596 research outputs found

    Convolution of multifractals and the local magnetization in a random field Ising chain

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    The local magnetization in the one-dimensional random-field Ising model is essentially the sum of two effective fields with multifractal probability measure. The probability measure of the local magnetization is thus the convolution of two multifractals. In this paper we prove relations between the multifractal properties of two measures and the multifractal properties of their convolution. The pointwise dimension at the boundary of the support of the convolution is the sum of the pointwise dimensions at the boundary of the support of the convoluted measures and the generalized box dimensions of the convolution are bounded from above by the sum of the generalized box dimensions of the convoluted measures. The generalized box dimensions of the convolution of Cantor sets with weights can be calculated analytically for certain parameter ranges and illustrate effects we also encounter in the case of the measure of the local magnetization. Returning to the study of this measure we apply the general inequalities and present numerical approximations of the D_q-spectrum. For the first time we are able to obtain results on multifractal properties of a physical quantity in the one-dimensional random-field Ising model which in principle could be measured experimentally. The numerically generated probability densities for the local magnetization show impressively the gradual transition from a monomodal to a bimodal distribution for growing random field strength h.Comment: An error in figure 1 was corrected, small additions were made to the introduction and the conclusions, some typos were corrected, 24 pages, LaTeX2e, 9 figure

    Orbits and phase transitions in the multifractal spectrum

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    We consider the one dimensional classical Ising model in a symmetric dichotomous random field. The problem is reduced to a random iterated function system for an effective field. The D_q-spectrum of the invariant measure of this effective field exhibits a sharp drop of all D_q with q < 0 at some critical strength of the random field. We introduce the concept of orbits which naturally group the points of the support of the invariant measure. We then show that the pointwise dimension at all points of an orbit has the same value and calculate it for a class of periodic orbits and their so-called offshoots as well as for generic orbits in the non-overlapping case. The sharp drop in the D_q-spectrum is analytically explained by a drastic change of the scaling properties of the measure near the points of a certain periodic orbit at a critical strength of the random field which is explicitly given. A similar drastic change near the points of a special family of periodic orbits explains a second, hitherto unnoticed transition in the D_q-spectrum. As it turns out, a decisive role in this mechanism is played by a specific offshoot. We furthermore give rigorous upper and/or lower bounds on all D_q in a wide parameter range. In most cases the numerically obtained D_q coincide with either the upper or the lower bound. The results in this paper are relevant for the understanding of random iterated function systems in the case of moderate overlap in which periodic orbits with weak singularity can play a decisive role.Comment: The article has been completely rewritten; the title has changed; a section about the typical pointwise dimension as well as several references and remarks about more general systems have been added; to appear in J. Phys. A; 25 pages, 11 figures, LaTeX2

    Nonlinear waves in a cylindrical Bose-Einstein condensate

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    We present a complete calculation of solitary waves propagating in a steady state with constant velocity v along a cigar-shaped Bose-Einstein trap approximated as infinitely-long cylindrical. For sufficiently weak couplings (densities) the main features of the calculated solitons could be captured by effective one-dimensional (1D) models. However, for stronger couplings of practical interest, the relevant solitary waves are found to be hybrids of quasi-1D solitons and 3D vortex rings. An interesting hierarchy of vortex rings occurs as the effective coupling constant is increased through a sequence of critical values. The energy-momentum dispersion of the above structures is shown to exhibit characteristics similar to a mode proposed sometime ago by Lieb within a strictly 1D model, as well as some rotonlike features.Comment: 10 pages, 12 figure

    Dark soliton states of Bose-Einstein condensates in anisotropic traps

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    Dark soliton states of Bose-Einstein condensates in harmonic traps are studied both analytically and computationally by the direct solution of the Gross-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The energy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. Large amplitude field modulation at a frequency resonant with the energy of a dark soliton is found to give rise to a state with multiple vortices. The Bogoliubov excitation spectrum of the soliton state contains complex frequencies, which disappear for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by propagation in real time.Comment: 11 pages, 8 embedded figures (two in color

    Experimental and numerical analysis of initial plasticity in P91 steel small punch creep samples

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    To date, the complex behaviour of small punch creep test (SPCT) specimens has not been completely understood, making the test hard to numerically model and the data difficult to interpret. This paper presents a novel numerical model able to generate results that match the experimental findings. For the first time, pre-strained uniaxial creep test data of a P91 steel at 600 °C have been implemented in a conveniently modified Liu and Murakami creep damage model in order to simulate the effects of the initial localised plasticity on the subsequent creep response of a small punch creep test specimen. Finite element (FE) results, in terms of creep displacement rate and time to failure, obtained by the modified Liu and Murakami model are in good agreement with experimental small punch creep test data. The rupture times obtained by the FE calculations which make use of the non-modified creep damage model are one order of magnitude shorter than those obtained by using the modified constitutive model. Although further investigation is needed, this novel approach has confirmed that the effects of initial localised plasticity, taking place in the early stages of small punch creep test, cannot be neglected. The new results, obtained by using the modified constitutive model, show a significant improvement with respect to those obtained by a state of the art creep damage constitutive model (the Liu and Murakami constitutive model) both in terms of minimum load-line displacement rate and time to rupture. The new modelling method will potentially lead to improved capability for SPCT data interpretatio

