54 research outputs found
A Pedagogy of Vulnerability: its Relevance to Diversity Teaching and ‘Humanising’ Higher Education
This paper attempts to unpack and propose an alternative to a frequent resistance towards generating discussion and exploration of uncomfortable or controversial topics within university teaching, in conjunction with encouraging academics to experiment with modelling authentic and courageous dialogues when addressing topics focussing on diversity, difference and intersectionality in the classroom. It presents reflections on adopting a ‘pedagogy of vulnerability’ in teaching and learning within higher education which dismantles the hierarchical dynamics of power between educators and learners. Via cultivating a co-learner stance for pursuing knowledge and wisdom, an activist motivation towards addressing matters of identity and social justice emerges. The qualities and practices of the vulnerable educator are described alongside their positive impact upon student participation, empowerment and engagement without ignoring the challenges and pitfalls of such approach in the context of institutional politics. Using the example of its application within teaching a counselling and psychotherapy degree at a university setting, it concludes with insights and a vision for its role in serving a more humane and relational higher education and an invitation for considering such a pedagogic approach in the context of different disciplines
Exploring the perceptions of Greek counsellors’ and counselling psychologists’ professional identity and training experience, through the lens of the first alumni graduates of a Greek state University
The field of Counselling as a profession and that of Counselling Psychology is a relatively new and developing discipline in Greece. As in other European countries, it is only in the recent years that this postgraduate training started to be delivered by a state/national University Institution in Greece. The present study focused on attempting to capture the qualitative experience of the first two cohorts of graduates from the 1st postgraduate programme in Counselling and Counselling Psychology delivered by the National and Kapodistrian University of Athens in collaboration with the Democritus University of Thrace. This data was collected via two focused group interviews using a thematic analysis approach which facilitated the immersion of the following main themes: motivating factors (for choosing such discipline), reflections on placements, the role of personal development, the evolving professional identity, issues of professional recognition, opportunities for employment, vision for the future.
In conclusion, the participants expressed the opinion that the provision of such a postgraduate programme by a Greek University was delivered in a rigorous way with high standards and has equipped them with the reflexivity and critical thinking required to build their professional identity and influence the developments still to come
Efficient integration of the variational equations of multi-dimensional Hamiltonian systems: Application to the Fermi-Pasta-Ulam lattice
We study the problem of efficient integration of variational equations in
multi-dimensional Hamiltonian systems. For this purpose, we consider a
Runge-Kutta-type integrator, a Taylor series expansion method and the so-called
`Tangent Map' (TM) technique based on symplectic integration schemes, and apply
them to the Fermi-Pasta-Ulam (FPU-) lattice of nonlinearly
coupled oscillators, with ranging from 4 to 20. The fast and accurate
reproduction of well-known behaviors of the Generalized Alignment Index (GALI)
chaos detection technique is used as an indicator for the efficiency of the
tested integration schemes. Implementing the TM technique--which shows the best
performance among the tested algorithms--and exploiting the advantages of the
GALI method, we successfully trace the location of low-dimensional tori.Comment: 14 pages, 6 figure
Low-dimensional q-Tori in FPU Lattices: Dynamics and Localization Properties
This is a continuation of our study concerning q-tori, i.e. tori of low
dimensionality in the phase space of nonlinear lattice models like the
Fermi-Pasta-Ulam (FPU) model. In our previous work we focused on the beta FPU
system, and we showed that the dynamical features of the q-tori serve as an
interpretational tool to understand phenomena of energy localization in the FPU
space of linear normal modes. In the present paper i) we employ the method of
Poincare - Lindstedt series, for a fixed set of frequencies, in order to
compute an explicit quasi-periodic representation of the trajectories lying on
q-tori in the alpha model, and ii) we consider more general types of initial
excitations in both the alpha and beta models. Furthermore we turn into
questions of physical interest related to the dynamical features of the q-tori.
