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At least 1,405 records · Page 78

Application of the Finite Element Method to Rotary Wing Aeroelasticity

A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.

Straub, F. K.↗

Upconverting Nanoparticles as Optical Sensors of Nano- to Micro-Newton Forces

Mechanical forces affect a myriad of processes, from bone growth to material fracture to touch-responsive robotics. While nano- to micro-Newton forces are prevalent at the microscopic scale, few methods have the nanoscopic size and signal stability to measure them in vivo or in situ. Here, we develop an optical force-sensing platform based on sub-25 nm NaYF 4 nanoparticles (NPs) doped with Yb 3+ , Er 3+ , and Mn 2+ . The lanthanides Yb 3+ and Er 3+ enable both photoluminescence and upconversion, while the energetically coupled d-metal Mn 2+ adds force tunability through its crystal field sensitivity. IN using a diamond anvil cell to exert up to 3.5 GPa pressure or ~10 μN force per particle, we track stress-induced spectral responses. The red (660 nm) to green (520, 540 nm) emission ratio varies linearly with pressure, yielding an observed color change from orange to red for α-NaYF 4 and from yellow–green to green for d-metal optimized β-NaYF 4 when illuminated in the near infrared. We record consistent readouts over multiple pressure cycles and hours of illumination. With the nanoscopic size, a dynamic range of 100 nN to 10 μN, and photostability, these nanoparticles lay the foundation for visualizing dynamic mechanical processes, such as stress propagation in materials and force signaling in organisms.

36 MATERIALS SCIENCE↗

Numerical Methods For Chemically Reacting Flows

Issues related to numerical stability, accuracy, and resolution discussed. Technical memorandum presents issues in numerical solution of hyperbolic conservation laws containing "stiff" (relatively large and rapidly changing) source terms. Such equations often used to represent chemically reacting flows. Usually solved by finite-difference numerical methods. Source terms generally necessitate use of small time and/or space steps to obtain sufficient resolution, especially at discontinuities, where incorrect mathematical modeling results in unphysical solutions.

Leveque, R. J.↗

The Influence of Modification on Crystal Lattice Stability of Austenite in Stainless Steel

Using the methods of electron diffraction microscopy and X-ray diffraction analysis, the influence of alloying of the austenitic steel, Grade 110H13, with chromium and vanadium, as well as high-melting, ultrafine-grained TiO{sub 2}, ZrO{sub 2} powders and Na{sub 3}AlF{sub 6} cryolite on its structural-phase state and microstructure is investigated. It is shown that the matrix of non-modified steel is completely austenitic and consists of an iron-based solid solution and the interstitial (C, N, O and other) and substitutional (Cr, V and other) atoms simultaneously. Alloying with chromium and vanadium changes neither its phase composition nor defect structure, while alloy modification results in qualitatively new structural features: γ → ε-transformation, high-intensity microtwinning, defect structure changes, and a sharp increase in the scalar dislocation density. The features of the deformation-induced microtwinning and ε-martensite plates identified in the modified steel promote revealing additional microtwin systems in the matrix γ-phase, which result in structural changes making it possible to classify it as a γ′-phase. It is found out that an introduction of modifying additions gives rise to the following sequence of structural-phase transformations: γ→γ′→(γ′ +ε). The experimental data obtained demonstrate that as a result of modification the crystal lattice transits into a low-stability state. This transition is accompanied by marked structural-phase changes consisting in the formation of several microtwin systems and γ → ε-transformation. These structural-phase changes in the modified steel are due to the crystal-lattice transition into the low-stability state, followed by new structural-phase alterations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Vibrational Control of a Nonlinear Elastic Panel

The paper is concerned with the stabilization of the nonlinear panel oscillation by an active control. The control is actuated by a combination of additive and parametric vibrational forces. A general method of vibrational control is presented for stabilizing panel vibration satisfying a nonlinear beam equation. To obtain analytical results, a perturbation technique is used in the case of weak nonlinearity. Possible application to other types of problems is briefly discussed.

Chow, P. L.↗

Early-stage human islet amyloid polypeptide aggregation: Mechanisms behind dimer formation

Amyloid aggregates of human islet amyloid polypeptide (hIAPP or human amylin) have long been implicated in the development of type II diabetes. While hIAPP is known to aggregate into amyloid fibrils, it is the early-stage prefibrillar species that have been proposed to be cytotoxic. A detailed picture of the early-stage aggregation process and relevant intermediates would be valuable in the development of effective therapeutics. Here, we use atomistic molecular dynamics simulations with a combination of enhanced sampling methods to examine the formation of the hIAPP dimer in water. Bias-exchange metadynamics calculations reveal relative conformational stabilities of the hIAPP dimer. Finite temperature string method calculations identify pathways for dimer formation, along with relevant free energy barriers and intermediate structures. We show that the initial stages of dimerization involve crossing a substantial free energy barrier to form an intermediate structure exhibiting transient beta-sheet character, before proceeding to form an entropically stabilized dimer structure.

