Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Arithmetic”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Enhancing phonon flow through one-dimensional interfaces by impedance matching

We extend concepts from microwave engineering to thermal interfaces and explore the principles of impedance matching in 1D. The extension is based on the generalization of acoustic impedance to nonlinear dispersions using the contact broadening matrix Γ(ω), extracted from the phonon self energy. For a single junction, we find that for coherent and incoherent phonons, the optimal thermal conductance occurs when the matching Γ(ω) equals the Geometric Mean of the contact broadenings. This criterion favors the transmission of both low and high frequency phonons by requiring that (1) the low frequency acoustic impedance of the junction matches that of the two contacts by minimizing the sum of interfacial resistances and (2) the cut-off frequency is near the minimum of the two contacts, thereby reducing the spillage of the states into the tunneling regime. For an ultimately scaled single atom/spring junction, the matching criterion transforms to the arithmetic mean for mass and the harmonic mean for spring constant. The matching can be further improved using a composite graded junction with an exponential varying broadening that functions like a broadband antireflection coating. There is, however, a trade off as the increased length of the interface brings in additional intrinsic sources of scattering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Molecular simulation of fluids with non-identical intermolecular potentials: Thermodynamic properties of 10-5 + 12-6 Mie potential binary mixtures

General methods for combining interactions between particles characterised by non-identical intermolecular potentials are investigated. The combination methods are tested by performing molecular dynamics simulations to determine the pressure, energy, isochoric and isobaric heat capacities, thermal expansion coefficient, isothermal compressibility, Joule-Thomson coefficient, and speed of sound of 10-5 + 12-6 Mie potential binary mixtures. In addition to the two non-identical Mie potentials, mixtures are also studied with non-identical intermolecular parameters. The combination methods are compared with results obtained by simply averaging the Mie exponents. When either the energy or size parameters are non-identical, very significant differences emerge in the thermodynamic properties predicted by the alternative combination methods. The isobaric heat capacity is the thermodynamic property that is most affected by the relative magnitude of the intermolecular potential parameters and the method for combining non-identical potentials. Either the arithmetic or geometric combination of potentials provides a simple and effective way of performing simulations involving mixtures of components characterised by non-identical intermolecular potentials, which is independent of their functional form.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural properties of a bone-ceramic composite as a promising material in spinal surgery

The paper describes the results of in vitro tests of composite bone-ceramic implants and procedures for modifying implant surfaces to enhance osteogenesis. Analysis of CBCI ESs demonstrated that they have a porous structure with the mean longitudinal pore size of 70 µm and the mean transverse pore size of 46 µm; surface pores are open, while inner pores are closed. Elemental analysis of the CBCI surface demonstrates that CBCIs are composed of aluminum and zirconium oxides and contain HA inclusions. Profilometry of the CBCI ES surface revealed the following deviations: the maximum deviation of the profile in the sample center is 15 µm and 16 µm on the periphery, while the arithmetical mean and mean square deviations of the profile are 2.65 and 3.4 µm, respectively. In addition, CBCI biodegradation products were pre-examined; a 0.9% NaCl solution was used as a comparison group. Potentially toxic and tissue accumulated elements, such as cadmium, cobalt, mercury, and lead, are present only in trace amounts and have no statistically significant differences with the comparison group, which precludes their potential toxic effects on the macroorganism. Ceramic-based CBCI may be effective and useful in medicine for restoration of the anatomic integrity and functions of the bone tissue.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Probing and exploiting the chaotic dynamics of a hydrodynamic photochemical oscillator to implement all the basic binary logic functions

The convective motions within a solution of a photochromic spiro-oxazine being irradiated by UV only on the bottom part of its volume, give rise to aperiodic spectrophotometric dynamics. In this paper, we study three nonlinear properties of the aperiodic time series: permutation entropy, short-term predictability and long-term unpredictability, and degree distribution of the visibility graph networks. After ascertaining the extracted chaotic features, we show how the aperiodic time series can be exploited to implement all the fundamental two-inputs binary logic functions (AND, OR, NAND, NOR, XOR, and XNOR) and some basic arithmetic operations (half-adder, full-adder, half-subtractor). This is possible due to the wide range of states a nonlinear system accesses in the course of its evolution. Therefore, the solution of the convective photochemical oscillator results in hardware for chaos-computing alternative to conventional complementary metal-oxide semiconductor-based integrated circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is therefore formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with application of accepted moves to the matrices delayed until after a predetermined number of moves, K . The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. Here this procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi- core CPUs and GPUs.

