A quantum molecular similarity analysis of changes in molecular electron density caused by basis set flotation and electric field application

Quantum molecular similarity (QMS) techniques are used to assess the response of the electron density of various small molecules to application of a static, uniform electric field. Likewise, QMS is used to analyze the changes in electron density generated by the process of floating a basis set. The results obtained show an interrelation between the floating process, the optimum geometry, and the presence of an external field. Cases involving the Le Chatelier principle are discussed, and an insight on the changes of bond critical point properties, self-similarity values and density differences is performed

Improvements in the ray tracing of implicit surfaces based on interval arithmetic

Las superfícies implícitas son útiles en muchas áreasde los gráficos por ordenador. Una de sus principales ventajas es que pueden ser fácilmente usadas como primitivas para modelado. Aun asi, no son muy usadas porque su visualización toma bastante tiempo. Cuando se necesita una visualización precisa, la mejor opción es usar trazado de rayos. Sin embargo, pequeñas partes de las superficies desaparecen durante la visualización. Esto ocurre por la truncación que se presenta en la representación en punto flotante de los ordenadores; algunos bits se puerden durante las operaciones matemáticas en los algoritmos de intersección. En este tesis se presentan algoritmos para solucionar esos problemas. La investigación se basa en el uso del Análisis Intervalar Modal el cual incluye herramientas para resolver problemas con incertidumbe cuantificada. En esta tesis se proporcionan los fundamentos matemáticos necesarios para el desarrollo de estos algoritmos.

Pleistocene geochronologies for fluvial sedimentary sequences: an archaeologist's perspective

Current models of Pleistocene fluvial system development and dynamics are assessed from the perspective of European Lower and Middle Palaeolithic stone tool assemblages recovered from fluvial secondary contexts. Fluvial activity is reviewed both in terms of Milankovitch-scale processes across the glacial/interglacial cycles of the Middle and Late Pleistocene, and in response to sub-Milankovitch scale, high-frequency, low-magnitude climatic oscillations. The chronological magnitude of individual phases of fluvial activity is explored in terms of radiocarbon-dated sequences from the Late Glacial and early Holocene periods. It is apparent that fluvial activity is associated with periods of climatic transition, both high and low magnitude, although system response is far more universal in the case of the high magnitude glacial/ interglacial transitions. Current geochronological tools do not permit the development of high-resolution sequences for Middle Pleistocene sediments, while localised erosion and variable system responses do not facilitate direct comparison with the ice core records. However, Late Glacial and early Holocene sequences indicate that individual fluvial activity phases are relatively brief in duration (e.g. 10(2) and 10(3) yr). From an archaeological perspective, secondary context assemblages can only be interpreted in terms of a floating geochronology, although the data also permit a reinvestigation of the problems of artefact reworking. Copyright (c) 2005 John Wiley I Sons, Ltd.

Thermopile radiometer signal conditioning for surface atmospheric radiation measurements

A highly stable microvolt amplifier for use with atmospheric broadband thermopile radiometers is described. The amplifier has a nominal gain of 500, for bipolar input signals in the range +/- 10 mV from a floating source. The noise level at the input is less than 5 mu V (at 100 k Omega input impedance), permitting instantaneous diffuse solar radiation measurements to 0.5 W m(-2) resolution with 12 bit analog to digital conversion. The temperature stability of gain is better than 5 ppm/degrees C (-4 to 20 degrees C). Averaged over a decade of use, the long term drift of the amplifier gain is less than similar to 0.02%/yr. As well as radiometers measuring solar and terrestrial radiations, the amplifier has also been successfully used with low level signals from thermocouples and ground heat flux plates.

