First order control for low-thrust interplanetary vehicles
First order control for low thrust interplanetary vehicles based on calculus of variations and Weierstrass E-function
FIRST ORDER EQUATION↗
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Some first-order perturbation energy values.
Computational formulas for first-order perturbation energy correction for singly excited singlet and triplet states of helium isoelectronic sequence
PERTURBATION THEORY↗
A first order iteration process for simultaneous equations
First order iteration process for solutions of simultaneous equations
NONLINEAR EQUATION↗
A first order iteration process for simultaneous equations.
First order iterative process for solving simultaneous equations to alter character of region where convergence is expected
Luther, H. A.↗
Improved first order interpolator
Data compression method enables first order interpolator to operate at higher speeds. Method requires same number of additions and subtractions but fewer multiplications than the conventional method.
Andrews, C. A.↗
Probability learning - First-order Markov structures of quarternary events
First order Markov structures of quaternary events applied to probability learning
Huff, E. M.↗
Random walk techniques in the solution of first order digital phase-locked loops
First order digital phase locked loops analysis for single channel command system, using random walk techniques
Holmes, J. K.↗
A recursively formulated first-order semianalytic artificial satellite theory based on the generalized method of averaging. Volume 1: The generalized method of averaging applied to the artificial satellite problem
A recursively formulated, first-order, semianalytic artificial satellite theory, based on the generalized method of averaging is presented in two volumes. Volume I comprehensively discusses the theory of the generalized method of averaging applied to the artificial satellite problem. Volume II presents the explicit development in the nonsingular equinoctial elements of the first-order average equations of motion. The recursive algorithms used to evaluate the first-order averaged equations of motion are also presented in Volume II. This semianalytic theory is, in principle, valid for a term of arbitrary degree in the expansion of the third-body disturbing function (nonresonant cases only) and for a term of arbitrary degree and order in the expansion of the nonspherical gravitational potential function.
Mcclain, W. D.↗
Asymptotic integration algorithms for nonhomogeneous, nonlinear, first order, ordinary differential equations
New methods for integrating systems of stiff, nonlinear, first order, ordinary differential equations are developed by casting the differential equations into integral form. Nonlinear recursive relations are obtained that allow the solution to a system of equations at time t plus delta t to be obtained in terms of the solution at time t in explicit and implicit forms. Examples of accuracy obtained with the new technique are given by considering systems of nonlinear, first order equations which arise in the study of unified models of viscoplastic behaviors, the spread of the AIDS virus, and predator-prey populations. In general, the new implicit algorithm is unconditionally stable, and has a Jacobian of smaller dimension than that which is acquired by current implicit methods, such as the Euler backward difference algorithm; yet, it gives superior accuracy. The asymptotic explicit and implicit algorithms are suitable for solutions that are of the growing and decaying exponential kinds, respectively, whilst the implicit Euler-Maclaurin algorithm is superior when the solution oscillates, i.e., when there are regions in which both growing and decaying exponential solutions exist.
Walker, K. P.↗
Tool reconstructs data input points corresponding to first order output graph
Tool aids in graphic determination of input values for any first order lag system of known gain and time constant where the corresponding output function is displayed graphically and can be described by a first order differential equation. This tool permits a rapid reconstruction of input points.
Biggs, R. E.↗
Magnetic field induced modification of a first-order ferromagnetic transition in Eu 2 In
Here, we present a comprehensive study of the temperature-and magnetic-field-dependent magnetization, specific heat, and local crystal structure across the first-order ferromagnetic–paramagnetic transition in Eu 2 In. Anomalies in the magnetocaloric response are observed near 𝐻 ≈ 25 kOe, including changes in field scaling of magnetic entropy, local entropy exponent, and universal master curve, which suggest an apparent weakening of the first-order character of the transition. However, quantitative analysis of the magnetocaloric parameters together with modified Arrott plots demonstrates that the transition remains first order up to at least 70 kOe. Specific-heat measurements reveal a field-induced splitting of the sharp zero-field anomaly into a doublet, providing a natural explanation for the change in the magnetocaloric response. Magnetic-field-dependent extended x-ray absorption fine structure (EXAFS) measurements show no detectable field-induced changes in the local coordination environment of Eu. We therefore attribute these observations to a magnetic-field-induced two-step transition process in Eu 2 In.
