1,191 research outputs found
Basic Understanding of Condensed Phases of Matter via Packing Models
Packing problems have been a source of fascination for millenia and their
study has produced a rich literature that spans numerous disciplines.
Investigations of hard-particle packing models have provided basic insights
into the structure and bulk properties of condensed phases of matter, including
low-temperature states (e.g., molecular and colloidal liquids, crystals and
glasses), multiphase heterogeneous media, granular media, and biological
systems. The densest packings are of great interest in pure mathematics,
including discrete geometry and number theory. This perspective reviews
pertinent theoretical and computational literature concerning the equilibrium,
metastable and nonequilibrium packings of hard-particle packings in various
Euclidean space dimensions. In the case of jammed packings, emphasis will be
placed on the "geometric-structure" approach, which provides a powerful and
unified means to quantitatively characterize individual packings via jamming
categories and "order" maps. It incorporates extremal jammed states, including
the densest packings, maximally random jammed states, and lowest-density jammed
structures. Packings of identical spheres, spheres with a size distribution,
and nonspherical particles are also surveyed. We close this review by
identifying challenges and open questions for future research.Comment: 33 pages, 20 figures, Invited "Perspective" submitted to the Journal
of Chemical Physics. arXiv admin note: text overlap with arXiv:1008.298
1 Bounds and Constructions for Granular Media Coding
AbstractâBounds on the rates of grain-correcting codes are presented. The lower bounds are GilbertâVarshamov-like ones, whereas the upper bounds improve on the previously known result by Mazumdar et al. Constructions of t-grain-correcting codes of length n for certain values of n and t are discussed. Finally, an infinite family of codes of rate approaching 1 that can detect an arbitrary number of grain errors is shown to exist. Index Termsâconvex optimization, GilbertâVarshamov bound, grain-correcting codes, granular media, lower bounds, magnetic recording, Markov chain, upper bounds. I
Theoretical studies on the mechanical behavior of granular materials under very low intergranular stresses
The salient aspects of the theoretical modeling of a conventional triaxial test (CTC) of a cohesionless granular medium with stress and strain rate loading are described. Included are a controllable gravitational body force and provision for low confining pressure and/or very low intergranular stress. The modeling includes rational, analytic, and numerical phases, all in various stages of development. The numerical evolutions of theoretical models will be used in final design stages and in the analysis of the experimental data. In this the experimental design stage, it is of special interest to include in the candidate considerations every anomaly found in preliminary terrestrial experimentation. Most of the anomalies will be eliminated by design or enhanced for measurement as the project progresses. The main aspect of design being not the physical apparatus but the type and trajectories of loading elected. The major considerations that have been treated are: appearance and growth of local surface aberrations, stress-power coefficients, strain types, optical strain, radial bead migration, and measures of rotation for the proper stress flux
Correcting Grain-Errors in Magnetic Media
This paper studies new bounds and code constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth. We derive new bounds on the maximum cardinality of a grain-error-correcting code and propose constructions of codes that correct grain-errors. We demonstrate that a permutation of the classical group codes (e.g., Constantin-Rao codes) can correct a single grain-error. In many cases of interest, our results improve upon the currently best known bounds and constructions. Some of the approaches adopted in the context of grain-errors may have application to related channel models
Green Facades and Living WallsâA Review Establishing the Classification of Construction Types and Mapping the Benefits
The green facades and living walls of vertical greenery systems (VGS) are gaining increasing importance as sustainable building design elements because they can improve the environmental impact of a building. The field could benefit from a comprehensive mapping out of VGS types, an improved classification and nomenclature system, and from linking the benefits to a specific construction type. Therefore, this research reviews existing VGS construction types and links associated benefits to them, clearly differentiating empirical from descriptive supporting data. The study adopted a scoping research review used for mapping a specific research field. A systematic literature review based on keywords identified 13 VGS construction typesâfour types of green facades, nine types of living walls, and ten benefits. Thermal performance, as a benefit of VGS, is the most broadly empirically explored benefit. Yet, further qualitative studies, including human perception of thermal comfort are needed. Improvements in air quality, reduction of noise, positive effects on hydrology, and visual benefits need much further empirical testing, as the current supporting data is mostly descriptive and based on the similarities with green roofs. The educational benefits of VGS has no supporting empirical evidence, while the social benefits have only been empirically evaluated through one identified study. Future progress of the field depends on the adoption of a clear VGS nomenclature system and further qualitative and quantitative empirical testing of VGS benefits, which should be clearly linked to a specific VGS construction type so that cross-comparison of studies is enabled
Combinatorial Methods in Coding Theory
This thesis is devoted to a range of questions in applied mathematics and signal processing motivated by applications in error correction, compressed sensing, and writing on non-volatile memories. The underlying thread of our results is the use of diverse combinatorial methods originating in coding theory and computer science.
The thesis addresses three groups of problems. The first of them is
aimed at the construction and analysis of codes for error correction. Here we examine properties of codes that are constructed using random and structured graphs and hypergraphs, with the main purpose of devising new decoding algorithms as well as estimating the distribution of Hamming weights in the resulting codes. Some of the results obtained give the best known estimates of the number of correctable errors for codes whose decoding relies on local operations on the graph.
In the second part we address the question of constructing sampling
operators for the compressed sensing problem. This topic has been
the subject of a large body of works in the literature. We propose
general constructions of sampling matrices based on ideas from coding theory that act as near-isometric maps on almost all sparse signal. This matrices can be used for dimensionality reduction and compressed sensing.
In the third part we study the problem of reliable storage of information in non-volatile memories such as flash drives. This problem gives rise to a writing scheme that relies on relative magnitudes of neighboring cells, known as rank modulation. We establish the exact asymptotic behavior of the size of codes for rank modulation and suggest a number of new general constructions of such codes based on properties of finite fields as well as combinatorial considerations
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
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Sight, sound, the chicken and the egg: Audio-visual co-dependency in music
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Amongst the modern day abundance of audio-visual media, where sounds represent everything from the swooping of virtual cameras through 3D spaces to the pressing of buttons and receiving of emails, and conversely where VJs routinely accompany live musical performance with an increasingly sophisticated language of abstract computer animation, the notion of music as a necessarily exclusively aural medium seems somewhat out of place. Psychological theories relating to the cognition of sound, in particular physical schema, accounting for the ubiquity of vertical plane pitch metaphors in most musical cultures, provide evidence of a deep-rooted spatially informed understanding of sound thus providing a common ground for both sound and vision in music. Furthermore, Western Classical composition is rife with examples of visually conceived forms from Bachâs Crab Canon (1747) to Xenakisâ architecturally inspired Metastasis (1954). However, in practice the gap between the listenerâs auditory experience and the composerâs visual concept is often insurmountable. Rising to Schaefferâs call for âPrimacy to the ear!â (Schaeffer, 1967, pp. 28-30), acousmatic composers have sought to derive music exclusively from experientially verifiable criteria. However, in its pervasiveness of other musical genres, no doubt aided by technologically and commercially driven domination of the pre-recorded over the live listening experience in the latter half of the twentieth century, such an approach has lead to the neglect of visual aspects in the live performance of much art-music. This research aims to begin to redress this balance through the composition of, largely computer realised, audio-visual works whose conception arises not from a superimposition of one medium upon another, but through the very relations between the media themselves. Utilising modern computersâ ability to synchronise physical and virtual visual events with synthesised sound in real time not only affords composers an invaluable tool for enhancing listenerâs perception of formal structures but also implies causal relationships between the sonic and the visual which can provide a base of intuitive understanding on which more complex formal ideas can be built.Sponsored by the Brunel University Isambard Scholarship
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