We focus on particular q-tori solutions describing low-frequency `packets' of
modes, and excitations of a small set of modes with an arbitrary distribution
in q-space. In the former case, we find formulae yielding an exponential
profile of energy localization, following an analysis of the size of the
leading order terms in the Poincare - Lindstedt series. In the latter case, we
explain the observed localization patterns on the basis of a rigorous result
concerning the propagation of non-zero terms in the Poincare - Lindstedt series
from zeroth to subsequent orders. Finally, we discuss the extensive (i.e.
independent of the number of degrees of freedom) properties of some q-tori
solutions.Comment: To appear in Physica D, 34 pages, 9 figure
Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method
As originally formulated, the Generalized Alignment Index (GALI) method of
chaos detection has so far been applied to distinguish quasiperiodic from
chaotic motion in conservative nonlinear dynamical systems. In this paper we
extend its realm of applicability by using it to investigate the local dynamics
of periodic orbits. We show theoretically and verify numerically that for
stable periodic orbits the GALIs tend to zero following particular power laws
for Hamiltonian flows, while they fluctuate around non-zero values for
symplectic maps. By comparison, the GALIs of unstable periodic orbits tend
exponentially to zero, both for flows and maps. We also apply the GALIs for
investigating the dynamics in the neighborhood of periodic orbits, and show
that for chaotic solutions influenced by the homoclinic tangle of unstable
periodic orbits, the GALIs can exhibit a remarkable oscillatory behavior during
which their amplitudes change by many orders of magnitude. Finally, we use the
GALI method to elucidate further the connection between the dynamics of
Hamiltonian flows and symplectic maps. In particular, we show that, using for
the computation of GALIs the components of deviation vectors orthogonal to the
direction of motion, the indices of stable periodic orbits behave for flows as
they do for maps.Comment: 17 pages, 9 figures (accepted for publication in Int. J. of
Bifurcation and Chaos
Energy localization on q-tori, long term stability and the interpretation of FPU recurrences
We focus on two approaches that have been proposed in recent years for the
explanation of the so-called FPU paradox, i.e. the persistence of energy
localization in the `low-q' Fourier modes of Fermi-Pasta-Ulam nonlinear
lattices, preventing equipartition among all modes at low energies. In the
first approach, a low-frequency fraction of the spectrum is initially excited
leading to the formation of `natural packets' exhibiting exponential stability,
while in the second, emphasis is placed on the existence of `q-breathers', i.e
periodic continuations of the linear modes of the lattice, which are
exponentially localized in Fourier space. Following ideas of the latter, we
introduce in this paper the concept of `q-tori' representing exponentially
localized solutions on low-dimensional tori and use their stability properties
to reconcile these two approaches and provide a more complete explanation of
the FPU paradox.Comment: 38 pages, 7 figure
A new class of integrable Lotka–Volterra systems
A parameter-dependent class of Hamiltonian (generalized) Lotka–Volterra systems is considered. We prove that this class contains Liouville integrable as well as superintegrable cases according to particular choices of the parameters. We determine sufficient conditions which result in integrable behavior, while we numerically explore the complementary cases, where these analytically derived conditions are not satisfied
Discrete Symmetry and Stability in Hamiltonian Dynamics
In this tutorial we address the existence and stability of periodic and
quasiperiodic orbits in N degree of freedom Hamiltonian systems and their
connection with discrete symmetries. Of primary importance in our study are the
nonlinear normal modes (NNMs), i.e periodic solutions which represent
continuations of the system's linear normal modes in the nonlinear regime. We
examine the existence of such solutions and discuss different methods for
constructing them and studying their stability under fixed and periodic
boundary conditions. In the periodic case, we employ group theoretical concepts
to identify a special type of NNMs called one-dimensional "bushes". We describe
how to use linear combinations such NNMs to construct s(>1)-dimensional bushes
of quasiperiodic orbits, for a wide variety of Hamiltonian systems and exploit
the symmetries of the linearized equations to simplify the study of their
destabilization. Applying this theory to the Fermi Pasta Ulam (FPU) chain, we
review a number of interesting results, which have appeared in the recent
literature. We then turn to an analytical and numerical construction of
quasiperiodic orbits, which does not depend on the symmetries or boundary
conditions. We demonstrate that the well-known "paradox" of FPU recurrences may
be explained in terms of the exponential localization of the energies Eq of
NNM's excited at the low part of the frequency spectrum, i.e. q=1,2,3,....
Thus, we show that the stability of these low-dimensional manifolds called
q-tori is related to the persistence or FPU recurrences at low energies.
Finally, we discuss a novel approach to the stability of orbits of conservative
systems, the GALIk, k=2,...,2N, by means of which one can determine accurately
and efficiently the destabilization of q-tori, leading to the breakdown of
recurrences and the equipartition of energy, at high values of the total energy
E.Comment: 50 pages, 13 figure
- …