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Multibody for Everybody (M4E) is an open-source symbolic dynamics modeling framework designed to automate the derivation of equations of motion and simulation of constrained multibody systems using the joint coordinate formulation.
Differential dynamic programming algorithms of second and first order for optimal control, considering nonlinear unconstrained and constrained problems
Numerical fluid dynamic models of mid-oceanic ridge axes were constructed using distributions of material properties constrained by seismic studies and thermal calculations. The calculations indicate that spreading is passive except for forces caused by density differences due to thermal expansion and partial melt. Except for geometric differences due to temperature distribution, one set of mechanical properties can adequately explain central rifts of slow ridges and central peaks of fast ridges. Viscous head loss in the upwelling material dominates at low spreading rates where material ascends through a narrow conduit. Thermal expansion and partial melting dominate at high spreading rates where a wide low viscosity crustal magma chamber is present. The preferred rheology is 10 to the 20th poise for the upwelling lithosphere; less than 5 x 10 to the 17th for the crustal magma chamber and axial intrusion zone at fast ridges, and a yield stress of 200 bars for the lithosphere. The calculation correctly predicts the existence of central peaks at 'hot-spot' ridges, where seismic evidence indicates a large magma chamber.
The structural design process for large transport aircraft is described. Critical loads must be determined from a large number of load cases within the flight maneuver envelope. The structural design is also constrained by considerations of producibility, reliability, maintainability, durability, and damage tolerance, as well as impact dynamics and multiple constraints due to flutter and aeroelasticity. Aircraft aeroelastic design considerations in three distinct areas of product development (preliminary design, advanced design, and detailed design) are presented and contrasted. The present state of the art is challenged to solve the practical difficulties associated with design, analysis, and redesign within cost and schedule constraints. The current practice consists of largely independent engineering disciplines operating with unorganized data interfaces. The need is then demonstrated for a well-planned computerized aeroelastic structural design optimization system operating with a common interdisciplinary data base. This system must incorporate automated interfaces between modular programs. In each phase of the design process, a common finite-element model for static and dynamic optimization is required to reduce errors due to modeling discrepancies. As the design proceeds from the simple models in preliminary design to the more complex models in advanced and detailed design, a means of retrieving design data from the previous models must be established.
A new family of gallium arsenide circuits for fine grained bit-systolic arithmetic arrays is introduced. This scheme combines features of two recent techniques of dynamic gallium arsenide FET logic and differential dynamic single-clock CMOS logic. The resulting circuits are fast and compact, with tightly constrained series FET propagation paths, low fanout, no dc power dissipation, and depletion FET implementation without level shifting diodes.
In order to understand the complex meteoroid environment that threatens spacecraft in near Earth space, ground based observational techniques provide us with an effective option for evaluating the important parameters of flux, speed, mass, density and directionality. While no observational method (in ]situ or ground based detectors) provides bias free measurements of direct quantities, there are several benefits to using the Earth as a detector for calibrating meteoroid models that extend to the inner Solar System and beyond Earth fs orbit. The Earth constantly interacts with meteoritic particles from comets and asteroids as they evolve from their parent objects through dynamical processes. Modeling these dynamical processes with a physics ]based approach can help reveal the causes of observational features but developing those models involves constraining sequences of poorly defined parameters. These parameters must be tuned to a particular detector that offers direct or indirect measurements of mass, density, flux and speed - the quantities used in evaluating penetration risk. The following topics will be discussed: a) Consistency between ground based and in.situ measurements of flux in Earth orbit. b) Consistency between radar and electro.optical speed determinations and agreement of these with dynamical studies. c) The fact that there are six sporadic sources which cannot be determined by integrated line of sight emissivity: Observations using IRAS or COBE cannot give you all important directionality needed for risk evaluations. d) The large collecting area of the Earth s atmosphere compared to in.situ detectors gives better number statistics in the threat regime. The NASA Meteoroid Environment Office utilizes ground based radar and electro.optical measurements to calibrate the Meteoroid Engineering Model (MEM). As MEM is an engineering design model our main emphasis is on threat size particle, speed, flux and directionality. However, MEM has acknowledged limitations particularly with regard to source strength as a function of mass and work is proceeding with improved distributions that will rectify many of these shortcomings.
While microscale helices with specified chirality are pervasive in biological systems, driving purely synthetic materials to self-organize into such useful structures remains a significant challenge. Through theory and simulations, we model the behavior of initially flat ribbons of gel-fiber composites and show that these materials self-organize into three-dimensional helices with the application of heat. We specifically focus on thermo-responsive gels, which shrink when heated to a point near the lower critical solubility temperature (LCST). Within the composite, regions of the LCST gel that lie far from the fibers can readily shrink in response to the increased temperature; however, near the fibers the network is inhibited from undergoing the heat-induced collapse. This competition between the constrained and the unconstrained regions of the heated sample plays a vital role in the structural evolution of the material. Additionally, we find that this dynamic process can be controlled through the careful placement of the fibers on the outer surface of the gel. We specifically identify fiber arrangements that lead to the formation of helical structures with controlled chirality. Moreover, we isolate scenarios where constraining the movement of one or both the free ends of the sample promotes and stabilizes the formation of helical structures with specified handedness. Such structurally tailored composites are useful for creating mechanically robust actuators, and “appendages” for soft robots that can controllably curl and uncurl with variations in temperature.