97 MATHEMATICS AND COMPUTING↗

DR-RINS: Digital real-time relative intensity noise suppressor for pump–probe spectroscopy and microscopy

Relative intensity noise (RIN) inherent in fiber lasers poses a serious obstacle to their use in pump–probe spectroscopy and imaging. RIN can be removed through an analog balanced detector, or, as we have previously shown, software adaptive noise cancellation (ANC) on digitized signals. One major drawback to software ANC is the added time required for digitizing and post-processing. In this article, we describe a design for ANC on a field-programmable gate array (FPGA), making use of high-level synthesis tools and fixed-point arithmetic to achieve real-time laser RIN suppression at 25 MHz sample rates. Unlike the software-ANC approach, the FPGA-ANC device can serve as a dedicated drop-in denoiser, placed between the detectors and a commercial lock-in amplifier. We demonstrate its application to transient absorption spectroscopy and microscopy, lowering the noise floor to ~17 dB above the shot noise limit. Furthermore, we demonstrate a dramatic improvement in data acquisition time from ~6 h to ~5 min in a real-time imaging scenario.

47 OTHER INSTRUMENTATION↗

Impact of areal-density asymmetries on the loss of confinement and ignition threshold in inertial confinement fusion capsules

In inertial confinement fusion implosion experiments, variations in the shell areal density reduce the shell’s inertia to confine the core pressure. Distorted capsules with large areal-density modulations decompress faster than uniform capsules in the disassembly phase. A simple 3-D analytic hot-spot model is derived to include the effects of low-mode areal-density modulations in the ignition criterion. The generalized 3-D ignition criterion for low modes is shown to depend on both the harmonic mean and the arithmetic mean of the areal density. Here, the “thin spots” in the shell are shown to dominate the loss of confinement as reflected by the harmonic mean definition of areal densities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Toward exascale whole-device modeling of fusion devices: Porting the GENE gyrokinetic microturbulence code to GPU

GENE solves the five-dimensional gyrokinetic equations to simulate the development and evolution of plasma microturbulence in magnetic fusion devices. The plasma model used is close to first principles and computationally very expensive to solve in the relevant physical regimes. In order to use the emerging computational capabilities to gain new physics insights, several new numerical and computational developments are required. Here, we focus on the fact that it is crucial to efficiently utilize GPUs (graphics processing units) that provide the vast majority of the computational power on such systems. In this paper, we describe the various porting approaches considered and given the constraints of the GENE code and its development model, justify the decisions made, and describe the path taken in porting GENE to GPUs. We introduce a novel library called gtensor that was developed along the way to support the process. Performance results are presented for the ported code, which in a single node of the Summit supercomputer achieves a speed-up of almost 15× compared to running on central processing unit (CPU) only. Typical GPU kernels are memory-bound, achieving about 90% of peak. Our analysis shows that there is still room for improvement if we can refactor/fuse kernels to achieve higher arithmetic intensity. We also performed a weak parallel scalability study, which shows that the code runs well on a massively parallel system, but communication costs start becoming a significant bottleneck.

Germaschewski, K. (ORCID:0000000284956354)↗

Scalar Breit interaction for molecular calculations

Variational treatment of the Dirac–Coulomb–Gaunt or Dirac–Coulomb–Breit two-electron interaction at the Dirac–Hartree–Fock level is the starting point of high-accuracy four-component calculations of atomic and molecular systems. In this work, we introduce, for the first time, the scalar Hamiltonians derived from the Dirac–Coulomb–Gaunt and Dirac–Coulomb–Breit operators based on spin separation in the Pauli quaternion basis. While the widely used spin-free Dirac–Coulomb Hamiltonian includes only the direct Coulomb and exchange terms that resemble nonrelativistic two-electron interactions, the scalar Gaunt operator adds a scalar spin–spin term. The spin separation of the gauge operator gives rise to an additional scalar orbit-orbit interaction in the scalar Breit Hamiltonian. Benchmark calculations of Au n (n = 2–8) show that the scalar Dirac–Coulomb–Breit Hamiltonian can capture 99.99% of the total energy with only 10% of the computational cost when real-valued arithmetic is used, compared to the full Dirac–Coulomb–Breit Hamiltonian. In conclusion, the scalar relativistic formulation developed in this work lays the theoretical foundation for the development of high-accuracy, low-cost correlated variational relativistic many-body theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

