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 $\geq3$, 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