected formulas for the brackets in Examples 2.27, 2.28 and 2.29. The corrections do not affect the exposition in any wa