Coordinates which diagonalize the kinetic energy of relative motion
General coordinate sets for diagonalizing relative kinetic energy of N particle system
Hirschfelder, J. O.↗
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Approximate Recovery and Relative Entropy I: General von Neumann Subalgebras
We prove the existence of a universal recovery channel that approximately recovers states on a von Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I von Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary von Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki–Masuda L p norms. We comment on applications to the quantum null energy condition.
79 ASTRONOMY AND ASTROPHYSICS↗
Computation of generalized and exact dispersion relations for longitudinal plasma waves in nonextensive statistics and the effects of the nonextensivity on the oscillation modes and damps
We have derived generalized dispersion relations for longitudinal waves in collisionless thermal plasma using linear Vlasov-Poisson kinetic model and nonextensive distributions for electrons. The Maxwellian limit of the dispersion relations, where the q-nonextensive parameter tends to one, is calculated. The generalized dispersion relations are reduced to polynomials for some specific values of q. The well-known modes of oscillations such as the Langmuir and electron acoustic waves have been obtained by solving the dispersion relations. Some new modes of oscillation are also found. Finally, the dependence of the oscillation modes and damps on q is discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Effect of minimal length uncertainty on the mass–radius relation of white dwarfs
Generalized uncertainty relation that carries the imprint of quantum gravity introduces a minimal length scale into the description of space–time. It effectively changes the invariant measure of the phase space through a factor (1+βp{sup 2}){sup −3} so that the equation of state for an electron gas undergoes a significant modification from the ideal case. It has been shown in the literature (Rashidi 2016) that the ideal Chandrasekhar limit ceases to exist when the modified equation of state due to the generalized uncertainty is taken into account. To assess the situation in a more complete fashion, we analyze in detail the mass–radius relation of Newtonian white dwarfs whose hydrostatic equilibria are governed by the equation of state of the degenerate relativistic electron gas subjected to the generalized uncertainty principle. As the constraint of minimal length imposes a severe restriction on the availability of high momentum states, it is speculated that the central Fermi momentum cannot have values arbitrarily higher than p{sub max}∼β{sup −1∕2}. When this restriction is imposed, it is found that the system approaches limiting mass values higher than the Chandrasekhar mass upon decreasing the parameter β to a value given by a legitimate upper bound. Instead, when the more realistic restriction due to inverse β-decay is considered, it is found that the mass and radius approach the values 1.4518 M{sub ⊙} and 601.18 km near the legitimate upper bound for the parameter β.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Adding Hierarchical Objects to Relational Database General-Purpose XML-Based Information Managements
NETMARK is a flexible, high-throughput software system for managing, storing, and rapid searching of unstructured and semi-structured documents. NETMARK transforms such documents from their original highly complex, constantly changing, heterogeneous data formats into well-structured, common data formats in using Hypertext Markup Language (HTML) and/or Extensible Markup Language (XML). The software implements an object-relational database system that combines the best practices of the relational model utilizing Structured Query Language (SQL) with those of the object-oriented, semantic database model for creating complex data. In particular, NETMARK takes advantage of the Oracle 8i object-relational database model using physical-address data types for very efficient keyword searches of records across both context and content. NETMARK also supports multiple international standards such as WEBDAV for drag-and-drop file management and SOAP for integrated information management using Web services. The document-organization and -searching capabilities afforded by NETMARK are likely to make this software attractive for use in disciplines as diverse as science, auditing, and law enforcement.
Lin, Shu-Chun↗
Spacecraft dynamics characterization and control system failure detection. Volume 3: Control system failure monitoring
We discuss the application of Generalized Parity Relations to two experimental flexible space structures, the NASA Langley Mini-Mast and Marshall Space Flight Center ACES mast. We concentrate on the generation of residuals and make no attempt to implement the Decision Function. It should be clear from the examples that are presented whether it would be possible to detect the failure of a specific component. We derive the equations from Generalized Parity Relations. Two special cases are treated: namely, Single Sensor Parity Relations (SSPR) and Double Sensor Parity Relations (DSPR). Generalized Parity Relations for actuators are also derived. The NASA Langley Mini-Mast and the application of SSPR and DSPR to a set of displacement sensors located at the tip of the Mini-Mast are discussed. The performance of a reduced order model that includes the first five models of the mast is compared to a set of parity relations that was identified on a set of input-output data. Both time domain and frequency domain comparisons are made. The effect of the sampling period and model order on the performance of the Residual Generators are also discussed. Failure detection experiments where the sensor set consisted of two gyros and an accelerometer are presented. The effects of model order and sampling frequency are again illustrated. The detection of actuator failures is discussed. We use Generalized Parity Relations to monitor control system component failures on the ACES mast. An overview is given of the Failure Detection Filter and experimental results are discussed. Conclusions and directions for future research are given.