    Eteokles in Spain? On Brecht’s Mein Bruder war ein Flieger

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    One of Bertolt Brecht’s most famous poems, Mein Bruder war ein Flieger, is often invoked as a manifesto for pacifist ideals, but some essential questions (who is the lyric I? what is the literal meaning of the poem?) have hardly received any attention. By evoking the poem’s nature as a Kinderlied, the context of its first publication, and its relationship with Brecht’s play Die Gewehre der Frau Carrar, this article tentatively identifies the source of its final pointe in a famous passage of Aeschylus’ Seven against Thebes, thereby suggesting—on the basis of textual comparisons—an example of far-reaching, ideological Antikerezeption in Brecht’s oeuvre, working all the way down to his Kalendergeschichten and to his Antigone

    Theropod Fauna from Southern Australia Indicates High Polar Diversity and Climate-Driven Dinosaur Provinciality

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    The Early Cretaceous fauna of Victoria, Australia, provides unique data on the composition of high latitude southern hemisphere dinosaurs. We describe and review theropod dinosaur postcranial remains from the Aptian–Albian Otway and Strzelecki groups, based on at least 37 isolated bones, and more than 90 teeth from the Flat Rocks locality. Several specimens of medium- and large-bodied individuals (estimated up to ∼8.5 metres long) represent allosauroids. Tyrannosauroids are represented by elements indicating medium body sizes (∼3 metres long), likely including the holotype femur of Timimus hermani, and a single cervical vertebra represents a juvenile spinosaurid. Single specimens representing medium- and small-bodied theropods may be referrable to Ceratosauria, Ornithomimosauria, a basal coelurosaur, and at least three taxa within Maniraptora. Thus, nine theropod taxa may have been present. Alternatively, four distinct dorsal vertebrae indicate a minimum of four taxa. However, because most taxa are known from single bones, it is likely that small-bodied theropod diversity remains underestimated. The high abundance of allosauroids and basal coelurosaurs (including tyrannosauroids and possibly ornithomimosaurs), and the relative rarity of ceratosaurs, is strikingly dissimilar to penecontemporaneous dinosaur faunas of Africa and South America, which represent an arid, lower-latitude biome. Similarities between dinosaur faunas of Victoria and the northern continents concern the proportional representatation of higher clades, and may result from the prevailing temperate–polar climate of Australia, especially at high latitudes in Victoria, which is similar to the predominant warm–temperate climate of Laurasia, but distinct from the arid climate zone that covered extensive areas of Gondwana. Most dinosaur groups probably attained a near-cosmopolitan distribution in the Jurassic, prior to fragmentation of the Pangaean supercontinent, and some aspects of the hallmark ‘Gondwanan’ fauna of South America and Africa may therefore reflect climate-driven provinciality, not vicariant evolution driven by continental fragmentation. However, vicariance may still be detected at lower phylogenetic levels

    NetTurnP – Neural Network Prediction of Beta-turns by Use of Evolutionary Information and Predicted Protein Sequence Features

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    UNLABELLED: β-turns are the most common type of non-repetitive structures, and constitute on average 25% of the amino acids in proteins. The formation of β-turns plays an important role in protein folding, protein stability and molecular recognition processes. In this work we present the neural network method NetTurnP, for prediction of two-class β-turns and prediction of the individual β-turn types, by use of evolutionary information and predicted protein sequence features. It has been evaluated against a commonly used dataset BT426, and achieves a Matthews correlation coefficient of 0.50, which is the highest reported performance on a two-class prediction of β-turn and not-β-turn. Furthermore NetTurnP shows improved performance on some of the specific β-turn types. In the present work, neural network methods have been trained to predict β-turn or not and individual β-turn types from the primary amino acid sequence. The individual β-turn types I, I', II, II', VIII, VIa1, VIa2, VIba and IV have been predicted based on classifications by PROMOTIF, and the two-class prediction of β-turn or not is a superset comprised of all β-turn types. The performance is evaluated using a golden set of non-homologous sequences known as BT426. Our two-class prediction method achieves a performance of: MCC=0.50, Qtotal=82.1%, sensitivity=75.6%, PPV=68.8% and AUC=0.864. We have compared our performance to eleven other prediction methods that obtain Matthews correlation coefficients in the range of 0.17-0.47. For the type specific β-turn predictions, only type I and II can be predicted with reasonable Matthews correlation coefficients, where we obtain performance values of 0.36 and 0.31, respectively. CONCLUSION: The NetTurnP method has been implemented as a webserver, which is freely available at http://www.cbs.dtu.dk/services/NetTurnP/. NetTurnP is the only available webserver that allows submission of multiple sequences

    J-Integral Calculation by Finite Element Processing of Measured Full-Field Surface Displacements

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    © 2017 The Author(s)A novel method has been developed based on the conjoint use of digital image correlation to measure full field displacements and finite element simulations to extract the strain energy release rate of surface cracks. In this approach, a finite element model with imported full-field displacements measured by DIC is solved and the J-integral is calculated, without knowledge of the specimen geometry and applied loads. This can be done even in a specimen that develops crack tip plasticity, if the elastic and yield behaviour of the material are known. The application of the method is demonstrated in an analysis of a fatigue crack, introduced to an aluminium alloy compact tension specimen (Al 2024, T351 heat condition)
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