New approach to terahertz diagnostics of human psychoemotional state

A new approach to terahertz (THz) diagnostics of the human psychoemotional state is proposed, based on the analysis of the THz contribution to the total signal while simultaneously recording the IR and THz emissions from the human body (hereinafter referred to as the IR – THz image). The developed image-processing algorithm allows extraction of the informative contribution determined by the THz radiation from the total signal perceived by the recording system. Simultaneous registration of the IR – THz images of the human face and the psychophysiological indicators are carried out in situations of physical stress (short-term intense physical exercise – squats functional test), electrical stimulation, and information stress (cognitive load – simple arithmetic mental calculations). The obtained data are compared with those of similar measurements at rest. It is shown that using cluster analysis of IR – THz images it is possible to divide the test subjects into classes according to the type of reaction of the circulatory system under stressful conditions. (paper)

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Effect of elastic anisotropy on thermally induced distortions of a laser beam in single cubic syngony crystals with radial cooling. Part I

We have studied thermally induced distortions of a beam in single cubic syngony crystals of all symmetry groups with an anisotropic elastic stiffness tensor. The arithmetic mean and the difference between the thermally induced phase incursions of eigenpolarisations, as well as the angle of incidence of these polarisations, are calculated for a long rod and a thin disk with radial cooling under uniform volume pumping of the active element. The position of the specific crystal orientations unrelated to its symmetry elements is investigated. The effective values of the thermo-optical constant Q in two specific orientations, as well as the thermo-optical constant P in an arbitrary orientation, are found. (invited paper)

36 MATERIALS SCIENCE↗

A holomorphic version of the Tate-Iwasawa method for unramified L-functions. I

Using the Tate-Iwasawa method the problem of meromorphic continuation and of the existence of a functional equation can be solved for the zeta and L-functions of one-dimensional arithmetical schemes. A new version of this method is put forward, which looks at the case of curves over a finite field and of unramified L-functions. The proof is based on a reduction of the problem to a Cousin problem on the Riemann sphere which is related to the curve under consideration. Bibliography: 16 titles.

97 MATHEMATICS AND COMPUTING↗

A COMPARISON OF THE VELOCITY PARAMETERS OF SiO v = 1, J = 1-0, and J = 2-1 MASER EMISSION IN LONG PERIOD VARIABLES

We present an analysis of velocity parameters derived from multi-epoch observations of the SiO maser spectra of 47 long period variables (LPVs). The velocity parameters are important to inform and constrain theoretical models of SiO maser emission and to extract information on binary orbits. Mira and R Aquarii (R Aqr) are two known binaries included in the program. The 47 LPVs are among 121 sources of the Australia Telescope National Facility Mopra telescope's monitoring program. Observations were carried out several times a year between 2008 and 2012 and are continuing. The SiO spectra are from the v = 1, J = 1-0 (43.122 GHz; hereafter J10) and the v = 1, J = 2-1 (86.2434 GHz; hereafter J21) transitions. For 41 of the 47 LPVs we observed both transitions nearly simultaneously in 457 observations. We have determined and compared the velocity centroids (VCs) and velocity ranges (VRs) of emission suffixed as above (10 and 21) for the two transitions: VC10, VC21, VR10, and VR21. The VCs of the two transitions are, on average, within 0.13 km s{sup -1} of each other but are sometimes separated by a few km s{sup -1}. The VC10s are, on average, slightly more positive than the VC21s. The values of the VCs in the two transitions have been compared to justify using both of these transitions to extract binary star orbital parameters. The arithmetic mean VR10 derived from 635 observations of 47 sources is 6.4 km s{sup -1} with a standard deviation of 3.4 km s{sup -1}, while the mean VR21 derived from 485 observations of 41 sources is 4.2 km s{sup -1} with a standard deviation of 2.8 km s{sup -1}. The number of occurrences of VR10 and VR21 versus VR have different distributions. The differences in the VRs indicate that the J21 and J10 emissions arise from dynamically different regions of the circumstellar environment.

