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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Design and Application of a High-Temperature Linear Ion Trap Reactor

A high-temperature linear ion trap reactor with hexapole design was homemade to study ion–molecule reactions at variable temperatures. The highest temperature for the trapped ions is up to 773 K, which is much higher than those in available reports. The reaction between V{sub 2}O{sub 6}{sup −} cluster anions and CO at different temperatures was investigated to evaluate the performance of this reactor. The apparent activation energy was determined to be 0.10 ± 0.02 eV, which is consistent with the barrier of 0.12 eV calculated by density functional theory. This indicates that the current experimental apparatus is prospective to study ion–molecule reactions at variable temperatures, and more kinetic details can be obtained to have a better understanding of chemical reactions that have overall barriers. .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Chemical Mass Shifts in a Digital Linear Ion Trap as Analytical Identity of o-, m-, and p-Xylene

Chemical mass shifts between isomeric ions of o-, m-, and p-xylene were measured using a digital linear ion trap, and the directions and values of the shifts were found to be correlated to the collision cross sections of the isomers. Both forward and reverse scans were used and the chemical shifts for each pair of isomers in scans of opposite directions were in opposite signs. Using different voltage settings (namely the voltage dividing ratio-VDR) of the ion trap allows adding high order field components in the quadrupole field and results in larger chemical mass shifts. The differential chemical mass shift which combined the shifts from forward and reverse scans doubled the amount of chemical shift, e.g., 0.077 Th between o- and p-xylene, enough for identification of the type of isomer without using an additional ion mobility spectrometer. The feature of equal and opposite chemical mass shifts also allowed to null out the chemical mass shift by calculating the mean m/z value between the two opposite scans and remove or reduce the mass error caused by chemical mass shift. .

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Optimized Electrostatic Linear Ion Trap for Charge Detection Mass Spectrometry

In charge detection mass spectrometry (CDMS), ions are passed through a detection tube and the m/z ratio and charge are determined for each ion. The uncertainty in the charge and m/z determinations can be dramatically reduced by embedding the detection tube in an electrostatic linear ion trap (ELIT) so that ions oscillate back and forth through the detection tube. The resulting time domain signal can be analyzed by fast Fourier transforms (FFTs). The ion’s m/z is proportional to the square of the oscillation frequency, and its charge is derived from the FFT magnitude. The ion oscillation frequency is dependent on the physical dimensions of the trap as well as the ion energy. A new ELIT has been designed for CDMS using the central particle method. In the new design, the kinetic energy dependence of the ion oscillation frequency is reduced by an order of magnitude. An order of magnitude reduction in energy dependence should have led to an order of magnitude reduction in the uncertainty of the m/z determination. In practice, a factor of four improvements was achieved. This discrepancy is probably mainly due to the trajectory dependence of the ion oscillation frequency. The new ELIT design uses a duty cycle of 50%. We show that a 50% duty cycle produces the lowest uncertainty in the charge determination. This is due to the absence of even-numbered harmonics in the FFT, which in turn leads to an increase in the magnitude of the peak at the fundamental frequency. .

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Simulation of Unidirectional Ion Ejection in an Asymmetric Half-Round Rod Electrode Linear Ion Trap Mass Analyzer

