Hypergeometric Formulas for Lattice Sums and Mahler Measures

We prove a variety of explicit formulas relating special values of generalized hypergeometric functions to lattice sums with four indices of summation. These results are related to Boyd’s conjectured identities between Mahler measures and special values of L-series of elliptic curves.

The EPR Paradox Implies A Minimum Achievable Temperature

We carefully examine the thermodynamic consequences of the repeated partial projection model for coupling a quantum system to an arbitrary series of environments under feedback control. This paper provides observational definitions of heat and work that can be realized in current laboratory setups. In contrast to other definitions, it uses only properties of the environment and the measurement outcomes, avoiding references to the `measurement' of the central system's state in any basis. These definitions are consistent with the usual laws of thermodynamics at all temperatures, while never requiring complete projective measurement of the entire system. It is shown that the back-action of measurement must be counted as work rather than heat to satisfy the second law. Comparisons are made to stochastic Schr\"{o}dinger unravelling and transition-probability based methods, many of which appear as particular limits of the present model. These limits show that our total entropy production is a lower bound on traditional definitions of heat that trace out the measurement device. Examining the master equation approximation to the process at finite measurement rates, we show that most interactions with the environment make the system unable to reach absolute zero. We give an explicit formula for the minimum temperature achievable in repeatedly measured quantum systems. The phenomenon of minimum temperature offers a novel explanation of recent experiments aimed at testing fluctuation theorems in the quantum realm and places a fundamental purity limit on quantum computers.Comment: 15 pages, 5 figures (submitted

Running Injuries Due to Strike Patterns

Running is a very repetitive activity that can lead to surmountable stresses to the body over time that could lead to injury. Running biomechanics can influence the effects that the body will experience. This paper will discuss the biomechanical effects that relate to two different strike patterns: rearfoot and forefoot. Research will be examined as to how the strike patterns can influence the major lower extremity joints: ankle, knee, and hip. Common injuries during running as related to strike pattern are also discussed through conclusions based on research studies

Range separation: The divide between local structures and field theories

This work presents parallel histories of the development of two modern theories of condensed matter: the theory of electron structure in quantum mechanics, and the theory of liquid structure in statistical mechanics. Comparison shows that key revelations in both are not only remarkably similar, but even follow along a common thread of controversy that marks progress from antiquity through to the present. This theme appears as a creative tension between two competing philosophies, that of short range structure (atomistic models) on the one hand, and long range structure (continuum or density functional models) on the other. The timeline and technical content are designed to build up a set of key relations as guideposts for using density functional theories together with atomistic simulation.Comment: Expanded version of a 30 minute talk delivered at the 2018 TSRC workshop on Ions in Solution, to appear in the March, 2019 issue of Substantia (https://riviste.fupress.net/index.php/subs/index

On the Differential Rotation of Massive Main Sequence Stars

To date, asteroseismology has provided core to surface differential rotation measurements in eight main-sequence stars. These stars, ranging in mass from $\sim$1.5-9$M_\odot$, show rotation profiles ranging from uniform to counter-rotation. Although they have a variety of masses, these stars all have convective cores and overlying radiative regions, conducive to angular momentum transport by internal gravity waves (IGW). Using two-dimensional (2D) numerical simulations we show that angular momentum transport by IGW can explain all of these rotation profiles. We further predict that should high mass, faster rotating stars be observed, the core to envelope differential rotation will be positive, but less than one.Comment: 5 pages, Accepted at ApJ