3,530 research outputs found

    Chemical Measurement and Fluctuation Scaling

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    Main abstract: Fluctuation scaling reports on all processes producing a data set. Some fluctuation scaling relationships, such as the Horwitz curve, follow exponential dispersion models which have useful properties. The mean-variance method applied to Poisson distributed data is a special case of these properties allowing the gain of a system to be measured. Here, a general method is described for investigating gain (G), dispersion (β), and process (α) in any system whose fluctuation scaling follows a simple exponential dispersion model, a segmented exponential dispersion model, or complex scaling following such a model locally. When gain and dispersion cannot be obtained directly, relative parameters, GR and βR, may be used. The method was demonstrated on data sets conforming to simple, segmented, and complex scaling. These included mass, fluorescence intensity, and absorbance measurements and specifications for classes of calibration weights. Changes in gain, dispersion, and process were observed in the scaling of these data sets in response to instrument parameters, photon fluxes, mathematical processing, and calibration weight class. The process parameter which limits the type of statistical process that can be invoked to explain a data set typically exhibited 04 possible. With two exceptions, calibration weight class definitions only affected β. Adjusting photomultiplier voltage while measuring fluorescence intensity changed all three parameters (0<α<0.8; 0<βR<3; 0<GR<4.1). The method provides a framework for calibrating and interpreting uncertainty in chemical measurement allowing robust compar ison of specific instruments, conditions, and methods. Supporting information abstract: On first inspection, fluctuation scaling data may appear to approximate a straight line when log transformed. The data presented in figure 5 of the main text gives a reasonable approximation to a straight line and for many purposes this would be sufficient. The purpose of the study of fluorescence intensity was to determine whether adjusting the voltage of a photomultiplier tube while measuring a fluorescent sample changes the process (α), the dispersion (β) and/or the gain (G). In this regard, the linear model established that PMT setting affects more than the gain. However, a detailed analysis beginning with testing for model mis-specification provides additional information. Specifically, Poisson behavior is only seen over a limited wavelength range in the 600 V and 700 V data sets

    On the Green-Functions of the classical offshell electrodynamics under the manifestly covariant relativistic dynamics of Stueckelberg

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    In previous paper derivations of the Green function have been given for 5D off-shell electrodynamics in the framework of the manifestly covariant relativistic dynamics of Stueckelberg (with invariant evolution parameter Ï„\tau). In this paper, we reconcile these derivations resulting in different explicit forms, and relate our results to the conventional fundamental solutions of linear 5D wave equations published in the mathematical literature. We give physical arguments for the choice of the Green function retarded in the fifth variable Ï„\tau.Comment: 16 pages, 1 figur

    Scaling Bounded Model Checking By Transforming Programs With Arrays

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    Bounded Model Checking is one the most successful techniques for finding bugs in program. However, model checkers are resource hungry and are often unable to verify programs with loops iterating over large arrays.We present a transformation that enables bounded model checkers to verify a certain class of array properties. Our technique transforms an array-manipulating (ANSI-C) program to an array-free and loop-free (ANSI-C) program thereby reducing the resource requirements of a model checker significantly. Model checking of the transformed program using an off-the-shelf bounded model checker simulates the loop iterations efficiently. Thus, our transformed program is a sound abstraction of the original program and is also precise in a large number of cases - we formally characterize the class of programs for which it is guaranteed to be precise. We demonstrate the applicability and usefulness of our technique on both industry code as well as academic benchmarks

    Towards a Realistic Equation of State of Strongly Interacting Matter

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    We consider a relativistic strongly interacting Bose gas. The interaction is manifested in the off-shellness of the equilibrium distribution. The equation of state that we obtain for such a gas has the properties of a realistic equation of state of strongly interacting matter, i.e., at low temperature it agrees with the one suggested by Shuryak for hadronic matter, while at high temperature it represents the equation of state of an ideal ultrarelativistic Stefan-Boltzmann gas, implying a phase transition to an effectively weakly interacting phase.Comment: LaTeX, figures not include

    Semigroup evolution in Wigner Weisskopf pole approximation with Markovian spectral coupling

