Linear Half-Space Problems in Kinetic Theory: Abstract Formulation and Regime Transitions

Half-space problems in the kinetic theory of gases are of great importance in the study of the asymptotic behavior of solutions of boundary value problems for the Boltzmann equation for small Knudsen numbers. In this work a generally formulated half-space problem, based on generalizations of stationary half-space problems in one spatial variable for the Boltzmann equation - for hard-sphere models of monatomic single species and multicomponent mixtures - is considered. The number of conditions on the indata at the interface needed to obtain well-posedness is investigated. Exponential fast convergence is obtained "far away" from the interface. In particular, the exponential decay at regime transitions - where the number of conditions on the indata needed to obtain well-posedness changes - for linearized kinetic half-space problems related to the half-space problem of evaporation and condensation in kinetic theory are considered. The regime transitions correspond to the transition between subsonic and supersonic evaporation/condensation, or the transition between evaporation and condensation. Near the regime transitions, slowly varying modes might occur, preventing uniform exponential speed of convergence there. By imposing extra conditions on the indata at the interface, the slowly varying modes can be eliminated near a regime transition, giving rise to uniform exponential speed of convergence near the regime transition. Values of the velocity of the flow at the far end, for which regime transitions take place are presented for some particular variants of the Boltzmann equation: for monatomic and polyatomic single species and mixtures, and the quantum variant for bosons and fermions.Comment: 37 page

Compactness property of the linearized Boltzmann collision operator for a multicomponent polyatomic gas

The linearized Boltzmann collision operator is fundamental in many studies of the Boltzmann equation and its main properties are of substantial importance. The decomposition into a sum of a positive multiplication operator, the collision frequency, and an integral operator is trivial. Compactness of the integral operator for monatomic single species is a classical result, while corresponding results for monatomic mixtures and polyatomic single species are more recently obtained. This work concerns the compactness of the operator for a multicomponent mixture of polyatomic species, where the polyatomicity is modeled by a discrete internal energy variable. With a probabilistic formulation of the collision operator as a starting point, compactness is obtained by proving that the integral operator is a sum of Hilbert-Schmidt integral operators and operators, which are uniform limits of Hilbert-Schmidt integral operators, under some assumptions on the collision kernel. The assumptions are essentially generalizations of the Grad's assumptions for monatomic single species. Self-adjointness of the linearized collision operator follows. Moreover, bounds on - including coercivity of - the collision frequency are obtained for a hard sphere like model. Then it follows that the linearized collision operator is a Fredholm operator, and its domain is also obtained.Comment: 32 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:2201.01365, arXiv:2201.0137

On the clinical assessment of persistent fatigue and pain

Patients with persistent fatigue and pain, most of them women, often struggle with decreased function and related concerns. They commonly receive an inconclusive investigation and a delayed diagnosis. Neuropathic aspects of the condition may be missed. Clinical screening is vital because it can support medical and healthcare decision-making early in the course of an illness. Two go-to tools of the typical assessment, the Beighton score and the pain drawing, are appreciated in praxis but lack substantial evidence base. The overarching aim of this thesis was to contribute to improvements in the management and diagnostics for these patients. All research questions originated from clinical praxis. The studies are based on data from one group among the very large population of patients who have persistent fatigue and pain: those presenting with suspected myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS). In study I, the Beighton score was evaluated within clinical routine assessment for its capacity to identify a physique with systemic joint laxity. Systemic joint laxity is a risk factor for developing persistent health issues and should warrant considerations in treatment. Normally, this feature would need to be assessed routinely in the investigation of persistent fatigue or pain. This study involved different competencies of the assessors (physician and physiotherapist). Despite these differences and a lack of joint training in the method, inter-rater reliability was acceptable, demonstrating the stability of the Beighton score as a measurement. The sum score, however, must not be interpreted as a definitive answer regarding whether systemic joint laxity is present but must be read instead within the context of a targeted medical history. Study II concerned the pain drawing used to assess body pain extent. Methods of interpretation, however, have not been standardized in clinic and little evidence is available regarding its use for assessing the cervical spine. Study II involved evaluation of a method of screening for cervicogenic headache using a standardized reading in which a predefined C2 pain pattern was applied. Dizziness/imbalance was strongly associated with the C2 pain pattern and those who presented with this pattern had more severe pain and lower health-related quality of life compared with those who did not present with it. Thus, the pain drawing with the C2 pain pattern could distinguish patients with a more complex pain picture. The strong association with dizziness/imbalance strengthened the relevance of the pattern in clinical assessment of cervicogenic headache. Paper III describes self-perceived health in the population with persistent fatigue and pain, from a biopsychosocial perspective. A comparison was made for two subgroups within the study population – those diagnosed with ME/CFS and those who were not but had a related symptom picture. Data were collected with several questionnaires on health-related factors. Characteristics of ME/CFS in this context were impaired tolerance for exertion (mental or physical), impaired energy levels, worse pain, and poorer general health. No between-group differences were found for signs of anxiety and depression, mental role functioning, and mental well-being, so that the identified ME/CFS characteristics did not emerge as causal in the health status of the ME /CFS- subgroup. In conclusion, the Beighton score and the pain drawing can aid in determining the nature and degree of a condition with persistent fatigue and pain. They appear to be tools to retain in the clinical assessment. Screening with the pain drawing also may be beneficial in supporting a patient-centred management and merits further development within the clinical assessment. The experience patients have with ME/CFS places this condition at the far end of the spectrum of persistent fatigue and pain

