Mean square of zeta function, circle problem and divisor problem revisited

This paper is closely related to the recent work [BW17] of the same authors and our purpose is to elaborate more on some of the results and methods from [BW17]. More specifically our goal is two-fold. Firstly, we will indicate how a simple variant related to Section 4 in [BW17] leads to the following improvements of Theorem 3 in [BW17]Comment: 23 page

Exploration of Tektite Formation Processes through Water and Metal Content Measurements

Impact events are a significant surface-modifying process on bodies lacking frequent resurfacing by atmospheric or igneous processes. To explore the effects of impacts on surface materials, we measured water and trace element compositions of tektites from Vietnam. Fourier transform infrared spectroscopy was used for water measurements and laser ablation inductively coupled plasma mass spectrometry was used for trace element measurements. Consistent with previous investigations of tektites, we found that the samples are depleted in volatile metals (e.g., Zn, Pb) as well as in water compared to the average continental crust, though water contents are high for rocks melted at atmospheric pressure. While Zn and Pb concentrations are linearly correlated with each other, there is no correlation between H 2 O and Zn or Pb contents. Combined with water contents of other tektites in the Australasian strewnfield, our results demonstrate that the source impact occurred at a wet site near the Indochina peninsula

Particle-in-cell experiments examine electron diffusion by whistler-mode waves: 1. Benchmarking with a cold plasma

Using a particle-in-cell code, we study the diffusive response of electrons due to wave particle interactions with whistler-mode waves. The relatively simple configuration of field-aligned waves in a cold plasma is used in order to benchmark our novel method, and to compare with previous works that used a different modelling technique. In this boundary-value problem, incoherent whistler-mode waves are excited at the domain boundary, and then propagate through the ambient plasma. Electron diffusion characteristics are directly extracted from particle data across all available energy and pitch-angle space. The ‘nature’ of the diffusive response is itself a function of energy and pitch-angle, such that the rate of diffusion is not always constant in time. However, after an initial transient phase, the rate of diffusion tends to a constant, in a manner that is consistent with the assumptions of quasilinear diffusion theory. This work establishes a framework for future investigations on the nature of diffusion due to whistler-mode wave-particle interactions, using particle-in-cell numerical codes with driven waves as boundary value problems

Variability of quasilinear diffusion coefficients for plasmaspheric hiss

In the Outer Radiation Belt, the acceleration and loss of high-energy electrons is largely controlled by wave-particle interactions. Quasilinear diffusion coefficients are an efficient way to capture the small-scale physics of wave-particle interactions due to magnetospheric wave modes such as plasmaspheric hiss. The strength of quasilinear diffusion coefficients as a function of energy and pitch-angle depends on both wave parameters and plasma parameters such as ambient magnetic field strength, plasma number density and composition. For plasmaspheric hiss in the magnetosphere, observations indicate large variations in the wave intensity and wavenormal angle, but less is known about the simultaneous variability of the magnetic field and number density. We use in-situ measurements from the Van Allen Probe mission to demonstrate the variability of selected factors that control the size and shape of pitch-angle diffusion coefficients: wave intensity, magnetic field strength and electron number density. We then compare with the variability of diffusion coefficients calculated individually from co-located and simultaneous groups of measurements. We show that the distribution of the plasmaspheric hiss diffusion coefficients is highly non-Gaussian with large variance, and that the distributions themselves vary strongly across the three phase-space bins studied. In most bins studied, the plasmaspheric hiss diffusion coefficients tend to increase with geomagnetic activity, but our results indicate that new approaches that include natural variability may yield improved parameterizations. We suggest methods like stochastic parameterization of wave-particle interactions could use variability information to improve modelling of the Outer Radiation Belt

Overexpression of Carnitine Palmitoyltransferase-1 in Skeletal Muscle Is Sufficient to Enhance Fatty Acid Oxidation and Improve High-Fat Diet–Induced Insulin Resistance

OBJECTIVE—Skeletal muscle insulin resistance is associated with lipid accumulation, but whether insulin resistance is due to reduced or enhanced flux of long-chain fatty acids into the mitochondria is both controversial and unclear. We hypothesized that skeletal muscle–specific overexpression of the muscle isoform of carnitine palmitoyltransferase 1 (CPT1), the enzyme that controls the entry of long-chain fatty acyl CoA into mitochondria, would enhance rates of fatty acid oxidation and improve insulin action in muscle in high-fat diet insulin-resistant rats