Publications

I describe the design, implementation, and usage of galpy, a python package for galactic-dynamics calculations. At its core, galpy consists of a general framework for representing galactic potentials both in python and in C (for accelerated computations); galpy functions, objects, and methods can generally take arbitrary combinations of these as arguments. Numerical orbit integration is supported with a variety of Runge-Kutta-type and symplectic integrators. For planar orbits, integration of the phase-space volume is also possible. galpy supports the calculation of action-angle coordinates and orbital frequencies for a given phase-space point for general spherical potentials, using state-of-the-art numerical approximations for axisymmetric potentials, and making use of a recent general approximation for any static potential. A number of different distribution functions (DFs) are also included in the current release; currently, these consist of two-dimensional axisymmetric and non-axisymmetric disk DFs, a three-dimensional disk DF, and a DF framework for tidal streams. I provide several examples to illustrate the use of the code. I present a simple model for the Milky Way's gravitational potential consistent with the latest observations. I also numerically calculate the Oort functions for different tracer populations of stars and compare them to a new analytical approximation. Additionally, I characterize the response of a kinematically warm disk to an elliptical m = 2 perturbation in detail. Overall, galpy consists of about 54,000 lines, including 23,000 lines of code in the module, 11,000 lines of test code, and about 20,000 lines of documentation. The test suite covers 99.6% of the code. galpy is available at http://github.com/jobovy/galpy with extensive documentation available at http://galpy.readthedocs.org/en/latest.

We introduce methods for large-scale Brownian Dynamics (BD) simulation of many rigid particles
of arbitrary shape suspended in a fluctuating fluid. Our method adds Brownian motion to the rigid
multiblob method [F. Balboa Usabiaga et al., Commun. Appl. Math. Comput. Sci. 11(2), 217-296
(2016)] at a cost comparable to the cost of deterministic simulations. We demonstrate that we can
efficiently generate deterministic and random displacements for many particles using preconditioned
Krylov iterative methods, if kernel methods to efficiently compute the action of the Rotne-Prager-
Yamakawa (RPY) mobility matrix and its “square” root are available for the given boundary conditions.
These kernel operations can be computed with near linear scaling for periodic domains using the
positively split Ewald method. Here we study particles partially confined by gravity above a no-
slip bottom wall using a graphical processing unit implementation of the mobility matrix-vector
product, combined with a preconditioned Lanczos iteration for generating Brownian displacements.
We address a major challenge in large-scale BD simulations, capturing the stochastic drift term that
arises because of the configuration-dependent mobility. Unlike the widely used Fixman midpoint
scheme, our methods utilize random finite differences and do not require the solution of resistance
problems or the computation of the action of the inverse square root of the RPY mobility matrix. We
construct two temporal schemes which are viable for large-scale simulations, an Euler-Maruyama
traction scheme and a trapezoidal slip scheme, which minimize the number of mobility problems to
be solved per time step while capturing the required stochastic drift terms. We validate and compare
these schemes numerically by modeling suspensions of boomerang-shaped particles sedimented near
a bottom wall. Using the trapezoidal scheme, we investigate the steady-state active motion in dense
suspensions of confined microrollers, whose height above the wall is set by a combination of thermal
noise and active flows. We find the existence of two populations of active particles, slower ones closer
to the bottom and faster ones above them, and demonstrate that our method provides quantitative
accuracy even with relatively coarse resolutions of the particle geometry.

We describe the treatment of Rashba spin-orbit coupling (SOC) in interacting many-fermion systems within the auxiliary-field quantum Monte Carlo framework, and present a set of illustrative results. These include numerically exact calculations on the ground-state properties of the spin-balanced, attractive two-dimensional Fermi gas, as well as a study of a tight-binding Hamiltonian with repulsive interaction. These systems are formally connected via the Hubbard Hamiltonian plus SOC, but cover different physics ranging from superfluidity and triplet pairing to SOC in real materials in the presence of strong interactions in localized orbitals. We carry out detailed benchmark studies of the method in the latter case when an approximation is needed to control the sign problem for repulsive Coulomb interactions. The methods presented here provide an approach for predictive computations in materials to study the interplay of SOC and strong correlation.

We investigate the interplay of spin-orbit coupling (SOC) and electronic correlations in Sr2RuO4 using dynamical mean-field theory. We find that SOC does not affect the correlation-induced renormalizations, which validates the Hund's metal picture of ruthenates even in the presence of the sizable SOC relevant to these materials. Nonetheless, SOC found to change significantly the electronic structure at k-points where a degeneracy applies in its absence. We explain why these two observations are consistent with one another and calculate effects of SOC on the correlated electronic structure. The magnitude of these effects is found to depend on the energy of the quasiparticle state under consideration, leading us to introduce the notion of an "energy-dependent quasiparticle spin-orbit coupling". This notion is generally applicable to all materials in which both the spin-orbit coupling and electronic correlations are sizable.

