16,174 research outputs found
Cosmic age, Statefinder and diagnostics in the decaying vacuum cosmology
As an extension of CDM, the decaying vacuum model (DV) describes the
dark energy as a varying vacuum whose energy density decays linearly with the
Hubble parameter in the late-times, , and
produces the matter component. We examine the high- cosmic age problem in
the DV model, and compare it with CDM and the Yang-Mills condensate
(YMC) dark energy model. Without employing a dynamical scalar field for dark
energy, these three models share a similar behavior of late-time evolution. It
is found that the DV model, like YMC, can accommodate the high- quasar APM
08279+5255, thus greatly alleviates the high- cosmic age problem. We also
calculate the Statefinder and the {\it Om} diagnostics in the model. It
is found that the evolutionary trajectories of and in the DV
model are similar to those in the kinessence model, but are distinguished from
those in CDM and YMC. The in DV has a negative slope and
its height depends on the matter fraction, while YMC has a rather flat , whose magnitude depends sensitively on the coupling.Comment: 12 pages, 4 figures, with some correction
Berry phase in a composite system
The Berry phase in a composite system with only one subsystem being driven
has been studied in this Letter. We choose two spin- systems with
spin-spin couplings as the composite system, one of the subsystems is driven by
a time-dependent magnetic field. We show how the Berry phases depend on the
coupling between the two subsystems, and what is the relation between these
Berry phases of the whole system and those of the subsystems.Comment: 4 pages, 6 figure
Geometric, Variational Integrators for Computer Animation
We present a general-purpose numerical scheme for time integration of Lagrangian dynamical systems—an important
computational tool at the core of most physics-based animation techniques. Several features make this
particular time integrator highly desirable for computer animation: it numerically preserves important invariants,
such as linear and angular momenta; the symplectic nature of the integrator also guarantees a correct energy
behavior, even when dissipation and external forces are added; holonomic constraints can also be enforced quite
simply; finally, our simple methodology allows for the design of high-order accurate schemes if needed. Two key
properties set the method apart from earlier approaches. First, the nonlinear equations that must be solved during
an update step are replaced by a minimization of a novel functional, speeding up time stepping by more than a
factor of two in practice. Second, the formulation introduces additional variables that provide key flexibility in the
implementation of the method. These properties are achieved using a discrete form of a general variational principle
called the Pontryagin-Hamilton principle, expressing time integration in a geometric manner. We demonstrate
the applicability of our integrators to the simulation of non-linear elasticity with implementation details
Discrete Lie Advection of Differential Forms
In this paper, we present a numerical technique for performing Lie advection
of arbitrary differential forms. Leveraging advances in high-resolution finite
volume methods for scalar hyperbolic conservation laws, we first discretize the
interior product (also called contraction) through integrals over Eulerian
approximations of extrusions. This, along with Cartan's homotopy formula and a
discrete exterior derivative, can then be used to derive a discrete Lie
derivative. The usefulness of this operator is demonstrated through the
numerical advection of scalar fields and 1-forms on regular grids.Comment: Accepted version; to be published in J. FoC
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