Vanschalkwyk, Christiaan M.↗
CoCr wear particles generated from CoCr alloy metal-on-metal hip replacements, and cobalt ions stimulate apoptosis and expression of general toxicology-related genes in monocyte-like U937 cells
Cobalt-chromium (CoCr) particles in the nanometre size range and their concomitant release of Co and Cr ions into the patients' circulation are produced by wear at the articulating surfaces of metal-on-metal (MoM) implants. This process is associated with inflammation, bone loss and implant loosening and led to the withdrawal from the market of the DePuy ASR™ MoM hip replacements in 2010. Ions released from CoCr particles derived from a resurfacing implant in vitro and their subsequent cellular up-take were measured by ICP-MS. Moreover, the ability of such metal debris and Co ions to induce both apoptosis was evaluated with both FACS and immunoblotting. qRT-PCR was used to assess the effects on the expression of lymphotoxin alpha (LTA), BCL2-associated athanogene (BAG1), nitric oxide synthase 2 inducible (NOS2), FBJ murine osteosarcoma viral oncogene homolog (FOS), growth arrest and DNA-damage-inducible alpha (GADD45A). ICP-MS showed that the wear debris released significant (p < 0.05) amounts of Co and Cr ions into the culture medium, and significant (p < 0.05) cellular uptake of both ions. There was also an increase (p < 0.05) in apoptosis after a 48 h exposure to wear debris. Analysis of qRT-PCR results found significant up-regulation (p < 0.05) particularly of NOS2 and BAG1 in Co pre-treated cells which were subsequently exposed to Co ions + debris. Metal debris was more effective as an inducer of apoptosis and gene expression when cells had been pre-treated with Co ions. This suggests that if a patient receives sequential bilateral CoCr implants, the second implant may be more likely to produce adverse effects than the first one. - Highlights: • Effects of CoCr nanoparticles and Co ions on U937 cells were investigated. • Ions released from wear debris play an important role in cellular response, • Toxicity of Co ions could be related to NO metabolic processes and apoptosis. • CoCr particles were a more effective inducer of apoptosis after cell priming. • CoCr particles were a more effective inducer of gene expression after cell priming.
60 APPLIED LIFE SCIENCES↗
TU-FG-209-05: Demonstration of the Line Focus Principle Using the Generalized Measured-Relative Object Detectability (GM-ROD) Metric
Purpose: Demonstrate and quantify the augmented resolution due to focalspot size decrease in images acquired on the anode side of the field, for both small and medium (0.3 and 0.6mm) focal-spot sizes using the experimental task-based GM-ROD metric. Theoretical calculations have shown that a medium focal-spot can achieve the resolution of a small focal-spot if acquired with a tilted anode, effectively providing a higher-output small focal-spot. Methods: The MAF-CMOS (micro-angiographic fluoroscopic complementary-metal-oxide semiconductor) detector (75µm pixel pitch) imaged two copper wire segments of different diameter and a pipeline stent at the central axis and on the anode side of the beam, achieved by tilting the x-ray C-arm (Toshiba Infinix) to 6° and realigning the detector with the perpendicular ray to correct for x-ray obliquity. The relative gain in resolution was determined using the GM-ROD metric, which compares images on the basis of the Fourier transform of the image and the measured NNPS. To emphasize the geometric unsharpness, images were acquired at a magnification of two. Results: Images acquired on the anode side were compared to those acquired on the central axis with the same target-area focal-spot to consider the effect of an angled tube, and for all three objects the advantage of the smaller effective focal-spot was clear, showing a maximum improvement of 36% in GM-ROD. The images obtained with the small focal-spot at the central axis were compared to those of the medium focal-spot at the anode side and, for all objects, the relative performance was comparable. Conclusion: For three objects, the GM-ROD demonstrated the advantage of the anode side focal-spot. The comparable performance of the medium focal-spot on the anode side will allow for a high-output small focal-spot; a necessity in endovascular image-guided interventions. Partial support from an NIH grant R01EB002873 and an equipment grant from Toshiba Medical Systems Corp.
60 APPLIED LIFE SCIENCES↗
Some dynamical aspects of the special and general theories of relativity
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Some dynamical aspects of the special and general theories of relativity
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Adamson, D.↗
Relation Between the Generalized Acoustic Analogy and Lilley's Contributions to Aeroacoustics
This paper reviews Lilley s reformulation of Lighthill s equation and shows that it can be obtained as a special case of a much more general acoustic analogy. It also shows how this generalized analogy can be used to eliminate some of the difficulties that arise when more conventional parallel flow analogies are applied to high speed jets. And, finally, some recent applications of these ideas are discussed.