An asymmetric trapping field was generated from an asymmetric half-round rod electrode linear ion trap (A-HreLIT), and its performance of unidirectional ion ejection was studied. Two different asymmetric structures of A-HreLITs were constructed, one rotating y electrode pairs toward an x electrode with an angle θ, and the other stretching one x electrode with a distance α. The center of trapping field was displaced away from the geometrical center of the ion trap, defined to be the midpoint along the axis of y between x electrodes, which leads to unidirectional ion ejection through one x electrode. Computer simulations were used to investigate the relationship between asymmetric geometric parameter of θ (or α) and analytical performance. Both structures could result in similar asymmetric trapping fields, which mainly composed of dipole, quadrupole, and hexapole fields. The dipole and hexapole fields were approximately proportional to the asymmetric geometric parameter of rotation angle θ (or stretch distance α). In simulation, ion trajectories and ion kinetic energy were calculated. For ions with m/z 609 Th, the simulation results showed that mass resolution of over 2400 (FWHM) and ion unidirectional ejection efficiency of nearly 90% were achieved in an optimized A-HreLIT. Ion detection efficiency of A-HreLIT could be improved significantly with only one ion detector, while maintaining a considerable mass resolution. Furthermore, the A-HreLIT could be driven by a traditional balanced RF power supply. These advantages make A-HreLIT suitable for developing miniaturized mass spectrometer with high performance. .

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2018

Operation and Performance of a Mass-Selective Cryogenic Linear Ion Trap

We report on the performance of a cryogenic 2D linear ion trap (cryoLIT) that is shown to be mass-selective in the temperature range of 17–295 K. As the cryoLIT is cooled, the ejection voltages during the mass instability scan decrease, which results in an effective mass shift to lower m/z relative to room temperature. This is attributed to a decrease in trap radius caused by thermal contraction. Additionally, the cryoLIT generates reproducible mass spectra from day-to-day, and is capable of performing stored waveform inverse Fourier transform (SWIFT) mass isolation of fragile N{sub 2}-tagged ions for the purpose of background-free infrared dissociation spectroscopy. .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Some new preconditioned generalized AOR methods for solving weighted linear least squares problems

In this paper, we propose some new preconditioned GAOR methods for solving weighted linear least squares problems and discuss their comparison results. Comparison results show that the convergence rates of the new preconditioned GAOR methods are better than those of the preconditioned GAOR methods presented by Shen et al. (Appl Math Mech Engl Ed 33(3):375–384, 2012) and Wang et al. (J Appl Math, doi: 10.1155/2012/563586 , 2012) whenever these methods are convergent. Finally, numerical experiments are provided to confirm the theoretical results obtained in this paper.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

An analytical method as a preconditioning modeling for systems of linear equations

In this paper, we propose a simple and practical preconditioner based on the homotopy analysis method. Furthermore, using this modeling, we design an efficient algorithm to solve linear systems. Within the computational framework, convection–diffusion equation candidates are investigated and evaluated. Finally, computational comparisons of the standard methods against preconditioned methods based on experiments are presented which illustrate the merits of the simplicity, power, and effectiveness of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Linear fractional differential equations and eigenfunctions of fractional differential operators

Eigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the analytical solution of some linear sequential fractional differential equations. As a first application, we discuss analytical solutions for the so-called fractional Helmholtz equation with one variable, obtained from the standard equation in one dimension by replacing the integer order derivative by the Riemann–Liouville fractional derivative. A second application consists of an initial value problem for a fractional wave equation in two dimensions in which the integer order partial derivative with respect to the time variable is replaced by the Caputo fractional derivative. The classical Mittag-Leffler functions are important in the theory of fractional calculus because they emerge as solutions of fractional differential equations. Starting with the solution of a specific fractional differential equation in terms of these functions, we find a way to express the exponential function in terms of classical Mittag-Leffler functions. A remarkable characteristic of this relation is that it is true for any value of the parameter n appearing in the definition of the functions, i.e., we have an infinite family of different expressions for e{sup x} in terms of classical Mittag-Leffler functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A cooperative conjugate gradient method for linear systems permitting efficient multi-thread implementation

