Discrete Line Spectra Research Articles

Recovery of discrete spectra radiated by substance in deep vacuum using integral approximation algorithm

Subject of Research. The topical spectroscopy inverse problem is considered: the recovery of a discrete (line) spectrum from the measured continuous spectrum and the spectrometer response (instrument, hardware, spread) function in the presence of noise. Method. The problem is reduced to solving a system of linear-nonlinear equations with respect to the intensities of lines entering linearly and the frequencies of lines entering nonlinearly in the spectrum. To solve the system of linear-nonlinear equations, an integral approximation algorithm is developed that combines the solution of a linear integral equation and a system of linear algebraic equations without solving non-linear equations. Main Results. The proposed solution makes it possible to determine the number of lines in the spectrum and their parameters and is confirmed by the solution of numerical examples. Practical Relevance. The proposed algorithm provides the increase of spectrometer resolution (resolve close lines and isolate weak lines from noise) by applying mathematical-computer processing of the discrete spectrum.

A kernel approach to deconvolution of the complex modulus in linear viscoelasticity

The relaxation spectrum of a viscoelastic material holds the key to describing its relaxation mechanisms at a molecular level. It also plays a fundamental role in accessing the molecular weight distribution, and in modelling the dynamics of complex fluids. The relaxation spectrum cannot be measured directly, but it may be locally determined from experimental measurements of viscoelastic response at a macroscopic level. In particular, the relaxation spectrum is a continuous distribution of relaxation times which may be recovered, at least locally, from measurements of the complex modulus of the material. Although mathematical expressions for the continuous spectrum have been known for well over a century, these were inaccessible to numerical implementation for decades. Regularization methods for approximating discrete line spectra were first introduced in the 1980s, but it was not until 2012 that methods for recovering continuous spectra in a mathematical framework were proposed. In this paper, we analyze spectrum recovery within the framework of reproducing kernel Hilbert spaces and identify such spaces as natural homes for the complex modulus and spectrum. Theorems are proved establishing the convergence of inverse operators expressed as series of derivatives of the complex modulus. This enables a detailed characterization of the native spaces of the real and imaginary parts of the complex modulus, and leads to a further theorem which identifies a hierarchy of trial spaces for the spectrum. Homeomorphic trial spaces for data and spectra are then specified in detail, and their efficacy demonstrated by means of a case study.

Quantum jumps, superpositions, and the continuous evolution of quantum states

The apparent dichotomy between quantum jumps on the one hand, and continuous time evolution according to wave equations on the other hand, provided a challenge to Bohr's proposal of quantum jumps in atoms. Furthermore, Schrödinger's time-dependent equation also seemed to require a modification of the explanation for the origin of line spectra due to the apparent possibility of superpositions of energy eigenstates for different energy levels. Indeed, Schrödinger himself proposed a quantum beat mechanism for the generation of discrete line spectra from superpositions of eigenstates with different energies.However, these issues between old quantum theory and Schrödinger's wave mechanics were correctly resolved only after the development and full implementation of photon quantization. The second quantized scattering matrix formalism reconciles quantum jumps with continuous time evolution through the identification of quantum jumps with transitions between different sectors of Fock space. The continuous evolution of quantum states is then recognized as a sum over continually evolving jump amplitudes between different sectors in Fock space.In today's terminology, this suggests that linear combinations of scattering matrix elements are epistemic sums over ontic states. Insights from the resolution of the dichotomy between quantum jumps and continuous time evolution therefore hold important lessons for modern research both on interpretations of quantum mechanics and on the foundations of quantum computing. They demonstrate that discussions of interpretations of quantum theory necessarily need to take into account field quantization. They also demonstrate the limitations of the role of wave equations in quantum theory, and caution us that superpositions of quantum states for the formation of qubits may be more limited than usually expected.

Research as a guide for curriculum development: An example from introductory spectroscopy. I. Identifying student difficulties with atomic emission spectra

This is the first of two closely related articles (Paper I and Paper II) that together illustrate how research in physics education has helped guide the design of instruction that has proved effective in improving student understanding of atomic spectroscopy. Most of the more than 1000 students who participated in this four-year investigation were science majors enrolled in the introductory calculus-based physics course at the University of Washington (UW) in Seattle, WA, USA. The others included graduate and undergraduate teaching assistants at UW and physics majors in introductory and advanced physics courses at the University of Zagreb, Zagreb, Croatia. About half of the latter group were preservice high school physics teachers. This article (Paper I) describes how several serious conceptual and reasoning difficulties were identified among students as they tried to relate a discrete line spectrum to the energy levels of atoms in a light source. Paper II illustrates how findings from this research informed the development of a tutorial that led to significant improvement in student understanding of atomic emission spectra.