59 BASIC BIOLOGICAL SCIENCES↗

Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential

In this work, we present trapped solitary wave solutions of a coupled nonlinear Schrödinger (NLS) system in 1 + 1 dimensions in the presence of an external, supersymmetric and complex $\mathcal{PT}$-symmetric potential. The Schrödinger system this work focuses on possesses exact solutions whose existence, stability, and spatio-temporal dynamics are investigated by means of analytical and numerical methods. Two different variational approximations are considered where the stability and dynamics of the solitary waves are explored in terms of eight and twelve time-dependent collective coordinates (CCs). We find regions of stability for specific potential choices as well as analytic expressions for the small oscillation frequencies in the CC approximation. Our findings are further supported by performing systematic numerical simulations of the NLS system.

97 MATHEMATICS AND COMPUTING↗

Numerical methods of solving a system of multi-dimensional nonlinear equations of the diffusion type

The principles of conservation and stability of difference schemes achieved using the iteration control method were examined. For the schemes obtained of the predictor-corrector type, the conversion was proved for the control sequences of approximate solutions to the precise solutions in the Sobolev metrics. Algorithms were developed for reducing the differential problem to integral relationships, whose solution methods are known, were designed. The algorithms for the problem solution are classified depending on the non-linearity of the diffusion coefficients, and practical recommendations for their effective use are given.

Agapov, A. V.↗

The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter

A control-system design method, Quadratic Optimal Cooperative Control Synthesis (CCS), is applied to the design of a Stability and Control Augmentation Systems (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design model, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing Vertol CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and Linear Quadratic Regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.

Townsend, Barbara K.↗

The application of quadratic optimal cooperative control synthesis to a CH-47 helicopter

A control-system design method, quadratic optimal cooperative control synthesis (CCS), is applied to the design of a stability and control augmentation system (SCAS). The CCS design method is different from other design methods in that it does not require detailed a priori design criteria, but instead relies on an explicit optimal pilot-model to create desired performance. The design method, which was developed previously for fixed-wing aircraft, is simplified and modified for application to a Boeing CH-47 helicopter. Two SCAS designs are developed using the CCS design methodology. The resulting CCS designs are then compared with designs obtained using classical/frequency-domain methods and linear quadratic regulator (LQR) theory in a piloted fixed-base simulation. Results indicate that the CCS method, with slight modifications, can be used to produce controller designs which compare favorably with the frequency-domain approach.

Townsend, Barbara K.↗

On the stability of numerical integration routines for ordinary differential equations.

Numerical integration methods for the solution of initial value problems for ordinary vector differential equations may be modelled as discrete time feedback systems. The stability criteria discovered in modern control theory are applied to these systems and criteria involving the routine, the step size and the differential equation are derived. Linear multistep, Runge-Kutta, and predictor-corrector methods are all investigated.

Glover, K.↗

GEMPIC: geometric electromagnetic particle-in-cell methods

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov–Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss’ law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

Physics↗

Effect of Surface Waviness on Transition in Three-Dimensional Boundary-Layer Flow

The effect of a surface wave on transition in three-dimensional boundary-layer flow over an infinite swept wing was studied. The mean flow computed using interacting boundary-layer theory, and transition was predicted using linear stability theory coupled with the empirical eN method. It was found that decreasing the wave height, sweep angle, or freestream unit Reynolds number, and increasing the freestream Mach number or suction level all stabilized the flow and moved transition onset to downstream locations.

Masad, Jamal A.↗

New Theoretical Technique Developed for Predicting the Stability of Alloys

When alloys are being designed for aeronautical and other applications, a substantial experimental effort is necessary to make incremental changes in the desired alloy properties. A scheme to narrow the field to the most promising candidates would substantially reduce the high cost of this experimental screening. Such a method for determining alloy properties, called the BFS (Bozzolo, Ferrante, and Smith) method, has been developed at the NASA Lewis Research Center. This method was used to calculate the thermal stability and mechanical strength of 200 alloys of Ni3Al, with Cu and Au impurities forming ternary and quaternary compounds. With recent advances in the method, almost any metallic impurity and crystal structure can be addressed. In addition, thermal effects can be addressed with Monte Carlo techniques. At present, an experimental program is in progress to verify these results. The method identified a small number of the most promising candidates from the 200 alloys with the largest negative heat of formation and the highest bulk modulus. This calculation required only 5 min of CPU time on a VAX computer. It is clear that semi-empirical methods have achieved the level of development and reliability to warrant examining this new approach to the problem of alloy design. The present work was meant to demonstrate, perhaps in a rather simple way, this power. This type of application of atomistic simulation methods can narrow the gap and improve the feedback between theoretical predictions and laboratory experimentation.

