Luminescence decays with underlying distributions: General properties and analysis with mathematical functions

In this work, an analysis of the general properties of the luminescence decay law is carried out. The conditions that a luminescence decay law must satisfy in order to correspond to a probability density function of rate constants are established. From an analysis of the general form of the luminescence decay law, it is concluded that the decay must be either exponential or sub-exponential for all times, in order to be represented by a distribution of rate constants H(k). Sub-exponentiality is nevertheless not a sufficient condition. Only decays that are completely monotonic have a probability density function of rate constants. The construction of the decay function from cumulant and moment expansions is studied, as well as the corresponding calculation of H(k) from a cumulant expansion. The asymptotic behavior of the decay laws is considered in detail, and the relation between this behavior and the form of H(k) for small k is explored. Several generalizations of the exponential decay function, namely the Kohlrausch, Becquerel, Mittag-Leffler and Heaviside decay functions, as well as the Weibull and truncated Gaussian rate constant distributions are discussed.     

Transverse pressure distributions in a simple model ear canal occluded by a hearing aid test fixture

The sound field in a model ear canal with a hearing aid test fixture has been investigated experimentally and theoretically. Large transverse variations of sound pressure level, as much as 20 dB at 8 kHz, were found across the inner face of the hearing aid. Variations are greatest near the outlet port of the receiver and the vent port. Deeper into the canal, the transverse variations are less significant and, at depths greater than 4 mm, only a longitudinal variation remains. The model canal was cylindrical, 7.5 mm diameter, and terminated with a Zwislocki coupler to represent absorption by the human middle ear. The outer end of the canal was driven by the receiver in the hearing aid test fixture, with the acoustic output entering the canal through a 1 mm port. The hearing aid was provided with a 20-mm-long vent, either 1 or 2 mm in diameter. The sound field inside the canal was measured using a specially designed 0.2-mm-diam probe microphone [Daigle and Stinson, J. Acoust. Soc. Am. 116, 2618 (2004)]. In parallel, calculations of the interior sound field were performed using a boundary element technique and found to agree well with measurements.     

How the cross-sectional discontinuity between ear canal and probe affects the ear canal length estimation

Many ear canal probes both deliver and measure sound via narrow tubes. This study investigates the effect of the cross-sectional discontinuity at the interface between ear canal models and the connecting tubes of a commercially available otoacoustic emission probe on the "acoustically" estimated cavity lengths. Rigid cavities having the same length but different diameters were produced, and modeled by the finite element method. Cavities with a diameter larger than 8 mm had acoustic lengths that considerably overestimated the real geometry. A length correction was derived, which, in most applications, compensates for the measurement errors emerging from the discontinuity effects.     

Diffusion,peer pressure,and tailed distributions

We present a general, physically motivated nonlinear and nonlocal advection equation in which the diffusion of interacting random walkers competes with a local drift arising from a kind of peer pressure. We show, using a mapping to an integrable dynamical system, that on varying a parameter the steady-state behavior undergoes a transition from the standard diffusive behavior to a localized stationary state characterized by a tailed distribution. Finally, we show that recent empirical laws on economic growth can be explained as a collective phenomenon due to peer pressure interaction.     

The mathematical background of chemical reactor analysis: I. Preliminaries. Batch reactors

The name “chemical reaction engineering” has been given to the branch of chemical engineering that focusses on the conditions which make for useful chemical transformation. Within this subdiscipline there are studies related primarily to the static and dynamic behavior of the reactor and of these the more analytical are rich in mathematical problems. In this paper the preliminary considerations of stoicheiometry, thermodynamics and chemical kinetics are outlined as background to a discussion of the batch reactor. The characteristic problems of other important reactor types will be taken up in a sequel.     

Parton distributions: a new global analysis

We present a new analysis of parton distributions of the proton. This incorporates a wide range of new data, an improved treatment of heavy flavours and a re-examination of prompt photon production. The new set (MRST) shows systematic differences from previous sets of partons which can be identified with particular features of the new data and with improvements in the analysis. We also investigate the sensitivities of the results to (i) the uncertainty in the determination of the gluon at large , (ii) the value of and (iii) the minimum cut on the data that are included in the global fit. Received: 23 March 1998 / Published online: 23 June 1998     

Synchronization and control in intrinsic and designed computation: an information-theoretic analysis of competing models of stochastic computation

We adapt tools from information theory to analyze how an observer comes to synchronize with the hidden states of a finitary, stationary stochastic process. We show that synchronization is determined by both the process's internal organization and by an observer's model of it. We analyze these components using the convergence of state-block and block-state entropies, comparing them to the previously known convergence properties of the Shannon block entropy. Along the way we introduce a hierarchy of information quantifiers as derivatives and integrals of these entropies, which parallels a similar hierarchy introduced for block entropy. We also draw out the duality between synchronization properties and a process's controllability. These tools lead to a new classification of a process's alternative representations in terms of minimality, synchronizability, and unifilarity.     

