Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles

Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function f(x, v; t). Adopting an alternative approach, previously introduced for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.

Nonlinear Field Line Random Walk and Generalized Compound Diffusion of Charged Particles

A new nonlinear theory for the perpendicular transport of charged particles is presented. This approach is based on an improved nonlinear treatment of field line random walk in combination with a generalized compound diffusion model. The generalized compound diffusion model is much more systematic and reliable, in comparison to previous theories. Furthermore, the new theory shows remarkably good agreement with test-particle simulations and heliospheric observations.

Towards a Critical Ecology of Child Development: Aligning the Theories of Bronfenbrenner and Bourdieu

Bronfenbrenner’s model of bio-ecological development has been utilized widely within the social sciences, in the field of human development, and in social work. Yet, while championing the rights of marginalised families and communities, Bronfenbrenner had under-theorized the role of power, agency and structure in shaping the ‘person-context’ interrelationship, life opportunities and social well-being. To respond to this deficit, this paper firstly outlines Bronfenbrenner’s ‘person, process, context, time’ model. Secondly, it then seeks to loosely align aspects of Bronfenbrenner’s model with Bourdieu’s analytical categories of habitus, field and capital. It is argued that these latter categories enable social workers to develop a critical ecology of child development, taking account of power and the interplay between agency and structure. The implications of the alignment for child and family social work are considered in the final section.