Resolution enhancement by nonlinear data processing. “HOGWASH” and the maximum entropy method

Two nonlinear methods for resolution enhancement of NMR data are investigated and compared. “HOGWASH” (modeled on a procedure employed in radioastronomy) and the maximum entropy method are applied to the same experimental free induction decay. In both cases, resolution enhancement is based on direct measurement of the instrumental lineshape of a reference signal known to be a singlet. The two approaches give comparable results, although HOGWASH requires much less computer time and memory than the maximum entropy method.     

Analysis of the maximum entropy principle “debate”

Jaynes's maximum entropy principle (MEP) is analyzed by considering in detail a recent controversy. Emphasis is placed on the inductive logical interpretation of probability and the concept of total knowledge. The relation of the MEP to relative frequencies is discussed, and a possible realm of its fruitful application is noted.     

Does the entropy of the Universe tend to a maximum?

Ordinary, macroscopic systems, naturally tend to a state of maximum entropy compatible with their constraints. However, this might not hold for gravity-dominated systems since their entropy may increase without bound unless this is precluded by the formation of a black hole. In this short note we suggest, based on the Hubble expansion history, that our Universe likely behaves as an ordinary system, i.e., that its entropy seems to tend to some maximum value.     

A new interpolating method based on the variation of spectra energy using CMOS array

A new interpolating method to enhance the resolution of gratings using complementary metal-oxide semiconductor (CMOS) according to the variation of some specified spectral light intensities during the motion of scale grating in a periodic separation is proposed. CMOS image sensor (pixel array 648×488) was also introduced as receiving device and its stability was verified experimentally. Many factors in the experiment were analyzed theoretically and contrasted with experiment. The advantages of this novel method were featured by CMOS and the specified spectral variation of the energy distribution was discussed.     

Is equilibrium always an entropy maximum?

A systematic development is given of the view that in the case of systems with long-range forces and which are therefore nonextensive (in some sense) some thermodynamic results do not hold. Among these is the relationU – TS + p = N and the Gibbs-Duhem equation. If a search for an equilibrium state is made by maximization of the entropy one may obtain misleading results because superadditivity may be violated. The considerations are worked out for a simple gas model, but they are relevant to black hole thermodynamics. Rather general conclusions can be drawn which transcend special systems.Based on a seminar given at the University of Florida, April 1983.On leave of absence from the Faculty of Mathematical Studies, University, Southampton S09 5NH, England.     

μSR in diamond

It has recently become possible to take advantage of the interesting properties of diamond, as the synthesis of diamond has reached a point that material with impurities in the low the part per billion range and residual strain in the order of ten nano-radians has been realized. Hyperfine interactions have played a key role in the study of diamond and the emergence of novel applications. This relates to the characterization of defects and the development of engineered few spin systems. A particular aspect of the defect studies is the elusive hydrogen defect. In μSR studies, muonium is considered a light isotope of hydrogen with very similar chemical properties, but with very interestingly different dynamical properties, due to its much lighter mass. It offers a unique opportunity to study the behaviour of hydrogen in diamond at very low concentrations. The studies have revealed details of the elementary muonium atom as well as a molecule involving muonium in the diamond lattice. The dynamics of the muonium, which include quantum diffusion and ionization have also been studied. This contribution reviews μSR in diamond in the context of diamond as a modern material hosting advanced applications.     

μSR research in semiconductors

Muon and muonium states in semiconductors especially silicon and germanium, have been the subject of SR research from the birth of the SR technique until the present. They are now under active investigation at at least three laboratories. Three different electronic states of the muon impurity have been firmly identified in silicon and more tentatively in germanium. This research has produced a significant amount of published literature which, due to the span of time and distance between the various experiments, shows large differences in technique, emphasis and style. I will attempt to present a coherent view of this literature distinghuishing the well-understood effects from those not understood.     

Detecting dynamical complexity changes in time series using the base-scale entropy

Timely detection of dynamical complexity changes in natural and man-made systems has deep scientific and practical meanings. We introduce a complexity measure for time series： the base-scale entropy. The definition directly applies to arbitrary real-word data. We illustrate our method on a practical speech signal and in a theoretical chaotic system. The results show that the simple and easily calculated measure of base-scale entropy can be effectively used to detect qualitative and quantitative dynamical changes.     