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    We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation (neglecting the background contribution) the evolution of a total system subspace is not an exact semigroup for the multi-channel decay, unless the projectors into eigesntates of the reduced evolution generator W(z)W(z) are orthogonal. In this case these projectors must be evaluated at different pole locations zα≠zβz_\alpha\neq z_\beta. Since the orthogonality relation does not generally hold at different values of zz, for example, when there is symmetry breaking, the semigroup evolution is a poor approximation for the multi-channel decay, even for a very weak coupling. Nevertheless, there exists a possibility not only to ensure the orthogonality of the W(z)W(z) projectors regardless the number of the poles, but also to simultaneously suppress the effect of the background contribution. This possibility arises when the theory is generalized to take into account interactions with an environment. In this case W(z)W(z), and hence its eigenvectors as well, are {\it independent} of zz, which corresponds to a structure of the coupling to the continuum spectrum associated with the Markovian limit.Comment: 9 pages, 3 figure

    Classical 5D fields generated by a uniformly accelerated point source

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    Gauge fields associated with the manifestly covariant dynamics of particles in (3,1)(3,1) spacetime are five-dimensional. In this paper we explore the old problem of fields generated by a source undergoing hyperbolic motion in this framework. The 5D fields are computed numerically using absolute time Ï„\tau-retarded Green-functions, and qualitatively compared with Maxwell fields generated by the same motion. We find that although the zero mode of all fields coincides with the corresponding Maxwell problem, the non-zero mode should affect, through the Lorentz force, the observed motion of test particles.Comment: 36 pages, 8 figure

    Control dependence for extended finite state machines

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    Though there has been nearly three decades of work on program slicing, there has been comparatively little work on slicing for state machines. One of the primary challenges that currently presents a barrier to wider application of state machine slicing is the problem of determining control dependence. We survey existing related definitions, introducing a new definition that subsumes one and extends another. We illustrate that by using this new definition our slices respect Weiser slicing’s termination behaviour. We prove results that clarify the relationships between our definition and older ones, following this up with examples to motivate the need for these differences

    Quantum Time and Spatial Localization: An Analysis of the Hegerfeldt Paradox

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    Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's theory of constraints. A parametrization invariant formulation is obtained by introducing time and energy operators for the relativistic particle and then treating the Klein-Gordon equation as a constraint. The standard, physical Hilbert space is recovered, via integration over proper time, from an augmented Hilbert space wherein time and energy are dynamical variables. It is shown that the Newton-Wigner position operator, being in this description a constant of motion, acts on states in the augmented space. States with strictly positive energy are non-local in time; consequently, position measurements receive contributions from states representing the particle's position at many times. Apparent superluminal propagation is explained by noting that, as the particle is potentially in the past (or future) of the assumed initial place and time of localization, it has time to propagate to distant regions without exceeding the speed of light. An inequality is proven showing the Hegerfeldt paradox to be completely accounted for by the hypotheses of subluminal propagation from a set of initial space-time points determined by the quantum time distribution arising from the positivity of the system's energy. Spatial localization can nevertheless occur through quantum interference between states representing the particle at different times. The non-locality of the same system to a moving observer is due to Lorentz rotation of spatial axes out of the interference minimum.Comment: This paper is identical to the version appearing in J. Math. Phys. 41; 6093 (Sept. 2000). The published version will be found at http://ojps.aip.org/jmp/. The paper (40 page PDF file) has been completely revised since the last posting to this archiv

    Multi-particle Correlations in Quaternionic Quantum Systems

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    We investigate the outcomes of measurements on correlated, few-body quantum systems described by a quaternionic quantum mechanics that allows for regions of quaternionic curvature. We find that a multi-particle interferometry experiment using a correlated system of four nonrelativistic, spin-half particles has the potential to detect the presence of quaternionic curvature. Two-body systems, however, are shown to give predictions identical to those of standard quantum mechanics when relative angles are used in the construction of the operators corresponding to measurements of particle spin components.Comment: REVTeX 3.0, 16 pages, no figures, UM-P-94/54, RCHEP-94/1
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