Source record↗

Ion Storage with the High Performance Antiproton Trap (HiPAT)

The matter antimatter reaction represents the densest form of energy storage/release known to modern physics: as such it offers one of the most compact sources of power for future deep space exploration. To take the first steps along this path, NASA-Marshall Space Flight Center is developing a storage system referred to as the High Performance Antiproton Trap (HiPAT) with a goal of maintaining 10(exp 12) particles for up to 18 days. Experiments have been performed with this hardware using normal matter (positive hydrogen ions) to assess the device's ability to hold charged particles. These ions are currently created using an electron gun method to ionize background gas; however, this technique is limited by the quantity that can be captured. To circumvent this issue, an ion source is currently being commissioned which will greatly increase the number of ions captured and more closely simulate actual operations expected at an antiproton production facility. Ions have been produced, stored for various time intervals, and then extracted against detectors to measure species, quantity and energy. Radio frequency stabilization has been tested as a method to prolong ion lifetime: results show an increase in the baseline 1/e lifetime of trapped particles from hours to days. Impurities in the residual background gas (typically carbon-containing species CH4, CO, CO2, etc.) present a continuing problem by reducing the trapped hydrogen population through the mechanism of ion charge exchange.

Martin, James↗

De Sitter decays to infinity

Bubbles of nothing are a class of vacuum decay processes present in some theories with compactified extra dimensions. We investigate the existence and properties of bubbles of nothing in models where the scalar pseudomoduli controlling the size of the extra dimensions are stabilized at positive vacuum energy, which is a necessary feature of any realistic model. We map the construction of bubbles of nothing to a four-dimensional Coleman-De Luccia problem and establish necessary conditions on the asymptotic behavior of the scalar potential for the existence of suitable solutions. We perform detailed analyses in the context of five-dimensional theories with metastable dS 4 x S 1 vacua, using analytic approximations and numerical methods to calculate the decay rate. We find that bubbles of nothing sometimes exist in potentials with no ordinary Coleman-De Luccia decay process, and that in the examples we study, when both processes exist, the bubble of nothing decay rate is typically faster. Our methods can be generalized to other stabilizing potentials and internal manifolds.

classical theories of gravity↗

Identification of multiple eigenmode growth rates in DIII-D and EAST tokamak plasmas

Here, the successful application of three-dimensional (3D) magnetohydrodynamic (MHD) spectroscopy in the stable DIII-D and EAST plasmas enables to directly extract the multi-mode plasma transfer function in tokamak experiments. The transfer function not only reveals the contribution of each dominant MHD eigenmode in the multi-model plasma response, but also quantifies the corresponding eigenvalue which is the critical stability index of MHD mode. The method performs the active detection of stable plasma by utilizing the upper and lower rows of internal coils to scan the frequency and poloidal spectrum of the applied 3D field, and reconstructing the multi-mode transfer functions model through the least square fitting of the plasma response measured by 3D-field magnetic sensors distributed at different poloidal locations. The results point to the potential development of an advanced strategy for tracking the plasma stability based on the extracted eigenvalues of stable modes. The improved understanding of the dominant eigenmodes' behavior in multi-mode plasma response through transfer function can also help to optimize the applied 3D fields for the purposes, such as the type-I edge localized mode suppression and the core stability control in future fusion reactors.

3D MHD spectroscopy↗

Gate‐Voltage Control of Borophene Structure Formation

Abstract Boron nanostructures are easily charged but how charge carriers affect their structural stability is unknown. We combined cluster expansion methods with first‐principles calculations to analyze the dependence of the preferred structure of two‐dimensional (2D) boron, or “borophene”, on charge doping controlled by a gate voltage. At a reasonable doping level of 3.12×10 14 cm −2 , the hollow hexagon concentration in the ground state of 2D boron increases to 1/7 from 1/8 in its charge‐neutral state. The numerical result for the dependence of hollow hexagon concentration on the doping level is well described by an analytical method based on an electron‐counting rule. Aside from in‐plane electronic bonding, the hybridization among out‐of‐plane boron orbitals is crucial for determining the relative stability of different sheets at a given doping level. Our results offer new insight into the stability mechanism of 2D boron and open new ways for the control of the lattice structure during formation.

Zhang, Zhuhua↗