Goldstein, M. E.↗
Derivation and generalization of the dispersion relation of rising-sun magnetron with sectorial and rectangular cavities
Field analysis method is used to derive the dispersion relation of rising-sun magnetron with sectorial and rectangular cavities. This dispersion relation is then extended to the general case in which the rising-sun magnetron can be with multi-group cavities of different shapes and sizes, and from which the dispersion relations of conventional magnetron, rising-sun magnetron, and magnetron-like device can be obtained directly. The results show that the relative errors between the theoretical and simulation values of the dispersion relation are less than 3%, the relative errors between the theoretical and simulation values of the cutoff frequencies of π mode are less than 2%. In addition, the influences of each structure parameter of the magnetron on the cutoff frequency of π mode and on the mode separation are investigated qualitatively and quantitatively, which may be of great interest to designing a frequency tuning magnetron.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Theory on excitations of drift Alfvén waves by energetic particles. II. The general fishbone-like dispersion relation
The theoretical framework of the general fishbone-like dispersion relation (GFLDR), presented and discussed in the Companion Paper [Phys. Plasmas 21, 072120 (2014)], is applied to cases of practical interest of shear/drift Alfvén waves (SAWs/DAWs) excited by energetic particles (EPs) in toroidal fusion plasmas. These applications demonstrate that the GFLDR provides a unified approach that allows analytical and numerical calculations of stability properties, as well as mode structures and, in general, nonlinear evolutions, based on different models and with different levels of approximation. They also show the crucial importance of kinetic descriptions, accurate geometries and boundary conditions for predicting linear as well as nonlinear SAW/DAW and EP behaviors in burning plasmas. Thus, the GFLDR unified theoretical framework elevates the interpretative capability for both experimental and numerical simulation results.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Embeddings and Integrable Charges for Extended Corner Symmetry
Not Available
79 ASTRONOMY AND ASTROPHYSICS↗
Generalization of the Manley-Rowe relations for non-periodic signals constrained in bandwidth with finite energy
General relations for the energy spectral densities of nonperiodic signals constrained in bandwidth in nonlinear reactances are derived. It is assumed that the charge-voltage characteristics of the reactances are polynomials. In addition certain conditions for the frequency bands of the signals must be met. By contrast with the Manley-Rowe relations integrals with respect to frequency appear instead of the ratios power over frequency. The integrands are energy spectral densities divided by frequency. For parametric devices inequalities can be derived for the ratios of the energy levels in the different circuits and the limiting frequencies of the energy spectral densities. With these inequalities it is possible to determine limits for the energy levels.
Proksch, P.↗
Order-Reduced Solution of the Nonlinear High-Fidelity Generalized Method of Cells Micromechanics Relations
The High-Fidelity Generalized Method of Cells (HFGMC) is one technique for accurately simulating nonlinear composite material behavior. The HFGMC uses a higher-order approximation for the subcell displacement field that allows for a more accurate determination of the subcell stressstrain fields at the cost of some computational efficiency. In order to reduce computational costs associated with the solution of the ensuing system of simultaneous equations, the HFGMC global system of equations for doubly-periodic repeating unit cells with nonlinear constituents was reduced in size through the use of a Petrov-Galerkin-based Proper Orthogonal Decomposition order-reduction scheme. A number of cases were presented that address the computational feasibility of using order-reduction techniques to solve solid mechanics problems involving complex microstructures.
order-reduction↗
Generalized conditional symmetries and related solutions of the Grad-Shafranov equation
The generalized conditional symmetry (GCS) method is applied to a specific case of the Grad–Shafranov (GS) equation, in cylindrical geometry assuming the existence of an axial symmetry. We investigate the conditions that yield the GS equation admitting a special class of second-order GCSs. The determining system for the unknown arbitrary functions is solved in several special cases and new exact solutions, including solitary waves, different in form and structure from the ones obtained using other nonclassical symmetry methods, are pointed out. Several plots of the level sets or flux surfaces of the new solutions as well as surfaces with vanishing flow are displayed. The obtained solutions can be useful for studying plasma equilibrium, transport phenomena, and magnetohydrodynamic stability.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Combination of TOPEX/POSEIDON Data with a Hydrographic Inversion for Determination of the Oceanic General Circulation and its Relation to Geoid Accuracy
A global estimate of the absolute oceanic general circulation from a geostrophic inversion of in situ hydrographic data is tested against and then combined with an estimate obtained from TOPEX/POSEIDON altimetric data and a geoid model computed using the JGM-3 gravity-field solution. Within the quantitative uncertainties of both the hydrographic inversion and the geoid estimate, the two estimates derived by very different methods are consistent. When the in situ inversion is combined with the altimetry/geoid scheme using a recursive inverse procedure, a new solution, fully consistent with both hydrography and altimetry, is found. There is, however, little reduction in the uncertainties of the calculated ocean circulation and its mass and heat fluxes because the best available geoid estimate remains noisy relative to the purely oceanographic inferences. The conclusion drawn from this is that the comparatively large errors present in the existing geoid models now limit the ability of satellite altimeter data to improve directly the general ocean circulation models derived from in situ measurements. Because improvements in the geoid could be realized through a dedicated spaceborne gravity recovery mission, the impact of hypothetical much better, future geoid estimates on the circulation uncertainty is also quantified, showing significant hypothetical reductions in the uncertainties of oceanic transport calculations. Full ocean general circulation models could better exploit both existing oceanographic data and future gravity-mission data, but their present use is severely limited by the inability to quantify their error budgets.
Ganachaud, Alexandre↗