This paper revisits, in a multi-thread context, the so-called multi-parameter or block conjugate gradient (B-CG) methods, first proposed as sequential algorithms by O’Leary and Brezinski, for the solution of the linear system Ax=b, for an n-dimensional symmetric positive definite matrix A. Instead of the scalar parameters of the classical CG algorithm, which minimizes a scalar functional at each iteration, multiple descent and conjugate directions are updated simultaneously. Implementation involves the use of multiple threads and the algorithm is referred to as cooperative CG (CCG) to emphasize that each thread now uses information that comes from the other threads. It is shown that for a sufficiently large matrix dimension n, the use of an optimal number of threads results in a worst case flop count of O(n{sup 7/3}) in exact arithmetic. Numerical experiments on a multi-core, multi-thread computer, for synthetic and real matrices, illustrate the theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A low-order block preconditioner for saddle point linear systems

A preconditioner is proposed for the large and sparse linear saddle point problems, which is based on a low-order three-by-three block saddle point form. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial for the preconditioned matrix are discussed. Numerical results show that the optimal convergence behavior can be achieved when the new preconditioner is used to accelerate the convergence rate of Krylov subspace methods such as GMRES.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Weak and strong orders of linear recurring sequences

The concept of the strong order of linear recurring sequence (LRS) is introduced in this paper. Necessary and sufficient conditions for the existence of the strong LRS order are derived. The strong LRS order is exploited for the formalization of the problem of the extension of a sequence from the available fragment (fragments) of that sequence. The definition of the strong LRS order opens new possibilities for formal sequence analysis whenever the weak LRS order of that sequence exists. Computational experiments with discrete iterative maps are used to illustrate the applicability of the strong LRS order in nonlinear system analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Compact video content representation for video coding using low multi-linear tensor rank approximation with dynamic core tensor order

Tensor is a multi-way representation of an entity that is widely used in many applications of mathematics and physics. The wide range of tensor algebra operations attract the researchers of graphical and vision field to identify unique methods for various applications such as segmentation, compression, indexing and so on. In this paper, low multi-linear rank approximation of a tensor is used for decomposition so as to perform compression on a video that is represented as a 4D tensor. Thus, the encoder has blocks for (1) multilinear rank approximation method so as to aid decomposition, (2) sparsity removal of residual data to reduce the required memory storage to a small level, (3) quantization on the sparse less residual data and (4) LZ77 dictionary coding for the video. The decoder uses a tensor reconstruction block along with residual error correction block that reduces loss/error in the reconstructed video. The size of core tensor is an important factor in rank approximation. It is identified at run time depending on the video contents. This size is determined adaptively using Tikhonov’s regularization method. The best value of core tensor size is identified with the corner of L-curve which preserves the video contents from heavy loss/error. Experimental results of the proposed work on comparison with H.264/AVC compression method indicate that the proposed method achieves up to 10% improvement in compression ratio with the least amount of loss and a maximum signal to noise ratio of 0.14. The proposed system gives better compression ratio than H.265 for videos with more number of frames without compromising quality.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

PCG method with Strang’s circulant preconditioner for Hermitian positive definite linear system in Riesz space fractional advection–dispersion equations

In this paper, preconditioned conjugate gradient (PCG) method with Strang’s circulant preconditioner is investigated to solve the Hermitian positive definite linear systems, which is result from the Crank–Nicolson (C-N) finite difference scheme with the weighted and shifted Grünwald difference (WSGD) operators to discretize the Riesz space fractional advection–dispersion equation (RSFADE). We show that the spectrum of the preconditioned matrix is clustered around 1, and the singular values of the preconditioned matrix are uniformly bounded away from zero under a certain condition, respectively; hence the PCG method, when applied to solving the preconditioned system, converges superlinearly. Moreover, the complexity in each iteration of the PCG method is O(Nlog N) via using the fast Fourier transforms, where N is the matrix size. Numerical experiments are included to demonstrate the effectiveness of our approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Regularization and index reduction for linear differential–algebraic systems

In this paper, a necessary and sufficient condition for the existence of a proportional semistate feedback is established such that the closed loop system is regular and of index at most two. The condition is characterized by a rank condition that involves only the original system coefficient matrices. Also, a new rank condition ensuring that a given linear time-invariant descriptor system is regular and of index at most some specific value is also derived. The developed theory is illustrated through physical and numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Numerical solution of linear and nonlinear hyperbolic telegraph type equations with variable coefficients using shifted Jacobi collocation method