Residual forcing necessary to close the MLTB on seasonal time scales are largest in regions of strongest surface heat flux forcing. Identifying the dominant source of error - surface heat flux error, mixed layer depth estimation, ocean dynamical forcing - remains a challenge in the eastern tropical oceans where ocean processes are very active. Improved sub-surface observations are necessary to better constrain errors. 1. Mixed layer depth evolution is critical to the seasonal evolution of mixed layer temperatures. It determines the inertia of the mixed layer, and scales the sensitivity of the MLTB to errors in surface heat flux and ocean dynamical forcing. This role produces timing impacts for errors in SST prediction. 2. Errors in the MLTB are larger than the historical 10Wm-2 target accuracy. In some regions, a larger accuracy can be tolerated if the goal is to resolve the seasonal SST cycle.
The problem is posed with the additional constraints that the dynamic controller uses only noise-corrupted outputs, and that its dimension is significantly lower than that of a Kalman filter. The unknown disturbance is viewed as an adversary which tries to maximize a performance criterion: a criterion that the controller gains attempt to minimize. The optimal controller gains are determined by solving a nonlinear matrix two-point boundary value problem.
Abstract Observations of core-collapse supernovae (CCSNe) reveal a wealth of information about the dynamics of the supernova ejecta and its composition but very little direct information about the progenitor. Constraining properties of the progenitor and the explosion requires coupling the observations with a theoretical model of the explosion. Here we begin with the CCSN simulations of Couch et al., which use a nonparametric treatment of the neutrino transport while also accounting for turbulence and convection. In this work we use the SuperNova Explosion Code to evolve the CCSN hydrodynamics to later times and compute bolometric light curves. Focusing on Type IIP SNe (SNe IIP), we then (1) directly compare the theoretical STIR explosions to observations and (2) assess how properties of the progenitor’s core can be estimated from optical photometry in the plateau phase alone. First, the distribution of plateau luminosities ( L 50 ) and ejecta velocities achieved by our simulations is similar to the observed distributions. Second, we fit our models to the light curves and velocity evolution of some well-observed SNe. Third, we recover well-known correlations, as well as the difficulty of connecting any one SN property to zero-age main-sequence mass. Finally, we show that there is a usable, linear correlation between iron core mass and L 50 such that optical photometry alone of SNe IIP can give us insights into the cores of massive stars. Illustrating this by application to a few SNe, we find iron core masses of 1.3–1.5 M ⊙ with typical errors of 0.05 M ⊙ . Data are publicly available online on Zenodo: doi: 10.5281/zenodo.6631964 .
A tetrahedron is a 4-node 6-strut pyramid structure which is being used by the NASA - Goddard Space Flight Center as the basic building block for a new approach to robotic motion. The struts are extendable; it is by the sequence of activities: strut-extension, changing the center of gravity and falling that the tetrahedron "moves". Currently, strut-extension is handled by human remote control. There is an effort underway to make the movement of the tetrahedron autonomous, driven by an attempt to achieve a goal. The approach being taken is to associate an intelligent agent with each node. Thus, the autonomous tetrahedron is realized as a constrained multi-agent system, where the constraints arise from the fact that between any two agents there is an extendible strut. The hypothesis of this work is that, by proper composition of such automated tetrahedra, robotic structures of various levels of complexity can be developed which will support more complex dynamic motions. This is the basis of the new approach to robotic motion which is under investigation. A Java-based simulator for the single tetrahedron, realized as a constrained multi-agent system, has been developed and evaluated. This paper reports on this project and presents a discussion of the structure and dynamics of the simulator.
