12,726 research outputs found
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
D-Branes in Field Theory
Certain gauge theories in four dimensions are known to admit semi-classical
D-brane solitons. These are domain walls on which vortex flux tubes may end.
The purpose of this paper is to develop an open-string description of these
D-branes. The dynamics of the domain walls is shown to be governed by a
Chern-Simons-Higgs theory which, at the quantum level, captures the classical
"closed string" scattering of domain wall solitons.Comment: 23 Pages, 3 figures. v2: reference adde
Estimating the direct and indirect impact of typhoons on plant performance: Evidence from Chinese manufacturers
We quantify the impact of typhoons on manufacturing plants in China. To this end we construct a panel data set of precisely geo-located plants and a plant-level measure of typhoon damage derived from storm track data and a wind field model. Our econometric results reveal that the impact on plant sales can be considerable, although the effects are relatively short-lived. Annual total costs to Chinese plants from typhoons are estimated to be in the range of US$ 3.2 billion (2017 prices), or about 1 per cent of average turnover. When we examine the channels by which plants react to a storm event we find that there is some buffering through an increase in debt and a reduction in liquidity. In terms of propagating the shock through foreign or domestic channels, our estimates suggest that plants prefer to reduce sales to domestic buyers more than foreign buyers and purchases from foreign rather than domestic suppliers. We also find some evidence of a negative indirect effect on turnover through spillovers from customers and a positive effect through damage to very nearby competitors
Description of spin transport and precession in spin-orbit coupling systems and a general equation of continuity
By generalizing the usual current density to a matrix with respect to spin
variables, a general equation of continuity satisfied by the density matrix and
current density matrix has been derived. This equation holds in arbitrary
spin-orbit coupling systems as long as its Hamiltonian can be expressed in
terms of a power series in momentum. Thereby, the expressions of the current
density matrix and a torque density matrix are obtained. The current density
matrix completely describes both the usual current and spin current as well;
while the torque density matrix describes the spin precession caused by a total
effective magnetic field, which may include a realistic and an effective one
due to the spin-orbit coupling. In contrast to the conventional definition of
spin current, this expression contains an additional term if the Hamiltonian
includes nonlinear spin-orbit couplings. Moreover, if the degree of the full
Hamiltonian , then the particle current must also be modified in order
to satisfy the local conservation law of number.Comment: 9 page
Towards granular hydrodynamics in two-dimensions
We study steady-state properties of inelastic gases in two-dimensions in the
presence of an energy source. We generalize previous hydrodynamic treatments to
situations where high and low density regions coexist. The theoretical
predictions compare well with numerical simulations in the nearly elastic
limit. It is also seen that the system can achieve a nonequilibrium
steady-state with asymmetric velocity distributions, and we discuss the
conditions under which such situations occur.Comment: 8 pages, 9 figures, revtex, references added, also available from
http://arnold.uchicago.edu/?ebn
Geometric Phase: a Diagnostic Tool for Entanglement
Using a kinematic approach we show that the non-adiabatic, non-cyclic,
geometric phase corresponding to the radiation emitted by a three level cascade
system provides a sensitive diagnostic tool for determining the entanglement
properties of the two modes of radiation. The nonunitary, noncyclic path in the
state space may be realized through the same control parameters which control
the purity/mixedness and entanglement. We show analytically that the geometric
phase is related to concurrence in certain region of the parameter space. We
further show that the rate of change of the geometric phase reveals its
resilience to fluctuations only for pure Bell type states. Lastly, the
derivative of the geometric phase carries information on both purity/mixedness
and entanglement/separability.Comment: 13 pages 6 figure
The effects of β-elemene on the expression of mTOR, HIF-1α, surviving in lung adenocarcinoma A549 cell
The purpose of this manuscript was to study the regulation effects of â-elemene combined with radiotherapy on three different gene expressions in lung adenocarcinoma A549 cell. mTOR gene, HIF-1á gene, Survivin gene were included in the gene group. Cell culture and RT-PCR were applied to finish this research. Hypoxia Control group, Hypoxia â-elemene group, Hypoxia â-elemene combined with irradiation group were set to compare the differences of three different gene expressions. The most active effects were found in the group of Hypoxia irradiation combined with â-elemene. In this group, the mTOR gene, HIF-1á gene, Survivin gene expressions were all down-regulated when compared with the single treatment groups, andthere were significantly statistical differences.Key words: â-elemene, A549, mTOR, HIF-1á, Survivin, Rhizoma Curcumae
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