123 research outputs found
Two sides of a coin: a critical review, and mathematical and phenomenological study of what we call hydromechanical coupling
In this paper a brief and critical review of the current literature on hydro-mechanical coupling is presented. Furthermore, anenhanced discrete element model is used to investigate the mutual relationship of soil water retention curve and suction stress curves and how the two are affected as a result of change in the initial porosity of the soil sample. The model revealed the suction stress values in wetting were less affected as in drying branch as a result of the change in the initial porosity of the soil sample
Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
We present a star product for noncommutative spaces of Lie type, including
the so called ``canonical'' case by introducing a central generator, which is
compatible with translations and admits a simple, manageable definition of an
invariant integral. A quasi-cyclicity property for the latter is shown to hold,
which reduces to exact cyclicity when the adjoint representation of the
underlying Lie algebra is traceless. Several explicit examples illuminate the
formalism, dealing with kappa-Minkowski spacetime and the Heisenberg algebra
(``canonical'' noncommutative 2-plane).Comment: 21 page
A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
We define and discuss classical and quantum gravity in 2+1 dimensions in the
Galilean limit. Although there are no Newtonian forces between massive objects
in (2+1)-dimensional gravity, the Galilean limit is not trivial. Depending on
the topology of spacetime there are typically finitely many topological degrees
of freedom as well as topological interactions of Aharonov-Bohm type between
massive objects. In order to capture these topological aspects we consider a
two-fold central extension of the Galilei group whose Lie algebra possesses an
invariant and non-degenerate inner product. Using this inner product we define
Galilean gravity as a Chern-Simons theory of the doubly-extended Galilei group.
The particular extension of the Galilei group we consider is the classical
double of a much studied group, the extended homogeneous Galilei group, which
is also often called Nappi-Witten group. We exhibit the Poisson-Lie structure
of the doubly extended Galilei group, and quantise the Chern-Simons theory
using a Hamiltonian approach. Many aspects of the quantum theory are determined
by the quantum double of the extended homogenous Galilei group, or Galilei
double for short. We study the representation theory of the Galilei double,
explain how associated braid group representations account for the topological
interactions in the theory, and briefly comment on an associated
non-commutative Galilean spacetime.Comment: 38 pages, 1 figure, references update
q-Quaternions and q-deformed su(2) instantons
We construct (anti)instanton solutions of a would-be q-deformed su(2)
Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant
noncommutative space] by reinterpreting the function algebra on the latter as a
q-quaternion bialgebra. Since the (anti)selfduality equations are covariant
under the quantum group of deformed rotations, translations and scale change,
by applying the latter we can generate new solutions from the one centered at
the origin and with unit size. We also construct multi-instanton solutions. As
they depend on noncommuting parameters playing the roles of `sizes' and
`coordinates of the centers' of the instantons, this indicates that the moduli
space of a complete theory will be a noncommutative manifold. Similarly, gauge
transformations should be allowed to depend on additional noncommutative
parameters.Comment: Latex file, 39 pages. Final version appeared in JM
Lattice Gauge Theory
We reformulate the Hamiltonian approach to lattice gauge theories such that,
at the classical level, the gauge group does not act canonically, but instead
as a Poisson-Lie group. At the quantum level, it then gets promoted to a
quantum group gauge symmetry. The theory depends on two parameters - the
deformation parameter and the lattice spacing . We show that the
system of Kogut and Susskind is recovered when , while
QCD is recovered in the continuum limit (for any ). We thus have the
possibility of having a two parameter regularization of QCD.Comment: 26 pages, LATEX fil
Improving communication between postgraduate researchers and the university library: a case study at De Montfort University Library and Learning Services
A well-established postgraduate researcher development program has existed at De Montfort University for many years. Library and Learning Services include modules on literature searching skills and critical appraisal. However, we recognized that researchers seemed to be disengaged with the services on offer. This concern informed a research project that considered the ways we could communicate better with researchers based on their needs. This paper explores the essential components of successful communication, such as context, timeliness and communication channels. An action-research approach was taken including focus groups and online surveys. The outcomes highlighted three significant crisis points, emphasizing the key times when researchers might need some intervention. The findings of this research identified the distinct needs of Postgraduate Researchers (PGRs) and how relevant and timely communication from the library can meet these needs. It also considers the impact of how communication has improved with researchers as a result of some of our interventions
Introduction to Quantum-Gravity Phenomenology
After a brief review of the first phase of development of Quantum-Gravity
Phenomenology, I argue that this research line is now ready to enter a more
advanced phase: while at first it was legitimate to resort to heuristic
order-of-magnitude estimates, which were sufficient to establish that
sensitivity to Planck-scale effects can be achieved, we should now rely on
detailed analyses of some reference test theories. I illustrate this point in
the specific example of studies of Planck-scale modifications of the
energy/momentum dispersion relation, for which I consider two test theories.
Both the photon-stability analyses and the Crab-nebula synchrotron-radiation
analyses, which had raised high hopes of ``beyond-Plankian'' experimental
bounds, turn out to be rather ineffective in constraining the two test
theories. Examples of analyses which can provide constraints of rather wide
applicability are the so-called ``time-of-flight analyses'', in the context of
observations of gamma-ray bursts, and the analyses of the cosmic-ray spectrum
near the GZK scale.Comment: 46 pages, LaTex. Based on lectures given at the 40th Karpacz Winter
School in Theoretical Physic
Hopf algebras and Markov chains: Two examples and a theory
The operation of squaring (coproduct followed by product) in a combinatorial
Hopf algebra is shown to induce a Markov chain in natural bases. Chains
constructed in this way include widely studied methods of card shuffling, a
natural "rock-breaking" process, and Markov chains on simplicial complexes.
Many of these chains can be explictly diagonalized using the primitive elements
of the algebra and the combinatorics of the free Lie algebra. For card
shuffling, this gives an explicit description of the eigenvectors. For
rock-breaking, an explicit description of the quasi-stationary distribution and
sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes
will only appear on the version on Amy Pang's website, the arXiv version will
not be updated.
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