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In this Tech. Note RHIC snakes and stable spin direction $\vector{n}$ 0 (s) are re-visited, based on OPERA-computed field maps of the former. The numerical simulations so undertaken provide various outcomes regarding RHIC optics and spin dynamics, in relation with orbital and focusing effects resulting from the use of this realistic 3-D representation of the snakes.
A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.
A new technique for analyzing complicated fluid flows in numerical simulations has been successfully tested. The analysis uses short time Lyapunov exponent contributions and the associated Lyapunov perturbation fields. A direct simulation of the Taylor-Couette flow just past the onset of chaos demonstrated that this new technique marks important times during the system evolution and identifies the important flow features at those times. This new technique will now be applied to a 'minimal' turbulent channel.
The photoreactions of halorhodopsin are complicated by the fact that the parent pigment and its photoproducts interact with chloride. Thus, in any photoreaction scheme at least four species have to be accounted for: HR565 and HR578 Cl-, as well as HR640 and HR520 Cl-. A photocycle scheme proposed earlier places the two main photointermediates of halorhodopsin, HR520 Cl- and HR640, into a single photocycle, with a chloride-dependent equilibrium between them [Oesterhelt, D., Hegemann, P., & Tittor, J. (1985) EMBO J. 4, 2351-2356]. This scheme, with the additional feature of direct photoproduction of HR640 from HR565, was tested in this work by using numerical solutions of the appropriate differential equations to simulate flash-induced absorption changes at 500 nm (production of HR520 Cl-) and at 660 nm (production of HR640). The time scale of the simulation was ms following the flash. Comparison of the simulated curves with experimental traces yielded a unique set of three rate constants. The proposed photocycle scheme and these rate constants predict well the shapes and amplitudes of flash traces at various chloride concentrations. It appears from the photocycle scheme, and the numerical values of rate constants, that chloride is bound with high affinity to the parent halorhodopsin molecule, but with much lower affinity to its main photointermediate. This may be the consequence of the fact that in the parent halorhodopsin in the retinal configuration is all-trans, but in the two photointermediates it is 13-cis.
It has been almost 50 years since humans last set foot on the Moon. With NASA’s Artemis program, the United States and its international and commercial partners are embarking on a new endeavor to explore the lunar surface. Before we return, we will have simulated every aspect of these future missions. Many of these models and simulations (M&S) will rely on well-known and commonly-used technologies, some of which trace their origins back to the Apollo program. However, M&S has advanced significantly, as have the underlying computational capabilities. As a result, we are able to model many more aspects of the Artemis vehicles and support systems with significantly improved detail and confidence. Accurately and efficiently modeling the lunar environment will be critical to simulating the Artemis elements and mission activities. This includes characterizing and modeling lunar topography, smaller craters, exposed surface rocks, lunar regolith, surface lighting, and ambient thermal environment. These are all necessary for understanding fundamental behaviors and performance of vehicles and support systems in the lunar environment and are often determining factors in the selection of exploration sites and defining mission profiles. The Astromaterials Research and Exploration Sciences (ARES) team in the Exploration Integration and Science Directorate at NASA’s Johnson Space Center (JSC) and the NASA Exploration Systems Simulations (NExSyS) team in the Simulation and Graphics Branch at JSC are developing and maintaining the Digital Lunar Exploration Sites (DLES) data, documentation, and software packages. This data is being fed directly into a diverse collection of graphics and simulation environments, where it is used to construct the closest known truth for numerous potential Lunar South Pole landing sites. DLES is available to projects across NASA and particularly the Artemis program to support coordinated digital representations of the lunar environment. This paper describes the fundamental need for DLES, the science data sets that are going into DLES, some of the processes used to integrate this data into DLES products, the basic products that constitute DLES, and some examples of DLES in use.
This document describes the partial derivatives for commonly estimated parameters including antenna positions, satellite position, and satellite velocity from a near-field VLBI delay model for Earth-orbiting satellites. This model was presented in the Journal of Geodesy by Jaron & Nothnagel (2019). In this context, we present a streamlined version of the near-field VLBI delay. From this simplified model, we deduce a delay rate expression and calculate partial derivatives, maintaining only the terms with significant impact on the computed derivatives’ magnitude. To verify the accuracy of the simplified model and the partial derivatives computed from it, we have created a simple simulation in Matlab of an Earth-orbiting satellite at the altitude of a typical Global Navigation Satellite Systems (GNSS) satellite. From this simulation, we compare the simplified and original delays, and we verify the magnitude and direction of the partial derivatives against the numerically computed derivatives from the original delay model. The partial derivatives and simplified VLBI delay model detailed here are implemented in Fortran in the open-source library VTD.