Kumar, Ajay [Ames Laboratory (AMES), Ames, IA (Uni↗
First-order formalism for β functions in bosonic sigma models from supersymmetry breaking
We consider the renormalization group flow equation for the two-dimensional sigma models with the Kähler target space. The first-order formulation allows us to treat perturbations in these models as current-current deformations. We demonstrate, however, that the conventional first-order formalism misses certain anomalies in the measure, and should be amended. We reconcile beta functions obtained within the conformal perturbation theory for the current-current deformations with traditional “geometric” results obtained in the background field methods, in this way resolving the peculiarities pointed out in O. Gamayun et al. [Peculiarities of beta functions in sigma models, J. High Energy Phys. 10 (2023) 097]. The result is achieved by the supersymmetric completion of the first-order sigma model.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
First-order and gradual phase transitions of ethane confined in MCM-41
The first-order phase transition of ethane confined in MCM-41, i.e., capillary condensation, has been measured using an isochoric cooling procedure by differential scanning calorimetry (DSC) under conditions ranging from 206 K and 1.1 bar up to the pore critical point (PCP). The PCP has also been determined using the three-line method developed earlier based on the vanishing heat of phase transition. As in the bulk phase, no first-order phase transition can occur above the critical point, which also implies that vapor can transform into liquid gradually by following a path around the critical point through the supercritical region. For the first time, the gradual phase transition is demonstrated with ethane in MCM-41, which is achieved through a multistep process with paths proceeding around the PCP without crossing the capillary-condensation curve. Finally, the occurrence of the gradual phase transition in nanopores, thus the confined supercriticality, is confirmed while our consistent DSC measurements are also well demonstrated.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
An analysis of a first-order polynomial predictor for data compression
Theoretical analysis of first order polynomial predictor for data compression
DATA COMPRESSOR↗
First-Order Frameworks for Managing Models in Engineering Optimization
Approximation/model management optimization (AMMO) is a rigorous methodology for attaining solutions of high-fidelity optimization problems with minimal expense in high- fidelity function and derivative evaluation. First-order AMMO frameworks allow for a wide variety of models and underlying optimization algorithms. Recent demonstrations with aerodynamic optimization achieved three-fold savings in terms of high- fidelity function and derivative evaluation in the case of variable-resolution models and five-fold savings in the case of variable-fidelity physics models. The savings are problem dependent but certain trends are beginning to emerge. We give an overview of the first-order frameworks, current computational results, and an idea of the scope of the first-order framework applicability.
Alexandrov, Natlia M.↗
Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws
We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.
Barth, Timothy↗
Aspects of reheating in first-order inflation
Studied here is reheating in theories where inflation is completed by a first-order phase transition. In the scenarios, the Universe decays from its false vacuum state by bubble nucleation. In the first stage of reheating, vacuum energy is converted into kinetic energy for the bubble walls. To help understand this phase, researchers derive a simple expression for the equation of state of a universe filled with expanding bubbles. Eventually, the bubble walls collide. Researchers present numerical simulations of two-bubble collisions clarifying and extending previous work by Hawking, Moss, and Stewart. The researchers' results indicate that wall energy is efficiently converted into coherent scalar waves. Also discussed is particle production due to quantum effects. These effects lead to the decay of the coherent scalar waves. They also lead to direct particle production during bubble-wall collisions. Researchers calculate particle production for colliding walls in both sine-Gordon and theta (4) theories and show that it is far more efficient in the theta (4) case. The relevance of this work for recently proposed models of first order inflation is discussed.
Watkins, Richard↗
On the Possibility of Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator
The first-order two-step nonlinear estimator, when applied to a problem of orbital navigation, is found to occasionally produce first step covariance matrices with very low eigenvalues at certain trajectory points. This anomaly is the result of the linear approximation to the first step covariance propagation. The study of this anomaly begins with expressing the propagation of the first and second step covariance matrices in terms of a single matrix. This matrix is shown to have a rank equal to the difference between the number of first step states and the number of second step states. Furthermore, under some simplifying assumptions, it is found that the basis of the column space of this matrix remains fixed once the filter has removed the large initial state error. A test matrix containing the basis of this column space and the partial derivative matrix relating first and second step states is derived. This square test matrix, which has dimensions equal to the number of first step states, numerically drops rank at the same locations that the first step covariance does. It is formulated in terms of a set of constant vectors (the basis) and a matrix which can be computed from a reference trajectory (the partial derivative matrix). A simple example problem involving dynamics which are described by two states and a range measurement illustrate the cause of this anomaly and the application of the aforementioned numerical test in more detail.
Garrison, James L.↗