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At least 73 records · Page 4

Detectors in weakly-coupled field theories

We initiate a study of asymptotic detector operators in weakly-coupled field theories. These operators describe measurements that can be performed at future null infinity in a collider experiment. In a conformal theory they can be identified with light-ray operators, and thus have a direct relation to the spectrum of the theory. After a general discussion of the underlying physical picture, we show how infrared divergences of general detector operators can be renormalized in perturbation theory, and how they give rise to detector anomalous dimensions. We discuss in detail how this renormalization can be performed at the intersections of the Regge trajectories where non-trivial mixing occurs, which is related to the poles in anomalous dimensions at special values of spin. Finally, we discuss novel horizontal trajectories in scalar theories and show how they contribute to correlation functions. Our calculations are done in the example of Φ 4 theory in d = 4 - ϵ dimensions, but the methods are applicable more broadly. At the Wilson-Fisher fixed point our results include an explicit expression for the Pomeron light-ray operator at two loops, as well as a prediction for the value of the Regge intercept at five loops.

47 OTHER INSTRUMENTATION↗

Cavity Swelling in Irradiated Materials

Cavity swelling, due to three-dimensional clustering of vacancies, is an undesirable isotropic volume expansion of materials under irradiation. This phenomenon occurs above stage-III recovery temperature where vacancies are mobile, between ~0.3–0.6 Tm where Tm is the absolute melting temperature. The primary mechanism for cavity swelling is “dislocation bias”, i.e., preferential absorption of interstitials by network dislocations, causing a vacancy supersaturation. Cavity swelling is highly temperature dependent and typically follows a bell-shaped curve with peak swelling occurring at an intermediate temperature. With increasing temperature, cavity size increases, and number density decreases logarithmically. With increasing dose, cavity swelling increases, but follows a hockey-stick type pattern, characterized by a low-swelling transient incubation period and then a steady-state regime. The incubation period, dominant in cavity nucleation, is dependent upon material’s chemistry and irradiation conditions such as dose rate/temperature. Cavity swelling increases linearly with dose in the steady-state regime, that is independent of chemistry and dose rate. This regime is dominated by cavity growth. Transmutation gases like He enhance cavity nucleation such that an early onset of cavity formation occurs. However, swelling magnitudes can be either increased or suppressed when He is present. Results in austenitic steels and Cu indicate that cavity swelling peaks at intermediate He/dpa ratios of ~10 appm He/dpa. The most effective method to mitigate cavity swelling is by increasing the fixed point-defect sink density, by promoting precipitation or dispersion strengthening.

Bhattacharya, Arunodaya↗

Some estimation formulae for continuous time-invariant linear systems

In this brief paper we examine a Riccati equation decomposition due to Reid and Lainiotis and apply the result to the continuous time-invariant linear filtering problem. Exploitation of the time-invariant structure leads to integration-free covariance recursions which are of use in covariance analyses and in filter implementations. A super-linearly convergent iterative solution to the algebraic Riccati equation (ARE) is developed. The resulting algorithm, arranged in a square-root form, is thought to be numerically stable and competitive with other ARE solution methods. Certain covariance relations that are relevant to the fixed-point and fixed-lag smoothing problems are also discussed.

Bierman, G. J.↗

Crustal deformation measurements in central Japan determined by a Global Positioning System fixed-point network

Results are presented from temporally dense measurements of crustal deformation associated with the convergence of the Eurasian (EUR), Pacific, North American, and Philippine Sea (PHS) plates, carried out in April 1988 by a 10-station GPS fixed-point network established in central Japan. Using regional orbit relaxation methods, the analysis of the first 17-month data revealed significant horizontal deformation across the Suruga trough. Namely, it was found that a site in the northern tip of PHS plate moved nearly westward with a velocity of 28 +/-5 mm per year, and a site at the southeastern tip of EUR plate moved south-southwestward with a velocity of 18 +/-5 mm per year. A significant vertical uplift with a velocity of 20 mm/yr was detected at a site inland of the Tokai district located in the Akaishi uplift zone and at a site on the Hatsushima Island in Sagami Bay.

