Evaporation and Discharge Dynamics of Highly Charged Multicomponent Droplets Generated by Electrospray Ionization

We investigate the Rayleigh discharge and evaporation dynamics of highly charged two-component droplets consisting principally of methanol with 2-methoxyethanol, tert-butanol, or m-nitrobenzyl alcohol. A phase Doppler anemometer (PDA) characterizes droplets generated by electrospray ionization (ESI) according to size, velocity, and charge as they move through a uniform electric field within an ion mobility spectrometer (IMS). Repeated field reversals result in droplet “ping-pong” through the PDA. This generates individual droplet histories of solvent evaporation behavior and the dynamics of charge loss to progeny droplets during Rayleigh discharge events. On average, methanol droplets discharge at 127% their Rayleigh limit of charge, q_R, and release 25% of the net charge. Charge loss from methanol/2-methoxyethanol droplets behaves similarly to pure 2-methoxyethanol droplets which release ~28% of their net charge. Binary methanol droplets containing up to 50% tert-butanol discharge at a lower percent q_R than pure methanol and release a greater fraction of their net charge. Mixed 99% methanol/1% m-nitrobenzyl alcohol droplets possess discharge characteristics similar to those of methanol. However, droplets of methanol containing 2% m-nitrobenzyl evaporate down to a fixed size and charge that remains constant with no observable discharges. Quasi-steady-state evaporation models accurately describe observed evaporation phenomena in which methanol/tert-butanol droplets evaporate at a rate similar to that of pure methanol and methanol/2-methoxyethanol droplets evaporate at a rate similar to that of 2-methoxyethanol. We compare these results to previous Rayleigh discharge experiments and discuss the implications for binary solvents in electrospray mass spectrometry (ESI-MS) and field-induced droplet ionization mass spectrometry (FIDI-MS)

HELIOS-K: An Ultrafast, Open-source Opacity Calculator for Radiative Transfer

We present an ultrafast opacity calculator that we name HELIOS-K. It takes a line list as an input, computes the shape of each spectral line and provides an option for grouping an enormous number of lines into a manageable number of bins. We implement a combination of Algorithm 916 and Gauss-Hermite quadrature to compute the Voigt profile, write the code in CUDA and optimise the computation for graphics processing units (GPUs). We restate the theory of the k-distribution method and use it to reduce $\sim 10^5$ to $10^8$ lines to $\sim 10$ to $10^4$ wavenumber bins, which may then be used for radiative transfer, atmospheric retrieval and general circulation models. The choice of line-wing cutoff for the Voigt profile is a significant source of error and affects the value of the computed flux by $\sim 10\%$. This is an outstanding physical (rather than computational) problem, due to our incomplete knowledge of pressure broadening of spectral lines in the far line wings. We emphasize that this problem remains regardless of whether one performs line-by-line calculations or uses the k-distribution method and affects all calculations of exoplanetary atmospheres requiring the use of wavelength-dependent opacities. We elucidate the correlated-k approximation and demonstrate that it applies equally to inhomogeneous atmospheres with a single atomic/molecular species or homogeneous atmospheres with multiple species. Using a NVIDIA K20 GPU, HELIOS-K is capable of computing an opacity function with $\sim 10^5$ spectral lines in $\sim 1$ second and is publicly available as part of the Exoclimes Simulation Platform (ESP; www.exoclime.org).Comment: Accepted by ApJ. 8 pages, 5 figure

Improved bounds on the number of ternary square-free words

Improved upper and lower bounds on the number of square-free ternary words are obtained. The upper bound is based on the enumeration of square-free ternary words up to length 110. The lower bound is derived by constructing generalised Brinkhuis triples. The problem of finding such triples can essentially be reduced to a combinatorial problem, which can efficiently be treated by computer. In particular, it is shown that the number of square-free ternary words of length n grows at least as 65^(n/40), replacing the previous best lower bound of 2^(n/17).Comment: 17 pages, AMS LaTeX. Paper has been completely rewritten and comprises new results on both lower and upper bounds. The Mathematica program mentioned in the article can be downloaded at http://mcs.open.ac.uk/ugg2/wordcomb/brinkhuistriples.

