Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Stress and Resilience in Combat-Related PTSD: Integration of Psychological Theory and Biological Mechanisms

Post-traumatic stress disorder (PTSD) is a debilitating psychiatric disorder that has a major impact on the ability to function effectively in daily life. PTSD may develop as a response to exposure to an event or events perceived as potentially harmful or life-threatening. It has high prevalence rates in the community, especially among vulnerable groups such as military personnel or those in emergency services. Despite extensive research in this field, the underlying mechanisms of the disorder remain largely unknown. The identification of risk factors for PTSD has posed a particular challenge as there can be delays in onset of the disorder, and most people who are exposed to traumatic events will not meet diagnostic criteria for PTSD. With the advent of the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM V), the classification for PTSD has changed from an anxiety disorder into the category of stress- and trauma-related disorders. This has the potential to refocus PTSD research on the nature of stress and the stress response relationship. This review focuses on some of the important findings from psychological and biological research based on early models of stress and resilience. Improving our understanding of PTSD by investigating both genetic and psychological risk and coping factors that influence stress response, as well as their interaction, may provide a basis for more effective and earlier intervention.

Information theory and resistance fluctuations in one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor we propose a distribution of maximum information entropy, constrained by the following physical requirements: (1) flux conservation, (2) time-reversal invariance, and (3) scaling with the length of the conductor of the two lowest cumulants of ω, where R=exp(iω→⋅Jbhat). The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

Microclimate and gas emissions in dairy buildings : Instrumentation, theory and measurements

The aim of this thesis was to develop measurement techniques and systems for measuring air quality and to provide information about air quality conditions and the amount of gaseous emissions from semi-insulated and uninsulated dairy buildings in Finland and Estonia. Specialization and intensification in livestock farming, such as in dairy production, is usually accompanied by an increase in concentrated environmental emissions. In addition to high moisture, the presence of dust and corrosive gases, and widely varying gas concentrations in dairy buildings, Finland and Estonia experience winter temperatures reaching below -40 ºC and summer temperatures above +30 ºC. The adaptation of new technologies for long-term air quality monitoring and measurement remains relatively uncommon in dairy buildings because the construction and maintenance of accurate monitoring systems for long-term use are too expensive for the average dairy farmer to afford. Though the documentation of accurate air quality measurement systems intended mainly for research purposes have been made in the past, standardised methods and the documentation of affordable systems and simple methods for performing air quality and emissions measurements in dairy buildings are unavailable. In this study, we built three measurement systems: 1) a Stationary system with integrated affordable sensors for on-site measurements, 2) a Wireless system with affordable sensors for off-site measurements, and 3) a Mobile system consisting of expensive and accurate sensors for measuring air quality. In addition to assessing existing methods, we developed simplified methods for measuring ventilation and emission rates in dairy buildings. The three measurement systems were successfully used to measure air quality in uninsulated, semi-insulated, and fully-insulated dairy buildings between the years 2005 and 2007. When carefully calibrated, the affordable sensors in the systems gave reasonably accurate readings. The spatial air quality survey showed high variation in microclimate conditions in the dairy buildings measured. The average indoor air concentration for carbon dioxide was 950 ppm, for ammonia 5 ppm, for methane 48 ppm, for relative humidity 70%, and for inside air velocity 0.2 m/s. The average winter and summer indoor temperatures during the measurement period were -7º C and +24 ºC for the uninsulated, +3 ºC and +20 ºC for the semi-insulated and +10 ºC and +25 ºC for the fully-insulated dairy buildings. The measurement results showed that the uninsulated dairy buildings had lower indoor gas concentrations and emissions compared to fully insulated buildings. Although occasionally exceeded, the ventilation rates and average indoor air quality in the dairy buildings were largely within recommended limits. We assessed the traditional heat balance, moisture balance, carbon dioxide balance and direct airflow methods for estimating ventilation rates. The direct velocity measurement for the estimation of ventilation rate proved to be impractical for naturally ventilated buildings. Two methods were developed for estimating ventilation rates. The first method is applicable in buildings in which the ventilation can be stopped or completely closed. The second method is useful in naturally ventilated buildings with large openings and high ventilation rates where spatial gas concentrations are heterogeneously distributed. The two traditional methods (carbon dioxide and methane balances), and two newly developed methods (theoretical modelling using Fick s law and boundary layer theory, and the recirculation flux-chamber technique) were used to estimate ammonia emissions from the dairy buildings. Using the traditional carbon dioxide balance method, ammonia emissions per cow from the dairy buildings ranged from 7 g day-1 to 35 g day-1, and methane emissions per cow ranged from 96 g day-1 to 348 g day-1. The developed methods proved to be as equally accurate as the traditional methods. Variation between the mean emissions estimated with the traditional and the developed methods was less than 20%. The developed modelling procedure provided sound framework for examining the impact of production systems on ammonia emissions in dairy buildings.