Context . The solar magnetic field plays an essential role in the formation, evolution, and dynamics of large-scale eruptive structures in the corona. The estimation of the coronal magnetic field, the ultimate driver of space weather, particularly in the ‘low’ and ‘middle’ corona, is presently limited due to practical difficulties. Data-driven time-dependent magnetofrictional modelling (TMFM) of active region magnetic fields has been proven to be a useful tool to study the corona. The input to the model is the photospheric electric field that is inverted from a time series of the photospheric magnetic field. Constraining the complete electric field, that is, including the non-inductive component, is critical for capturing the eruption dynamics. We present a detailed study of the effects of optimisation of the non-inductive electric field on the TMFM of AR 12473. Aims . We aim to study the effects of varying the non-inductive electric field on the data-driven coronal simulations, for two alternative parametrisations. By varying parameters controlling the strength of the non-inductive electric field, we wish to explore the changes in flux rope formation and their early evolution and other parameters, for instance, axial flux and magnetic field magnitude. Methods . We used the high temporal and spatial resolution cadence vector magnetograms from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). The non-inductive electric field component in the photosphere is critical for energising and introducing twist to the coronal magnetic field, thereby allowing unstable configurations to be formed. We estimated this component using an approach based on optimising the injection of magnetic energy. Results . Our data show that flux ropes are formed in all of the simulations except for those with the lower values of these optimised parameters. However, the flux rope formation, evolution and eruption time varies depending on the values of the optimisation parameters. The flux rope is formed and has overall similar evolution and properties with a large range of non-inductive electric fields needed to determine the non-inductive electric field component that is critical for energising and introducing twist to the coronal magnetic field. Conclusions . This study shows that irrespective of non-inductive electric field values, flux ropes are formed and erupted, which indicates that data-driven TMFM can be used to estimate flux rope properties early in their evolution without needing to employ a lengthy optimisation process.
Partial differential equation (PDE)-constrained optimization problems arise in a variety of scientific and engineering applications, such as topology optimization, electrodynamics, fluid dynamics, and structural dynamics. However, these problems are often challenging and computationally expensive to solve, due to the need to solve the PDEs within the optimization loop. One approach to reducing the computational cost of these methods while providing convergence guarantees is through inexact trust region methods; this method uses lower fidelity solutions of the PDE at early stages of the optimization and adjusts the required accuracy of inexact PDE solvers as the optimization progresses. In this work, we explore the use of machine learning based surrogate models with these inexact trust region methods. We first demonstrate the potential of this approach by using Gaussian processes as the surrogate model and test this on a simple PDE-constrained optimization problem. We then document explorations into improving the computational costs of evolutional deep neural network / neural Galerkin methods, with the eventual goal of using these methods with the inexact trust region algorithms. We are able to speed up these approaches, albeit at the cost of lower accuracy.
In examining the role of time in mental workload, the authors present a different perspective from which to view the problem of assessment. Mental workload is plotted in three dimensions, whose axes represent effective time for action, perceived distance from desired goal state, level of effort required to achieve the time-constrained goal. This representation allows the generation of isodynamic workload contours that incorporate the factors of operator skill and equifinality of effort. An adaptive interface for dynamic task reallocation is described that uses this form of assessment to reconcile the joint aims of stable operator loading and acceptable primary task performance by the total system.
TRAPPIST-1 is a nearby ultra-cool dwarf that is host to a remarkable planetary system consisting of seven transiting planets. The orbital properties and radii of the planets have been well constrained, and recently, the masses of the inner six planets have been measured with additional ground- and space-based photometric observations. Large uncertainties in these mass measurements have prevented a robust analysis of the planetary compositions. Here, we perform many thousands of N-body dynamical simulations with planet properties perturbed from the observed values and identify those that are stable for millions of years. This allows us to identify self-consistent orbital solutions that can be used in future studies. From our range of dynamical masses, we find that most of the planets are consistent with an Earth-like composition, where TRAPPIST-1f is likely to have a volatile-rich envelope.
TRAPPIST-1 is a nearby ultra-cool dwarf that is host to a remarkable planetary system consisting of seven transiting planets. The orbital properties and radii of the planets have been well constrained, and recently, the masses of the inner six planets have been measured with additional ground- and space-based photometric observations. Large uncertainties in these mass measurements have prevented a robust analysis of the planetary compositions. Here, we perform many thousands of N-body dynamical simulations with planet properties perturbed from the observed values and identify those that are stable for millions of years. This allows us to identify self-consistent orbital solutions that can be used in future studies. From our range of dynamical masses, we find that most of the planets are consistent with an Earth-like composition, where TRAPPIST-1f is likely to have a volatile-rich envelope.
TRAPPIST-1 is a nearby ultra-cool dwarf that is host to a remarkable planetary system consisting of seven transiting planets. The orbital properties and radii of the planets have been well constrained, and recently, the masses of the inner six planets have been measured with additional ground- and space-based photometric observations. Large uncertainties in these mass measurements have prevented a robust analysis of the planetary compositions. Here, we perform many thousands of N-body dynamical simulations with planet properties perturbed from the observed values and identify those that are stable for millions of years. This allows us to identify self-consistent orbital solutions that can be used in future studies. From our range of dynamical masses, we find that most of the planets are consistent with an Earth-like composition, where TRAPPIST-1f is likely to have a volatile-rich envelope.
Abstract An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near‐term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H 4 , H 2 O, and BeH 2 molecules, where it yields compact variational ansätze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is shown through a set of AVQITE calculations of quantum spin models. Finally, quantum Lanczos calculations are demonstrated alongside AVQITE without additional quantum resource costs.