Compactness property of the linearized Boltzmann collision operator for a mixture of monatomic and polyatomic species

The linearized Boltzmann collision operator has a central role in many important applications of the Boltzmann equation. Recently some important classical properties of the linearized collision operator for monatomic single species were extended to multicomponent monatomic gases and polyatomic single species. For multicomponent polyatomic gases, the case where the polyatomicity is modelled by a discrete internal energy variable was considered lately. Here we considers the corresponding case for a continuous internal energy variable. Compactness results, saying that the linearized operator can be decomposed into a sum of a positive multiplication operator, the collision frequency, and a compact operator, bringing e.g., self-adjointness, is extended from the classical result for monatomic single species, under reasonable assumptions on the collision kernel. With a probabilistic formulation of the collision operator as a starting point, the compactness property is shown by a decomposition, such that the terms are, or at least are uniform limits of, Hilbert-Schmidt integral operators and therefore are compact operators. Moreover, bounds on - including coercivity of - the collision frequency are obtained for a hard sphere like, as well as hard potentials with cutoff like, models, from which Fredholmness of the linearized collision operator follows, as well as its domain.Comment: 38 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2212.02160, arXiv:2201.01365, arXiv:2201.0137

Inverse photoemission in strongly correlated electron systems

Based on exact results for small clusters of 2D t-J model we demonstrate the existence of several distinct `channels' in its inverse photoemission (IPES) spectrum. Hole-like quasiparticles can either be annihilated completely, or leave behind a variable number of spin excitations, which formed the `dressing cloud' of the annihilated hole. In the physical parameter regime the latter processes carry the bulk of IPES weight and although the Fermi surface takes the form of hole pockets, the distribution of spectal weight including these `magnon-bands' in the IPES spectrum is reminiscent of free electrons. The emerging scenario for Fermiology and spectral weight distribution is shown to be consistent with photoemission, inverse photemission and de Haas--van Alphen experiments on cuprate superconductors.Comment: Revtex file, 4 PRB pages + three figures appended as uu-encoded postscript. Hardcopies of figures (or the entire manuscript) can also be obtained by e-mail request to: [email protected]

International Business Potential for Analytics of Room Utilization

Many universities worldwide have large campuses which they are trying to maintain and administer in the best way possible. Their infrastructure often includes numerous auditoriums with access to the Internet by the Wi-Fi standard. MazeMap and Cisco have developed a solution which can geographically track Wi-Fi clients within a building. This solution makes it possible to count the number of people in a room through depersonalized data. On an international level, the student numbers are increasing and many space and timetable managers are struggling to find enough lecture halls for their students. The occupancy status of a room at any given time can thus be crucial information for them. This thesis aims to find the international business potential for the Wi-Fi analytics service from MazeMap. The technological solution has some limitations, and they are assessed with emphasis on their commercial impact. In order to investigate the business potential, a global space management survey has been conducted and the market has been investigated. The survey received 60 responses. In the results, 61.7% of the institutions had shortages of larger lecture halls and 35.6% were struggling with the efficiency of use. 13.3% were willing to pay an annual subscription fee of more than $35,000 for a solution that could help them optimize their utilization by 20%. There was a correlation between the willingness to pay and space shortages. The investigation found that the utilization rates predicted by scheduled lecture hours were higher than the actual rates in many cases. After contributing to the survey, one British university made an enquiry for more information about the service, and stated that they were looking for such a service. They further indicated that they could be interested in participating in a pilot project. The British market showed the more promising results, while Australia, Canada and Switzerland share some characteristics and findings which could indicate a similar demand. Based on the findings and results, a business model proposal was built. The model includes bundling and possible integration with timetable systems, and was designed with the Business Model Canvas

Hold thou My Hand

https://digitalcommons.library.umaine.edu/mmb-me/1093/thumbnail.jp

ADHD i arbeidslivet. En kvalitativ studie av mennesker med ADHD sine opplevelser og behov for tilrettelegging i arbeidslivet

Denne masteroppgaven har som formål å vise utfordringer så vel som fordeler med ADHD diagnosen knyttet til det å fungere i samfunnet. Jeg har brukt kvalitativ forskningsmetode og intervjuet syv personer med ADHD, hvor vi får innblikk i deres erfaringer med utdanning og arbeidsliv. Studien tar for seg hvordan disse menneskene har fungert i skolesammenheng, i arbeidslivet og livet generelt. Litteraturen som er brukt i oppgaven er stemplingsteori belyst med Goffman og Becker sine teorier om avvik. ADHD diagnosen bærer med seg stigma ettersom den i mange tilfeller kan være ganske synlig i form av for eksempel hyperaktivitet. Medikaliseringsbergrepet gir også et bredere bilde av temaet og brukes i denne studien til å gi en bedre forståelse av hva det vil si å faktisk få diagnosen, da det for mange er det en lettelse når de kan sette en merkelapp på sine utfordringer. Arbeidslivet er en arena de aller fleste av oss skal innom i løpet av livet, og der skal man forhåpentligvis tilbringe mange år. Derfor er det viktig at dette er en plass hvor man føler på mestring og tilhørighet. Litteratur om arbeidslivet og NAV sin posisjon i forhold til personer med ADHD viser hvor viktig tilrettelegging er for de som trenger det. Forskning viser at det er lettere for personer med ADHD å falle utenfor arbeidslivet og at mange sliter på skolen. Dette er bakgrunn for at jeg har ønsket å finne ut om det er behov for tilrettelegging i arbeidslivet