14 research outputs found
Force Dipole Interactions in Tubular Fluid Membranes
We construct viscous fluid flow sourced by a force dipole embedded in a
cylindrical fluid membrane, coupled to external embedding fluids. We find
analytic expressions for the flow, in the limit of infinitely long and thin
tubular membranes. We utilize this solution to formulate the in-plane dynamics
of a pair of pusher-type dipoles along the cylinder surface. We find that a
mutually perpendicular dipole pair generically move together along helical
geodesics. Since the cylindrical geometry breaks the in-plane rotational
symmetry of the membrane, there is a difference in flows along the axial and
transverse directions of the cylinder. This in turn leads to anisotropic
hydrodynamic interaction between the dipoles and is remarkably different from
flat and spherical fluid membranes. In particular, the flow along the compact
direction of the cylinder has a local rigid rotation term (independent of the
angular coordinate but decays along the axis of the cylinder). Due to this
feature of the flow, we observe that the interacting dipole pair initially
situated along the axial direction exhibits an overall drift along the compact
angular direction of the tubular fluid membrane. We find that the drift for the
dipole pair increases linearly with time. Our results are relevant for
non-equilibrium dynamics of motor proteins in tubular membranes arising in
nature, as well as in-vitro experiments (25)
Closed-form solutions of spinning, eccentric binary black holes at 1.5 post-Newtonian order
The closed-form solution of the 1.5 post-Newtonian (PN) accurate binary black
hole (BBH) Hamiltonian system has proven to be difficult to obtain for a long
time since its introduction in 1966. Closed-form solutions of the PN BBH
systems with arbitrary parameters (masses, spins, eccentricity) are required
for modeling the gravitational waves (GWs) emitted by them. Accurate models of
GWs are crucial for their detection by LIGO/Virgo and LISA. Only recently, two
solution methods for solving the BBH dynamics were proposed in arXiv:1908.02927
(without using action-angle variables), and arXiv:2012.06586, arXiv:2110.15351
(action-angle based). This paper combines the ideas laid out in the above
articles, fills the missing gaps and provides the two solutions which are fully
1.5PN accurate. We also present a public Mathematica package BBHpnToolkit which
implements these two solutions and compares them with a fully numerical
treatment. The level of agreement between these solutions provides a numerical
verification for all the five actions constructed in arXiv:2012.06586, and
arXiv:2110.15351. This paper hence serves as a stepping stone for pushing the
action-angle-based solution to 2PN order via canonical perturbation theory.Comment: 13 pages, 3 figure
Interpolating from Bianchi Attractors to Lifshitz and AdS Spacetimes
We construct classes of smooth metrics which interpolate from Bianchi
attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or
geometries in the UV. While we do not obtain these metrics
as solutions of Einstein gravity coupled to a simple matter field theory, we
show that the matter sector stress-energy required to support these geometries
(via the Einstein equations) does satisfy the weak, and therefore also the
null, energy condition. Since Lifshitz or geometries can in
turn be connected to spacetime, our results show that there is no
barrier, at least at the level of the energy conditions, for solutions to arise
connecting these Bianchi attractor geometries to spacetime. The
asymptotic spacetime has no non-normalizable metric deformation turned
on, which suggests that furthermore, the Bianchi attractor geometries can be
the IR geometries dual to field theories living in flat space, with the
breaking of symmetries being either spontaneous or due to sources for other
fields. Finally, we show that for a large class of flows which connect two
Bianchi attractors, a C-function can be defined which is monotonically
decreasing from the UV to the IR as long as the null energy condition is
satisfied. However, except for special examples of Bianchi attractors
(including AdS space), this function does not attain a finite and non-vanishing
constant value at the end points.Comment: 37 pages, 12 figures, The comment regarding the behavior of
C-function for general Bianchi Types appearing in IR or UV clarified, the
relation of Type IX with for made more precise
and a comment regarding type V added in the conclusio