A mathematical analysis: From memristor to fracmemristor

The memristor is also a basic electronic component, just like resistors, capacitors and inductors. It is a nonlinear device with memory characteristics. In 2008, with HP's announcement of the discovery of the TiO₂ memristor, the new memristor system, memory capacitor (memcapacitor) and memory inductor (meminductor) were derived. Fractional-order calculus has the characteristics of non-locality, weak singularity and long term memory which traditional integer-order calculus does not have, and can accurately portray or model real-world problems better than the classic integer-order calculus. In recent years, researchers have extended the modeling method of memristor by fractional calculus, and proposed the fractional-order memristor, but its concept is not unified. This paper reviews the existing memristive elements, including integer-order memristor systems and fractional-order memristor systems. We analyze their similarities and differences, give the derivation process, circuit schematic diagrams, and an outlook on the development direction of fractional-order memristive elements.     

Estimation of eardrum acoustic pressure and of ear canal length from remote points in the canal

Sound pressure distributions in the human ear canal, whether unoccluded or occluded with ear molds, were studied using a probe tube technique. On average, for frequencies below 6 kHz, the measuring probe tube had to be placed within 8 mm of the vertical plane containing the top of the eardrum (TOD), determined optically, in order to obtain sound pressure magnitudes within 6 dB of "eardrum pressure." To obtain that accuracy in all of the eight subjects studied, the probe had to be within 6 mm of the TOD. Since probe location relative to the drum has to be known, a purely acoustic method was developed which can be conveniently used to localize the probe-tip position, utilizing the standing wave property of the sound pressure in the ear canal. The acoustically estimated "drum location" generally lay between the optically determined vertical planes containing the TOD and the umbo. On average, the "drum location" fell 1 mm medial to the TOD. Of the 32 estimates made acoustically in various occluded and unoccluded conditions in 14 subjects, 30 estimates lay within a +/- 2-mm range of this average.     

Johnson's SB distribution function as applied in the mathematical representation of particle size distributions. Part 1: Theoretical background and numerical simulation

An investigation was carried out of the transformation between the number, length, surface and volume size distributions expressed by Johnson's S_B distribution function – the bounded log-normal distribution function. As is well known, if any of the number, length, surface and volume distributions is log-normal, all the others will also be log-normal. Theoretical analysis suggests that the S_B function may have a similar property. This was confirmed by a computer-aided numerical simulation, in which emphasis was given to the transformation between successive order size distributions, i.e. ?_i(x) → ?_{i + 1}(x) or ?_i(x) → ?_{i ? 1}(x). The numerical results can be applied to the particle size distribution transformation because this transformation can generally be made step by step, for example, ?_i → ?_i?1 (x) → ?_{i ? 2}(x) → … → ?_j(x) for ?_i(x) → ?_j(x) ( i > j).     

Angular distributions of elastic and quasi elastic heavy-ion collisions. pattern analysis

From classical in-beam spectroscopy on the¹⁰⁶Cd+¹²C reaction, unambiguousγ-ray assignments have been done for¹¹⁶Xe,¹¹⁶I and¹¹⁶Te nuclei. The ground band levels observed in¹¹⁶Xe have been compared to those of heavier even-even xenon isotopes and to the IBA theoretical predictions. In addition, using the newγ-ray assignments, evaporation cross-sections of the¹¹⁸Xe compound nucleus have been estimated and compared to the evaporation model calculations.     

Single InAs/GaAs quantum dots: Photocurrent and cross-sectional AFM analysis

Photocurrent (PC) spectroscopy is employed to study the carrier escape from self-assembled InAs/GaAs quantum dots (QDs) embedded in a Schottky photodiode structure. As a function of the applied field, we detect a shift of the exciton ground-state transition due to the quantum-confined Stark effect (). The tunneling time, which is directly related to the observed photocurrent linewidth due to τ/(2Γ), changes by a factor of five in the photocurrent regime. The measured linewidth dependency on the electric field is modeled by a simple 1D WKB approximation for the tunneling process, which shows that the energetic position of the wetting layer is important for the measured tunneling time out of the dot. In addition to that we present cross-sectional atomic force measurements (AFM) of the investigated photodiode structure. The method needs a minimum of time and sample preparation (cleaving and etching) to obtain the dot density, dot distribution, and give an estimate of the dot dimensions. Etching only the cleaved surface of the sample opens up the opportunity to determine the properties of a buried dot layer before or even after device fabrication.     

