479 research outputs found
Some examples of exponentially harmonic maps
The aim of this paper is to study some examples of exponentially harmonic
maps. We study such maps firstly on flat euclidean and Minkowski spaces and
secondly on Friedmann-Lema\^ itre universes. We also consider some new models
of exponentially harmonic maps which are coupled with gravity which happen to
be based on a generalization of the lagrangian for bosonic strings coupled with
dilatonic field.Comment: 16 pages, 5 figure
A Mass Bound for Spherically Symmetric Black Hole Spacetimes
Requiring that the matter fields are subject to the dominant energy
condition, we establish the lower bound for the
total mass of a static, spherically symmetric black hole spacetime. ( and denote the area and the surface gravity of the horizon,
respectively.) Together with the fact that the Komar integral provides a simple
relation between and the strong energy condition,
this enables us to prove that the Schwarzschild metric represents the only
static, spherically symmetric black hole solution of a selfgravitating matter
model satisfying the dominant, but violating the strong energy condition for
the timelike Killing field at every point, that is, .
Applying this result to scalar fields, we recover the fact that the only black
hole configuration of the spherically symmetric Einstein-Higgs model with
arbitrary non-negative potential is the Schwarzschild spacetime with constant
Higgs field. In the presence of electromagnetic fields, we also derive a
stronger bound for the total mass, involving the electromagnetic potentials and
charges. Again, this estimate provides a simple tool to prove a ``no-hair''
theorem for matter fields violating the strong energy condition.Comment: 16 pages, LATEX, no figure
Are there static texture?
We consider harmonic maps from Minkowski space into the three sphere. We are
especially interested in solutions which are asymptotically constant, i.e.
converge to the same value in all directions of spatial infinity. Physical
3-space can then be compactified and can be identified topologically (but not
metrically!) with a three sphere. Therefore, at fixed time, the winding of the
map is defined. We investigate whether static solutions with non-trivial
winding number exist. The answer which we can proof here is only partial: We
show that within a certain family of maps no static solutions with non-zero
winding number exist. We discuss the existing static solutions in our family of
maps. An extension to other maps or a proof that our family of maps is
sufficiently general remains an open problem.Comment: 12 page Latex file, 1 postscript figure, submitted to PR
Examining the Evidence Base for Forensic Case Formulation: An Integrative Review of Recent Research
In the past decade, forensic case formulation (FCF) has become a key activity in many forensic services. However, the evidence base for FCF remains limited. This integrative review aimed to identify and evaluate all FCF research conducted since the lack of understanding within this field was highlighted by several academics in 2011. A rigorous literature search led to the identification of 14 studies fitting the inclusion criteria. Studies were critically evaluated and synthesised to create a summary of the recent research, to identify remaining gaps in our understanding, and to create an agenda for future research
QCD Strings as Constrained Grassmannian Sigma Model:
We present calculations for the effective action of string world sheet in R3
and R4 utilizing its correspondence with the constrained Grassmannian sigma
model. Minimal surfaces describe the dynamics of open strings while harmonic
surfaces describe that of closed strings. The one-loop effective action for
these are calculated with instanton and anti-instanton background, reprsenting
N-string interactions at the tree level. The effective action is found to be
the partition function of a classical modified Coulomb gas in the confining
phase, with a dynamically generated mass gap.Comment: 22 pages, Preprint: SFU HEP-116-9
Is diagnosis enough to guide interventions in mental health? Using case formulation in clinical practice
While diagnosis has traditionally been viewed as an essential concept in medicine, particularly when selecting treatments, we suggest that the use of diagnosis alone may be limited, particularly within mental health. The concept of clinical case formulation advocates for collaboratively working with patients to identify idiosyncratic aspects of their presentation and select interventions on this basis. Identifying individualized contributing factors, and how these could influence the person\u27s presentation, in addition to attending to personal strengths, may allow the clinician a deeper understanding of a patient, result in a more personalized treatment approach, and potentially provide a better clinical outcome.<br /
Calibrated Sub-Bundles in Non-Compact Manifolds of Special Holonomy
This paper is a continuation of math.DG/0408005. We first construct special
Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on
the cotangent bundle of S^n by looking at the conormal bundle of appropriate
submanifolds of S^n. We find that the condition for the conormal bundle to be
special Lagrangian is the same as that discovered by Harvey-Lawson for
submanifolds in R^n in their pioneering paper. We also construct calibrated
submanifolds in complete metrics with special holonomy G_2 and Spin(7)
discovered by Bryant and Salamon on the total spaces of appropriate bundles
over self-dual Einstein four manifolds. The submanifolds are constructed as
certain subbundles over immersed surfaces. We show that this construction
requires the surface to be minimal in the associative and Cayley cases, and to
be (properly oriented) real isotropic in the coassociative case. We also make
some remarks about using these constructions as a possible local model for the
intersection of compact calibrated submanifolds in a compact manifold with
special holonomy.Comment: 20 pages; for Revised Version: Minor cosmetic changes, some
paragraphs rewritten for improved clarit
Mean Curvature Flow of Spacelike Graphs
We prove the mean curvature flow of a spacelike graph in of a map from a closed Riemannian
manifold with to a complete Riemannian manifold
with bounded curvature tensor and derivatives, and with
sectional curvatures satisfying , remains a spacelike graph,
exists for all time, and converges to a slice at infinity. We also show, with
no need of the assumption , that if , or if and
, constant, any map is trivially
homotopic provided where
, in case , and
in case . This largely extends some known results for
constant and compact, obtained using the Riemannian structure
of , and also shows how regularity theory on the mean
curvature flow is simpler and more natural in pseudo-Riemannian setting then in
the Riemannian one.Comment: version 5: Math.Z (online first 30 July 2010). version 4: 30 pages:
we replace the condition by the the weaker one .
The proofs are essentially the same. We change the title to a shorter one. We
add an applicatio
Constant-angle surfaces in liquid crystals
We discuss some properties of surfaces in R3 whose unit normal has constant angle with an assigned direction field. The constant angle condition can be rewritten as an Hamilton-Jacobi equation correlating the surface and the direction field. We focus on examples motivated by the physics of interfaces in liquid crystals and of layered fluids, and discuss the properties of the constant-angle surfaces when the direction field is singular along a line (disclination) or at a point (hedgehog defect
A class of extremising sphere-valued maps with inherent maximal tori symmetries in SO(n)
In this paper we consider an energy functional depending on the norm of the gradient and seek to extremise it over an admissible class of Sobolev maps defined on an annulus and taking values on the unit sphere whilst satisfying suitable boundary conditions. We establish the existence of an infinite family of solutions with certain symmetries to the associated nonlinear Euler-Lagrange system in even dimensions and discuss the stability of such extremisers by way of examining the positivity of the second variation of the energy at these solutions
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