Optica Creates CDF Content on the Web for Optics

Optica can be used to create interactive, dynamic Computable Document Format (CDF) content on the web of optical systems for teaching optics and sharing of optical models. The implications of this new paradigm could be revolutionary for the optics community. Since Optica can import the file formats of other popular optical design software packages, such as Zemax and Code V, the consequences of this new format could be quite far ranging. In particular, we hope to provide an online service for users of other optical modeling packages to upload their data files and immediately link to an interactive web-based model of their specific optical design. As such, new users not need purchase Optica or Mathematica to begin reaping the benefits of CDF. In this presentation, we will demonstrate how Optica can be used to generate CDF material and discuss our strategy to exploit this exciting new format.

Wolfram MathModelica and Mathematica Analysis and Design Workshop

Learn how to use Mathematica when designing and analyzing MathModelica models. In this workshop you will learn how to analyze simulation results as well as learn how to get MathModelica model equations into Mathematica to analyze and design your dynamic system.

Wolfram MathModelica—Control Design

With the release of Version 8, tools for control design have been included in Mathematica. Together with Wolfram MathModelica, it will give you all the tools you need to design controllers for advanced systems. This seminar will show you how you can develop a model of a dynamic system in MathModelica and design its control system in Mathematica.

Symbolic Computing Package and Its Application to Mathematical Physics

The Symbolic Computing package is a Mathematica add-on package that facilitates symbolic computation in Mathematica. It enables display and interpretation of derivatives, differential vector operators, and brackets using the traditional notation based on the low-level box language and contains more than 500 user-defined functions for manipulation and evaluation of various mathematical expressions. These functions can be categorized into:

• Basic Algebra
• Complex Variables
• Differential Calculus
• Display and Graphics
• Elementary Functions
• Equation Solving
• Equations
• Export of Data
• Flow Control
• Formula Manipulation
• Fourier Analysis
• Function Analysis
• Geometry
• Integral Calculus
• Numerical Functions
• Operator Analysis
• Patterns
• Polynomials and Series
• Products
• Rules
• Special Functions
• String Operations
• Summations
• Symbols
• Trigonometric Functions
• Variables
• Vectors and Matrices

The development of the package and application to mathematical physics, especially classical mechanics, electromagnetism, and quantum mechanics, will be presented.

Quantum Mechanics on the GPU

Mathematica 8 provides tools for running code on your computer's GPU using either CUDA or OpenCL. These tools lower the barriers to GPU computing dramatically. I will show how by writing a small amount of GPU kernel code that you can use to solve interesting quantum mechanics problems on your GPU. Speed-ups of several orders of magnitude can be obtained even on modest graphics cards. Once your GPU function is written, it can used just like any other Mathematica function, making dynamic visualization of your results easy.

Direct Exoplanet Imaging Using Advanced Post Processing in Mathematica

HR 8799 is one of only three exoplanetary systems observed with direct imaging. Discovered in 2008, it is currently the only multiple-exoplanetary system discovered with this method. The ability to measure the planet's orbital motion is critical to understanding this system. Indeed, orbital information brings insight into the dynamics, stability, and formation mechanisms for the planets. Yet measuring the orbital motion is a very difficult task because of the long-period orbits (50–500 year), which requires long time baselines and high-precision astrometry. We present the precovery of the three planets HR 8799b, c, and d using the archival dataset of the star HR 8799 obtained with the Hubble Space Telescope (HST) NICMOS coronagraph in 1998. This data provides a 10-year baseline with the discovery images, and therefore offers a very unique opportunity to constrain their orbital motion now. Recent dynamical studies of this system showed that it is mostly unstable with only a few possible stable solutions involving mean motion resonances. We study the compatibility of a few of these stable scenarios with the new astrometric data, and offer new dynamical constraints on the HR 8799 system. These results were achieved by developing sophisticated image-processing and orbit-fitting techniques using Mathematica, where we apply a statistical approach to get high-precision astrometry and then test for compatibility with previously published stable solutions.

