782 research outputs found
Finitary topos for locally finite, causal and quantal vacuum einstein gravity
No full textThe pentalogy (Mallios, A. and Raptis, I. (2001). International Journal of Theoretical Physics 40, 1885; Mallios, A. and Raptis, I. (2002). International Journal of Theoretical Physics 41, 1857; Mallios, A. and Raptis, I. (2003).International Journal of Theoretical Physics 42, 1479; Mallios, A. and Raptis, I. (2004). 'paper-book'/research monograph); I. Raptis (2005). International Journal of Theoretical Physics (to appear)is brought to its categorical climax by organizing the curved finitary spacetime sheaves of quantumcausal sets involved therein, on which a finitary (:locally finite), singularity-free, background manifold independent and geometrically prequantized version of the gravitational vacuum Einstein field equations were seen to hold, into a topos structure [InlineMediaObject not available: see fulltext.]. We show that the category of finitary differential triads [InlineMediaObject not available: see fulltext.] is a finitary instance of an elementary topos proper in the original sense dueto Lawvere and Tierney. We present in the light of Abstract Differential Geometry (ADG) a Grothendieck-type of generalization of Sorkin's finitary substitutes of continuous spacetime manifoldtopologies, the latter's topological refinement inverse systems of locally finite coverings and their associated coarse graining sieves, the upshot being that [InlineMediaObject not available: see fulltext.] is also a finitary example of a Grothendieck topos. In the process, we discover that the subobject classifier Ω fcq of [InlineMediaObject not available: see fulltext.] is a Heyting algebra type of object, thus we infer that the internal logic of our finitary topos is intuitionistic, as expected. We also introduce the new notion of 'finitary differential geometric morphism' which, as befits ADG, gives a differential geometric slant to Sorkin's purely topological acts of refinement (:coarse graining). Based on finitary differential geometric morphisms regarded as natural transformations of the relevant sheaf categories, we observe that the functorial ADG-theoretic version of the principle of general covariance of GeneralRelativity is preserved under topological refinement. The paper closes with a thorough discussion of four future routes we could take in order to further develop our topos-theoretic perspective on ADG-gravity along certain categorical trends in current quantum gravity research. © Springer Science+Business Media, LLC 2007
Finitary-algebraic 'resolution' of the inner Schwarzschild singularity
No full textA 'resolution' of the interior singularity of the spherically symmetric Schwarzschild solution of the Einstein equations for the gravitational field of a point-particle is carried out entirely and solely by finitistic and algebraic means. To this end, the background differential spacetime manifold and, in extenso, Differential Calculus-free purely algebraic (:sheaf-theoretic) conceptual and technical machinery of Abstract Differential Geometry (ADG) is employed. As in previous works [Mallios, A. and Raptis, I. (2001). Finitary spacetime sheaves of quantum causal sets: Curving quantum causality. International Journal of Theoretical Physics, 40, 1885 [gr-qc/0102097]; Mallios, A. and Raptis, I. (2002). Finitary Čech-de Rham cohomology. International Journal of Theoretical Physics, 41, 1857 [gr-qc/0110033]; Mallios, A. and Raptis, I. (2003). Finitary, causal and quantal vacuum Einstein gravity. International Journal of Theoretical Physics 42, 1479 [gr-qc/0209048]], which this paper continues, the starting point for the present application of ADG is Sorkin's finitary (:locally finite) poset (:partially ordered set) substitutes of continuous manifolds in their Gel'fand-dual picture in terms of discrete differential incidence algebras and the finitary spacetime sheaves thereof. It is shown that the Einstein equations hold not only at the finitary poset level of 'discrete events,' but also at a suitable 'classical spacetime continuum limit' of the said finitary sheaves and the associated differential triads that they define ADG-theoretically. The upshot of this is two-fold: On the one hand, the field equations are seen to hold when only finitely many events or 'degrees of freedom' of the gravitational field are involved, so that no infinity or uncontrollable divergence of the latter arises at all in our inherently finitistic-algebraic scenario. On the other hand, the law of gravity-still modelled in ADG by a differential equation proper-does not break down in any (differential geometric) sense in the vicinity of the locus of the point-mass as it is traditionally maintained in the usual manifold-based analysis of spacetime singularities in General Relativity (GR). At the end, some brief remarks are made on the potential import of ADG-theoretic ideas in developing a genuinely background-independent Quantum Gravity (QG). A brief comparison between the 'resolution' proposed here and a recent resolution of the inner Schwarzschild singularity by Loop QG means concludes the paper. © 2006 Springer Science+Business Media, Inc
Must fermentation progress monitoring by polymer coated capacitive vapour sensor arrays
No full textThe present work deals with the task of monitoring the fermentation progress of grape must with a gas sensor array, without the use of pre-concentrator steps. The sensor array consists of eighrt interdigitated capacitors, coated with different polymeric materials through a well, formatted around the capacitor. The fermentation process of a particular must was duplicated under laboratory conditions and monitored in terms of (a) standard chemical analysis and (b) the response of the sensor array to the headspace of must samples, on a daily basis. PCA analysis revealed that a successful fermentation follows a distinct curve not related to that obtained from a series of equivalent pure ethanol solutions ©2009 IEEE