Torque in mooring chain. Part 1: Background and theory

Chain in both its forms - common (or stud-less) and stud-link - has many engineering applications. It is widely used as a component in the moorings of offshore floating systems, where its ruggedness and corrosion resistance make it an attractive choice. Chain exhibits some interesting behaviour in that when straight and subject to an axial load it does not twist or generate any torque, but if twisted or loaded when in a twisted condition it behaves in a highly non-linear manner, with the torque dependent upon the level of twist and axial load. Clearly an understanding of the way in which chains may behave and interact with other mooring components (such as wire rope, which also exhibits coupling between axial load and generated torque) when they are in service is essential. However, the sizes of chain that are in use in offshore moorings (typical bar diameters are 75 mm and greater) are too large to allow easy testing. This paper, which is in two parts, aims to address the issues and considerations relevant to torque in mooring chain. The first part introduces a frictionless theory that predicts the resultant torques and 'lift' in the links as non-dimensionalized functions of the angle of twist. Fortran code is presented in an Appendix, which allows the reader to make use of the analysis. The second part of the paper presents results from experimental work on both stud-less (41 mm) and stud-link (20.5 and 56 mm) chains. Torsional data are presented in both 'constant twist' and 'constant load' forms, as well as considering the lift between the links.

Perspex machine XI: topology of the transreal numbers

The transreal numbers are a total number system in which even, arithmetical operation is well defined even-where. This has many benefits over the real numbers as a basis for computation and, possibly, for physical theories. We define the topology of the transreal numbers and show that it gives a more coherent interpretation of two's complement arithmetic than the conventional integer model. Trans-two's-complement arithmetic handles the infinities and 0/0 more coherently, and with very much less circuitry, than floating-point arithmetic. This reduction in circuitry is especially beneficial in parallel computers, such as the Perspex machine, and the increase in functionality makes Digital Signal Processing chips better suited to general computation.

Perspex machine VII: The universal perspex machine

The perspex machine arose from the unification of projective geometry with the Turing machine. It uses a total arithmetic, called transreal arithmetic, that contains real arithmetic and allows division by zero. Transreal arithmetic is redefined here. The new arithmetic has both a positive and a negative infinity which lie at the extremes of the number line, and a number nullity that lies off the number line. We prove that nullity, 0/0, is a number. Hence a number may have one of four signs: negative, zero, positive, or nullity. It is, therefore, impossible to encode the sign of a number in one bit, as floating-, point arithmetic attempts to do, resulting in the difficulty of having both positive and negative zeros and NaNs. Transrational arithmetic is consistent with Cantor arithmetic. In an extension to real arithmetic, the product of zero, an infinity, or nullity with its reciprocal is nullity, not unity. This avoids the usual contradictions that follow from allowing division by zero. Transreal arithmetic has a fixed algebraic structure and does not admit options as IEEE, floating-point arithmetic does. Most significantly, nullity has a simple semantics that is related to zero. Zero means "no value" and nullity means "no information." We argue that nullity is as useful to a manufactured computer as zero is to a human computer. The perspex machine is intended to offer one solution to the mind-body problem by showing how the computable aspects of mind and. perhaps, the whole of mind relates to the geometrical aspects of body and, perhaps, the whole of body. We review some of Turing's writings and show that he held the view that his machine has spatial properties. In particular, that it has the property of being a 7D lattice of compact spaces. Thus, we read Turing as believing that his machine relates computation to geometrical bodies. We simplify the perspex machine by substituting an augmented Euclidean geometry for projective geometry. This leads to a general-linear perspex-machine which is very much easier to pro-ram than the original perspex-machine. We then show how to map the whole of perspex space into a unit cube. This allows us to construct a fractal of perspex machines with the cardinality of a real-numbered line or space. This fractal is the universal perspex machine. It can solve, in unit time, the halting problem for itself and for all perspex machines instantiated in real-numbered space, including all Turing machines. We cite an experiment that has been proposed to test the physical reality of the perspex machine's model of time, but we make no claim that the physical universe works this way or that it has the cardinality of the perspex machine. We leave it that the perspex machine provides an upper bound on the computational properties of physical things, including manufactured computers and biological organisms, that have a cardinality no greater than the real-number line.

