442 research outputs found
Pierre Duhemâs philosophy and history of science
LEITE (FĂĄbio Rodrigo) â STOFFEL (Jean-François), Introduction (pp. 3-6). BARRA (Eduardo Salles de O.) â SANTOS (Ricardo Batista dos), Duhemâs analysis of Newtonian method and the logical priority of physics over metaphysics (pp. 7-19). BORDONI (Stefano), The French roots of Duhemâs early historiography and epistemology (pp. 20-35). CHIAPPIN (JosĂ© R. N.) â LARANJEIRAS (CĂĄssio Costa), Duhemâs critical analysis of mechaÂniÂcism and his defense of a formal conception of theoretical phyÂsics (pp. 36-53). GUEGUEN (Marie) â PSILLOS (Stathis), Anti-Âscepticism and epistemic humility in Pierre Duhemâs philosophy of science (pp. 54-72). LISTON (Michael), Duhem : images of science, historical continuity, and the first crisis in physics (pp. 73-84). MAIOCCHI (Roberto), Duhem in pre-war Italian philosÂophy : the reasons of an absence (pp. 85-92). HERNĂNDEZ MĂRQUEZ (VĂctor Manuel), Was Pierre Duhem an «esprit de finesse» ? (pp. 93-107). NEEDHAM (Paul), Was Duhem justified in not distinguishing between physical and chemical atomism ? (pp. 108-111). OLGUIN (Roberto Estrada), «Bon sens» and «noĂ»s» (pp. 112-126). OLIVEIRA (Amelia J.), Duhemâs legacy for the change in the historiography of science : An analysis based on Kuhnâs writings (pp. 127-139). PRĂNCIPE (JoĂŁo), PoincarĂ© and Duhem : Resonances in their first epistemological reflecÂtions (pp. 140-156). MONDRAGON (DamiĂĄn Islas), Book review of «Pierre Duhem : entre fĂsica y metafĂsica» (pp. 157-159). STOFFEL (Jean-François), Book review of P. Duhem : «La thĂ©orie physique : son objet, sa structure» / edit. by S. Roux (pp. 160-162). STOFFEL (Jean-François), Book review of St. Bordoni : «When historiography met epistemology» (pp. 163-165)
Estudio sobre convergencia y dinåmica de los métodos de Newton, Stirling y alto orden
Las matemĂĄticas, desde el origen de esta ciencia, han estado al servicio de la
sociedad tratando de dar respuesta a los problemas que surgĂan. Hoy en dĂa sigue
siendo asĂ, el desarrollo de las matemĂĄticas estĂĄ ligado a la demanda de otras
ciencias que necesitan dar soluciĂłn a situaciones concretas y reales.
La mayorĂa de los problemas de ciencia e ingenierĂa no pueden resolverse
usando ecuaciones lineales, es por tanto que hay que recurrir a las ecuaciones no
lineales para modelizar dichos problemas (Amat, 2008; véase también Argyros y
Magreñån, 2017, 2018), entre otros. El conflicto que presentan las ecuaciones no
lineales es que solo en unos pocos casos es posible encontrar una soluciĂłn Ășnica,
por tanto, en la mayor parte de los casos, para resolverlas hay que recurrir a los
métodos iterativos. Los métodos iterativos generan, a partir de un punto inicial,
una sucesiĂłn que puede converger o no a la soluciĂłn
Recommended from our members
Numerical modelling of tidal flows in the Arabian gulf
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The main purpose of this thesis is the prediction of tidal movements in the Gulf, which are essential factors for shipping,
fishing, and coast protection. The search for suitable predictions of tide propagation and flow problems has undergone a great
advance with the arrival of the digital computer. The development of numerical methods permits the formulation of different
efficient hydrodynamic models to compute every tide phenomenon with precision and to handle a great amount of information. A two dimensional hydrodynamic model for tidal flow in the Arabian Gulf is developed. The basic hydrodynamic equations are solved with an explicit finite difference method using a staggered grid to reproduce the various tidal constituents in the Arabian Gulf Tidal forcing term at the open boundary (Strait of Harmouz) is approximated in a novel way. A detailed discussion is presented on the treatment of open and closed boundaries.
Simulations have been made over several representative tidal cycles using this finite difference model, and the results compare favourably with existing data in different locations in the Arabian Gulf. Contour diagrams for amplitudes and phases are presented for the four dominant constituents M2 (principal lunar), S2 (principal solar), K, (lunar solar diurinal) and O, (principal lunar diurnal) in the Arabian Gulf. Due to the explicit nature of
the finite difference scheme, this hydrodynamic model can be efficiently implemented on parallel as well as serial computers
Recommended from our members
Poincaré and the Three Body Problem
The purpose of the thesis is to present an account of Henri Poincare's famous memoir on the three body problem, the final version of which was published in Acta Mathematica in 1890 as the prize-winning entry in King Oscar II's 60th birthday competition. The memoir is reknowned both for its role in providing the foundations for Poincare's celebrated three volume MĂ©thodes Nouvelles de la MĂ©canique CĂ©leste, and for containing the first mathematical description of chaotic behaviour in a dynamical system.
