715 research outputs found
Stochastic B-series analysis of iterated Taylor methods
For stochastic implicit Taylor methods that use an iterative scheme to
compute their numerical solution, stochastic B--series and corresponding growth
functions are constructed. From these, convergence results based on the order
of the underlying Taylor method, the choice of the iteration method, the
predictor and the number of iterations, for It\^o and Stratonovich SDEs, and
for weak as well as strong convergence are derived. As special case, also the
application of Taylor methods to ODEs is considered. The theory is supported by
numerical experiments
The development of linked databases and environmental modelling systems for decision-making in London
A basic requirement for a city's growth is the availability of land, raw material and water. For continued and sustainable development of today’s cities we must be able to meet these basic requirements whilst being mindful of the environment and its relationship with anthropogenic activity. The heterogeneous and complex nature of urban systems where there are obvious environmental and anthropogenic inter-dependencies necessitates a more holistic approach to decision-making. New developments such as linked databases of environmental data and integrated environmental modelling systems provide new ways of organising cross-disciplinary information and a means to apply this to explain, explore and predict the urban systems response to environmental change. In this paper we show how, accessibility to linked databases, detailed understanding of the geology and integrated environmental modelling solutions has the potential to provide decision-makers and policy developers with the science based information needed to understand and address these challenges
Sequential pivotal mechanisms for public project problems
It is well-known that for several natural decision problems no budget
balanced Groves mechanisms exist. This has motivated recent research on
designing variants of feasible Groves mechanisms (termed as `redistribution of
VCG (Vickrey-Clarke-Groves) payments') that generate reduced deficit. With this
in mind, we study sequential mechanisms and consider optimal strategies that
could reduce the deficit resulting under the simultaneous mechanism. We show
that such strategies exist for the sequential pivotal mechanism of the
well-known public project problem. We also exhibit an optimal strategy with the
property that a maximal social welfare is generated when each player follows
it. Finally, we show that these strategies can be achieved by an implementation
in Nash equilibrium.Comment: 19 pages. The version without the appendix will appear in the Proc.
2nd International Symposium on Algorithmic Game Theory, 200
Universally Coupled Massive Gravity, II: Densitized Tetrad and Cotetrad Theories
Einstein's equations in a tetrad formulation are derived from a linear theory
in flat spacetime with an asymmetric potential using free field gauge
invariance, local Lorentz invariance and universal coupling. The gravitational
potential can be either covariant or contravariant and of almost any density
weight. These results are adapted to produce universally coupled massive
variants of Einstein's equations, yielding two one-parameter families of
distinct theories with spin 2 and spin 0. The theories derived, upon fixing the
local Lorentz gauge freedom, are seen to be a subset of those found by
Ogievetsky and Polubarinov some time ago using a spin limitation principle. In
view of the stability question for massive gravities, the proven non-necessity
of positive energy for stability in applied mathematics in some contexts is
recalled. Massive tetrad gravities permit the mass of the spin 0 to be heavier
than that of the spin 2, as well as lighter than or equal to it, and so provide
phenomenological flexibility that might be of astrophysical or cosmological
use.Comment: 2 figures. Forthcoming in General Relativity and Gravitatio
Towards a quantitative phase-field model of two-phase solidification
We construct a diffuse-interface model of two-phase solidification that
quantitatively reproduces the classic free boundary problem on solid-liquid
interfaces in the thin-interface limit. Convergence tests and comparisons with
boundary integral simulations of eutectic growth show good accuracy for
steady-state lamellae, but the results for limit cycles depend on the interface
thickness through the trijunction behavior. This raises the fundamental issue
of diffuse multiple-junction dynamics.Comment: 4 pages, 2 figures. Better final discussion. 1 reference adde
Recommended from our members
General closed-form basket option pricing bounds
This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known. Moreover, the basket value is not required to be positive. We test our new price approximations on different multivariate models, allowing for jumps and stochastic volatility. Numerical examples are discussed and benchmarked against Monte Carlo simulations. All bounds are general and do not require any additional assumption on the characteristic function, so our methods may be employed also to non-affine models. All bounds involve the computation of one-dimensional Fourier transforms; hence, they do not suffer from the curse of dimensionality and can be applied also to high-dimensional problems where most existing methods fail. In particular, we study two kinds of price approximations: an accurate lower bound based on an approximating set and a fast bounded approximation based on the arithmetic-geometric mean inequality. We also show how to improve Monte Carlo accuracy by using one of our bounds as a control variate
Eutectic colony formation: A phase field study
Eutectic two-phase cells, also known as eutectic colonies, are commonly
observed during the solidification of ternary alloys when the composition is
close to a binary eutectic valley. In analogy with the solidification cells
formed in dilute binary alloys, colony formation is triggered by a
morphological instability of a macroscopically planar eutectic solidification
front due to the rejection by both solid phases of a ternary impurity that
diffuses in the liquid. Here we develop a phase-field model of a binary
eutectic with a dilute ternary impurity and we investigate by dynamical
simulations both the initial linear regime of this instability, and the
subsequent highly nonlinear evolution of the interface that leads to fully
developed two-phase cells with a spacing much larger than the lamellar spacing.
We find a good overall agreement with our recent linear stability analysis [M.
Plapp and A. Karma, Phys. Rev. E 60, 6865 (1999)], which predicts a
destabilization of the front by long-wavelength modes that may be stationary or
oscillatory. A fine comparison, however, reveals that the assumption commonly
attributed to Cahn that lamella grow perpendicular to the envelope of the
solidification front is weakly violated in the phase-field simulations. We show
that, even though weak, this violation has an important quantitative effect on
the stability properties of the eutectic front. We also investigate the
dynamics of fully developed colonies and find that the large-scale envelope of
the composite eutectic front does not converge to a steady state, but exhibits
cell elimination and tip-splitting events up to the largest times simulated.Comment: 18 pages, 18 EPS figures, RevTeX twocolumn, submitted to Phys. Rev.
Measurement of the B0-anti-B0-Oscillation Frequency with Inclusive Dilepton Events
The - oscillation frequency has been measured with a sample of
23 million \B\bar B pairs collected with the BABAR detector at the PEP-II
asymmetric B Factory at SLAC. In this sample, we select events in which both B
mesons decay semileptonically and use the charge of the leptons to identify the
flavor of each B meson. A simultaneous fit to the decay time difference
distributions for opposite- and same-sign dilepton events gives ps.Comment: 7 pages, 1 figure, submitted to Physical Review Letter
- …