84 research outputs found
An Inverse Mass Expansion for Entanglement Entropy in Free Massive Scalar Field Theory
We extend the entanglement entropy calculation performed in the seminal paper
by Srednicki for free real massive scalar field theories in 1+1, 2+1 and 3+1
dimensions. We show that the inverse of the scalar field mass can be used as an
expansion parameter for a perturbative calculation of the entanglement entropy.
We perform the calculation for the ground state of the system and for a
spherical entangling surface at third order in this expansion. The calculated
entanglement entropy contains a leading area law term, as well as subleading
terms that depend on the regularization scheme, as expected. Universal terms
are non-perturbative effects in this approach. Interestingly, this perturbative
expansion can be used to approximate the coefficient of the area law term, even
in the case of a massless scalar field in 2+1 and 3+1 dimensions. The presented
method provides the spectrum of the reduced density matrix as an intermediate
result, which is an important advantage in comparison to the replica trick
approach. Our perturbative expansion underlines the relation between the area
law and the locality of the underlying field theory.Comment: 35 pages, 5 figure
Salient Features of Dressed Elliptic String Solutions on S
We analyse several physical aspects of the dressed elliptic strings
propagating on and of their counterparts in
the Pohlmeyer reduced theory, i.e. the sine-Gordon equation. The solutions are
divided into two wide classes; kinks which propagate on top of elliptic
backgrounds and those which are non-localised periodic disturbances of the
latter. The former class of solutions obey a specific equation of state that is
in principle experimentally verifiable in systems which realize the sine-Gordon
equation. Among both of these classes, there appears to be a particular class
of interest the closed dressed strings. They in turn form four distinct
subclasses of solutions. Unlike the closed elliptic strings, these four
subclasses, exhibit interactions among their spikes. These interactions
preserve a carefully defined turning number, which can be associated to the
topological charge of the sine-Gordon counterpart. One particular class of
those closed dressed strings realizes instabilities of the seed elliptic
solutions. The existence of such solutions depends on whether a superluminal
kink with a specific velocity can propagate on the corresponding elliptic
sine-Gordon solution. Finally, the dispersion relations of the dressed strings
are studied. A qualitative difference between the two wide classes of dressed
strings is discovered. This would be an interesting subject for investigation
in the dual field theory.Comment: 75 pages, 27 figure
Dressed Elliptic String Solutions on RxS^2
We obtain classical string solutions on RxS^2 by applying the dressing method
on string solutions with elliptic Pohlmeyer counterparts. This is realized
through the use of the simplest possible dressing factor, which possesses just
a pair of poles lying on the unit circle. The latter is equivalent to the
action of a single Backlund transformation on the corresponding sine-Gordon
solutions. The obtained dressed elliptic strings present an interesting
bifurcation of their qualitative characteristics at a specific value of a
modulus of the seed solutions. Finally, an interesting generic feature of the
dressed strings, which originates from the form of the simplest dressing factor
and not from the specific seed solution, is the fact that they can be
considered as drawn by an epicycle of constant radius whose center is running
on the seed solution. The radius of the epicycle is directly related to the
location of the poles of the dressing factor.Comment: 47 pages, 2 figure
Advanced computer architecture specification for automated weld systems
This report describes the requirements for an advanced automated weld system and the associated computer architecture, and defines the overall system specification from a broad perspective. According to the requirements of welding procedures as they relate to an integrated multiaxis motion control and sensor architecture, the computer system requirements are developed based on a proven multiple-processor architecture with an expandable, distributed-memory, single global bus architecture, containing individual processors which are assigned to specific tasks that support sensor or control processes. The specified architecture is sufficiently flexible to integrate previously developed equipment, be upgradable and allow on-site modifications
Development of a Computer Architecture to Support the Optical Plume Anomaly Detection (OPAD) System
The NASA OPAD spectrometer system relies heavily on extensive software which repetitively extracts spectral information from the engine plume and reports the amounts of metals which are present in the plume. The development of this software is at a sufficiently advanced stage where it can be used in actual engine tests to provide valuable data on engine operation and health. This activity will continue and, in addition, the OPAD system is planned to be used in flight aboard space vehicles. The two implementations, test-stand and in-flight, may have some differing requirements. For example, the data stored during a test-stand experiment are much more extensive than in the in-flight case. In both cases though, the majority of the requirements are similar. New data from the spectrograph is generated at a rate of once every 0.5 sec or faster. All processing must be completed within this period of time to maintain real-time performance. Every 0.5 sec, the OPAD system must report the amounts of specific metals within the engine plume, given the spectral data. At present, the software in the OPAD system performs this function by solving the inverse problem. It uses powerful physics-based computational models (the SPECTRA code), which receive amounts of metals as inputs to produce the spectral data that would have been observed, had the same metal amounts been present in the engine plume. During the experiment, for every spectrum that is observed, an initial approximation is performed using neural networks to establish an initial metal composition which approximates as accurately as possible the real one. Then, using optimization techniques, the SPECTRA code is repetitively used to produce a fit to the data, by adjusting the metal input amounts until the produced spectrum matches the observed one to within a given level of tolerance. This iterative solution to the original problem of determining the metal composition in the plume requires a relatively long period of time to execute the software in a modern single-processor workstation, and therefore real-time operation is currently not possible. A different number of iterations may be required to perform spectral data fitting per spectral sample. Yet, the OPAD system must be designed to maintain real-time performance in all cases. Although faster single-processor workstations are available for execution of the fitting and SPECTRA software, this option is unattractive due to the excessive cost associated with very fast workstations and also due to the fact that such hardware is not easily expandable to accommodate future versions of the software which may require more processing power. Initial research has already demonstrated that the OPAD software can take advantage of a parallel computer architecture to achieve the necessary speedup. Current work has improved the software by converting it into a form which is easily parallelizable. Timing experiments have been performed to establish the computational complexity and execution speed of major components of the software. This work provides the foundation of future work which will create a fully parallel version of the software executing in a shared-memory multiprocessor system
