Optimal taxation in a growth model with public consumption and home production

In a neoclassical growth model with public consumption, we show the following Pareto optimal tax rules. The government should tax leisure and private consumption at the same rate, and subsidize net investment at the same rate it taxes net capital income. Also, it should tax capital income more heavily than labor income. In an extension for home production, the additional rule is to tax investment for home production at the same rate of the tax on private market consumption. These tax and subsidy rates should be constant over time except the initial tax rate on capital income.

Dark-Ages Reionisation & Galaxy Formation Simulation XVI: The Thermal Memory of Reionisation

Intergalactic medium temperature is a powerful probe of the epoch of reionisation, as information is retained long after reionisation itself. However, mean temperatures are highly degenerate with the timing of reionisation, with the amount heat injected during the epoch, and with the subsequent cooling rates. We post-process a suite of semi-analytic galaxy formation models to characterise how different thermal statistics of the intergalactic medium can be used to constrain reionisation. Temperature is highly correlated with redshift of reionisation for a period of time after the gas is heated. However as the gas cools, thermal memory of reionisation is lost, and a power-law temperature-density relation is formed, $T = T_0(1+\delta)^{1-\gamma}$ with $\gamma \approx 1.5$. Constraining our model against observations of electron optical depth and temperature at mean density, we find that reionisation likely finished at $z_{\rm{reion}} = 6.8 ^{+ 0.5} _{-0.8}$ with a soft spectral slope of $\alpha = 2.8 ^{+ 1.2} _{-1.0}$. By restricting spectral slope to the range $[0.5,2.5]$ motivated by population II synthesis models, reionisation timing is further constrained to $z_{\rm{reion}} = 6.9 ^{+ 0.4} _{-0.5}$. We find that, in the future, the degeneracies between reionisation timing and background spectrum can be broken using the scatter in temperatures and integrated thermal history.Comment: 17 pages, 17 figures, Accepted for publication in MNRA

The characteristics of billows generated by internal solitary waves

The spatial and temporal development of shear-induced overturning billows associated with breaking internal solitary waves is studied by means of a combined laboratory and numerical investigation. The waves are generated in the laboratory by a lock exchange mechanism and they are simulated numerically via a contour-advective semi-Lagrangian method. The properties of individual billows (maximum height attained, time of collapse, growth rate, speed, wavelength, Thorpe scale) are determined in each case, and the billow interaction processes are studied and classified. For broad flat waves, similar characteristics are seen to those in parallel shear flow, but, for waves not at the conjugate flow limit, billow characteristics are affected by the spatially varying wave-induced shear flow. Wave steepness and wave amplitude are shown to have a crucial influence on determining the type of interaction that occurs between billows and whether billow overturning can be arrested. Examples are given in which billows (i) evolve independently of one another, (ii) pair with one another, (iii) engulf/entrain one another and (iv) fail to completely overturn. It is shown that the vertical extent a billow can attain (and the associated Thorpe scale of the billow) is dependent on wave amplitude but that its value saturates once a given amplitude is reached. It is interesting to note that this amplitude is less than the conjugate flow limit amplitude. The number of billows that form on a wave is shown to be dependent on wavelength; shorter waves support fewer but larger billows than their long-wave counterparts for a given stratification.PostprintPeer reviewe

Dehydrative etherification reactions of glycerol with alcohols catalyzed by recyclable nanoporous aluminosilicates: telescoped routes to glyceryl ethers

Catalytic strategies for the efficient transformation of abundant sustainable bioderived molecules, such as glycerol, into higher value more useful products is an important research goal. In this study, we demonstrate that atom efficient dehydrative etherification reactions of glycerol with activated alcohols are effectively catalyzed by nanoporous aluminosilicate materials in dimethylcarbonate (DMC) to produce the corresponding 1-substituted glyceryl ethers in high yield. By carrying out the reaction in acetone, it is possible to capitalize on the ability of these materials to catalyze the corresponding acetalization reaction, allowing for the development of novel, telescoped acetalization-dehydrative etherification reaction sequences to selectively produce protected solketal derivatives. These materials also catalyze the telescoped reaction of glycerol with <i>tert</i>-butanol (TBA) in acetone to produce the corresponding solketal mono <i>tert</i>-butyl ether product in high yield, providing a potential route to convert glycerol directly into a useful and sustainable fuel additive

Efficient Reionization in a Large Hydrodynamic Galaxy Formation Simulation

Accuracy in the topology and statistics of a simulated Epoch of Reionization (EoR) are vital to draw connections between observations and physical processes. While full radiative transfer models produce the most accurate reionization models, they are highly computationally expensive, and are infeasible for the largest cosmological simulations. Instead, large simulations often include EoR models that are pre-computed via the initial density field, or post-processed where feedback effects are ignored. We introduce Astrid-ES, a resimulation of the Astrid epoch of reionisation $20 > z > 5.5$ which includes an on-the-fly excursion-set reionization algorithm. Astrid-ES produces more accurate reionization histories without significantly impacting the computational time. This model directly utilises the star particles produced in the simulation to calculate the EoR history and includes a UV background which heats the gas particles after their reionization. We contrast the reionization topology and statistics in Astrid-ES with the previously employed parametric reionisation model, finding that in Astrid-ES, ionised regions are more correlated with galaxies, and the 21cm power-spectrum shows an increase in large scale power. We calculate the relation between the size of HII regions and the UV luminosity of the brightest galaxy within them. Prior to the overlap phase, we find a power-law fit of $\mathrm{log} (R) = -0.314 M_\mathrm{UV} - 2.550 \mathrm{log}(1+z) + 7.408$ with a standard deviation $\sigma_R < 0.15 \mathrm{dex}$ across all mass bins. We also examine the properties of halos throughout reionization, finding that while the properties of halos in the simulation are correlated with the redshift of reionisation, they are not greatly affected by reionisation itself.Comment: 12 pages, 11 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Societ