The GENGA Code: Gravitational Encounters in N-body simulations with GPU Acceleration

We describe an open source GPU implementation of a hybrid symplectic N-body integrator, GENGA (Gravitational ENcounters with Gpu Acceleration), designed to integrate planet and planetesimal dynamics in the late stage of planet formation and stability analyses of planetary systems. GENGA uses a hybrid symplectic integrator to handle close encounters with very good energy conservation, which is essential in long-term planetary system integration. We extended the second order hybrid integration scheme to higher orders. The GENGA code supports three simulation modes: Integration of up to 2048 massive bodies, integration with up to a million test particles, or parallel integration of a large number of individual planetary systems. We compare the results of GENGA to Mercury and pkdgrav2 in respect of energy conservation and performance, and find that the energy conservation of GENGA is comparable to Mercury and around two orders of magnitude better than pkdgrav2. GENGA runs up to 30 times faster than Mercury and up to eight times faster than pkdgrav2. GENGA is written in CUDA C and runs on all NVIDIA GPUs with compute capability of at least 2.0.Comment: Accepted by ApJ. 18 pages, 17 figures, 4 table

Asymptotic estimates for interpolation and constrained approximation in H2 by diagonalization of Toeplitz operators

Sharp convergence rates are provided for interpolation and approximation schemes in the Hardy space H-2 that use band-limited data. By means of new explicit formulae for the spectral decomposition of certain Toeplitz operators, sharp estimates for Carleman and Krein-Nudel'man approximation schemes are derived. In addition, pointwise convergence results are obtained. An illustrative example based on experimental data from a hyperfrequency filter is provided

Stochasticity & Predictability in Terrestrial Planet Formation

Terrestrial planets are thought to be the result of a vast number of gravitational interactions and collisions between smaller bodies. We use numerical simulations to show that practically identical initial conditions result in a wide array of final planetary configurations. This is a result of the chaotic evolution of trajectories which are highly sensitive to minuscule displacements. We determine that differences between systems evolved from virtually identical initial conditions can be larger than the differences between systems evolved from very different initial conditions. This implies that individual simulations lack predictive power. For example, there is not a reproducible mapping between the initial and final surface density profiles. However, some key global properties can still be extracted if the statistical spread across many simulations is considered. Based on these spreads, we explore the collisional growth and orbital properties of terrestrial planets which assemble from different initial conditions (we vary the initial planetesimal distribution, planetesimal masses, and giant planet orbits). Confirming past work, we find that the resulting planetary systems are sculpted by sweeping secular resonances. Configurations with giant planets on eccentric orbits produce fewer and more massive terrestrial planets on tighter orbits than those with giants on circular orbits. This is further enhanced if the initial mass distribution is biased to the inner regions. In all cases, the outer edge of the system is set by the final location of the $\nu_6$ resonance and we find that the mass distribution peaks at the $\nu_5$ resonance. Using existing observations, we find that extrasolar systems follow similar trends. Although differences between our numerical modelling and exoplanetary systems remain, we suggest that CoRoT-7, HD 20003, and HD 20781 may host undetected giant planets.Comment: replaced to match published version, 20 pages, 11 figures, published in MNRAS, simulation outputs available at https://cheleb.net/astro/sp15

Spin Hall Effect in Atoms

We propose an optical means to realize a spin hall effect (SHE) in neutral atomic system by coupling the internal spin states of atoms to radiation. The interaction between the external optical fields and the atoms creates effective magnetic fields that act in opposite directions on "electrically" neutral atoms with opposite spin polarizations. This effect leads to a Landau level structure for each spin orientation in direct analogy with the familiar SHE in semiconductors. The conservation and topological properties of the spin current, and the creation of a pure spin current are discussed.Comment: 4 pages, 2 figure; Final versio

Existence And Uniqueness For Nonlinear Neutral-differential Equations

Fixed point theorems are used to prove existence and uniqueness of the C1 solution of the initial-value problem for a functional-differential equation of neutral type. © 1971, American Mathematical Society. All Rights Reserved