Signal Processing

Computational Integration of Biomedical Research Workflows at the Oregon National Primate Research Center

The Oregon National Primate Research Center (ONPRC) is one of eight NPRCs applying animal models in developing therapies for AIDS, metabolic and neurodegenerative disease, and reproductive health. Research into human disease is complemented by veterinary medicine in development of methods and resources to support animal husbandry—capabilities crucial to engineering breeding colonies that are supportive of evolving research needs. An additional challenge concerns allocation of animals to competing research projects, in particular doing so in a way that is fair to scientific, economic, and ethical perspectives. In accordance with these needs, Mathematica technologies are revolutionizing ONPRC efforts to transform organizational workflows throughout, from powering market-based mechanisms for animal allocation to providing automated animal-record extracts for researchers to integrating surgical and animal-care activity to related work across the consortium of NPRCs. First-of-a-kind capabilities have been developed in minimal time and at minimal expense, substantiating the claim that Mathematica offers a months-to-days improvement in development efficiency. The diversity of deployment mechanisms make the Mathematica product accessible to users throughout the organization, from animal care technicians to veterinarians to researchers and staff.

Some accomplishments include reduction of surgical staff coupled with reduction in process variation and improvement in procedural discipline and efficiency, online access to animal information strengthening integration of research and husbandry, and generation of datasets in minutes that previously would have required hours and days (if possible at all.) Never before at ONPRC has "IT" evoked expressions like "... Amazing what you can do," "...Love it...," "This is cool," and simply "Awesome."

GPS Timing-Code-Based Positioning in Mathematica

Global Positioning System (GPS) receiver positions are computed from observed timing-code pseudoranges between GPS satellites and the receiver plus the coordinates computed for the satellites at transmission time. The Mathematica code reads observations and satellite ephemerides from RINEX files, computes satellite positions using orbital mechanics, computes and corrects the pseudorange error budget, to compute the final position using a nonlinear least-squares adjustment of the multi-lateration problem. Tests show computed positions agree with published control coordinates within the standard error expected for code-only GPS positioning.

A Formal Approach for Modeling and Simulation

Modeling some behaviors of a system is a complex multi-step and multi-layered description process closely related to the numerical simulation and visualization of these behaviors. At the bottom level layer, physical characteristics are defined in terms of quantities and associated to symbols, units, and values. At the top level layer, systems are expressed as a set of interconnected components involving such quantities. Intermediate layers are used to express how components are acting on each other, how quantities are dependent together, and how that can be effectively represented in terms of equations with the help of physical formalisms and theories. By adding a few constructions, we show how to turn the rich programming and mathematical language of Mathematica into a generic declarative modeling language that is rich enough to represent the most complex models of large-scale systems. Ad-hoc compilers are then able to produce from these source models any kind of simulation code as target. An industrial application of these theoretical concerns has led to the development of an integrated environment for modeling and simulation used by one of the leaders in the aircraft industry for the design of flight dynamics models and the automatic generation of components of the flight simulators.

Impact of Slowing Spin on the Trajectory of a Baseball

A flying baseball in the air not only is subject to gravity's pull, it is also subject to air resistance. A spinning ball in addition to these two forces experiences a spin-dependent force. We consider a practical scenario where the speed dependent drag force not only retards the motion, it slows the spin as well. The analysis of the kinematic and dynamic of the proposed scenario entails solving super nonlinear coupled ODEs. Utilizing Mathematica's NDSolve function, we solve these equations numerically. We compile numeric and graphic lists of quantities of interests versus their comparative counterparts of non-retarded case.

Visual Depth Perception and Mathematica

A translating observer viewing a rigid environment experiences "motion parallax," the relative movement upon the observer's retina of variously positioned objects in the scene. This retinal movement of images provides a cue to the relative depth of objects in the environment; however, retinal motion alone cannot mathematically determine the relative depth of objects. Also, Nadler, et al. (Nature 2008) showed that monkeys cannot perceive even "near" or "far" without an extra retinal signal. Nawrot and Joyce (Vis Res 2006) showed experimentally that the ratio of the rate of image motion on the retina and the rate of smooth eye pursuit was important in perception of depth from lateral motion. Nawrot and Stroyan (Vis Res 2009 and J of Math Bio 2011) developed a mathematical theory of the motion/pursuit ratio and verified that people use this cue in central vision. Nadler, Nawrot, et al. (Neuron 2009) showed that monkeys use the extra retinal pursuit signal neurologically to perceive depth sign. Work is ongoing to understand the role of the motion/pursuit ratio, psychophysically, neurologically, and mathematically. Mathematica is playing an important role in the discoveries and communication across disciplines because it can provide powerful, but easy-to-use interactive graphical programs in accessible ways.

Image Processing Workshop

This workshop will explore some of Mathematica's powerful image processing capabilities. We will focus on rapid prototyping of image processing algorithms and develop step-by-step solutions for a variety of problems. Moreover, we will show how to make use of Mathematica's built-in features to improve performance and to easily create powerful interactive tools.