Automatic Generation of Matrix Element Derivatives for Tight Binding Models

Tight binding (TB) models are one approach to the quantum mechanical many particle problem. An important role in TB models is played by hopping and overlap matrix elements between the orbitals on two atoms, which of course depend on the relative positions of the atoms involved. This dependence can be expressed with the help of Slater-Koster parameters, which are usually taken from tables. Recently, a way to generate these tables automatically was published. If TB approaches are applied to simulations of the dynamics of a system, also derivatives of matrix elements can appear. In this work we give general expressions for first and second derivatives of such matrix elements. Implemented in a computer program they obviate the need to type all the required derivatives of all occuring matrix elements by hand.Comment: 11 pages, 2 figure

Resonators coupled to voltage-biased Josephson junctions: From linear response to strongly driven nonlinear oscillations

Motivated by recent experiments, where a voltage biased Josephson junction is placed in series with a resonator, the classical dynamics of the circuit is studied in various domains of parameter space. This problem can be mapped onto the dissipative motion of a single degree of freedom in a nonlinear time-dependent potential, where in contrast to conventional settings the nonlinearity appears in the driving while the static potential is purely harmonic. For long times the system approaches steady states which are analyzed in the underdamped regime over the full range of driving parameters including the fundamental resonance as well as higher and sub-harmonics. Observables such as the dc-Josephson current and the radiated microwave power give direct information about the underlying dynamics covering phenomena as bifurcations, irregular motion, up- and down conversion. Due to their tunability, present and future set-ups provide versatile platforms to explore the changeover from linear response to strongly nonlinear behavior in driven dissipative systems under well defined conditions.Comment: 12 pages, 11 figure

Prevalence of hormone prescription and education for cis and trans women by medical trainees

PREVALENCE OF HORMONE PRESCRIPTION AND EDUCATION FOR CIS AND TRANS WOMEN BY MEDICAL TRAINEES AUTHORS Madison Meister, BA Candidate; Emily J Noonan, PhD, MA; Laura A. Weingartner, PhD, MS BACKGROUND Hormone replacement therapy is a common healthcare practice for contraception, hormone control, and menopause treatment. Transgender patients may also take hormones to affirm their gender identity, such as feminizing hormones (estrogen), for transgender women. Studying how trainees discuss hormone risks for both cis and trans women can demonstrate if disparities exist and how we may address them to overcome healthcare barriers. METHODS Fifty videos were analyzed of third-year medical students taking patient histories from standardized patients, including 28 cis women and 22 trans women. Students had previously completed LGBTQ clinical skills training, and patients reported taking estrogen purchased online for acne control (cis) or gender-affirming (trans) purposes. Videos were analyzed for the presence and context of hormone health risk discussion, student knowledge, and whether the student agreed to prescribe hormones. RESULTS Of the 90% (n=43) of students who agreed to prescribe hormones, 47% (n=20) prescribed conditionally. Conditions included: pending lab results, desire to research hormones, or checking with attending physicians. A larger proportion of trans women were prescribed hormones (95% or 21/22) compared to cisgender women (79% or 22/28). While similar proportions of students discussed hormone risks between patient groups, students discussed their knowledge or discomfort prescribing hormones more frequently with trans women (27% or n=6/22) than cis women (18% or n=5/28). DISCUSSION We expected students to prescribe combined estrogen-progestin oral contraception to cis women. These data show students more readily prescribed estrogen for gender-affirming purposes, suggesting that LGBTQ clinical skills interventions may help prepare students to provide gender-affirming care

Thermal diffusion of supersonic solitons in an anharmonic chain of atoms

We study the non-equilibrium diffusion dynamics of supersonic lattice solitons in a classical chain of atoms with nearest-neighbor interactions coupled to a heat bath. As a specific example we choose an interaction with cubic anharmonicity. The coupling between the system and a thermal bath with a given temperature is made by adding noise, delta-correlated in time and space, and damping to the set of discrete equations of motion. Working in the continuum limit and changing to the sound velocity frame we derive a Korteweg-de Vries equation with noise and damping. We apply a collective coordinate approach which yields two stochastic ODEs which are solved approximately by a perturbation analysis. This finally yields analytical expressions for the variances of the soliton position and velocity. We perform Langevin dynamics simulations for the original discrete system which fully confirm the predictions of our analytical calculations, namely noise-induced superdiffusive behavior which scales with the temperature and depends strongly on the initial soliton velocity. A normal diffusion behavior is observed for very low-energy solitons where the noise-induced phonons also make a significant contribution to the soliton diffusion.Comment: Submitted to PRE. Changes made: New simulations with a different method of soliton detection. The results and conclusions are not different from previous version. New appendixes containing information about the system energy and soliton profile

Mixed convection in a rotating porous cavity having local heater

Numerical simulation of convective heat transfer inside a rotating porous square cavity with local heater of constant temperature has been performed. Governing equations formulated on the basis of mass, momentum and energy conservation laws written using the dimensionless stream function, vorticity and temperature have been solved by the finite difference method. The effects of Rayleigh and Taylor numbers on periodic flow and heat transfer have been studied

Asymptotic adaptive methods for multi-scale problems in fluid mechanics

This paper reports on the results of a three-year research effort aimed at investigating and exploiting the role of physically motivated asymptotic analysis in the design of numerical methods for singular limit problems in fluid mechanics. Such problems naturally arise, among others, in combustion, magneto-hydrodynamics and geophysical fluid mechanics. Typically, they are characterized by multiple space and/or time scales and by the disturbing fact that standard computational techniques fail entirely, are unacceptably expensive, or both. The challenge here is to construct numerical methods which are robust, uniformly accurate, and efficient through different asymptotic regimes and over a wide range of relevant applications. Summaries of multiple scales asymptotic analyses for low Mach number flows, magnetohydrodynamics at small Mach and Alfv´en numbers, and of multiple scales atmospheric flows are provided. These reveal singular balances between selected terms in the respective governing equations within the considered flow regimes. These singularities give rise to problems of severe stiffness, stability, or to dynamic range issues in straightforward numerical discretizations. Aformal mathematical framework for the multiple scales asymptotics is then summarized using the example of multiple length scale – single time scale asymptotics for low Mach number flows. The remainder of the paper focuses on the construction of numerical discretizations for the respective full governing equation systems. These discretizations avoid the pitfalls of singular balances by exploiting the asymptotic results. Importantly, the asymptotics are not used here to derive simplified equation systems, which are then solved numerically. Rather, we aim at numerically integrating the full equation sets and at using the asymptotics only to construct discretizations that do not deteriorate as a singular limit is approached. One important ingredient of this strategy is the numerical identification of a singular limit regime given a set of discrete numerical state variables. This problem is addressed in an exemplary fashion for multiple length – single time scale low Mach number flows in one space dimension. The strategy allows a dynamic determination of an instantaneous relevant Mach number, and it can thus be used to drive the appropriate adjustment of the numerical discretizations when the singular limit regime is approached