The cellular cytoskeleton is an active material, driven out of equilibrium by molecular motor proteins. It is not understood how the collective behaviors of cytoskeletal networks emerge from the properties of the network's constituent motor proteins and filaments. Here we present experimental results on networks of stabilized microtubules in Xenopus oocyte extracts, which undergo spontaneous bulk contraction driven by the motor protein dynein, and investigate the effects of varying the initial microtubule density and length distribution. We find that networks contract to a similar final density, irrespective of the length of microtubules or their initial density, but that the contraction timescale varies with the average microtubule length. To gain insight into why this microscopic property influences the macroscopic network contraction time, we developed simulations where microtubules and motors are explicitly represented. The simulations qualitatively recapitulate the variation of contraction timescale with microtubule length, and allowed stress contributions from different sources to be estimated and decoupled.

We describe, using first principles calculations, the way in which the inherent broken symmetry at the surface of (0001) sapphire leads to a surface dipole and, with applied strain, to a piezoelectric effect. While the bulk form of sapphire has inversion symmetry and thus no net electrical dipole or piezoelectricity, our ab initio calculations show that a large surface dipole emerges. Furthermore, the magnitude of this dipole responds to imposed strain, i.e., a surface piezoelectric effect in an otherwise centro-symmetric non-piezoelectric material. Numerically, the surface piezoelectric response is as strong as a single unit cell of a bulk piezoelectric with e31=0.31 C/m2. Given the importance and widespread use of sapphire as a substrate, this dipole and its response can play an important role in surface chemistry as well as for the coupling of electronic devices fabricated on top of the sapphire surface. The mechanism presented here may be relevant in other materials with corundum structure.

A body submerged in active matter feels the swim pressure through a kinetic accumulation boundary layer on its surface. The boundary layer results from a balance between translational diffusion and advective swimming and occurs on the microscopic length scale $$\lambda^{-1} = \delta/\sqrt{2[1 + \frac{1}{6}(\ell/\delta)^2]}$$. Here $$\delta = \sqrt{D_T\tau_R}$$, $$D_T$$ is the Brownian translational diffusivity, $$\tau_R$$ is the reorientation time and $$\ell = U_0\tau_R$$ is the swimmer's run length, with $$U_0$$ the swim speed. In this work we analyze the swim pressure on arbitrary shaped bodies by including the effect of local shape curvature in the kinetic boundary layer. When $$\delta\ll L$$ and $$\ell \ll L$$, where $$L$$ is the body size, the leading order effects of curvature on the swim pressure are found analytically to scale as $$J_S\lambda\delta^2/L$$, where $$J_S$$ is twice the (non-dimensional) mean curvature. Particle-tracking simulations and direct solutions to the Smoluchowski equation governing the probability distribution of the active particles show that $\lambda\delta^2/L$ is a universal scaling parameter not limited to the regime $$\delta, \ell\ll L$$. The net force exerted on the body by the swimmers is found to scale as $$\bF^{net} /\left(n^\infty k_sT_s L^2\right) = f(\lambda\delta^2/L)$$, where $$f(x)$$ is a dimensionless function that is quadratic when $$x\ll1$$ and linear when $$x\sim 1$$. Here, $$k_sT_s = \zeta U_0^2\tau_R/6$$ defines the `activity' of the swimmers, with $$\zeta$$ the drag coefficient, and $$n^\infty$$ is the uniform number density of swimmers far from the body. We discuss the connection of this boundary layer to continuum mechanical descriptions of active matter and briefly present how to include hydrodynamics into this purely kinetic study.

Engineering effective electronic parameters is a major focus in condensed matter physics. Their dynamical modulation opens the possibility of creating and controlling physical properties in systems driven out of equilibrium. In this work, we demonstrate that the Hubbard U, the on-site Coulomb repulsion in strongly correlated materials, can be modified on femtosecond time scales by a strong nonresonant laser excitation in the prototypical charge transfer insulator NiO. Using our recently developed time-dependent density functional theory plus self-consistent U (TDDFT+U) method, we demonstrate the importance of a dynamically modulated U in the description of the high-harmonic generation of NiO. Our study opens the door to novel ways of modifying effective interactions in strongly correlated materials via laser driving, which may lead to new control paradigms for field-induced phase transitions and perhaps laser-induced Mott insulation in charge-transfer materials.

Chemically active Brownian particles with surface catalytic reactions may repel each other due to diffusiophoretic interactions in the reaction and product concentration fields. The system behavior can be described by a “chemical” coupling parameter $$\Gamma_c$$ that compares the strength of diffusiophoretic repulsion to Brownian motion, and by a mapping to the classical electrostatic one component plasma (OCP) system. When confined to a constant-volume domain, body-centered cubic (bcc) crystals spontaneously form from random initial configurations when the repulsion is strong enough to overcome Brownian motion. Face-centered cubic (fcc) crystals may also be stable. The “melting point” of the “liquid-to-crystal transition” occurs at $$\Gamma_c \approx 140$$ for both bcc and fcc lattices.