This paper considers the optimal energy management for a microgrid. The goal of optimal energy management is to minimize the total generation cost while meeting total demand and satisfying individual generator output limits. To achieve this goal, we develop a distributed algorithm based on the consensus theory and gradient estimation technique. Compared to the existing algorithms with diminishing step-sizes, the proposed algorithm enjoys a faster convergence speed due to the fixed step-size, and thus increases the computation speed, and reduces the computation and communication burden. The proposed distributed algorithm is applicable to both fixed and time-varying directed communication networks. We show that the convergence of the proposed distributed algorithm is achieved if the fixed communication network is strongly connected, or if the time-varying communication network is uniformly jointly strongly connected. Numerical simulation results are used to illustrate and demonstrate the effectiveness of the proposed algorithm.
A series of observing system simulation experiments have been performed in order to assess the potential impact of marine surface wind data on numerical weather prediction. In addition to conventional data, the experiments simulated the time-continuous assimilation of remotely sensed marine surface wind or temperature sounding data. The wind data were fabricated directly for model grid points intercepted by a Seasat-1 scatterometer swath and were assimilated into the lowest active level (945 mb) of the model using a localized successive correction method. It is shown that Seasat wind data can greatly improve numerical weather forecasts due to better definition of specific features. The case of the QE II storm is examined.
Two methods are presented for a direct Monte Carlo evaluation of the surface entropy S(s) of a liquid interacting by specified, volume-independent potentials. The first method is based on an application of the approach of Ferrenberg and Swendsen (1988, 1989) to Monte Carlo simulations at two different temperatures; it gives much more reliable results for S(s) in liquid Si than previous calculations based on numerical differentiation. The second method expresses the surface entropy directly as a canonical average at fixed temperature.
Opposed Jet Burner (OJB) tools have been used extensively by the authors to measure Flame Strength (FS) extinction limits of laminar H2/N2 air and (recently) hydrocarbon (HC) air Counterflow Diffusion Flames (CFDFs) at one atm. This paper details normalization of FSs of N2- diluted H2 and HC systems to account for effects of fuel composition, temperature, pressure, jet diameter, inflow Reynolds number, and inflow velocity profile (plug, contoured nozzle; and parabolic, straight tube). Normalized results exemplify a sensitive accurate means of validating, globally, reduced chemical kinetic models at approx. 1 atm and the relatively low temperatures approximating the loss of non-premixed idealized flameholding, e.g., in scramjet combustors. Laminar FS is defined locally as maximum air input velocity, U(sub air), that sustains combustion of a counter-jet of g-fuel at extinction. It uniquely characterizes a fuel. And global axial strain rate at extinction (U(sub air) normalized by nozzle or tube diameter, D(sub n or (sub t)) can be compared directly with computed extinction limits, determined using either a 1-D Navier Stokes stream-function solution, using detailed transport and finite rate chemistry, or (better yet) a detailed 2-D Navier Stokes numerical simulation. The experimental results define an idealized flameholding reactivity scale that shows wide ranging (50 x) normalized FS s for various vaporized-liquid and gaseous HCs, including, in ascending order: JP-10, methane, JP-7, n-heptane, n-butane, propane, ethane, and ethylene. Results from H2 air produce a unique and exceptionally strong flame that agree within approx. 1% of a recent 2-D numerically simulated FS for a 3 mm tube-OJB. Thus we suggest that experimental FS s and/or FS ratios, for various neat and blended HCs w/ and w/o additives, offer accurate global tests of chemical kinetic models at the Ts and Ps of extinction. In conclusion, we argue the FS approach is more direct and fundamental, for assessing, e.g., idealized scramjet flameholding potentials, than measurements of laminar burning velocity or blowout in a Perfectly Stirred Reactor, because the latter characterize premixed combustion in the absence of aerodynamic strain. And FS directly measures a chemical kinetic characteristic of non-premixed combustion at typical flameholding temperatures. It mimics conditions where gfuels are typically injected into a subsonic flameholding recirculation zone that captures air, where the effects of aerodynamic strain and associated multi-component diffusion become important.
Topology establishes a unifying framework for a diverse range of scientific areas including particle physics, cosmology, and condensed matter physics. One of the most fascinating manifestations of topology in the context of condensed matter is the topological Hall effect, and its relative: the Skyrmion Hall effect. Skyrmions are stable vortex-like spin configurations in certain chiral magnets, and when subject to external electric currents can drift in the transverse direction to the current. These quasi-particles are characterised by a conserved topological charge which in the Skyrmion Hall effect plays the role of electric charges in the ordinary Hall effect. Recently, it has been shown that liquid crystals endowed with chiral properties serve as an ideal testbed for the fundamental investigation of topological solitons, including their two- and three-dimensional realisations. Here, we show experimentally and numerically that three-dimensional solitons aka "torons" exhibit a Hall-like effect when driven by shear flows: the torons are deflected in the direction perpendicular to the shear plane. The experimental results are rationalised in terms of the dynamic Ericksen-Leslie equations, which predict the emergence of the transverse component of the net mass flow, the magnitude of which scales as the 3rd power of the shear rate. The perturbation analysis highlights an interplay of the viscous and chiral elastic torques as the mechanism for the emergence of net transverse currents. Numerical simulations demonstrate, however, that torons are not merely dragged by the flow but move with their own transverse speed, much larger than the average flow velocity in the transverse direction. Our findings may enable responsive microfluidic applications relying on soft topological solitons.
