61,399 research outputs found

    Non-Gaussian numerical errors versus mass hierarchy

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    We probe the numerical errors made in renormalization group calculations by varying slightly the rescaling factor of the fields and rescaling back in order to get the same (if there were no round-off errors) zero momentum 2-point function (magnetic susceptibility). The actual calculations were performed with Dyson's hierarchical model and a simplified version of it. We compare the distributions of numerical values obtained from a large sample of rescaling factors with the (Gaussian by design) distribution of a random number generator and find significant departures from the Gaussian behavior. In addition, the average value differ (robustly) from the exact answer by a quantity which is of the same order as the standard deviation. We provide a simple model in which the errors made at shorter distance have a larger weight than those made at larger distance. This model explains in part the non-Gaussian features and why the central-limit theorem does not apply.Comment: 26 pages, 7 figures, uses Revte

    Basic physical and chemical processes in space radiation effects on polymers

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    The effects of space ionizing radiation on polymers is investigated in terms of operative physical and chemical processes. A useful model of charged particle impact with a polymer was designed. Principle paths of molecular relaxation were identified and energy handling processes were considered. The focus of the study was on energy absorption and the immediately following events. Further study of the radiation degradation of polymers is suggested

    Optical Studies of Metal- Semiconductor Transmutations Produced by Intercalation

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    Spectra of the alkali metal intercalation products of MoS2 and NbSc2 arc interpreted in terms of a previously published band model

    High-Accuracy Calculations of the Critical Exponents of Dyson's Hierarchical Model

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    We calculate the critical exponent gamma of Dyson's hierarchical model by direct fits of the zero momentum two-point function, calculated with an Ising and a Landau-Ginzburg measure, and by linearization about the Koch-Wittwer fixed point. We find gamma= 1.299140730159 plus or minus 10^(-12). We extract three types of subleading corrections (in other words, a parametrization of the way the two-point function depends on the cutoff) from the fits and check the value of the first subleading exponent from the linearized procedure. We suggest that all the non-universal quantities entering the subleading corrections can be calculated systematically from the non-linear contributions about the fixed point and that this procedure would provide an alternative way to introduce the bare parameters in a field theory model.Comment: 15 pages, 9 figures, uses revte

    Thermal measurement and modeling of multi-die packages

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    Thermal measurement and modeling of multi-die packages became a hot topic recently in different fields like RAM chip packaging or LEDs / LED assemblies, resulting in vertical (stacked) and lateral arrangement. In our present study we show results for a mixed arrangement: an opto-coupler device has been investigated with 4 chips in lateral as well as vertical arrangement. In this paper we give an overview of measurement and modeling techniques and results for stacked and MCM structures, describe our present measurement results together with our structure function based methodology of validating the detailed model of the package being studied. Also, we show how to derive junction-to-pin thermal resistances with a technique using structure functions.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

    A Guide to Precision Calculations in Dyson's Hierarchical Scalar Field Theory

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    The goal of this article is to provide a practical method to calculate, in a scalar theory, accurate numerical values of the renormalized quantities which could be used to test any kind of approximate calculation. We use finite truncations of the Fourier transform of the recursion formula for Dyson's hierarchical model in the symmetric phase to perform high-precision calculations of the unsubtracted Green's functions at zero momentum in dimension 3, 4, and 5. We use the well-known correspondence between statistical mechanics and field theory in which the large cut-off limit is obtained by letting beta reach a critical value beta_c (with up to 16 significant digits in our actual calculations). We show that the round-off errors on the magnetic susceptibility grow like (beta_c -beta)^{-1} near criticality. We show that the systematic errors (finite truncations and volume) can be controlled with an exponential precision and reduced to a level lower than the numerical errors. We justify the use of the truncation for calculations of the high-temperature expansion. We calculate the dimensionless renormalized coupling constant corresponding to the 4-point function and show that when beta -> beta_c, this quantity tends to a fixed value which can be determined accurately when D=3 (hyperscaling holds), and goes to zero like (Ln(beta_c -beta))^{-1} when D=4.Comment: Uses revtex with psfig, 31 pages including 15 figure

    Spatiotemporal symmetries in the disynaptic canal-neck projection

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    The vestibular system in almost all vertebrates, and in particular in humans, controls balance by employing a set of six semicircular canals, three in each inner ear, to detect angular accelerations of the head in three mutually orthogonal coordinate planes. Signals from the canals are transmitted to eight (groups of) neck motoneurons, which activate the eight corresponding muscle groups. These signals may be either excitatory or inhibitory, depending on the direction of head acceleration. McCollum and Boyle have observed that in the cat the relevant network of neurons possesses octahedral symmetry, a structure that they deduce from the known innervation patterns (connections) from canals to muscles. We rederive the octahedral symmetry from mathematical features of the probable network architecture, and model the movement of the head in response to the activation patterns of the muscles concerned. We assume that connections between neck muscles can be modeled by a “coupled cell network,” a system of coupled ODEs whose variables correspond to the eight muscles, and that this network also has octahedral symmetry. The network and its symmetries imply that these ODEs must be equivariant under a suitable action of the octahedral group. It is observed that muscle motoneurons form natural “push-pull pairs” in which, for given movements of the head, one neuron produces an excitatory signal, whereas the other produces an inhibitory signal. By incorporating this feature into the mathematics in a natural way, we are led to a model in which the octahedral group acts by signed permutations on muscle motoneurons. We show that with the appropriate group actions, there are six possible spatiotemporal patterns of time-periodic states that can arise by Hopf bifurcation from an equilibrium representing an immobile head. Here we use results of Ashwin and Podvigina. Counting conjugate states, whose physiological interpretations can have significantly different features, there are 15 patterns of periodic oscillation, not counting left-right reflections or time-reversals as being different. We interpret these patterns as motions of the head, and note that all six types of pattern appear to correspond to natural head motions

    Friction force microscopy : a simple technique for identifying graphene on rough substrates and mapping the orientation of graphene grains on copper

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    At a single atom thick, it is challenging to distinguish graphene from its substrate using conventional techniques. In this paper we show that friction force microscopy (FFM) is a simple and quick technique for identifying graphene on a range of samples, from growth substrates to rough insulators. We show that FFM is particularly effective for characterizing graphene grown on copper where it can correlate the graphene growth to the three-dimensional surface topography. Atomic lattice stick–slip friction is readily resolved and enables the crystallographic orientation of the graphene to be mapped nondestructively, reproducibly and at high resolution. We expect FFM to be similarly effective for studying graphene growth on other metal/locally crystalline substrates, including SiC, and for studying growth of other two-dimensional materials such as molybdenum disulfide and hexagonal boron nitride

    Dispersion strengthening in vanadium microalloyed steels processed by simulated thin slab casting and direct charging. Part 2 - chemical characterisation of dispersion strengthening precipitates

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    The composition of the sub-15 nm particles in six related vanadium high strength low alloy steels, made by simulated thin slab direct charged casting, has been determined using electron energy loss spectroscopy (EELS). Such particles are considered to be responsible for dispersion hardening. For the first time, particles down to 4 nm in size have had their composition fully determined. In all the steels, the particles were nitrogen and vanadium rich and possibly slightly sub-stoichiometric carbonitrides. Equilibrium thermodynamics predicted much higher carbon to metal atomic ratios than observed in all cases so that kinetics and mechanical deformation clearly control the precipitation process. Thus it is important to formulate the steel with this in mind
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