Polymer/BaTiO3 nanocomposites based chemocapacitive sensors
No full textThe performance of novel capacitive sensors, based on PHEMA-BaTiO3 composite films, is presented. The changes in capacitance response upon exposure to various levels of humidity and ethanol vapor are studied in order to evaluate the effect of incorporated BaTiO3 on the sensitivity-selectivity of the sensors. © 2008 Elsevier B.V. All rights reserved
Characterization of polymer layers for silicon micromachined bilayer chemical sensors using white light interferometry
No full textThe swelling behavior of polymer layers used in silicon micromachined bilayer structures is studied using white light interferometry. The study focuses on poly-hydroxy-ethyl-methacrylate (PHEMA) films and their behavior in terms of film expansion, response time and sensitivity upon exposure to methanol and ethanol vapors. Thin films of PHEMA exhibit higher relative swelling than thicker films, in the presence of methanol, as well as lower diffusion coefficients corresponding to higher response times. © 2005 Published by Elsevier B.V
Finitary Čech-de Rham cohomology
No full textThe present paper continues (Mallios & Rapfis, International Journal of Theoretical Physics, 2001, 40, 1885) and studies the curved finitary spacetime sheaves of incidence algebras presented therein from a Čech cohomological perspective. In particular, we entertain the possibility of constructing a nontrivial de Rham complex on these finite dimensional algebra sheaves along the lines of the first author's axiomatic approach to differential geometry via the theory of vector and algebra sheaves (Mallios, Geometry of Vector Sheaves. An Axiomtic Approach to Differential Geometry, Vols. 1-2, Kluwer, Dordrecht, 1998a; Mathematica Japonica (International Plaza), 1998b, 48, 93). The upshot of this study is that important "classical" differential geometric constructions and results usually thought of as being intimately associated with C∞-smooth manifolds carry through, virtually unaltered, to the finitary-algebraic regime with the help of some quite universal, because abstract, ideas taken mainly from sheaf-cohomology as developed in Mallios (1998a,b). At the end of the paper, and due to the fact that the incidence algebras involved have been interpreted as quantum causal sets (Raptis, International Journal of Theoretical Physics, 2000, 39, 1233; Mallios & Rapfis, 2001), we discuss how these ideas may be used in certain aspects of current research on discrete Lorentzian quantum gravity
Polymer-BaTiO 3 composites: Dielectric constant and vapor sensing properties in chemocapacitor applications
No full textEvaluation of a chemocapacitive sensor array for the detection of vapor analytes and their mixtures
No full textPolymer coated microfabricated interdigitated electrodes arrays for gas sensing applications
No full textInterDigitated Capacitive (IDC) sensor arrays are fabricated with conventional microelectronics-micromachining technologies on quartz substrates. After fabrication, a polymeric well is patterned around each IDC to precisely define the sensing area and thus deposit coatings of various polymers, by drop casting, in a reproducible and controlled manner. The gas sensing performance of the IDC array is presented for humidity and p-xylene.</jats:p
Finitary, Causal, and Quantal Vacuum Einstein Gravity
No full textWe continue recent work (Mallios and Raptis, International Journal of Theoretical Physics 40, 1885, 2001; in press) and formulate the gravitational vacuum Einstein equations, over a locally finite space-time by using the basic axiomatics, techniques, ideas, and working philosophy of Abstract Differential Geometry. The main kinematical structure involved, originally introduced and explored in (Mallios and Raptis, International Journal of Theoretical Physics 40, 1885, 2001), is a curved principal finitary space-time sheaf of incidence algebras, which have been interpreted as quantum causal sets, together with a nontrivial locally finite spin-Loretzian connection on it which lays the structural foundation for the formulation of a covariant dynamics of quantum causality in terms of sheaf morphisms. Our scheme is innately algebraic and it supports a categorical version of the principle of general covariance that is manifestly independent of a background C∞-smooth space-time manifold M. Thus, we entertain the possibility of developing a "fully covariant" path integral-type of quantum dynamical scenario for these connections that avoids ab initio various problems that such a dynamics encounters in other current quantization schemes for gravity-either canonical (Hamiltonian) or covariant (Lagrangian)-involving an external, base differential space-time manifold, namely, the choice of a diffeomorphism-invariant measure on the moduli space of gauge-equivalent (self-dual) gravitational spin-Lorentzian connections and the (Hilbert space) inner product that could in principle be constructed relative to that measure in the quantum theory-the so-called "inner product problem," as well as the "problem of time" that also involves the Diff(M) "structure group" of the classical C∞-smooth space-time continuum of general relativity. Hence, by using the inherently algebraico-sheaf-theoretic and calculus-free ideas of Abstract Differential Geometry, we are able to draw preliminary, albeit suggestive, connections between certain nonperturbative (canonical or covariant) approaches to quantum general relativity (e.g., Ashtekar's new variables and the loop formalism that has been developed along with them) and Sorkin et al.'s causal set program As it were, we "noncommutatively algebraize," "differential geomenize" and, as a result, dynamically vary causal sets. At the end, we anticipate various consequences that such a scenario for a locally finite, causal and quantal vacuum Einstein gravity might have for the obstinate (from the viewpoint of the smooth continuum) problem of C∞-smooth space-time singularities
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