The telegraph equation is one of the important equations of mathematical physics. In this work, a spectral collocation scheme is proposed for the numerical solutions of one- and two-dimensional linear telegraph equations and telegraph equations with nonlinear forcing term. The homogeneous initial and boundary conditions are satisfied exactly by expanding the unknown variable using polynomial bases of functions which are built upon the Jacobi polynomials. The suggested scheme is successfully developed for the aforementioned problem with nonhomogeneous data. Extensive numerical experiments are presented to verify the efficiency of the proposed scheme.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Non-linear Wire Rope Isolator Model to Enhance Transportation Simulation of Fragile Equipment

Abstract Introduction Wire rope isolators are often used as means of vibration isolation for the transportation of fragile machine equipment. When deployed as suspension systems in a transportation scenario, a simple spring–damper model is often used to predict the dynamic loads that act on the structure being transported. However, this simple model has proved to be too simplistic to be used in the development of an accurate numerical model that can predict the vibration levels experienced by the inner components of fragile equipment during its transportation. This paper describes the experimental tests conducted on a wire rope isolator used for the transportation of the prototype SSR1 cryomodule. Materials and methods A hysteretic Bouc–Wen model has been used to analytically describe the force–deformation relationship of the wire rope isolators. The developed model of the isolator has been implemented in a larger model to simulate the actual transportation of the prototype SSR1 cryomodule, a section of the new PIP-II linear accelerator under construction at Fermilab. A series of multibody dynamic simulations with rigid and flexible components was used to numerically determine the acceleration of some critical components. Results and conclusions An actual experimental transportation was simulated using two numerical models: the developed Bouc–Wen model and a conventional spring–damper model. It is shown how the Bouc–Wen formulation of the isolator characteristics drastically improves the correspondence between experimental and simulated results if compared to a spring–damper model, especially in the range of 0–30 Hz which is the most critical for transportation problems.

42 ENGINEERING↗
DOE OSTI2017

Linear dichroism of DNA: Characterization of the orientation distribution function caused by hydrodynamic shear

Linear dichroism provides information on the orientation of chromophores part of, or bound to, an orientable molecule such as DNA. For molecular alignment induced by hydrodynamic shear, the principal axes orthogonal to the direction of alignment are not equivalent. Thus, the magnitude of the flow-induced change in absorption for light polarized parallel to the direction of flow can be more than a factor of two greater than the corresponding change for light polarized perpendicular to both that direction and the shear axis. The ratio of the two flow-induced changes in absorption, the dichroic increment ratio, is characterized using the orthogonal orientation model, which assumes that each absorbing unit is aligned parallel to one of the principal axes of the apparatus. The absorption of the alienable molecules is characterized by components parallel and perpendicular to the orientable axis of the molecule. The dichroic increment ratio indicates that for the alignment of DNA in rectangular flow cells, average alignment is not uniaxial, but for higher shear, as produced in a Couette cell, it can be. The results from the simple model are identical to tensor models for typical experimental configuration. Approaches for measuring the dichroic increment ratio with modern dichrometers are further discussed.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2018

Micromechanical modeling of non-linear stress-strain behavior of polycrystalline microcracked materials under tension

The stress-strain behavior of microcracked polycrystalline materials (such as ceramics or rocks) under conditions of tensile, displacement-controlled, loading is discussed. Micromechanical explanation and modeling of the basic features, such as non-linearity and hysteresis in stress-strain curves, is developed, with stable microcrack propagation and “roughness” of intergranular cracks playing critical roles. Experiments involving complex loading histories were done on large- and medium grain size β-eucryptite ceramic. As a result, the model is shown to reproduce the basic features of the observed stress-strain curves.

36 MATERIALS SCIENCE↗