Next-to-leading order gravitational spin1-spin2 coupling with Kaluza-Klein reduction

We use the recently proposed Kaluza-Klein (KK) reduction over the time dimension, within an effective field theory (EFT) approach, to calculate the next to leading order (NLO) gravitational spin1-spin2 interaction between two spinning compact objects. It is shown here that to NLO in the spin1-spin2 interaction, the reduced KK action within the stationary approximation is sufficient to describe the gravitational interaction, and that it simplifies calculation substantially. We also find here that the gravito-magnetic vector field defined within the KK decomposition of the metric mostly dominates the mediation of the interaction. Our results coincide with those calculated in the ADM Hamiltonian formalism, and we provide another explanation for the discrepancy with the result previously derived within the EFT approach, thus demonstrating clearly the equivalence of the ADM Hamiltonian formalism and the EFT action approach.Comment: 12 pages, revtex4-1, 3 figures; v2: reference added; v3: edited, section 3 elaborated; v4: publishe

Lie discrete symmetries of lattice equations

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the discrete symmetries of the discrete Painlev\'e I equation and of the Toda lattice equation

A Lattice Simulation of the SU(2) Vacuum Structure

In this article we analyze the vacuum structure of pure SU(2) Yang-Mills using non-perturbative techniques. Monte Carlo simulations are performed for the lattice gauge theory with external sources to obtain the effective potential. Evidence from the lattice gauge theory indicating the presence of the unstable mode in the effective potential is reported.Comment: 12 pages, latex with revtex style, figures avalable by e-mail: [email protected]

Expanding perfect fluid generalizations of the C-metric

We reexamine Petrov type D gravitational fields generated by a perfect fluid with spatially homogeneous energy density and in which the flow lines form a timelike non-shearing and non-rotating congruence. It is shown that the anisotropic such spacetimes, which comprise the vacuum C-metric as a limit case, can have \emph{non-zero} expansion, contrary to the conclusion in the original investigation by Barnes (Gen. Rel. Grav. 4, 105 (1973)). This class consists of cosmological models with generically one and at most two Killing vectors. We construct their line element and discuss some important properties. The methods used in this investigation incite to deduce testable criteria regarding shearfree normality and staticity op Petrov type $D$ spacetimes in general, which we add in an appendix.Comment: 16 pages, extended and amended versio

14.6-GHz LiNbO/sub 3/ microdisk photonic self-homodyne RF receiver

Nonlinear optical modulation combined with simultaneous photonic and RF resonance in an LiNbO/sub 3/ microdisk modulator is used to create a self-homodyne photonic RF receiver. Carrier and sidebands are mixed in the optical domain, and the modulated optical signal is detected using a photodetector. The photodetector has a bandwidth matched to the baseband signal. It filters out the high-frequency components and generates the baseband photocurrent. Receiver operation is demonstrated by demodulating up to 100-Mb/s digital data from a 14.6-GHz carrier frequency without any high-speed electronic components. A bit error rate of 10/sup -9/ is measured for 10-Mb/s downconverted digital data at -15-dBm received RF power. Preliminary results of employing this photonic RF receiver in a short-distance Ku-band wireless link demonstrate the potential of using high-quality optical microresonators in RF receiver applications

A design of actuation mechanisms for use in 'huggable' robotic teddy bear

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006.Includes bibliographical references.Silent, back drivable actuators were necessary for the Huggable teddy bear, a robotic companion for use in therapeutic applications. The benefits of pet therapy include a reduction in stress and an increase in rate of healing. The Huggable teddy bear will attempt to offer the same benefits through a life-like interaction with the user. Consequently, the actuators were created to be compact due to the small size of the robot. Actuators were also designed to interface with the motor control board used in the Huggable and allow for feedback for use in position control. Care was taken in the design process to address the issues of manufacturing and assembly. The two mechanisms designed for the Huggable were an eyebrow mechanism and an ear mechanism. The eyebrow mechanism has 2 degrees of freedom (DOF). This was done using a symmetrical design which couples the motion of outer eyebrows together and the motion of the inner eyebrows together. The Ear mechanism has only 1 DOF and is cable driven. These mechanisms will allow the Huggable teddy bear to provide emotional feedback as well as create a realistic response to stimulus. Up to this point, the designs and mechanisms have been built. Testing of the design will follow to ensure life-like interaction with the user.by Levi Lalla.S.B

A new two-dimensional lattice model that is "consistent around a cube"

For two-dimensional lattice equations one definition of integrability is that the model can be naturally and consistently extended to three dimensions, i.e., that it is "consistent around a cube" (CAC). As a consequence of CAC one can construct a Lax pair for the model. Recently Adler, Bobenko and Suris conducted a search based on this principle and certain additional assumptions. One of those assumptions was the "tetrahedron property", which is satisfied by most known equations. We present here one lattice equation that satisfies the consistency condition but does not have the tetrahedron property. Its Lax pair is also presented and some basic properties discussed.Comment: 8 pages in LaTe

Lie Symmetries and Exact Solutions of First Order Difference Schemes

We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted to the symmetries considered. The invariant difference schemes can be so chosen that their solutions coincide exactly with those of the original differential equation.Comment: Minor changes and journal-re

Difference schemes with point symmetries and their numerical tests

Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new difference schemes are tested as numerical methods. The obtained numerical solutions are shown to be much more accurate than those obtained by standard methods without an increase in cost. For an example involving a solution with a singularity in the integration region the symmetry preserving scheme, contrary to standard ones, provides solutions valid beyond the singular point.Comment: 26 pages 7 figure