Search results for "RIEMANN"
showing 10 items of 254 documents
On the volume of unit vector fields on spaces of constant sectional curvature
2004
A unit vector field X on a Riemannian manifold determines a submanifold in the unit tangent bundle. The volume of X is the volume of this submanifold for the induced Sasaki metric. It is known that the parallel fields are the trivial minima.
Transportation-cost inequality on path spaces with uniform distance
2008
Abstract Let M be a complete Riemannian manifold and μ the distribution of the diffusion process generated by 1 2 ( Δ + Z ) where Z is a C 1 -vector field. When Ric − ∇ Z is bounded below and Z has, for instance, linear growth, the transportation-cost inequality with respect to the uniform distance is established for μ on the path space over M . A simple example is given to show the optimality of the condition.
Set valued Kurzweil-Henstock-Pettis integral
2005
It is shown that the obvious generalization of the Pettis integral of a multifunction obtained by replacing the Lebesgue integrability of the support functions by the Kurzweil--Henstock integrability, produces an integral which can be described -- in case of multifunctions with (weakly) compact convex values -- in terms of the Pettis set-valued integral.
A Birkhoff type integral and the Bourgain property in a locally convex space
2007
An integral, called the $Bk$-integral, for functions taking values in a locally convex space is defined. Properties of $Bk$-integrable functions are considered and the relations with other integrals are studied. Moreover the $Bk$-integrability of bounded functions is compared with the Bourgain property.
Logos, Pathos and Ethos in Ackroyd's Plato's Papers via an Interdisciplinary Psycho-philosophical Approach
2014
Abstract The present moral crisis of humanity will be closely considered in Ackroyd's Plato's Papers via Riemann's Theorem of Earth Mapping, Kelly's Personal Construct theory and Plato's Idea of the Third Man with a view to showing that only the generally assumed relationship between logos and ethos could rescue the mentality of the entire world and retrieve temporality and morality. For this approach to be successfully turned to good account the Aristotelian concepts of Logos (the thinking part of the intellect) mediating with Pathos (the feeling self) through the actions of his acting self, the personal Ethos, will be employed in relation to Ackroyd's character, Plato, the philosopher-ora…
Solutions via double wave ansatz to the 1-D non-homogeneous gas-dynamics equations
2020
Abstract In this paper classes of double wave solutions of the 1D Euler system describing a ideal fluid in the non-homogeneous case have been determined. In order that the analytical procedure under interest to hold, suitable model laws for the source term involved in the governing model were characterized. Finally such a class of exact double wave solutions has been used for solving some problems of interest in nonlinear wave propagation.
High-order methods for the simulation of hydromagnetic instabilities in core-collapse supernovae
2011
AbstractWe present an assessment of the accuracy of a recently developed MHD code used to study hydromagnetic flows in supernovae and related events. The code, based on the constrained transport formulation, incorporates unprecedented ultra-high-order methods (up to 9th order) for the reconstruction and the most accurate approximate Riemann solvers. We estimate the numerical resistivity of these schemes in tearing instability simulations.
Numerical Relativistic Hydrodynamics
2008
High Resolution Shock Capturing (HRSC) techniques achieve highly accurate numerical approximations (formally second order or better) in smooth regions of the flow, and capture the motion of unresolved steep gradients without creating spurious oscillations. I will show how these techniques have been extended to relativistic hydrodynamics, making it possible to explore some challenging astrophysical scenarios. I will review recent literature concerning the main properties of different special relativistic Riemann solvers, and discuss several test problems which are commonly used to evaluate the performance of numerical methods in relativistic hydrodynamics. In the second part, I will illustra…
A powerful hydrodynamic booster for relativistic jets
2006
Velocities close to the speed of light are a robust observational property of the jets observed in microquasars and AGNs, and are expected to be behind much of the phenomenology of GRBs. Yet, the mechanism boosting relativistic jets to such large Lorentz factors is still essentially unknown. Building on recent general-relativistic, multidimensional simulations of progenitors of short GRBs, we discuss a new effect in relativistic hydrodynamics which can act as an efficient booster in jets. This effect is purely hydrodynamical and occurs when large velocities tangential to a discontinuity are present in the flow, yielding Lorentz factors $\Gamma \sim 10^2-10^3$ or larger in flows with moderat…
Meson-Baryon Interactions in Unitarized Chiral Perturbation Theory
2002
Meson-Baryon Interactions can be successfully described using both Chiral Symmetry and Unitarity. The $s-$wave meson-baryon scattering amplitude is analyzed in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry in the potential. Two body coupled channel unitarity is exactly preserved. The needed two particle irreducible matrix amplitude is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. Off-shell behavior is parameterized in terms of low energy constants. The relation to the heavy baryon limit is discussed. The position of the complex poles in the second Riemann sheet of the scattering amplitude determine masses and widths baryonic reson…