7,716 research outputs found

    Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory

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    We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their substantial value for problems ranging in scale from molecules to the entire solar system. In this article, we suggest two possible reasons for the paucity relative to spherical harmonics. The first is essentially historical---ellipsoidal harmonics developed during the late 19th century and early 20th, when it was found that only the lowest-order harmonics are expressible in closed form. Each higher-order term requires the solution of an eigenvalue problem, and tedious manual computation seems to have discouraged applications and theoretical studies. The second explanation is practical: even with modern computers and accurate eigenvalue algorithms, expansions in ellipsoidal harmonics are significantly more challenging to compute than those in Cartesian or spherical coordinates. The present implementations reduce the "barrier to entry" by providing an easy and free way for the community to begin using ellipsoidal harmonics in actual research. We demonstrate our implementation using the specific and physiologically crucial problem of how charged proteins interact with their environment, and ask: what other analytical tools await re-discovery in an era of inexpensive computation?Comment: 25 pages, 3 figure

    Ephemeral properties and the illusion of microscopic particles

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    Founding our analysis on the Geneva-Brussels approach to quantum mechanics, we use conventional macroscopic objects as guiding examples to clarify the content of two important results of the beginning of twentieth century: Einstein-Podolsky-Rosen's reality criterion and Heisenberg's uncertainty principle. We then use them in combination to show that our widespread belief in the existence of microscopic particles is only the result of a cognitive illusion, as microscopic particles are not particles, but are instead the ephemeral spatial and local manifestations of non-spatial and non-local entities

    Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector

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    Terahertz (THz) imaging has the ability to see through otherwise opaque materials. However, due to the long wavelengths of THz radiation ({\lambda}=300{\mu}m at 1THz), far-field THz imaging techniques are heavily outperformed by optical imaging in regards to the obtained resolution. In this work we demonstrate near-field THz imaging with a single-pixel detector. We project a time-varying optical mask onto a silicon wafer which is used to spatially modulate a pulse of THz radiation. The far-field transmission corresponding to each mask is recorded by a single element detector and this data is used to reconstruct the image of an object placed on the far side of the silicon wafer. We demonstrate a proof of principal application where we image a printed circuit board on the underside of a 115{\mu}m thick silicon wafer with ~100{\mu}m ({\lambda}/4) resolution. With subwavelength resolution and the inherent sensitivity to local conductivity provided by the THz probe frequencies, we show that it is possible to detect fissures in the circuitry wiring of a few microns in size. Imaging systems of this type could have other uses where non-invasive measurement or imaging of concealed structures with high resolution is necessary, such as in semiconductor manufacturing or in bio-imaging

    Dust heating by the interstellar radiation field in models of turbulent molecular clouds

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    We have calculated the radiation field, dust grain temperatures, and far infrared emissivity of numerical models of turbulent molecular clouds. When compared to a uniform cloud of the same mean optical depth, most of the volume inside the turbulent cloud is brighter, but most of the mass is darker. There is little mean attenuation from center to edge, and clumping causes the radiation field to be somewhat bluer. There is also a large dispersion, typically by a few orders of magnitude, of all quantities relative to their means. However, despite the scatter, the 850 micron emission maps are well correlated with surface density. The fraction of mass as a function of intensity can be reproduced by a simple hierarchical model of density structure.Comment: 32 pages, 14 figures, submitted to Ap

    Efficient computation of hashes

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    The sequential computation of hashes at the core of many distributed storage systems and found, for example, in grid services can hinder efficiency in service quality and even pose security challenges that can only be addressed by the use of parallel hash tree modes. The main contributions of this paper are, first, the identification of several efficiency and security challenges posed by the use of sequential hash computation based on the Merkle-Damgard engine. In addition, alternatives for the parallel computation of hash trees are discussed, and a prototype for a new parallel implementation of the Keccak function, the SHA-3 winner, is introduced
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