Functional microdomains in G-protein-coupled receptors: the conserved arginine-cage motif in the gonadotropin-releasing hormone receptor

An Arg present in the third transmembrane domain of all rhodopsin-like G-protein-coupled receptors is required for efficient signal transduction. Mutation of this Arg in the gonadotropin-releasing hormone receptor to Gln, His, or Lys abolished or severely impaired agonist-stimulated inositol phosphate generation, consistent with Arg having a role in receptor activation. To investigate the contribution of the surrounding structural domain in the actions of the conserved Arg, an integrated microdomain modeling and mutagenesis approach has been utilized. Two conserved residues that constrain the Arg side chain to a limited number of conformations have been identified. In the inactive wild-type receptor, the Arg side chain is proposed to form an ionic interaction with Asp3.49(138). Experimental results for the Asp3. 49(138) --> Asn mutant receptor show a modestly enhanced receptor efficiency, consistent with the hypothesis that weakening the Asp3. 49(138)-Arg3.50(139) interaction by protonation of the Asp or by the mutation to Asn favors activation. With activation, the Asp3. 49(138)-Arg3.50(139) ionic bond would break, and the unrestrained Arg would be prevented from orienting itself toward the water phase by a steric clash with Ile3.54(143). The mutation Ile3.54(143) --> Ala, which eliminates this clash in simulations, causes a marked reduction in measured receptor signaling efficiency, implying that solvation of Arg3.50(139) prevents it from functioning in the activation of the receptor. These data are consistent with residues Asp3.49(138) and Ile3.54(143) forming a structural motif, which helps position Arg in its appropriate inactive and active receptor conformations

Tests of Spurious Transport in Smoothed Particle Hydrodynamics

We have performed a series of systematic tests to evaluate the effects of spurious transport in three-dimensional smoothed particle hydrodynamics (SPH) calculations. Our tests investigate (i) particle diffusion, (ii) shock heating, (iii) numerical viscosity, and (iv) angular momentum transport. The results are useful for quantifying the accuracy of the SPH scheme, especially for problems where shear flows or shocks are present, as well as for problems where true hydrodynamic mixing is relevant. We examine the different forms of artificial viscosity (AV) which have been proposed by Monaghan, by Hernquist & Katz, and by Balsara. For each form, our tests suggest a single set of values for the AV parameters $\alpha$ and $\beta$ (coefficients of the linear and quadratic terms) which are appropriate in a large number of situations. We also discuss how these parameters should be adjusted depending on the goals of the particular application. We find that both the Hernquist & Katz and Balsara forms introduce relatively small amounts of numerical viscosity. Furthermore, both Monaghan's and Balsara's AV do well at treating shocks and at limiting the amount of spurious mixing. For these reasons, we endorse the Balsara AV for use in a broad range of applications.Comment: 49 pages, 26 figures as 30 postscript files, submitted to The Journal of Computational Physic

Does the external remote controller’s reading correspond to the actual lengthening in magnetic-controlled growing rods?

Purpose Magnetic-controlled growing rods (MCGRs) are now routinely used in many centres to treat early-onset scoliosis (EOS). MCGR lengthening is done non-invasively by the external remote controller (ERC). Our experience suggests that there may be a discrepancy between the reported rod lengthening on the ERC and the actual rod lengthening. The aim of this study was to investigate this discrepancy. Methods This was a prospective series. Eleven patients who were already undergoing treatment for EOS using MCGRs were included in this study. Results One hundred and ninety-two sets of ultrasound readings were obtained (96 episodes of rod lengthening on dual-rod constructs) and compared to their ERC readings. Only 15/192 (7.8%) readings were accurate; 27 readings (14.9%) were false positive; and 8 readings (4.2%) were an underestimation while 142 readings (74.0%) were an overestimation by the ERC. Average over-reporting by the ERC was 5.31 times of the actual/ultrasound reading. When comparing interval radiographs with lengthening obtained on ultrasound, there was a discrepancy with an average overestimation of 1.35 times with ultrasound in our series. There was a significant difference between ERC and USS (p = 0.01) and ERC and XR (p = 0.001). However, there was no significant difference between USS and XR (p > 0.99). Conclusion The reading on the ERC does not equate to the actual rod lengthening. The authors would recommend that clinicians using the MCGR for the treatment of early-onset scoliosis include pre- and post-extension imaging (radiographs or ultrasound) to confirm extension lengths at each outpatient extension. In centres with ultrasound facilities, we would suggest that patients should have ultrasound to monitor each lengthening after distraction but also 6-month radiographs