Perspex machine VIII: axioms of transreal arithmetic

Transreal arithmetic is a total arithmetic that contains real arithmetic, but which has no arithmetical exceptions. It allows the specification of the Universal Perspex Machine which unifies geometry with the Turing Machine. Here we axiomatise the algebraic structure of transreal arithmetic so that it provides a total arithmetic on any appropriate set of numbers. This opens up the possibility of specifying a version of floating-point arithmetic that does not have any arithmetical exceptions and in which every number is a first-class citizen. We find that literal numbers in the axioms are distinct. In other words, the axiomatisation does not require special axioms to force non-triviality. It follows that transreal arithmetic must be defined on a set of numbers that contains{-8,-1,0,1,8,&pphi;} as a proper subset. We note that the axioms have been shown to be consistent by machine proof.

Numerical precision requirements on the Multiband Ultra-Wideband system for practical consumer electronic devices

This paper discusses the requirements on the numerical precision for a practical Multiband Ultra-Wideband (UWB) consumer electronic solution. To this end we first present the possibilities that UWB has to offer to the consumer electronics market and the possible range of devices. We then show the performance of a model of the UWB baseband system implemented using floating point precision. Then, by simulation we find the minimal numerical precision required to maintain floating-point performance for each of the specific data types and signals present in the UWB baseband. Finally, we present a full description of the numerical requirements for both the transmit and receive components of the UWB baseband. The numerical precision results obtained in this paper can then be used by baseband designers to implement cost effective UWB systems using System-on-Chip (SoC), FPGA and ASIC technology solutions biased toward the competitive consumer electronics market(1).

Modelling fixed plant and algal dynamics in rivers: an application to the River Frome

The development of eutrophication in river systems is poorly understood given the complex relationship between fixed plants, algae, hydrodynamics, water chemistry and solar radiation. However there is a pressing need to understand the relationship between the ecological status of rivers and the controlling environmental factors to help the reasoned implementation of the Water Framework Directive and Catchment Sensitive Farming in the UK. This research aims to create a dynamic, process-based, mathematical in-stream model to simulate the growth and competition of different vegetation types (macrophytes, phytoplankton and benthic algae) in rivers. The model, applied to the River Frome (Dorset, UK), captured well the seasonality of simulated vegetation types (suspended algae, macrophytes, epiphytes, sediment biofilm). Macrophyte results showed that local knowledge is important for explaining unusual changes in biomass. Fixed algae simulations indicated the need for the more detailed representation of various herbivorous grazer groups, however this would increase the model complexity, the number of model parameters and the required observation data to better define the model. The model results also highlighted that simulating only phytoplankton is insufficient in river systems, because the majority of the suspended algae have benthic origin in short retention time rivers. Therefore, there is a need for modelling tools that link the benthic and free-floating habitats.

Perspex machine X: software development

The Perspex Machine arose from the unification of computation with geometry. We now report significant redevelopment of both a partial C compiler that generates perspex programs and of a Graphical User Interface (GUI). The compiler is constructed with standard compiler-generator tools and produces both an explicit parse tree for C and an Abstract Syntax Tree (AST) that is better suited to code generation. The GUI uses a hash table and a simpler software architecture to achieve an order of magnitude speed up in processing and, consequently, an order of magnitude increase in the number of perspexes that can be manipulated in real time (now 6,000). Two perspex-machine simulators are provided, one using trans-floating-point arithmetic and the other using transrational arithmetic. All of the software described here is available on the world wide web. The compiler generates code in the neural model of the perspex. At each branch point it uses a jumper to return control to the main fibre. This has the effect of pruning out an exponentially increasing number of branching fibres, thereby greatly increasing the efficiency of perspex programs as measured by the number of neurons required to implement an algorithm. The jumpers are placed at unit distance from the main fibre and form a geometrical structure analogous to a myelin sheath in a biological neuron. Both the perspex jumper-sheath and the biological myelin-sheath share the computational function of preventing cross-over of signals to neurons that lie close to an axon. This is an example of convergence driven by similar geometrical and computational constraints in perspex and biological neurons.

