2,313 research outputs found
Continuation-conjugate gradient methods for the least squares solution of nonlinear boundary value problems
We discuss in this paper a new combination of methods for solving nonlinear boundary value problems containing a parameter. Methods of the continuation type are combined with least squares formulations, preconditioned conjugate gradient algorithms and finite element approximations.
We can compute branches of solutions with limit points, bifurcation points, etc.
Several numerical tests illustrate the possibilities of the methods discussed in the present paper; these include the Bratu problem in one and two dimensions, one-dimensional bifurcation and perturbed bifurcation problems, the driven cavity problem for the Navier–Stokes equations
The Topology of Branching Universes
The purpose of this paper is to survey the possible topologies of branching
space-times, and, in particular, to refute the popular notion in the literature
that a branching space-time requires a non-Hausdorff topology
Simulasi Penanganan Potensi Aliran Debris di Gunung Sago (Studi Kasus di Batang Lakin, Kecamatan Lareh Sago Halaban, Kabupaten Lima Puluh Kota)
The regions in foothills of Sago mountain are flood-prone area due to debris flow. As occurred on March 22, 2010, there has been a catastrophic overflow of debris flow from Sago mountain. The disaster resulted in severe damage around the rivers downstream Sago mountains, including Batang Lakin river. This research study debris flow potential and how to mitigate it in Batang Lakin river, West Sumatra. Analysis of potential debris flow hazard of Batang Lakin river and alternative debris mitigation is simulated using the debris flow simulator Kanako 2D version 2.051. Simulation is important for verifying effect of controlling flow of debris prior to construction work carried out. Rain data input was calculated based on fifty years time period and one hundred years time period Research findings show that at Batang Lakin river, debris flow occurred and overflowing river channel. Alternative countermeasure chosen is sabo dam. For fifty years period when debris flow peak discharge of 59.50 m3/second required 2 units of sabo dams (closed type) with positions at Sta 0 +200 (Sabo height 6 m) and at Sta 0 +450 (Sabo height 4 m). For one hundred years period when debris flow peak discharge of 62.66 m3/second required 2 units of sabo dams (closed type) with positions at Sta 0 +200 (Sabo height 6 m) and at Sta 0 +450 (Sabo height 5 m) to prevent overflow of debris flow to the settlement. Thus, the right efforts to control debris flow on Batang Lakin is the sabo dam
Late time behaviour of the maximal slicing of the Schwarzschild black hole
A time-symmetric Cauchy slice of the extended Schwarzschild spacetime can be
evolved into a foliation of the -region of the spacetime by maximal
surfaces with the requirement that time runs equally fast at both spatial ends
of the manifold. This paper studies the behaviour of these slices in the limit
as proper time-at-infinity becomes arbitrarily large and gives an analytic
expression for the collapse of the lapse.Comment: 18 pages, Latex, no figure
Topology Change and Causal Continuity
The result that, for a scalar quantum field propagating on a ``trousers''
topology in 1+1 dimensions, the crotch singularity is a source for an infinite
burst of energy has been used to argue against the occurrence of topology
change in quantum gravity. We draw attention to a conjecture due to Sorkin that
it may be the particular type of topology change involved in the trousers
transition that is problematic and that other topology changes may not cause
the same difficulties. The conjecture links the singular behaviour to the
existence of ``causal discontinuities'' in the spacetime and relies on a
classification of topology changes using Morse theory. We investigate various
topology changing transitions, including the pair production of black holes and
of topological geons, in the light of these ideas.Comment: Latex, 28 pages, 10 figures, small changes in text (one figure
removed), conclusions remain unchanged. Accepted for publication in Physical
Review
Vacuum Spacetimes with Future Trapped Surfaces
In this article we show that one can construct initial data for the Einstein
equations which satisfy the vacuum constraints. This initial data is defined on
a manifold with topology with a regular center and is asymptotically
flat. Further, this initial data will contain an annular region which is
foliated by two-surfaces of topology . These two-surfaces are future
trapped in the language of Penrose. The Penrose singularity theorem guarantees
that the vacuum spacetime which evolves from this initial data is future null
incomplete.Comment: 19 page
Probabilistic Description of Traffic Breakdowns
We analyze the characteristic features of traffic breakdown. To describe this
phenomenon we apply to the probabilistic model regarding the jam emergence as
the formation of a large car cluster on highway. In these terms the breakdown
occurs through the formation of a certain critical nucleus in the metastable
vehicle flow, which enables us to confine ourselves to one cluster model. We
assume that, first, the growth of the car cluster is governed by attachment of
cars to the cluster whose rate is mainly determined by the mean headway
distance between the car in the vehicle flow and, may be, also by the headway
distance in the cluster. Second, the cluster dissolution is determined by the
car escape from the cluster whose rate depends on the cluster size directly.
The latter is justified using the available experimental data for the
correlation properties of the synchronized mode. We write the appropriate
master equation converted then into the Fokker-Plank equation for the cluster
distribution function and analyze the formation of the critical car cluster due
to the climb over a certain potential barrier. The further cluster growth
irreversibly gives rise to the jam formation. Numerical estimates of the
obtained characteristics and the experimental data of the traffic breakdown are
compared. In particular, we draw a conclusion that the characteristic intrinsic
time scale of the breakdown phenomenon should be about one minute and explain
the case why the traffic volume interval inside which traffic breakdown is
observed is sufficiently wide.Comment: RevTeX 4, 14 pages, 10 figure
Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method
We will present results of a numerical integration of a maximally sliced
Schwarzschild black hole using a smooth lattice method. The results show no
signs of any instability forming during the evolutions to t=1000m. The
principle features of our method are i) the use of a lattice to record the
geometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADM
equations to the lattice and iii) the use of the Bianchi identities to assist
in the computation of the curvatures. No other special techniques are used. The
evolution is unconstrained and the ADM equations are used in their standard
form.Comment: 47 pages including 26 figures, plain TeX, also available at
http://www.maths.monash.edu.au/~leo/preprint
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