Shimada, Seiichi↗

Infrared fixed point of the SU(3) gauge theory with 𝑁 𝑓 = 10 flavors

We use lattice simulations and the continuous renormalization group method, based on the gradient flow, to calculate the 𝛽 function and anomalous dimensions of the SU(3) gauge theory with 𝑁 𝑓 = 10 flavors of fermions in the fundamental representation. We employ several improvements to extend the range of available renormalized couplings, including the addition of heavy Pauli-Villars bosons to reduce cutoff effects and the combination of a range of gradient flow transformations. While in the weak coupling regime our result is consistent with those of earlier studies, our techniques allow us to study the system at much stronger couplings than previously possible. We find that the renormalization group 𝛽 function develops a zero, corresponding to an infrared-stable fixed point, at gradient-flow coupling 𝑔 2 = 15.0⁢(5). We also determine the mass and tensor anomalous dimensions: At the fixed point we find 𝛾 𝑚 ≃0.6, suggesting that this system might be deep inside the conformal window.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Fast Multigrid Techniques in Total Variation-Based Image Reconstruction

Existing multigrid techniques are used to effect an efficient method for reconstructing an image from noisy, blurred data. Total Variation minimization yields a nonlinear integro-differential equation which, when discretized using cell-centered finite differences, yields a full matrix equation. A fixed point iteration is applied with the intermediate matrix equations solved via a preconditioned conjugate gradient method which utilizes multi-level quadrature (due to Brandt and Lubrecht) to apply the integral operator and a multigrid scheme (due to Ewing and Shen) to invert the differential operator. With effective preconditioning, the method presented seems to require Omicron(n) operations. Numerical results are given for a two-dimensional example.

Oman, Mary Ellen↗

A fast implicit solver for semiconductor models in one space dimension

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved with a variety of methods. A key algorithmic component in all the approaches considered here is a recently developed sweeping algorithm for Vlasov-Poisson systems. A synthetic acceleration scheme has been implemented to accelerate the convergence of iterative solvers by using the solution to a drift-diffusion equation as a preconditioner. The performance of four iterative solvers and their accelerated variants has been compared on problems modeling semiconductor devices with various electron mean-free-path.

97 MATHEMATICS AND COMPUTING↗

Closed-Form Solutions for the Equations of Motion of the Heavy Symmetrical Top with One Point Fixed

The Equations of Motion (EOM) for the Heavy Symmetrical Top with One Point Fixed are highly non-linear. The literature describes the numerical methods that are used to resolve this Classical system including modern tools i.e. the Runge-Kutta Fourth Order method. It is more difficult to derivate closed-form solutions for the EOM and as mentioned in the literature it is not always possible to find the close-form solution for all the EOM. Fortunately, there are a few examples available that will serve as a guide to move further on in this topic. It is the purpose of this paper to find a methodology that will produce the solutions for a given subset of EOM that fulfill certain requisites. The report is organized as follows: it starts with a very short summary of the literature available on this topic and quickly follows into the derivation of the EOM using the Euler-Lagrange method. The Routhian will be used to reduce the size of the expression. It continues with the formulation of the Classical cubic function (f(u)) through a novel process. The roots of f(u) are of the outmost importance to be able to find the EOM closed-form solution, and once the final roots are selected the general method that will produce the closed-form solutions is presented. Two sets of examples are included to show the validity of the process and comparisons of the results from the closed-form solutions vs. the numerical results for these examples are shown.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Hybrid state vector methods for structural dynamic and aeroelastic boundary value problems

A computational technique is developed that is suitable for performing preliminary design aeroelastic and structural dynamic analyses of large aspect ratio lifting surfaces. The method proves to be quite general and can be adapted to solving various two point boundary value problems. The solution method, which is applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. A mixed variational formulation is presented that conveniently yields a useful form for these state vector differential equations. Solutions to these equations are obtained by employing an integrating matrix method. The application of an integrating matrix provides a discretization of the differential equations that only requires solutions of standard linear matrix systems. It is demonstrated that matrix partitioning can be used to reduce the order of the required solutions. Results are presented for several example problems in structural dynamics and aeroelasticity to verify the technique and to demonstrate its use. These problems examine various types of loading and boundary conditions and include aeroelastic analyses of lifting surfaces constructed from anisotropic composite materials.

Lehman, L. L.↗

Sinusoidal transform coding

It has been shown that an analysis/synthesis system based on a sinusoidal representation of speech leads to synthetic speech that is essentially perceptually indistinguishable from the original. Strategies for coding the amplitudes, frequencies and phases of the sine waves have been developed that have led to a multirate coder operating at rates from 2400 to 9600 bps. The encoded speech is highly intelligible at all rates with a uniformly improving quality as the data rate is increased. A real-time fixed-point implementation has been developed using two ADSP2100 DSP chips. The methods used for coding and quantizing the sine-wave parameters for operation at the various frame rates are described.