Research as a guide for curriculum development: An example from introductory spectroscopy. II. Addressing student difficulties with atomic emission spectra

This is the second of two closely related articles (Paper I and Paper II) that together illustrate how research in physics education has helped guide the design of instruction that has proved effective in improving student understanding of atomic spectroscopy. Most of the more than 1000 students who participated in this four-year investigation were science majors enrolled in the introductory calculus-based physics course at the University of Washington (UW) in Seattle, WA, USA. The others included graduate and undergraduate teaching assistants at UW and physics majors in introductory and advanced physics courses at the University of Zagreb, Zagreb, Croatia. About half of the latter group were preservice high school physics teachers. Paper I describes how several conceptual and reasoning difficulties were identified among university students as they tried to relate a discrete line spectrum to the energy levels of atoms in a light source. This second article (Paper II) illustrates how findings from this research informed the development of a tutorial that led to improvement in student understanding of atomic emission spectra.

A novel modulation scheme for short range polymer optical fiber communications

To make use of the spectrum of a step-index polymer optical fiber (SI-POF) channel, a hybrid modulation scheme is proposed combining discrete multi-tone modulation and M-ary position phase shift keying. The discrete line spectrum interference and sideband interference components of the new modulation scheme are analyzed. The waveform optimization factor and a new numerical symbol generating approach are introduced to strengthen the anti-interference capability of the system. Offline processing with an arbitrary waveform generator and digital storage oscilloscope is used to investigate the transmission performance. A transmission rate of 510.5 Mbps is achieved for a 50 m SI-POF in an intensity modulated direct detection system using eye-safe resonant cavity light-emitting diodes and a PIN diode at red 650 nm. The experimental verification demonstrates that, using the new methodology, an additional bit rate of 19.5 Mbps in the low signal-to-noise ratio region is obtained. Furthermore there 6 dB power is saved at a bit error rate (BER) of 1×10−4, so better spectral efficiency can be achieved. It is demonstrated that the proposed scheme can offer better BER performance and make a better compromise between transmission rate, power consumption, spectral efficiency and BER.

SOME NUMERICAL AND EXPERIMENTAL OBSERVATIONS ON THE GROWTH OF OSCILLATIONS IN AN X-BAND GUNN OSCILLATOR

The dynamics of the onset of oscillations in a wave guide cavity based Gunn Oscillator (GO) has been critically examined through numerical simulations and experimental studies. The transition of the GO from a non-oscillatory to an oscillatory state and the same in the reverse direction occurs at different critical values of the dc bias voltage applied to the GO. In presence of a weak RF field in GO cavity, oscillations with broad band continuous spectrum and multiple discrete line spectrum are observed at the GO output for different values of dc bias below the above mentioned critical values. Analysing the numerically obtained time series data, chaos quantifiers have been obtained to prove the occurrence of the chaotic oscillations in the GO. Experimental results and observations of numerical simulation show good qualitative agreement.

Capture Gamma-ray Libraries for Nuclear Applications

Author(s): Sleaford, B.W. | Abstract: The neutron capture reaction is useful in identifying and analyzing the gamma-ray spectrum from an unknown assembly as it gives unambiguous information on its composition. This can be done passively or actively where an external neutron source is used to probe an unknown assembly. There are known capture gamma-ray data gaps in the ENDF libraries used by transport codes for various nuclear applications. The Evaluated Gamma-ray Activation file (EGAF) is a new thermal neutron capture database of discrete line spectra and cross sections for over 260 isotopes that was developed as part of an IAEA Coordinated Research Project. EGAF has been used to improve the capture gamma production in ENDF libraries. For medium to heavy nuclei the quasi continuum contribution to the gamma cascades is not experimentally resolved. The continuum contains up to 90percent of all the decay energy an is modeled here with the statistical nuclear structure code DICEBOX. This code also provides a consistency check of the level scheme nuclear structure evaluation. The calculated continuum is of sufficient accuracy to include in the ENDF libraries. This analysis also determines new total thermal capture cross sections and provides an improved RIPL database. For higher energy neutron capture there is less experimental data available making benchmarking of the modeling codes more difficult. We use CASINO, a version of DICEBOX that is modified for this purpose. This can be used to simulate the neutron capture at incident neutron energies up to 20 MeV to improve the gamma-ray spectrum in neutron data libraries used for transport modelling of unknown assemblies.

Nonlinear photoelectron emission from metal surfaces induced by short laser pulses: the effects of field enhancement by surface plasmons

Nonlinear electron emission processes induced by surface plasmon oscillations have been studied both experimentally and theoretically. The measured above-threshold electron spectra extend up to energies whose appearance cannot be explained solely by standard non-perturbative methods, which predict photon energy separated discrete energy line spectra with the known fast fall - plateau - cutoff envelope shape, even when taking the large field enhancement into account. The theoretical analysis of our data, based on the concept of plasmon-induced near-field effects, gives reasonably good explanation and qualitative agreement in the whole intensity range.