Energy spectra and energy correlations in the decayH→ZZ→μ+μ−μ+μ−

It is shown that in the sequential decay $H \to ZZ \to (f_1 \bar f_1 ) + (f_2 \bar f_2 )$ , the energy distribution of the final state particles provides a simple and powerful test of theHZZ vertex. For a standard Higgs boson, the energy spectrum of any final fermion, in the rest frame ofH, is predicted to be dΓ/dx～1+β⁴?2(x?1)², with $\beta = \sqrt {1 - 4m_Z^2 /m_H^2 } $ and 1?β≤x=4E/m _H ≤1+β. By contrast, the spectrum for a pseudoscalar Higgs is dΓ/dx～β²+(x?1)². There are characteristic energy correlations betweenf ₁ andf ₂ and betweenf ₁ andf ₂. These considerations are applied to the “gold-plated” reactionH→ZZ→μ⁺μ^?μ⁺μ^?, including possible effects ofCP-violation in theHZZ coupling. Our formalism also yields the energy spectra and correlations of leptons in the decay $H \to W^ + W^ - \to l^ + v_l l^ - \bar v_l $ .     

Investigation of the GdMn2O5 multiferroic by the μSR method

The GdMn₂O₅ multiferroic (a ceramic sample and a sample consisting of a large array of randomly oriented single crystals with linear dimensions 2–3 mm) has been studied by the μSR method within the temperature range 10–300 K. Three anomalies in the temperature behavior of the parameters of the muon polarization relaxation function, namely, close to the phase transition driven by the onset of long-range magnetic order in the manganese ion subsystem (T _N1 = 40–41 K), near the lock-in transition initiated by an abrupt change of the wave vector of magnetic order (T _L = 35 K), and close to the Gd³⁺ ion ordering temperature (T _N2 = 15 K), have been found. An analysis of the time spectra of muon spin precession in the internal magnetic field of the samples has revealed two positions of preferable muon localization sites in samples, which differ in precession frequencies and the character of their behavior with temperature. The lower-frequency precession driven by Mn⁴⁺ ions, ferromagnetic Mn4⁺-Mn⁴⁺ + muonium complexes, and Gd³⁺ions is observed throughout the temperature region T < T _N1 and is practically independent of temperature. At temperatures T < T _L = 35 K, a higher-frequency precession associated with Mn³⁺ ions appears also. It is characterized by a temperature dependence ～(T/T _N1)^β with the index β = 0.39, which is typical of Heisenberg-type 3D magnets. For T < T _N1, a deficiency of the rest total asymmetry is observed. This phenomenon can probably be assigned to formation of muonium, which suggests that charge transfer processes play an important role in formation of long-range magnetic order.     

μSR investigation of cupric oxide

TF and ZFSR-investigations were performed on high purity CuO powder. By TF measurements a phase transition to the ordered state was observed at 227K. A commensurate-incommensurate phase transition was detected at 213K by ZF measurements. In the commensurate phase we observed the Larmor precession. Four signals were detected below 55K, but by increasing temperature above 190K, precession became having only one component. This fact may be explained by muons tunneling between equivalent sites. In the incommensurate phase the Larmor precession was not detected because of too large damping.     

μ+SR in imperfect solids

The use of ⁺SR as a probe of point defects in metals is discussed. The importance of separating the effects due to the presence of the muon from those intrinsic to the defect-host system is stressed. It is suggested that studies of magnetic impurities in non-magnetic hosts may yield data which are relatively probe-independent. A theoretical analysis of the depolarization of muons coupled to magnetic impurities is outlined. It is pointed out that measurements of the field dependence of the depolarization rate can give information about impurity spin correlation times.Work performed under the auspices of the U. S. Department of Energy.     

Error of the local sound field’s maximum frequency shifts in shallow water

The error in determining the position of the spectral maximum of a signal against Gaussian white noise is considered. The sensitivity of the monitoring method based on measuring the frequency shifts of the field maximum is estimated. For a specific case of a Gaussian signal’s spectrum and the medium perturbed by background internal waves, results of calculations are presented.     