Mcaulay, Robert J.↗

Highly accelerated life testing (HALT): A review from a statistical perspective

Despite its use in one form or another for at least four decades, HALT and related techniques [e.g., highly accelerated-stress screening (HASS) and stress audits (HASA)] are not well understood within the statistical community and remain controversial. This largely reflects a conflict in motivation between engineers, testing under harsh conditions to discover and eliminate failure modes, and statisticians, taking a more cautious approach to develop quantitative estimates of parameters such as mean time between failures (MTBF). Here, this review article will clarify HALT concepts and methods and explain where it fits within the universe of methods that involve the application of accelerating factors to compress the time required to evaluate or enhance product reliability. A major distinction is between methods such as HALT, a high-stress test-analyze-fix-test iterative process directed at improving reliability by discovering and fixing weak points in a design, and quantitative accelerated life testing (QALT), whose goal is the estimation of product life for a fixed design. We discuss methods such as physics of failure that offer some hope of bridging the gap between the qualitative nature of HALT, and purely quantitative statistical methods. We present a variety of engineering applications of HALT including metal fatigue, piping and pressure vessels, structural damage, radiation damage, and rotating machinery. We also discuss potential synergies between HALT and QALT, such as rapid identification, through HALT, of failure modes requiring quantitative analysis. For further study, extensive references to the applicable literature are provided as well as an appendix that describes related methods.

97 MATHEMATICS AND COMPUTING↗

Automated Parameter Studies Using a Cartesian Method

Computational Fluid Dynamics (CFD) is now routinely used to analyze isolated points in a design space by performing steady-state computations at fixed flight conditions (Mach number, angle of attack, sideslip), for a fixed geometric configuration of interest. This "point analysis" provides detailed information about the flowfield, which aides an engineer in understanding, or correcting, a design. A point analysis is typically performed using high fidelity methods at a handful of critical design points, e.g. a cruise or landing configuration, or a sample of points along a flight trajectory.

Murman, Scott M.↗

On the Development of Order and Interfaces during the Growth of Ultrathin La 2 CuO 4 Films by Molecular Beam Epitaxy

While the atomic structure of interfaces in complex oxide heterostructures created by epitaxial growth has been investigated extensively, few studies have been conducted on how interfaces form and restructure at the initial stage of film growth. The dynamic aspects of the growth behavior can strongly influence the final interfacial atomic structure, which may lead to the emergence of interface-specific properties, such as the rise of interfacial superconductivity between certain Ruddlesden-Popper oxide materials. In this report, the structural development of La2CuO 4 thin films grown by molecular beam epitaxy on a LaSrAlO 4 substrate is investigated by X-ray diffraction measurements with rapid scans over a volume of reciprocal space. This method provides far more detailed information on interface formation than traditional fixed-point measurements. The results show that the atomic structure of the interface becomes fully established after just a single unit cell of growth. Interestingly, restructuring continues to occur within the topmost half to one unit cell of the film during the deposition process. However, diffraction intensity oscillations from both reflection high-energy electron and X-ray measurements stabilize only after the growth of two unit cells, indicating that the growth front morphology continues to evolve until the start of the third unit cell. This multimodal investigation provides insights into the atomic processes taking place during layered oxide interface formation, including the dynamical rearrangement of LaO and CuO 2 layers. Such information is not only relevant to the engineering and optimization of functional layer structures but can also be critical for ultrathin films.

36 MATERIALS SCIENCE↗

Calculation of permanent magnet arrangements for stellarators: a linear least-squares method

A problem arising in several engineering areas is to design magnets outside a volume that produce a desired magnetic field inside it. One instance of this problem is stellarator design, where it has recently been shown that permanent magnets can provide the required shaping of the magnetic field. Here we demonstrate a robust and efficient algorithm REGCOIL_PM to calculate the spatial distribution of these permanent magnets. The procedure involves a small number of fixed-point iterations, with a linear least-squares problem solved at each step. Furthermore, the method exploits the Biot–Savart Law's exact linearity in magnetization density and approximate linearity in magnet size, for magnets far from the target region. No constraint is placed on the direction of magnetization, so Halbach solutions are found naturally, and the magnitude of the magnetization can be made uniformly equal to a target value.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A strawman targeting technique for spinner spacecraft in the presence of pointing uncertainty

A graphical method that allows the selection of the attitude orientation of a spinner spacecraft prior to the application of a single fixed magnitude velocity change to effect a desired orbit transfer is presented. The selection of the final pointing vector along or opposite to which the desired Delta-V is applied, takes into account pointing errors due to initial attitude determination uncertainty and execution errors introduced during the rhumb line precession of the spin axis. The characterization of the target space in terms of any achieved orbit parameters of interest as well as the final pointing uncertainty is sufficient to determine the right final attitude that insures satisfaction of mission requirements.

