An essential need for many model-based robot control algorithms is the ability to quickly and accurately compute partial derivatives of equations motion. State art approaches this problem often use analytical methods based on chain rule applied existing dynamics algorithms. Although these are an improvement over finite differences in terms accuracy, they not always most efficient. In paper, we ...

adapted from R. S. Lakes, Modern Physics Letters B, 30 (24) 1650319 (9 pages) (2016). Abstract Chiral dielectrics are considered from the perspective of continuum representations of spatial heterogeneity. Static effects in isotropic chiral dielectrics are predicted, provided the electric field has nonzero third spatial derivatives. The effects are compared with static chiral phenomena in Cosser...

Two finite difference discretization schemes for approximating the spatial derivatives in the diffusion equation in spherical coordinates with variable diffusivity are presented and analyzed. The numerical solutions obtained by the discretization schemes are compared for five cases of the functional form for the variable diffusivity: (I) constant diffusivity, (II) temporally-dependent diffusivi...

We establish new existence results for the Einstein constraint equations for mean extrinsic curvature arbitrarily far from constant. The results hold for rescaled background metric in the positive Yamabe class, with freely specifiable parts of the data sufficiently small, and with matter energy density not identically zero. Two technical advances make these results possible: A new topological f...

Hitherto no method, to our knowledge, was known to incorporate spatial phase shifting for the measurement of pure in-plane displacements. We demonstrate that the modified Duffy two-aperture configuration [Opt. Lett. 22, 1958 (1996)], which is sensitive to only the in-plane displacement component and offers increased sensitivity, lends itself to measurement with spatial phase shifting. The confi...

This paper applies the global radial basis functions as a spatial collocation scheme for solving the Options Pricing model. Diierent numerical time integration schemes are employed for the time derivative of the model. It is shown that the major numerical error is from the time integration instead of the spatial approximation by comparing with the analytical solution. Since the basis functions ...

We consider open superstring partition function Z on the disc in time-dependent tachyon background T = f(xi)e μx0 where the profile function f depends on spatial coordinates. We compute Z to second order in derivatives of f and compare the result with some previously suggested effective actions depending only on first derivatives of the tachyon field. We also compute the target-space stress-ene...