On the propagation of a weak shock front: Theory and application

In this paper the kinematics of a weak shock front governed by a hyperbolic system of conservation laws is studied. This is used to develop a method for solving problems, involving the propagation of nonlinear unimodal waves. It consists of first solving the nonlinear wave problem by moving along the bicharacteristics of the system and then fitting the shock into this solution field, so that it satisfies the necessary jump conditions. The kinematics of the shock leads in a natural way to the definition of ldquoshock-raysrdquo, which play the same role as the ldquoraysrdquo in a continuous flow. A special case of a circular cylinder introduced suddenly in a constant streaming flow is studied in detail. The shock fitted in the upstream region propagates with a velocity which is the mean of the velocities of the linear and the nonlinear wave fronts. In the downstream the solution is given by an expansion wave.

Non-Abelian monopoles break color. II. Field theory and quantum mechanics

Many grand unified theories (GUT's) predict non-Abelian monopoles which are sources of non-Abelian (and Abelian) magnetic flux. In the preceding paper, we discussed in detail the topological obstructions to the global implementation of the action of the "unbroken symmetry group" H on a classical test particle in the field of such a monopole. In this paper, the existence of similar topological obstructions to the definition of H action on the fields in such a monopole sector, as well as on the states of a quantum-mechanical test particle in the presence of such fields, are shown in detail. Some subgroups of H which can be globally realized as groups of automorphisms are identified. We also discuss the application of our analysis to the SU(5) GUT and show in particular that the non-Abelian monopoles of that theory break color and electroweak symmetries.

Using Lifespan developmental theory and methods as a viable alternative to the study of generational differences at work

I agree with Costanza and Finkelstein (2015) that it is futile to further invest in the study of generational differences in the work context due to a lack of appropriate theory and methods. The key problem with the generations concept is that splitting continuous variables such as age or time into a few discrete units involves arbitrary cutoffs and atheoretical groupings of individuals (e.g., stating that all people born between the early 1960s and early 1980s belong to Generation X). As noted by methodologists, this procedure leads to a loss of information about individuals and reduced statistical power (MacCallum, Zhang, Preacher, & Rucker, 2002). Due to these conceptual and methodological limitations, I regard it as very difficult if not impossible to develop a “comprehensive theory of generations” (Costanza & Finkelstein, p. 20) and to rigorously examine generational differences at work in empirical studies.

Influences on novice drivers' speed selection - a systematic review: Application and limitations of theory and methodology

Background Excessive speed is a primary contributing factor to young novice road trauma, including intentional and unintentional speeds above posted limits or too fast for conditions. The objective of this research was to conduct a systematic review of recent investigations into novice drivers’ speed selection, with particular attention to applications and limitations of theory and methodology. Method Systematic searches of peer-reviewed and grey literature were conducted during September 2014. Abstract reviews identified 71 references potentially meeting selection criteria of investigations since the year 2000 into factors that influence (directly or indirectly) actual speed (i.e., behaviour or performance) of young (age <25 years) and/or novice (recently-licensed) drivers. Results Full paper reviews resulted in 30 final references: 15 focused on intentional speeding and 15 on broader speed selection investigations. Both sets identified a range of individual (e.g., beliefs, personality) and social (e.g., peer, adult) influences, were predominantly theory-driven and applied cross-sectional designs. Intentional speed investigations largely utilised self-reports while other investigations more often included actual driving (simulated or ‘real world’). The latter also identified cognitive workload and external environment influences, as well as targeted interventions. Discussion and implications Applications of theory have shifted the novice speed-related literature beyond a simplistic focus on intentional speeding as human error. The potential to develop a ‘grand theory’ of intentional speeding emerged and to fill gaps to understand broader speed selection influences. This includes need for future investigations of vehicle-related and physical environment-related influences and methodologies that move beyond cross-sectional designs and rely less on self-reports.