Kechichian, J. A.↗

First Terrestrial Soft X-ray Aurora Observations by Chandra

Northern polar "auroral" regions of Earth was observed by High-Resolution Camera in imaging mode (T32C-I) aboard Chandra X-Ray Observatory (CXO) during mid December 2003 - mid April 2004. Ten CXO observations, each approximately 20 min duration, were made in a non-conventional method (due to CXO technical issues), such that Chandra was aimed at a fixed point in sky and the Earth's polar cusp was allowed to drift through the HRC-I field-of-view. The observations were performed when CXO was near apogee and timed during northern winter mostly near midnight (6 hr), except two observations which occurred around 1200 UT, so that northern polar region is entirely in dark and solar fluoresced x-ray contamination can be avoided. These observations were aimed at searching the Earth's soft x-ray aurora and to do a comparative study with Jupiter's x-ray aurora, where a pulsating x-ray hot-spot near the northern magnetic pole has been observed by Chandra that implies a particle source region near Jupiter's magnetopause, and entry of heavy solar wind ions due to high-latitude reconnection as a viable explanation for the soft x-ray emissions. The first Chandra soft (0.1-2 keV) x-ray observations of Earth's aurora show that it is highly variable (intense arc, multiple arcs, diffuse, at times almost absent). In at least one of the observations an isolated blob of emission is observed where we expect cusp to be: giving indication of solar wind charge-exchange signature in x-rays. We are comparing the Chandra x-ray observations with observations at other wavelengths and particle data from Earth-orbiting satellites and solar wind measurements from near-Earth ACE and SOH0 spacecraft. Preliminary results from these unique CXO-Earth observations will be presented and discussed.

Bhardwaj, Anil↗

Bifurcation Analysis Using Rigorous Branch and Bound Methods

For the study of nonlinear dynamic systems, it is important to locate the equilibria and bifurcations occurring within a specified computational domain. This paper proposes a new approach for solving these problems and compares it to the numerical continuation method. The new approach is based upon branch and bound and utilizes rigorous enclosure techniques to yield outer bounding sets of both the equilibrium and local bifurcation manifolds. These sets, which comprise the union of hyper-rectangles, can be made to be as tight as desired. Sufficient conditions for the existence of equilibrium and bifurcation points taking the form of algebraic inequality constraints in the state-parameter space are used to calculate their enclosures directly. The enclosures for the bifurcation sets can be computed independently of the equilibrium manifold, and are guaranteed to contain all solutions within the computational domain. A further advantage of this method is the ability to compute a near-maximally sized hyper-rectangle of high dimension centered at a fixed parameter-state point whose elements are guaranteed to exclude all bifurcation points. This hyper-rectangle, which requires a global description of the bifurcation manifold within the computational domain, cannot be obtained otherwise. A test case, based on the dynamics of a UAV subject to uncertain center of gravity location, is used to illustrate the efficacy of the method by comparing it with numerical continuation and to evaluate its computational complexity.

Smith, Andrew P.↗

Recent Advances to Estimation of Fixed-Interface Modal Models Using Dynamic Substructuring

In 2010, Allen & Mayes proposed to estimate the fixed-interface modes of a structure by measuring the modes of the structure bolted to a fixture and then applying constraints to the fixture using the transmission simulator method. While the method proved useful, and has indeed been used in studies since that point, a few peculiarities were noted. First, in some cases the estimated fixed-base natural frequencies were observed to converge very slowly to the true values (in simulated experiments) as the number of constraints was increased. To formulate these constraints, prior studies used only the free-interface modes of the fixture or the measured modes of the assembly. This work extends that to consider other sets of constraints, showing improved results. Furthermore, in some prior studies it has been observed that there were errors of more than 10% in the natural frequencies even when the fixture motion was hundreds of times smaller than the motion of the structure of interest (and so it had presumably been removed). This work explores this phenomenon, seeking to use the strain energy in the fixture, to the extent that it can be estimated using a test-analysis model for the fixture, as a metric to predict frequency error. The proposed methods are explored by applying them to simulated measurements from a beam and from the NASA Space Launch System coupled to the Mobile Launcher.

Allen, Mathew S.↗