Valence-Change of Eu and Its Effects on the Luminescent Properties of Sr2MgSi2O7:Eu,Dy

Long afterglow phosphors of Sr2MgSi2O7:Eu,Dy were prepared by high temperature solid state reaction in oxidation atmospheres, and then were treated sequentially in reducing atmosphere --> oxidation atmosphere --> reducing atmosphere. The crystal structure of the samples was investigated by using powder X-ray diffraction (XRD). The measurements of the photoluminescence and the thermoluminescence properties suggest the difference in the luminescent properties between Eu2+ and Eu3+. Eu3+ ions occupy two different sites, and their emission spectra consist of four discrete line spectra, due to the 5D0 --> 7F1 (590 nm), 5D0 --> 7F2 (618 nm), 5D0 --> 7F4 (703 nm) and the 5D2 --> 7F3 (510 nm) transitions. But in contrast, the emission spectrum of Eu2+ is characteristic of a broadband spectrum due to the 4f(7) --> 4f(6) 5d(1) transition. The luminescence of Sr2MgSi2O7:Eu2+,Dy3+ displays both higher intensity and longer decay than that of Sr2MgSi2O7:Eu3+,Dy3+. The emissions from Dy3+ are detected in all samples, indicating that Dy3+ ions act not only the trap center but also the luminescence center in the host lattice of Sr2MgSi2O7.

Formation of the continuous visible emission spectrum of pulsed discharge in cesium vapor

The formation of a continuous emission spectrum of pulsed discharge in high-pressure cesium vapor (P ≤ 1 bar) has been experimentally studied under conditions of increased power deposited in discharge. Experimental data well agree with the results of theoretical calculations. Physical mechanisms underlying the observed phenomenon are discussed. It is shown that, as the pumping current pulse amplitude is increased from 15 to 80 A, a discrete line spectrum transforms into the continuous spectrum. This is accompanied by an increase in the light yield (from 15 to 85 lm/W) and color-rendering index (from 86 to 98).

Polarization Resolved Laser-Induced Breakdown Spectroscopy of Al

It is shown that the continuous background of the laser-induced breakdown spectrum of Al produced by 800 nm femtosecond pulses is strongly polarized. Use of a polarizer to filter out the background significantly improves the signal/noise and signal/background ratios of the discrete line spectrum. The effects of the laser pulse energy, focal position, incidence and detection angles, and the polarization plane of the laser were investigated. Polarization resolved laser-induced breakdown spectroscopy (PRLIBS) is much less sensitive to these variables than conventional, ungated fs-LIBS, making this a much more versatile analytical tool. These measurements reveal qualitatively different mechanisms for the continuous and discrete parts of the spectrum.

Low distortion slow light in flat Brillouin gain spectrum by using optical frequency comb

We present a novel method for realizing a slow light with a broadband flat Brillouin gain and low distortion by using an optical frequency comb. We obtained a pump light consisting of 20 discrete line spectra using an optical frequency comb generation technique and a flat SBS gain with a 200 MHz bandwidth. We have realized a large relative pulse delay of 2.46 while suppressing the broadening factor to less than 1.19 for a pulse with a duration of 5.44 ns.

Evolution of the Near-UV Emission Spectrum Associated with the Reduction Process in Microwave Iron Making

The structure of the emission spectrum in the near-UV range (240 nm-310 nm) changes drastically from the continuous spectrum to a discrete line spectrum with increasing sample temperature during the carbothermic reduction of magnetite in a 2.45 GHz microwave multimode furnace. The continuous spectrum can be assigned as a cathodoluminescence of magnetite. The dynamic evolution of the spectrum from continuous to discrete represents the progress of the reduction from magnetite to iron.

Simulation of Rayleigh-Faded Mobile-to-Mobile Communication Channels

Mobile-to-mobile channels find increasing applications in futuristic intelligent transport systems, ad hoc mobile wireless networks, and relay-based cellular networks. Their statistical properties are quite different from typical cellular radio channels, thereby requiring new methods for their simulation. This paper proposes a double-ring model to simulate the mobile-to-mobile local scattering environment, and develops sum-of-sinusoids (SoS)-based models for simulating such channels. The proposed models produce waveforms having desired statistical properties with good accuracy, and also remove some drawbacks of an existing model derived by using the discrete line spectrum simulation method.