Ear canal acoustic distortion at 2f1-f2 from human ears: relation to other emissions and perceived combination tones

Two aspects of the intermodulation distortion product at 2f1-f2 generated by normal human ears and measured acoustically in the ear canal were studied: (1) its relation to tone-evoked and spontaneous otoacoustic emissions, and (2) its relation to the perceived combination tone at the same frequency. With regard to (1), substantial differences among ears in the detectability of emissions were observed; ears tended to exhibit all or none of the emission types that were sought. Within ears possessing emissions, the magnitudes of tone-evoked emissions and acoustic distortion showed a similar dependence on frequency. With regard to (2), a three-primary-tone stimulus was employed to ask whether the ear canal acoustic distortion tone is canceled under the same stimulus conditions that produce perceptual cancellation. Simultaneous cancellation of perceptual and acoustic distortion was produced rarely. Results are interpreted qualitatively with a model in which primary tones produce distortion at their interaction region within the cochlea; this distortion propagates to the distortion-frequency place where it mediates perception. This same distortion wave produces emission components at additional locations, including the primary-tone interaction region, which sum vectorially to mediate the emitted acoustic distortion product.     

Physical and mathematical analysis of a wind model

Summary We have carried out a mathematical and physical analysis of the instabilities present in a one-layer wind model. The single terms of the basic equation have been discussed, pointing out their influence on the accuracy of the solution and their relationship to the possible instabilities. Possible improvements of the model in different directions are indicated in the final discussion.

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Riassunto Si effettua un’analisi matematica e fisica delle instabilità presenti nel modello del vento ad uno strato. Si discutono i singoli termini dell’equazione di base, sottolineando la loro influenza sulla accuratezza della soluzione e la loro relazione con le instabilità possibili. Nella discussione finale si indicano possibili miglioramenti del modello in diverse direzioni.

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Резюме Проводится математический и физический анализ неустойчивостей, возникающих в одно-слойной модели ветра. Обсуждаются отдельные члены базисного уравнения. Отмечается влияние этих членов на точность решения и их связь с возможными неустойчивостями. Указываются возможные улучцения обсуждаемой модели в различных напавлениях.

     

Introduction to focus issue: mixed mode oscillations: experiment, computation, and analysis

Mixed mode oscillations (MMOs) occur when a dynamical system switches between fast and slow motion and small and large amplitude. MMOs appear in a variety of systems in nature, and may be simple or complex. This focus issue presents a series of articles on theoretical, numerical, and experimental aspects of MMOs. The applications cover physical, chemical, and biological systems.     

Solar particle event dose and dose-rate distributions: parameterization of dose-time profiles, with subsequent dose-rate analysis.

Calculations of total dose and equivalent dose as functions of time, as well as dose-rate and equivalent dose rate since event start are presented for fifteen of the larger solar particle events that occurred during the period between November 1987 and August 1991. The doses, dose-equivalents, and rates presented are for exposures to the skin, ocular lens, and bone marrow behind a thickness of aluminum shielding which provides protection comparable to that of a thin spacecraft. The calculated dose vs time profiles are parameterized using a Weibull cumulative distribution as the fitting function. Parameters are determined using least-squares techniques. Fitted curves are then differentiated to produce smoothed dose-rate curves for each of the events. These results provide a useful starting point for the development of methods to predict the cumulative doses and times to reach various dose limits from a limited number of dosimeter measurements early in the evolution of a solar particle event.     

Quantum computation: Algorithms and Applications

As the prospect of commercial quantum computers turns ever more real in recent times, research in quantum algorithms becomes the center of attention. Due to the strong parallelism of quantum computing in Hilbert space, ordinarily intractable calculation problems could now be solved very efficiently with non-classical means. To exploit parallelism, creative quantum algorithms are required so that efficient quantum oracles can be tailor-designed to specific computation needs. Therefore, in the quest for quantum supremacy, quantum algorithms and their related applications are as important as the quantum computer hardware. This article covers the basic concepts of quantum computation and reviews some important quantum algorithms and their applications.