Low frequency characteristic parameters measurement of vented-box loudspeaker system using total least squares method

I.IntroductiollThecomputeraideddesign(CAD)techniqueisanadvancedmethodforthedesignofvented-boxloudspeakersystemsI1l,whichisbasedontheThiele-Sma.llparametersofloudspeakersIa]andthefowfrequencycharpeteristicparametersofvelltedboxloudspeakersystems.TheThiele-Smallparametersofloudspeakersandsomeofthelowfrequellcycharacteristicparametersofvellted-boxloudspeakersystemshavebeendeterIIilnedbyfrequencyUomainmeth.dI3'4]foralongtime.Themaindisadwtagesofthismethodarecomplicatedandtimeconsuming.TheThi…     

An investigation into the maximum entropy production principle in chaotic Rayleigh–Bénard convection

The hypothesis is made that the temperature and velocity fields in Rayleigh–Bénard convection can be expressed as a superposition of the active modes with time-dependent amplitudes, even in the chaotic regime. The maximum entropy production principle is interpreted as a variational principle in which the amplitudes of the modes are the variational degrees of freedom. For a given Rayleigh number, the maximum heat flow for any set of amplitudes is sought, subject only to the constraints that the energy equation be obeyed and the fluid be incompressible. The additional hypothesis is made that all temporal correlations between modes are zero, so that only the mean-squared amplitudes are optimising variables. The resulting maximal Nusselt number is close to experimental determinations. The Nusselt number would appear to be simply related to the number of active modes, in particular the number of distinct vertical modes. It is significant that reasonable results are obtained for the optimised Nusselt number in that the dynamics (the Navier–Stokes equation) is not used as a constraint. This suggests grounds for optimism that the maximum entropy production principle, interpreted in this variational manner, can provide a reasonable guide to the dynamic steady states of non-equilibrium systems whose detailed dynamics are unknown.     

μSR studies of YFeMnO4

Muon spin relaxation (SR) studies were carried out on YFeMnO₄. Two interesting phenomena were found in measurements of longitudinal relaxation time spectra atT>T _cusp for a single crystal: (1) difference of the relaxation rates between the directions parallel with and perpendicular to thec-axis, and (2) suppression of local field fluctuations in a longitudinal external field. The spectra atT >T _cusp were reproduced with the function exp[-(₀ t)]. The results are discussed under a picture of the magnetic spin fluctuations of triangular antiferromagnets.     

μSR studies in heavily doped GaAs

Transverse-field (TF) and longitudinal-field (LF) ⁺ SR measurements have been made on conducting GaAsSi (n-type 10¹⁸ cm^–3) and GaAsZn (p-type 10¹⁹ cm^–3) from 20 mK to 200 K. At low temperatures in GaAsSi, the frequency spectra show a large diamagnetic signal as well as broad lines due to bond-centered muonium (Mu _BC ). This broadening is attributed to spin exchange interactions with charge carriers in impurity bands. Only the diamagnetic signal is observed in GaAsZn. The field dependence of the TF diamagnetic relaxation rate at 5 K can be explained by the combined electric quadrupolar and Zeeman interaction between the muon and the surrounding nuclei and the temperature scan at TF=1.5 T indicates that the mechanisms responsible for the broadening are temperature independent. The candidates for the diamagnetic species are discussed in view of these results.This work is partially supported by the Natural Sciences and Engineering Research Council of Canada, the Welch Foundation (C-1048 [TLE], D-1053 [RLL]) and the U.S. National Science Foundation (DMR-8917639 [TLE, BH]).     

Feasibility of measuring the average sizes of diamagnetic domains by the μSR 2 method

Abtract One of the simplest examples of possible application of the μSR ² method for estimating the sizes of diamagnetic domains is analyzed in detail. The domains have been observed for the first time by means of the μ SR method in beryllium [G. Solt, C. Baines, V. S. Egorov et al., Hyperfine Interactions 104, 257 (1997)]. Results are given from a computer simulation of a μSR ² experiment to measure domain sizes in Be. An algorithm is described for processing the experimental results. It is graphically demonstrated that domain sizes can be estimated within the accelerator operating time allocated for an ordinary μSR experiment. Zh. éksp. Teor. Fiz. 115, 2133–2142 (June 1999)     

Track reconstruction using the TSF method for the BESm main drift chamber

We describe the algorithm to reconstruct the charged tracks for BESⅢmain drift chamber at BEPCⅡ,including the track finding and fitting.With a new method of the Track Segment Finder(TSF), the results of present study indicate that the algorithm can reconstruct the charged tracks over a wide range of momentum with high efficiency,while improving the robustness against the background noise in the drift chamber.The overall performances,including spatial resolution,momentum resolution and secondary vertices reconstruction efficiency,etc.satisfy the requirements of BESⅢexperiment.