Bulletin of the American Physical Society
2006 APS April Meeting
Saturday–Tuesday, April 22–25, 2006; Dallas, TX
Session H14: Novel Techniques |
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Chair: Ron Mickens, Clark Atlanta University Room: Hyatt Regency Dallas Cumberland I |
Sunday, April 23, 2006 8:30AM - 8:42AM |
H14.00001: New CP-violation and preferred-frame tests with polarized electrons Claire Cramer, Blayne Heckel, Ted Cook, Eric Adelberger We report new results from our torsion pendulum test for spin-coupled interactions. Our experiment uses the torque produced on a spin-polarized torsion pendulum containing 8$\times10^{22}$ polarized electrons as a sensitive measure of weak spin-coupled forces. Results can be interpreted as constraints on CP-violating interactions between the pendulum's polarized electrons and unpolarized matter in the surrounding environment, velocity-dependent interactions, and preferred-frame effects that would cause the electrons to precess about a direction fixed in inertial space. When interpreted in the context of Kosteleck\'y's Standard Model Extension, limits on CPT and Lorentz violating parameters are at the level of 10$^{-22}$~eV in the electron sector. These represent a factor of one hundred improvement over previously reported results, and should be compared to the benchmark value $m_e^2/M_{\rm P}= 2 \times 10^{-17}$~eV. [Preview Abstract] |
Sunday, April 23, 2006 8:42AM - 8:54AM |
H14.00002: $^3$He Relaxation Study at Low Temperature for the Neutron Electric Dipole Moment Experiment Qiang Ye The search for the existence of a nonzero neutron electric dipole moment (EDM) is a direct search of time reversal symmetry violation and has the potential to reveal new sources of CP violation beyond the Standard Model and may have a significant impact on our understanding of baryogenesis. A new experiment has been proposed to provide a new way to measure the neutron EDM with unprecedented sensitivity. The experiment requires that the $^3$He polarization to have little or negligible loss during each measurement period. Therefore, understanding the relaxation mechanism of polarized $^3$He and maintaining its polarization at the unique nEDM experimental conditions is essential. We have studied the longitudinal relaxation time of $^3$He vapor for the first time from a deuterated tetraphenyl butadiene (d-TPB) coated acrylic cell in a diluted mixture of $^{3}$He-$^{4}$He at a temperature of 1.9K and first set of results will be reported. A d-TPB coated acrylic cells will be used in the neutron EDM experiment. It is important to extend our current work down to $\sim$500mK and to a $^3$He concentration closer to that of the nEDM experiment. Such measurements are being planned with the use of a dilution refrigerator and a SQUID setup for the monitoring of the $^3$He polarization. [Preview Abstract] |
Sunday, April 23, 2006 8:54AM - 9:06AM |
H14.00003: Calculating Periodic Solutions to `Truly Nonlinear' Oscillatory ODE's Ronald Mickens `Truly nonlinear' oscillators (in one dimension) are modeled by second-order,ordinary differential equations having the form $$\ddot x + f(x)=\epsilon g(x,\dot x),\leqno(*)$$ where the elastic restoring force $f(x)$ does not contain a linear term, $\epsilon$ is a positive parameter (which may or may not be small), and $g(x,\dot x)$ is a polynomial function of $(x, \dot x)$. A particular example of $f(x)$ is $$f(x)=x^{\frac pq},\quad p=(2n+1),\quad q=(2m+1),\leqno(**)$$ where $(n,m)$ are non-negative integers. The significant issue for Eq.~($*$) is that analytical approximations to its periodic solutions can be calculated. In general, when $\epsilon$ is small, Eq.~($*$) does not have a mathematical structure such that the standard perturbation methods can be used. We demonstrate that an iteration procedure can be formulated such that excellent approximations to the periodic solutions are obtained for the ODE given by Eq.~($*$). The method is illustrated by applying it to the case where $f(x)=x^3$ and $\epsilon=0$. [Preview Abstract] |
Sunday, April 23, 2006 9:06AM - 9:18AM |
H14.00004: Analysis of the Lev Ginzburg Equation Michael Bellamy, Ronald Mickens A second-order differential equation taking the form $$\ddot x=f(x,\dot x,p)\leqno(*)$$ was derived by Ginzburg$^1$. In this ODE, $\dot x$ and $\ddot x $ represent the first and second derivatives with respect to time; and $p$ stands for four parameters, $p=(p_1,p_2, p_3,p_4)$, where $(p_1,p_2,p_3)$ are non-negative and $p_4$ can be of either sign. The function $f$ is linear in $x$, but quadratic in $\dot x$. Ginzburg's main purpose in constructing this equation was to take into consideration the ``inertial behavior of biological populations." However, this ODE can also be used to model a variety of physical dynamical systems.$^2$ With four parameters, there is a broad range of possible solution behaviors. Our present purpose is to prove that limit-cycle behavior can occur for Eq.~($*$) under the appropriate conditions on the parameters. We demonstrate this result by means of the Hopf bifurcation theory.$^3$ References $^1$L. Ginzburg and M. Colyvan, Ecological Orbits (Oxford, New York, 2004). $^2$S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley; Reading, MA; 1994). $^3$E. Beltrami, Mathematics for Dynamic Modeling (Academic Press, Boston, 1987). [Preview Abstract] |
Sunday, April 23, 2006 9:18AM - 9:30AM |
H14.00005: An Approach to Modeling Extreme Loading of Structures using Peridynamics Paul Demmie Peridynamics is a theory of continuum mechanics that is formulated in terms of integral equations rather than partial differential equations. It assumes that particles in a continuum interact across a finite distance as in molecular dynamics. The integral equations remain valid regardless of any fractures or other discontinuities that may emerge due to loading. In contrast, the differential equations of classical theory break down when a discontinuity appears. Peridynamics predicts the deformation and failure of structures under dynamic loading, especially failure due to fracture. Cracks emerge spontaneously as a result of the equations of motion and material model and grow in whatever direction is energetically favorable. The implementation does not require a separate law that tells cracks when and where to grow. We describe peridynamics theory and provide some examples of its application as implemented in the EMU computer code. EMU is mesh free. Therefore, it does not use elements, and there are no geometrical objects connecting the grid points. Hence, there is no need for a mesh generator when modeling complex structures. Only the generation of grid points is required. [Preview Abstract] |
Sunday, April 23, 2006 9:30AM - 9:42AM |
H14.00006: 3D real holographic image movies are projected into a volumetric display using dynamic digital micromirror device (DMD) holograms. Michael L. Huebschman, Jeremy Hunt, Harold R. Garner The Texas Instruments Digital Micromirror Device (DMD) is being used as the recording medium for display of pre-calculated digital holograms. The high intensity throughput of the reflected laser light from DMD holograms enables volumetric display of projected real images as well as virtual images. A single DMD and single laser projector system has been designed to reconstruct projected images in a 6''x 6''x 4.5'' volumetric display. The volumetric display is composed of twenty-four, 6''-square, PSCT liquid crystal plates which are each cycled on and off to reduce unnecessary scatter in the volume. The DMD is an XGA format array, 1024x768, with 13.6 micron pitch mirrors. This holographic projection system has been used in the assessment of hologram image resolution, maximum image size, optical focusing of the real image, image look-around, and physiological depth cues. Dynamic movement images are projected by transferring the appropriately sequenced holograms to the DMD at movie frame rates. [Preview Abstract] |
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