Wave scattering by an axisymmetric ice floe of varying thickness

The problem of water wave scattering by a circular ice floe, floating in fluid of finite depth, is formulated and solved numerically. Unlike previous investigations of such situations, here we allow the thickness of the floe (and the fluid depth) to vary axisymmetrically and also incorporate a realistic non-zero draught. A numerical approximation to the solution of this problem is obtained to an arbitrary degree of accuracy by combining a Rayleigh–Ritz approximation of the vertical motion with an appropriate variational principle. This numerical solution procedure builds upon the work of Bennets et al. (2007, J. Fluid Mech., 579, 413–443). As part of the numerical formulation, we utilize a Fourier cosine expansion of the azimuthal motion, resulting in a system of ordinary differential equations to solve in the radial coordinate for each azimuthal mode. The displayed results concentrate on the response of the floe rather than the scattered wave field and show that the effects of introducing the new features of varying floe thickness and a realistic draught are significant.

Evolutionary and revolutionary effects of transcomputation

Mathematics in Defence 2011 Abstract. We review transreal arithmetic and present transcomplex arithmetic. These arithmetics have no exceptions. This leads to incremental improvements in computer hardware and software. For example, the range of real numbers, encoded by floating-point bits, is doubled when all of the Not-a-Number(NaN) states, in IEEE 754 arithmetic, are replaced with real numbers. The task of programming such systems is simplified and made safer by discarding the unordered relational operator,leaving only the operators less-than, equal-to, and greater than. The advantages of using a transarithmetic in a computation, or transcomputation as we prefer to call it, may be had by making small changes to compilers and processor designs. However, radical change is possible by exploiting the reliability of transcomputations to make pipelined dataflow machines with a large number of cores. Our initial designs are for a machine with order one million cores. Such a machine can complete the execution of multiple in-line programs each clock tick

Characterization and antimicrobial efficacy against E. coli of a helium/air plasma at atmospheric pressure created in a plastic package

A plasma source, sustained by the application of a floating high voltage (±15 kV) to parallel-plate electrodes at 50 Hz, has been achieved in a helium/air mixture at atmospheric pressure (P = 105 Pa) contained in a zip-locked plastic package placed in the electrode gap. Some of the physical and antimicrobial properties of this apparatus were established with a view to ascertain its performance as a prototype for the disinfection of fresh produce. The current–voltage (I–V) and charge–voltage (Q–V) characteristics of the system were measured as a function of gap distance d, in the range (3 × 103 ≤ Pd ≤ 1.0 × 104 Pa m). The electrical measurements showed this plasma source to exhibit the characteristic behaviour of a dielectric barrier discharge in the filamentary mode and its properties could be accurately interpreted by the two-capacitance in series model. The power consumed by the discharge and the reduced field strength were found to decrease quadratically from 12.0 W to 4.5 W and linearly from 140 Td to 50 Td, respectively, in the range studied. Emission spectra of the discharge were recorded on a relative intensity scale and the dominant spectral features could be assigned to strong vibrational bands in the 2+ and 1− systems of N2 and ${\rm N}_2^+$ , respectively, with other weak signatures from the NO and OH radicals and the N+, He and O atomic species. Absolute spectral intensities were also recorded and interpreted by comparison with the non-equilibrium synthetic spectra generated by the computer code SPECAIR. At an inter-electrode gap of 0.04 m, this comparison yielded typical values for the electron, vibrational and translational (gas) temperatures of (4980 ± 100) K, (2700 ± 200) K and (300 ± 100) K, respectively and an electron density of 1.0 × 1017 m−3. A Boltzmann plot also provided a value of (3200 ± 200 K) for the vibrational temperature. The antimicrobial efficacy was assessed by studying the resistance of both Escherichia coli K12 its isogenic mutants in soxR, soxS, oxyR, rpoS and dnaK selected to identify possible cellular responses and targets related with 5 min exposure to the active gas in proximity of, but not directly in, the path of the discharge filaments. Both the parent strain and mutants populations were significantly reduced by more than 1.5 log cycles in these conditions, showing the potential of the system. Post-treatment storage studies showed that some transcription regulators and specific genes related to oxidative stress play an important role in the E. coli repair mechanism and that plasma exposure affects specific cell regulator systems.