2,951 research outputs found
On the Geometric Principles of Surface Growth
We introduce a new equation describing epitaxial growth processes. This
equation is derived from a simple variational geometric principle and it has a
straightforward interpretation in terms of continuum and microscopic physics.
It is also able to reproduce the critical behavior already observed, mound
formation and mass conservation, but however does not fit a divergence form as
the most commonly spread models of conserved surface growth. This formulation
allows us to connect the results of the dynamic renormalization group analysis
with intuitive geometric principles, whose generic character may well allow
them to describe surface growth and other phenomena in different areas of
physics
Dynamic Scaling of Non-Euclidean Interfaces
The dynamic scaling of curved interfaces presents features that are
strikingly different from those of the planar ones. Spherical surfaces above
one dimension are flat because the noise is irrelevant in such cases. Kinetic
roughening is thus a one-dimensional phenomenon characterized by a marginal
logarithmic amplitude of the fluctuations. Models characterized by a planar
dynamical exponent , which include the most common stochastic growth
equations, suffer a loss of correlation along the interface, and their dynamics
reduce to that of the radial random deposition model in the long time limit.
The consequences in several applications are discussed, and we conclude that it
is necessary to reexamine some experimental results in which standard scaling
analysis was applied
Stochastic growth equations on growing domains
The dynamics of linear stochastic growth equations on growing substrates is
studied. The substrate is assumed to grow in time following the power law
, where the growth index is an arbitrary positive number.
Two different regimes are clearly identified: for small the interface
becomes correlated, and the dynamics is dominated by diffusion; for large
the interface stays uncorrelated, and the dynamics is dominated by
dilution. In this second regime, for short time intervals and spatial scales
the critical exponents corresponding to the non-growing substrate situation are
recovered. For long time differences or large spatial scales the situation is
different. Large spatial scales show the uncorrelated character of the growing
interface. Long time intervals are studied by means of the auto-correlation and
persistence exponents. It becomes apparent that dilution is the mechanism by
which correlations are propagated in this second case.Comment: Published versio
Geometrical approach to tumor growth
Tumor growth has a number of features in common with a physical process known
as molecular beam epitaxy. Both growth processes are characterized by the
constraint of growth development to the body border, and surface diffusion of
cells/particles at the growing edge. However, tumor growth implies an
approximate spherical symmetry that makes necessary a geometrical treatment of
the growth equations. The basic model was introduced in a former article [C.
Escudero, Phys. Rev. E 73, 020902(R) (2006)], and in the present work we extend
our analysis and try to shed light on the possible geometrical principles that
drive tumor growth. We present two-dimensional models that reproduce the
experimental observations, and analyse the unexplored three-dimensional case,
for which new conclusions on tumor growth are derived
How the experience of being diagnosed with borderline personality disorder affects relations with others and one’s self-perception - an existential phenomenological study
Having worked as a psychologist in both the UK and Lima, Peru, working with
patients who present a variety of conditions ranging from a depression to severe cases
of schizophrenia, I became concerned by the way in which patients reacted to their
diagnoses and in particular by the negative response of patients diagnosed with
Borderline Personality Disorder (BPD). I also perceived that the lack of a clear and
accepted diagnosis caused significant confusion regarding the condition for patients,
carers and professionals. This led me to question the value of the diagnoses in the
process of understanding and helping people with emotional distress or psychological
problems. This study is a response to my experience and the experience participants
expressed through me
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