79 ASTRONOMY AND ASTROPHYSICS↗

Periodic analysis of solar activity and its link with the Arctic oscillation phenomenon

Based on spectrum analysis, we provide the arithmetic expressions of the quasi 11 yr cycle, 110 yr century cycle of relative sunspot numbers, and quasi 22 yr cycle of solar magnetic field polarity. Based on a comparative analysis of the monthly average geopotential height, geopotential height anomaly, and temperature anomaly of the northern hemisphere at locations with an air pressure of 500 HPa during the positive and negative phases of AO (Arctic Oscillation), one can see that the abnormal warming period in the Arctic region corresponds to the negative phase of AO, while the anomalous cold period corresponds to its positive phase. This shows that the abnormal change in the Arctic region is an important factor in determining the anomalies of AO. In accordance with the analysis performed using the successive filtering method, one can see that the AO phenomenon occurring in January shows a clear quasi 88 yr century cycle and quasi 22 yr decadal cycle, which are closely related to solar activities. The results of our comparative analysis show that there is a close inverse relationship between the solar activities (especially the solar magnetic field index changes) and the changes in the 22 yr cycle of the AO occurring in January, and that the two trends are basically opposite of each other. That is to say, in most cases after the solar magnetic index MI rises from the lowest value, the solar magnetic field turns from north to south, and the high-energy particle flow entering the Earth's magnetosphere increases to heat the polar atmosphere, thus causing the AO to drop from the highest value; after the solar magnetic index MI drops from the highest value, the solar magnetic field turns from south to north, and the solar high-energy particle flow passes through the top of the Earth's magnetosphere rather than entering it to heat the polar atmosphere. Thus the polar temperature drops, causing the AO to rise from the lowest value. In summary, the variance contribution rate of the changes in the quasi 110 yr century cycle and quasi 22 yr decadal cycle for the AO reaches 62.9%, indicating that solar activity is an important driving factor of the AO.

79 ASTRONOMY AND ASTROPHYSICS↗

A comparison of the velocity parameters of SiO V = 1, J = 1 − 0, and J = 2 − 1 maser emission in semiregular variables

We have determined and compared the SiO maser velocity parameters of semiregular variables in the v = 1, J = 1 − 0 (J10{sup 1}) and the v = 1, J = 2 − 1 (J21) transitions. Fourteen sources in the Mopra SiO Maser Catalogue are classified as semiregular variables of types SR, SRa, SRb, or SRc. (L2 Puppis, an SRa star with an unusual SiO maser spectrum, has been analyzed individually.) We have previously presented the overall and phase dependent velocity parameters of SiO masers associated with long period variables (LPVs) of well-established periods and maxima. A comparison of the velocity centroid (VC) difference, VC21–VC10, shows mixed results for the variable types. Some differences are negative and some positive. The SRc difference is negative, large, and relatively stable. The SRb difference has the widest distribution. The velocity ranges (VRs) of the maser emission have been compared using arithmetic averages, Gaussian fits to the distributions, and Weibull fits to the distributions. For LPVs, SRs, SRas, and SRcs the VR10 is one to a few km s{sup −1} greater than the VR21. SRcs have the largest VRs by a factor of two or three indicating the greater range over which the conditions necessary for masers to originate exist in these supergiant stars. SRbs are the only classification of semiregular variable in which the VR21 exceeds the VR10. The larger VR21 compared to VR10 for SRbs appears in all comparisons. The difference in the SRb SiO maser velocity parameters may be due to a difference in the oscillation mechanism of the star. The suggested overtone oscillations of SRbs may affect the circumstellar cloud dynamics. Little theoretical work has specifically addressed the masers in semiregular variables. Qualitative comparisons of the data with the existing models of the SiO masers in LPVs are made.

79 ASTRONOMY AND ASTROPHYSICS↗

GRay: A MASSIVELY PARALLEL GPU-BASED CODE FOR RAY TRACING IN RELATIVISTIC SPACETIMES

We introduce GRay, a massively parallel integrator designed to trace the trajectories of billions of photons in a curved spacetime. This graphics-processing-unit (GPU)-based integrator employs the stream processing paradigm, is implemented in CUDA C/C++, and runs on nVidia graphics cards. The peak performance of GRay using single-precision floating-point arithmetic on a single GPU exceeds 300 GFLOP (or 1 ns per photon per time step). For a realistic problem, where the peak performance cannot be reached, GRay is two orders of magnitude faster than existing central-processing-unit-based ray-tracing codes. This performance enhancement allows more effective searches of large parameter spaces when comparing theoretical predictions of images, spectra, and light curves from the vicinities of compact objects to observations. GRay can also perform on-the-fly ray tracing within general relativistic magnetohydrodynamic algorithms that simulate accretion flows around compact objects. Making use of this algorithm, we calculate the properties of the shadows of Kerr black holes and the photon rings that surround them. We also provide accurate fitting formulae of their dependencies on black hole spin and observer inclination, which can be used to interpret upcoming observations of the black holes at the center of the Milky Way, as well as M87, with the Event Horizon Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗

PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity, the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