Trajectories in Logarithmic Potentials

Trajectories in logarithmic potentials are investigated by taking as example the motion of an electron within a cylindrical capacitor. The solution of the equation of motion in plane polar coordinates, (r,{\phi}) is attained by forming a series expansion of r and of 1/r as a function of {\phi}. The terms of the series contain polynomials, the recurrence relation of which is given, together with some further characteristics. By the comparison-theorem of infinite series, the convergence of the solution is demonstraded. The simplest trajectories in logarithmic potentials are represented by rosette type orbits with a period of 4{\pi}/3, and by circular paths.Comment: 17 pages, 5 figure

Combining music and life story work to enhance participation in family interaction in semantic dementia: a longitudinal study of one family's experience.

Background: Semantic dementia is a rarer dementia, classified as a type of frontotemporal dementia and a variant of primary progressive aphasia. Studies examining conversation in this condition and interventions to enhance participation in family life present as gaps in the research literature. Methods: Working with one family on a longitudinal basis, this study used conversation analysis and narrative analysis to provide a detailed assessment of communication . This information was used to design an individually tailored life story intervention to facilitate family interaction: a co-produced life story music DVD. Results: This intervention offered the family a resource that allowed the person with semantic dementia to display areas of retained competence and enhanced participation in interaction in a way that was not typically present in everyday conversation. Conclusions: It is argued that fostering greater opportunities for such in-the-moment connections is an important goal for intervention, particularly when language may be significantly compromised

The effect of improvisational music therapy on the treatment of depression: protocol for a randomised controlled trial

Background. Music therapy is frequently offered to individuals suffering from depression. Despite the lack of research into the effects of music therapy on this population, anecdotal evidence suggests that the results are rather promising. The aim of this study is to examine whether improvisational, psychodynamically orientated music therapy in an individual setting helps reduce symptoms of depression and improve other health-related outcomes. In particular, attention will be given to mediator agents, such as musical expression and interaction in the sessions, as well as to the explanatory potential of EEG recordings in investigating emotion related music perception of individuals with depression. Methods. 85 adults (18–50 years of age) with depression (ICD-10: F 32 or F33) will be randomly assigned to an experimental or a control condition. All participants will receive standard care, but the experimental group will be offered biweekly sessions of improvisational music therapy over a period of 3 months. A blind assessor will measure outcomes before testing, after 3 months, and after 6 months. Discussion. This study aims to fill a gap in knowledge as to whether active (improvisational) music therapy applied to people with depression improves their condition. For the first time in this context, the mediating processes, such as changes in musical expression and interaction during the course of therapy, will be objectively investigated, and it is expected that the results will provide new insights into these processes. Furthermore, the findings are expected to reveal whether music related emotional experiences, as measured by EEG, can be utilized in assessing a depressive client's improvement in the therapy. The size and the comprehensiveness of the study are sufficient for generalizing its findings to clinical practice as well as to further music therapy research. Trial registration. ISRCTN84185937peerReviewe

HOMESIDE: Home-based family caregiver-delivered music and reading interventions for people living with dementia: Protocol of a randomised controlled trial

Introduction: Pharmacological interventions to address behavioural and psychological symptoms of dementia (BPSD) can have undesirable side effects, therefore non-pharmacological approaches to managing symptoms may be preferable. Past studies show that music therapy can reduce BPSD, and other studies have explored how formal caregivers use music in their caring roles. However, no randomised study has examined the effects on BPSD of music interventions delivered by informal caregivers (CGs) in the home setting. Our project aims to address the need for improved informal care by training cohabiting family CGs to implement music interventions that target BPSD, and the quality of life (QoL) and well-being of people with dementia (PwD) and CGs. Methods and analysis: A large international three-arm parallel-group randomised controlled trial will recruit a sample of 495 dyads from Australia, Germany, UK, Poland and Norway. Dyads will be randomised equally to standard care (SC), a home-based music programme plus SC, or a home-based reading programme plus SC for 12 weeks. The primary outcome is BPSD of PwD (measured using the Neuropsychiatric Inventory-Questionnaire). Secondary outcomes will examine relationship quality between CG and PwD, depression, resilience, competence, QoL for CG and QoL for PwD. Outcomes will be collected at baseline, at the end of the 12-week intervention and at 6 months post randomisation. Resource Utilisation in Dementia will be used to collect economic data across the life of the intervention and at 6-month follow-up. We hypothesise that the music programme plus SC will generate better results than SC alone (primary comparison) and the reading programme plus SC (secondary comparison). Ethics and dissemination: Ethical approval has been obtained for all countries. Results will be presented at national and international conferences and published in scientific journals and disseminated to consumer and caregiver representatives and the community