Interactions between a flexible beam and a fluid in a channel are of great relevance to biological hairy surfaces, aquatic vegetation, marine life (e.g., fish gills), and many industrial systems alike. While steady state response of a beam to such flows is fairly well-explored, their behavior in the transient regime is not fully understood. Here, a series of numerical simulations are performed to study the laminar Couette flow of an incompressible viscous fluid past an elastic beam in a two-dimensional channel. The flexible beam is perpendicular to the direction of flow, and its base is fixed to the stationary bottom of the channel. We measure the evolution of the Vogel exponent, drag reduction, and reconfiguration number during the transient and steady-state response of the fluid–structure system for different geometrical and physical properties. Our benchmark shows a good agreement between numerical and experimental observations. Our results show that the system's steady-state response at different bulk-fluid velocities can be reproduced by investigating the shear flow response during the transient regime. We define a new variable that characterizes the evolution of the local velocity profile in the proximity of the free end of the beam and use that to characterize the transient-regime response. The analysis yields insight into the competing effects of elasticity of the beam and non-linear flow response.
Kinetic descriptions of runaway electrons (REs) are usually based on Fokker-Planck models that determine the probability distribution function of REs in 2-dimensional momentum space. Despite the simplification involved, the Fokker-Planck equation can rarely be solved analytically and direct numerical approaches [e.g., continuum and particle-based Monte Carlo (MC)] can be time consuming, especially in the computation of asymptotic-type observables including the runaway probability, the slowing-down and runaway mean times, and the energy limit probability. In this study, we present a novel backward MC approach to these problems based on backward stochastic differential equations that describe the dynamics of the runaway probability by means of the Feynman-Kac theory. The key ingredient of the backward MC algorithm is to place all the particles in a runaway state and simulate them backward from the terminal time to the initial time. As such, our approach can provide much faster convergence than direct MC methods (by significantly reducing the number of particles required to achieve a prescribed accuracy) while at the same time maintaining the advantages of particle-based methods (compared to continuum approaches). The proposed algorithm is unconditionally stable and can be parallelized as easy as the direct MC method, and its extension to dimensions higher than two is straightforward, thus paving the way for conducting large-scale RE simulation.
The development of numerical software for engineering applications requires the validation of the code against experimental benchmark datasets. To support the validation of SAS4A/SASSYS-1 in simulating the single-phase natural circulation within nuclear reactor systems, high-precision steady-state experiments are performed to capture single-phase natural circulation phenomena on an existing scaled facility with comprehensive instrumentation. Forced convection tests are designed precisely capturing the facility’s critical thermal-hydraulic parameters required for one-dimensional modeling, and a comprehensive single-phase natural circulation dataset is obtained with well-documented experimental uncertainty and facility description. Analysis and discussion based on the finalized dataset confirm the dataset’s ability in capturing dominant phenomena and address important physical interpretation of parameters. The dataset reported in this project provides a valuable benchmark resource for the validation of system analysis codes under single-phase natural circulation inside nuclear reactors. Validation of SAS4A/SASSYS-1 is then performed against the obtained benchmark dataset to confirm the capability of its physics model in simulating the steady-state single-phase natural circulation. The experimental facility is modeled in the candidate code. Solution verification is performed using Richardson-extrapolation-based estimators to quantify and restrict numerical errors from discretization. Numerical uncertainty originating from finite maximum pseudo-transient time is also quantified and restricted. Input uncertainty provided by the benchmark dataset is forward propagated through the candidate code, directly quantifying the simulation output in a Monte Carlo approach. The composition of the output uncertainty is further determined by the estimators of Sobol’ indices through a variance-based sensitivity analysis. With uncertainty quantified for each individual condition, detailed comparison between the simulation results and experimental data is performed covering the whole dataset, which shows consistent agreement for all important quantities. The validation activity reported in this project demonstrates that SAS4A/SASSYS-1 can predict the primary parameters with satisfactorily accuracy under steady-state single-phase natural circulation.
