title: Nonlinear development of the kink instability in coronal flux tubes

authors: Craig, Ian J.D.

abstract: Solar prominences and flares are believed to be caused by rapid release of magnetic energy stored in coronal magnetic fields. Recent studies of the linear phase of ideal MHD instabilities has shown that energy release is slow and weak, so it is therefore important to study the nonlinear phase to see if this provides a mechanism for significant energy release. In this paper we describe a Lagrangian numerical scheme for simulating nonlinear evolution of ideal MHD equilibria and apply it to an unstable finite Gold-Hoyle flux tube, line-tied to perfectly conducting endplates. The ensuing kink instability develops considerably faster than linear theory would predict, and eventually (over typically 100 Alfvén time scales) a new kinked equilibrium is attained, in which current sheets appear to be present. Little magnetic energy is lost in the ideal MHD phase, but resistive instabilities in the current sheets could lead to much more explosive energy release. Numerical studies of nonlinear interactions indicate that growth of the unstable kink mode is suppressed by the presence of other modes, which offers a possible explanation of the observed longevity of coronal loops.

text: Nonlinear development of the kink instability in coronal flux tubes Solar prominences and flares are believed to be caused by rapid release of magnetic energy stored in coronal magnetic fields. Recent studies of the linear phase of ideal MHD instabilities has shown that energy release is slow and weak, so it is therefore important to study the nonlinear phase to see if this provides a mechanism for significant energy release. In this paper we describe a Lagrangian numerical scheme for simulating nonlinear evolution of ideal MHD equilibria and apply it to an unstable finite Gold-Hoyle flux tube, line-tied to perfectly conducting endplates. The ensuing kink instability develops considerably faster than linear theory would predict, and eventually (over typically 100 Alfvén time scales) a new kinked equilibrium is attained, in which current sheets appear to be present. Little magnetic energy is lost in the ideal MHD phase, but resistive instabilities in the current sheets could lead to much more explosive energy release. Numerical studies of nonlinear interactions indicate that growth of the unstable kink mode is suppressed by the presence of other modes, which offers a possible explanation of the observed longevity of coronal loops.

year: 1990

title: Divisibility by 3 of even multiperfect numbers of abundancy 3 and 4

authors: Broughan, Kevin A.

subjects: maths

abstract: We say a number is flat if it can be written as a non-trivial power of 2 times an odd squarefree number. The power is the “exponent” and the number of odd primes the “length”. Let N be flat and 4-perfect with exponent a and length m. If a ≢ 1 mod 12, then a is even. If a is even and 3 ∤ N then m is also even. If a ≡ 1 mod 12 then 3 | N and m is even. If N is flat and 3-perfect and 3 ∤ N, then if a a ≡ 1 mod 12, a is even. If
a ≡ 1 mod 12 then m is odd. If N is flat and 3 or 4-perfect then it is divisible by at least one Mersenne prime, but not all odd prime divisors are Mersenne. We also give some conditions for the divisibility by 3 of an arbitrary even 4-perfect number.

text: Divisibility by 3 of even multiperfect numbers of abundancy 3 and 4 We say a number is flat if it can be written as a non-trivial power of 2 times an odd squarefree number. The power is the “exponent” and the number of odd primes the “length”. Let N be flat and 4-perfect with exponent a and length m. If a ≢ 1 mod 12, then a is even. If a is even and 3 ∤ N then m is also even. If a ≡ 1 mod 12 then 3 | N and m is even. If N is flat and 3-perfect and 3 ∤ N, then if a a ≡ 1 mod 12, a is even. If
a ≡ 1 mod 12 then m is odd. If N is flat and 3 or 4-perfect then it is divisible by at least one Mersenne prime, but not all odd prime divisors are Mersenne. We also give some conditions for the divisibility by 3 of an arbitrary even 4-perfect number.

year: 2010

title: Media coverage of 'decades of disparity' in ethnic mortality in Aotearoa.

authors: Hodgetts, Darrin

subjects: psychology

abstract: For some time we have known that factors such as economic prosperity, community cohesion, and social justice bear on health. These societal influences are particularly pertinent to the health of indigenous groups, such as Maori, who are still responding to processes of colonization. In July 2003 the New Zealand Ministry of Health published a report entitled  Decades of Disparity , which proposed (among other things) that neoliberal policies of the last two decades impacted negatively on mortality rates for Maori and Pacific peoples, when compared with Pakeha. In this article we explore media coverage of this report through analyses of media releases, radio, television and newspaper items. It is argued that as the story evolved media increasingly challenged the importance of societal determinants of health, preferring individual level explanations. As a result coverage failed to give due emphasis to structural health concerns for Maori, which necessitate social change.

text: Media coverage of 'decades of disparity' in ethnic mortality in Aotearoa. For some time we have known that factors such as economic prosperity, community cohesion, and social justice bear on health. These societal influences are particularly pertinent to the health of indigenous groups, such as Maori, who are still responding to processes of colonization. In July 2003 the New Zealand Ministry of Health published a report entitled  Decades of Disparity , which proposed (among other things) that neoliberal policies of the last two decades impacted negatively on mortality rates for Maori and Pacific peoples, when compared with Pakeha. In this article we explore media coverage of this report through analyses of media releases, radio, television and newspaper items. It is argued that as the story evolved media increasingly challenged the importance of societal determinants of health, preferring individual level explanations. As a result coverage failed to give due emphasis to structural health concerns for Maori, which necessitate social change.

year: 2004