14,959 research outputs found
Numerical Methods for Solving One Dimensional Problems With a Moving Boundary
This thesis describes some methods which were employed to compute approximate solutions to partial differential equations with moving boundaries verifying the existing numerical solutions, modifying the techniques and applying them to new problems. The problems considered were the determination of the temperature in melting ice and of the concentration of oxygen diffusion in both one dimensional cartesian and axially symmetric cylindrical coordinates. For the melting ice problem the methods studied included variable time step methods with difference formulae and different methods of calculating the variable time step, and also a transformation to fix the moving boundary using a conventional finite difference technique on the known domain. The diffusion problem had a singularity on the initial boundary. The singularity was treated by using an approximate analytical solution and the numerical solution found by a finite difference method with fixed time and space steps and a Lagrange-type formula near the moving boundary
Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque
New exact analytic solutions are introduced for the rotational motion of a
rigid body having two equal principal moments of inertia and subjected to an
external torque which is constant in magnitude. In particular, the solutions
are obtained for the following cases: (1) Torque parallel to the symmetry axis
and arbitrary initial angular velocity; (2) Torque perpendicular to the
symmetry axis and such that the torque is rotating at a constant rate about the
symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial
angular velocity perpendicular to the symmetry axis, with the torque being
fixed with the body. In addition to the solutions for these three forced cases,
an original solution is introduced for the case of torque-free motion, which is
simpler than the classical solution as regards its derivation and uses the
rotation matrix in order to describe the body orientation. This paper builds
upon the recently discovered exact solution for the motion of a rigid body with
a spherical ellipsoid of inertia. In particular, by following Hestenes' theory,
the rotational motion of an axially symmetric rigid body is seen at any instant
in time as the combination of the motion of a "virtual" spherical body with
respect to the inertial frame and the motion of the axially symmetric body with
respect to this "virtual" body. The kinematic solutions are presented in terms
of the rotation matrix. The newly found exact analytic solutions are valid for
any motion time length and rotation amplitude. The present paper adds further
elements to the small set of special cases for which an exact solution of the
rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The
following typos present in the Journal version are HERE corrected: 1)
Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3)
Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6
Stable Monopole-Antimonopole String Background in SU(2) QCD
Motivated by the instability of the Savvidy-Nielsen-Olesen vacuum we make a
systematic search for a stable magnetic background in pure SU(2) QCD. It is
shown that a pair of axially symmetric monopole and antimonopole strings is
stable, provided that the distance between the two strings is less than a
critical value. The existence of a stable monopole-antimonopole string
background strongly supports that a magnetic condensation of
monopole-antimonopole pairs can generate a dynamical symmetry breaking, and
thus the magnetic confinement of color in QCD.Comment: 7 page
Mixed-isotope Bose-Einstein condensates in Rubidium
We consider the ground state properties of mixed Bose-Einstein condensates of
87Rb and 85Rb atoms in the isotropic pancake trap, for both signs of the
interspecies scattering length. In the case of repulsive interspecies
interaction, there are the axially-symmetric and symmetry-breaking ground
states. The threshold for the symmetry breaking transition, which is related to
appearance of a zero dipole-mode, is found numerically. For attractive
interspecies interactions, the two condensates assume symmetric ground states
for the numbers of atoms up to the collapse instability of the mixture.Comment: Revised; 21 pages, 5 figures, submitted to Physical Review
On the Post-linear Quadrupole-Quadrupole Metric
The Hartle-Thorne metric defines a reliable spacetime for most astrophysical
purposes, for instance for the simulation of slowly rotating stars. Solving the
Einstein field equations, we added terms of second order in the quadrupole
moment to its post-linear version in order to compare it with solutions found
by Blanchet in the frame of the multi-polar post-Minkowskian framework. We
first derived the extended Hartle-Thorne metric in harmonic coordinates and
then showed agreement with the corresponding post-linear metric from Blanchet.
We also found a coordinate transformation from the post-linear Erez-Rosen
metric to our extended Hartle-Thorne spacetime. It is well known that the
Hartle-Thorne solution can be smoothly matched with an interior perfect fluid
solution with physically appropriate properties. A comparison among these
solutions provides a validation of them. It is clear that in order to represent
realistic solutions of self-gravitating (axially symmetric) matter
distributions of perfect fluid, the quadrupole moment has to be included as a
physical parameter
- …