Refractory boron compounds for high performance: Theory and experiment

We have shown that novel synthesis methods combined with careful evaluation of DFT phonon calculations provides new insight into boron compounds including a capacity to predict Tc for AlB2-type superconductors.

The Systems Theory Framework of career development: 20 years of contribution to theory and practice

The development and sustained contribution of the Systems Theory Framework to career development theory and practice is well documented in national and international literatures. In addition to its contribution to theory integration, it has added to the growing literature on connecting career theory and practice, in particular for non-Western populations. In addition, it has been the basis of the development of a broad array of constructivist approaches to career counselling, and indeed specific reflective career assessment activities. This article begins with a brief history of the Systems Theory Framework which is then followed by a rationale for its development. The contribution of the Systems Theory Framework to theory and practice is then described prior to concluding comments by the authors.

Scattering theory and the discrete linear optimal control problem

This paper deals with the interpretation of the discrete-time optimal control problem as a scattering process in a discrete medium. We treat the discrete optimal linear regulator, constrained end-point and servo and tracking problems, providing a unified approach to these problems. This approach results in an easy derivation of the desired results as well as several new ones.

Precipitate growth with composition-dependent diffusivity: Comparison between theory and phase field simulations

We consider the growth of an isolated precipitate when the matrix diffusivity depends on the composition. We have simulated precipitate growth using the Cahn-Hilliard model, and find good agreement between our results and those from a sharp interface theory for systems with and without a dilatational misfit. With misfit, we report (and rationalize) an interesting difference between systems with a constant diffusivity and those with a variable diffusivity in the matrix.

Thermoelectric power in ultrathin films, quantum wires and carbon nanotubes under classically large magnetic field: Simplified theory and relative comparison

We study the thermoelectric power under classically large magnetic field (TPM) in ultrathin films (UFs), quantum wires (QWs) of non-linear optical materials on the basis of a newly formulated electron dispersion law considering the anisotropies of the effective electron masses, the spin-orbit splitting constants and the presence of the crystal field splitting within the framework of k.p formalism. The results of quantum confined III-V compounds form the special cases of our generalized analysis. The TPM has also been studied for quantum confined II-VI, stressed materials, bismuth and carbon nanotubes (CNs) on the basis of respective dispersion relations. It is found taking quantum confined CdGeAs2, InAs, InSb, CdS, stressed n-InSb and Bi that the TPM increases with increasing film thickness and decreasing electron statistics exhibiting quantized nature for all types of quantum confinement. The TPM in CNs exhibits oscillatory dependence with increasing carrier concentration and the signature of the entirely different types of quantum systems are evident from the plots. Besides, under certain special conditions, all the results for all the materials gets simplified to the well-known expression of the TPM for non-degenerate materials having parabolic energy bands, leading to the compatibility test. (C) 2009 Elsevier B.V. All rights reserved.

Binding of nucleobases with single-walled carbon nanotubes: Theory and experiment

We report the binding energy of various nucleobases (guanine (G), adenine (A), thymine (T) and cytosine (C)) with (5,5) single-walled carbon nanotube (SWNT) calculated using first-principle Hartre–Fock method (HF) together with classical force field. The binding energy without including the solvation effects of water decreases in the order G>A>T>C. The inclusion of solvation energy changes the order of binding preference to be G>T>A>C. Using isothermal titration (micro) calorimetry experiments, we also show the relative binding affinity to be T>A>C, in agreement with our calculations.