While the aurora has attracted attention for millennia, important questions remain unanswered. Foremost is how auroral electrons are accelerated before colliding with the ionosphere and producing auroral light. Powerful Alfvén waves are often found traveling Earthward above auroras with sufficient energy to generate auroras, but there has been no direct measurement of the processes by which Alfvén waves transfer their energy to auroral electrons. Here, we show laboratory measurements of the resonant transfer of energy from Alfvén waves to electrons under conditions relevant to the auroral zone. Experiments are performed by launching Alfvén waves and simultaneously recording the electron velocity distribution. Numerical simulations and analytical theory support that the measured energy transfer process produces accelerated electrons capable of reaching auroral energies. The experiments, theory, and simulations demonstrate a clear causal relationship between Alfvén waves and accelerated electrons that directly cause auroras.
Magnetic fields and their dynamical interplay with matter in galaxy clusters contribute to the physical properties and evolution of the intracluster medium. However, the current understanding of the origin and properties of cluster magnetic fields is still limited by observational challenges. In this article, we map the magnetic fields at hundreds-kpc scales of five clusters RXC J1314.4-2515, Abell 2345, Abell 3376, MCXC J0352.4-7401, and El Gordo using the synchrotron intensity gradient technique in conjunction with high-resolution radio observations from the Jansky Very Large Array (JVLA) and the Karoo Array Telescope (MeerKAT). We demonstrate that the magnetic field orientation of radio relics derived from synchrotron intensity gradient is in agreement with that obtained with synchrotron polarization. Most importantly, the synchrotron intensity gradient is not limited by Faraday depolarization in the cluster central regions and allows us to map magnetic fields in the radio halos of RXC J1314.4-2515 and El Gordo. We find that magnetic fields in radio halos exhibit a preferential direction along the major merger axis and show turbulent structures at higher angular resolution. The results are consistent with expectations from numerical simulations, which predict turbulent magnetic fields in cluster mergers that are stirred and amplified by matter motions.
Proper scaling in turbulent planar plumes is investigated in this study using a scaling patch approach. Based on the scaled boundary conditions, a proper velocity scale for the mean axial flow is the plume centerline velocity U ref = U ctr , and a proper temperature scale for the temperature excess is Θ ref = T ctr – T ∞ , where T ctr is the plume centerline temperature and T ∞ is the ambient fluid temperature. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity, mean momentum, and mean energy equations, respectively, the following is found: (1) a proper scale for the mean transverse flow is V ref = ( d δ / d x ) U ctr , where d δ / d x is the growth rate of the plume width. (2) A proper scale for the Reynolds shear stress is R vu , ref = U ctr V ref = ( d δ / d x ) U ctr 2 , a mix of the scales for the mean axial and transverse flows. (3) A proper scale for the turbulent heat flux is R v θ , ref = V ref Θ ctr , a mix of the scales for the mean transverse flow and mean temperature excess. The mean transverse flow thus plays a critical role in the scaling of turbulent planar plumes. Approximate functions are developed for the scaled mean transverse flow, Reynolds shear stress, and turbulent temperature flux, and are found to agree favorably with experimental and numerical simulation data. The integral analysis of the mean momentum equation yields a Richardson number Ri, which remains invariant in the axial direction. The Richardson number is defined as Ri = def g β Θ ctr δ t / ( U ctr V ref ) ≈ 1 / 2 , where g is the gravitational acceleration, β is the thermal expansion coefficient, and δ t is the plume half-width based on the mean temperature profile. This Richardson number arises directly from the scaling patch analysis of the mean momentum equation, including both the streamwise and transverse velocity scales.
Here, we discuss the stability properties of the solutions of the general nonlinear Schrödinger equation in 1 + 1 dimensions in an external potential derivable from a parity-time ($ \newcommand{\PT}{\mathcal{PT}} \PT$ ) symmetric superpotential $W(x)$ that we considered earlier in Kevrekidis et al (2015 Phys. Rev. E 92 042901). In particular we consider the nonlinear partial differential equation $ \{i \, \partial_t + \partial_x^2 - V(x) + g \vert \psi(x, t) \vert ^{2\kappa} \} \, \psi(x, t) = 0 \>, $ for arbitrary nonlinearity parameter κ, where $g= \pm1$ and V is the well known Pöschl–Teller potential which we allow to be repulsive as well as attractive. Using energy landscape methods, linear stability analysis as well as a time dependent variational approximation, we derive consistent analytic results for the domains of instability of these new exact solutions as a function of the strength of the external potential and κ. For the repulsive potential we show that there is a translational instability which can be understood in terms of the energy landscape as a function of a stretching parameter and a translation parameter being a saddle near the exact solution. In this case, numerical simulations show that if we start with the exact solution, the initial wave function breaks into two pieces traveling in opposite directions. If we explore the slightly perturbed solution situations, a 1% change in initial conditions can change significantly the details of how the wave function breaks into two separate pieces. For the attractive potential, changing the initial conditions by 1% modifies the domain of stability only slightly. For the case of the attractive potential and negative g perturbed solutions merely oscillate with the oscillation frequencies predicted by the variational approximation.