Resolution enhancement of spectra using differentiation

The analysis of measured spectra, when it reduces to finding the positions and heights of spectral lines, becomes an extremely difficult problem when the lines are closely spaced and broadened to the point where overlapping occurs, and explicit models for the shape of the peaks are unknown. For the widely used nonlinear fitting methods, good starting values cannot be found by direct inspection of the spectra. Sometimes, it is even impossible to determine the number of overlapping spectral lines. Resolution enhancement procedures aim to undo the broadening in order to go back towards the original situation. Traditional resolution rules-of-thumb, such as the Rayleigh, Houston and Sparrow criteria, must be replaced by computational procedures which invoke appropriate assumptions about the broadening of the spectral lines. Measured spectra can be viewed as convolutions between known smooth kernels and discrete line spectra. In this way, the determination of positions and heights of the spectral lines can be recast as a deconvolution problem. Unfortunately, the theory which guarantees the effectiveness of deconvolution requires smoothness of the solution and, as a consequence, does not apply to discrete line spectra. However, discrete line spectra only need to be approximated by spectral peaks which satisfy the smoothness criteria required by the regularization theory in order to formulate a suitable deconvolution framework. In this paper, the corresponding deconvolution problem is solved effectively using a numerical differentiation procedure which plays a derivative spectroscopy enhancement role. When compared with similar deconvolution methods, its enhanced performance is confirmed by theoretical error analysis which identifies a sense in which this method has best possible convergence rates. In practice, the method provides good starting values for the positions of the lines for the nonlinear fitting methods. Sometimes, the ‘starting values’ are so good that a subsequent nonlinear fitting step is not necessary. By modelling the spectra as probability measures in an appropriate Hilbert space framework, estimates are derived that characterize the nature of the smoothing performed by the regularization recovery methodology proposed. The paper concludes with an examination, using the Hilbert space framework, of the trade-off between resolution and the various types of error that occur in a measured spectrum.

Factors affecting the UV emission from pulsed surface discharges

The emission properties of pulsed electrical discharges propagating across the surfaces of PET, PP, PTFE, UPVC, and PVDF in various gases have been investigated. The optical spectra from the discharges have been recorded over the 200-500 nm bandwidth and the effect of the interaction between the pulsed discharge and the substrate material studied. The gases used were air, argon, and SF/sub 6/ at pressures in the range 0.1-1 bar. In comparison to the other gases, SF/sub 6/ was found to produce the most intense continuum and line emission within the 200-300 nm spectral region. The substrate material was found to affect both the intensity of continuum spectra and the content of the discrete line spectra. When PTFE was employed, the continuum spectra was more intense compared to that of the other materials. In contrast, the use of PVC resulted in a considerable modification to the composition of the discrete line spectra.

'Two-level', Stokes, and anti-Stokes pumping of a nuclear gamma laser with anisotropic hidden inversion

Recoil in radiative gamma transitions leads to a discrete line spectrum of absorption and emission resonances in an ensemble of free nuclei. This opens up the possibility of efficient pumping of such nuclei and of hidden inversion in an nonstandard 'optical' scheme without participation of the third auxiliary level, as well as in Stokes and anti-Stokes schemes. Quantitative estimates are given for several nuclides.

Many-electron singularity in aggregate X-ray line and photoelectron spectra

It is generally admitted that the many-electron effects govern the shape of the discrete X-ray line and photoemission spectra. This phenomenon has been studied in bulk metals (Mahan, Nozieres and de Dominicis model) where it is characterized by two effects: the Anderson orthogonality between the initial and final ground states and the $$|E|^{\alpha _H - 1} $$ spectrum behaviour, whereE is the emitted particle energy defect (with respect to the one-electron energy) and α H (with 0<α H <1) and exponent related to the phase shifts δ at the Fermi level due to the localised hole potential. We study these two effects in limited media (closed loop shape withN=10 to 30 atoms). We observe that, asN increases, the ground state overlap tends toward zero in a way which is surprisingly close to the Anderson $$N^{ - \alpha _H /2} $$ behaviour. TheE spectra are also obtained. They are very different from the bulk which will lead to asymmetry parameters smaller for aggregates than for the bulk. A discussion of the experimental results is presented.

Relationship between forced expiratory flow and tracheal sounds. Possible effect of vortices on flow.

We measured both tracheal sounds and forced expiratory flows simultaneously in 20 normal subjects and 4 patients with stenosis of the main bronchus. Spectral analysis of the tracheal sounds revealed development of discrete line spectra, the frequencies of which ranged between 488 and 942 Hz. There was a positive correlation between these frequencies and the peak flows (r = 0.601). We speculate that the origin of these line spectra are vortices rather than the vibrations of the wall. It is postulated that the pressure drops caused by vortices make the airways more susceptible to collapse and may lead to flow limitation.