A historical context is provided both through consideration of the problem itself and through a discussion of Poincaré's earlier work which relates to the mathematics developed in the memoir. The organisation of the Oscar competition, which was undertaken by Gösta Mittag-Leffler, is also described. This not only provides an insight into the late 19th century European mathematical community but also reveals that after the prize had been awarded Poincare found an important error in his work and substantially revised the memoir prior to its publication in Acta. The discovery of a printed version of the original memoir personally annotated by Poincaré has allowed for a detailed comparative study of the mathematics contained in both versions of the memoir. The error is explained and it is shown that it was only as a result of its correction that Poincaré discovered the chaotic behaviour now associated with the memoir.
The contemporary reception of the memoir is discussed and Poincaré's subsequent work in celestial mechanics and related topics is examined. Through the consideration of sources up to 1920 the influence and impact of the memoir on the progress of the three body problem and on dynamics in general is assessed
Safety criteria for aperiodic dynamical systems
The
use of
dynamical
system models
is
commonplace
in
many areas of science and
engineering.
One is
often
interested in
whether
the
attracting solutions
in these
models are
robust
to perturbations of
the
equations of motion.
This
question
is
extremely
important
in
situations where
it is
undesirable
to have
a
large
response
to
perturbations
for
reasons
of safety.
An
especially
interesting
case occurs when the
perturbations are aperiodic and
their
exact
form is
unknown.
Unfortunately,
there is
a
lack
of
theory in the literature that
deals
with
this
situation.
It
would
be
extremely useful to have
a practical
technique that
provides
an upper
bound
on the size of the
response
for
an arbitrary perturbation of given
size.
Estimates
of
this form
would allow the
simple
determination
of safety criteria
that
guarantee
the response
falls
within some pre-specified safety
limits. An
excellent area
of application
for this technique
would
be
engineering systems.
Here
one
is frequently
faced
with
the
problem of obtaining safety criteria
for
systems
that in
operational use are
subject
to unknown, aperiodic perturbations.
In this thesis I
show
that
such safety criteria are easy to obtain
by
using
the
concept
of persistence
of
hyperbolicity. This
persistence result
is
well
known in the theory
of
dynamical systems.
The formulation I
give
is functional
analytic
in
nature and
this has
the
advantage
that it is
easy
to
generalise and
is
especially suited to the
problem of
unknown,
aperiodic perturbations.
The
proof
I
give of
the
persistence
theorem
provides
a
technique
for
obtaining
the
safety estimates we want and
the
main part of
this thesis is
an
investigation into how this
can
be
practically
done.
The
usefulness of
the technique is illustrated through two
example systems,
both
of
which are
forced
oscillators.
Firstly, I
consider
the
case where
the
unforced oscillator
has
an asymptotically stable equilibrium.
A
good application of this is the
problem of
ship stability.
The
model
is
called
the
escape equation and
has been
argued to
capture
the relevant
dynamics
of a ship at sea.
The
problem is to find
practical criteria
that
guarantee
the
ship
does not capsize or go
through large
motions when there are external
influences like
wind and waves.
I
show
how
to
provide good criteria which ensure a safe
response when
the
external
forcing is
an arbitrary,
bounded function
of
time. I
also
consider
in
some
detail the
phased-locked loop. This is
a periodically forced
oscillator
which
has
an attracting periodic solution that is
synchronised
(or
phase-locked) with
the
external
forcing. It is interesting to
consider the
effect of small aperiodic variations
in the
external
forcing. For hyperbolic
solutions
I
show that the
phase-locking persists and
I
give
a method
by
which one can
find
an upperbound
on
the
maximum size of
the
response
Extreme sea levels around the coast of Southern Africa
Bibliography: pages 96-100.Tide gauge data from ten ports around the coast of Southern Africa are used to study the nature and behaviour of extreme high sea levels with a view towards predicting the likelihood of extremes occurring in the future. A recorded sea level height can be thought of as a combination of an astronomical tide and a weather determined component. In Southern Africa tides are typically 2 to 2.5 metres in range and the non-tidal residual accounts for up to 50 cm. Sea level is governed by local tides and local meteorology and there is great similarity in the magnitudes and timing at all ports. However tides are found to be the dominant contribution to extreme levels, hence the long term character of tidal variations is important in Southern African extremes. The fortnightly, equinoctial and 4.4 year tidal cycles determine the expected sea level extremes. A prediction technique developed here makes use of the tidal dominance by calculating the likelihood of exceedance for a specific month in a particular year. For any month the highest tide is known and an extreme will depend on the necessary surge occurring. Probability is derived from the surge distribution for that month, carried out for each month in a year, and the results presented as an exceedance chart
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