Spectrum Preprocessing in the OPAD System
To determine the readiness of a rocket engine, and facilitate decisions on continued use of the engine before servicing is required, high-resolution optical spectrometers are used to acquire spectra from the exhaust plume. Such instruments are in place at the Technology Test Bed (TTB) stand at Marshall Space Flight Center (MSFC) and the A1 stand at Stennis Space Center (SSC). The optical spectrometers in place have a wide wavelength range covering the visible and near-infrared regions, taking approximately 8000 measurements at about one Angstrom spacing every half second. In the early stages of this work, data analysis was done manually. A simple spectral model produced a theoretical spectrum for given amount of elements and an operator visually matched the theoretical and real spectra. Currently, extensive software is being developed to receive data from the spectrometer and automatically generate an estimate of element amounts in the plume. It will result in fast and reliable analysis, with the capability of real-time performance. This software is the result of efforts of several groups but mainly it has been developed and used by scientists and combustion engineers, in their effort of understanding the underlying physical processes and phenomena and creating visualization and report generation facilities. Most of the software has been developed using the IDL language and programming environment which allows for extensive data visualization. Although this environment has been very beneficial, the resulting programs execute very slowly and are not easily portable to more popular, real-time environments. The need for portability and high speed of execution is becoming more apparent as the software matures moving out of the experimentation stage and into the production stage where ease of use and short response time are the most desirable features. The purpose of the work described here is to assist the scientists who developed the original IDL-based version in the conversion of the software into the real-time, production version. Specifically, a section of the software devoted to the preprocessing of the spectra has been converted into the C language. In addition, parts of this software which may be improved have been identified, and recommendations are given to improve the functionality and ease of use of the new version
Task scheduling in dataflow computer architectures
Dataflow computers provide a platform for the solution of a large class of computational problems, which includes digital signal processing and image processing. Many typical applications are represented by a set of tasks which can be repetitively executed in parallel as specified by an associated dataflow graph. Research in this area aims to model these architectures, develop scheduling procedures, and predict the transient and steady state performance. Researchers at NASA have created a model and developed associated software tools which are capable of analyzing a dataflow graph and predicting its runtime performance under various resource and timing constraints. These models and tools were extended and used in this work. Experiments using these tools revealed certain properties of such graphs that require further study. Specifically, the transient behavior at the beginning of the execution of a graph can have a significant effect on the steady state performance. Transformation and retiming of the application algorithm and its initial conditions can produce a different transient behavior and consequently different steady state performance. The effect of such transformations on the resource requirements or under resource constraints requires extensive study. Task scheduling to obtain maximum performance (based on user-defined criteria), or to satisfy a set of resource constraints, can also be significantly affected by a transformation of the application algorithm. Since task scheduling is performed by heuristic algorithms, further research is needed to determine if new scheduling heuristics can be developed that can exploit such transformations. This work has provided the initial development for further long-term research efforts. A simulation tool was completed to provide insight into the transient and steady state execution of a dataflow graph. A set of scheduling algorithms was completed which can operate in conjunction with the modeling and performance tools previously developed. Initial studies on the performance of these algorithms were done to examine the effects of application algorithm transformations as measured by such quantities as number of processors, time between outputs, time between input and output, communication time, and memory size
Classical solutions of -deformed coset models
We obtain classical solutions of \l-deformed \s-models based on
and coset manifolds. Using two different
sets of coordinates, we derive two distinct classes of solutions. The first
class is expressed in terms of hyperbolic and trigonometric functions, whereas
the second one in terms of elliptic functions. We analyze their properties
along with the boundary conditions and discuss string systems that they
describe. It turns out that there is an apparent similarity between the
solutions of the second class and the motion of a pendulum.Comment: 36+9 pages, 8 figure
Entanglement of Harmonic Systems in Squeezed States
The entanglement entropy of a free scalar field in its ground state is
dominated by an area law term. It is noteworthy, however, that the study of
entanglement in scalar field theory has not advanced far beyond the ground
state. In this paper, we extend the study of entanglement of harmonic systems,
which include free scalar field theory as a continuum limit, to the case of the
most general Gaussian states, namely the squeezed states. We find the
eigenstates and the spectrum of the reduced density matrix and we calculate the
entanglement entropy. Finally, we apply our method to free scalar field theory
in 1+1 dimensions and show that, for very squeezed states, the entanglement
entropy is dominated by a volume term, unlike the ground-state case. Even
though the state of the system is time-dependent in a non-trivial manner, this
volume term is time-independent. We expect this behaviour to hold in higher
dimensions as well, as it emerges in a large-squeezing expansion of the
entanglement entropy for a general harmonic system.Comment: 44 pages + 29 pages appendix, 13 figure
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