880 research outputs found

    Anomalous diffusion associated with nonlinear fractional derivative Fokker-Planck-like equation: Exact time-dependent solutions

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    We consider the d=1d=1 nonlinear Fokker-Planck-like equation with fractional derivatives tP(x,t)=Dγxγ[P(x,t)]ν\frac{\partial}{\partial t}P(x,t)=D \frac{\partial^{\gamma}}{\partial x^{\gamma}}[P(x,t) ]^{\nu}. Exact time-dependent solutions are found for ν=2γ1+γ \nu = \frac{2-\gamma}{1+ \gamma} (<γ2-\infty<\gamma \leq 2). By considering the long-distance {\it asymptotic} behavior of these solutions, a connection is established, namely q=γ+3γ+1q=\frac{\gamma+3}{\gamma+1} (0<γ20<\gamma \le 2), with the solutions optimizing the nonextensive entropy characterized by index qq . Interestingly enough, this relation coincides with the one already known for L\'evy-like superdiffusion (i.e., ν=1\nu=1 and 0<γ20<\gamma \le 2). Finally, for (γ,ν)=(2,0)(\gamma,\nu)=(2, 0) we obtain q=5/3q=5/3 which differs from the value q=2q=2 corresponding to the γ=2\gamma=2 solutions available in the literature (ν<1\nu<1 porous medium equation), thus exhibiting nonuniform convergence.Comment: 3 figure

    Comparison between dispersed nuclear power plants and a nuclear energy center at a hypothetical site on Kentucky Lake, Tennessee

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    The thermal, ecological, and social impacts of a 40-reactor NEC are compared to impacts from four 10-reactor NECs and ten 4-reactor power plants. The comparison was made for surrogate sites in western Tennessee. The surrogate site for the 40-reactor NEC is located on Kentucky Lake. A layout is postulated for ten clusters of four reactors each with 2.5-mile spacing between clusters. The plants use natural-draft cooling towers. A transmission system is proposed for delivering the power (48,000 MW) to five load centers. Comparable transmission systems are proposed for the 10-reactor NECs and the 4-reactor dispersed sites delivering power to the same load centers. (auth

    Beyond the binary collision approximation for the large-qq response of liquid 4^4He

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    We discuss corrections to the linear response of a many-body system beyond the binary collision approximation. We first derive for smooth pair interactions an exact expression of the response 1/q2\propto 1/q^2, considerably simplifying existing forms and present also the generalization for interactions with a strong, short-range repulsion. We then apply the latter to the case of liquid 4^4He. We display the numerical influence of the 1/q21/q^2 correction around the quasi-elastic peak and in the low-intensity wings of the response, far from that peak. Finally we resolve an apparent contradiction in previous discussions around the fourth order cumulant expansion coefficient. Our results prove that the large-qq response of liquid 4^4He can be accurately understood on the basis of a dynamical theory.Comment: 19 p. Figs. available on reques

    Renormalization Scheme Dependence and the Problem of Theoretical Uncertainties in Next-Next-to-Leading Order QCD Predictions

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    Renormalization scheme uncertainties in the next-next-to-leading order QCD predictions are discussed. To obtain an estimate of these uncertainties it is proposed to compare predictions in all schemes that do not have unnaturally large expansion coefficients. A concrete prescription for eliminating the unnatural schemes is given, based on the requirement that large cancellations in the expression for the characteristic renormalization scheme invariant should be avoided. As an example the QCD corrections to the Bjorken sum rule are considered. The importance of the next-next-to-leading order corrections for a proper evaluation of perturbative QCD predictions is emphasized.Comment: 15 pages, 3 figures,Late

    Exploring skewed parton distributions with two body models on the light front II: covariant Bethe-Salpeter approach

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    We explore skewed parton distributions for two-body, light-front wave functions. In order to access all kinematical regimes, we adopt a covariant Bethe-Salpeter approach, which makes use of the underlying equation of motion (here the Weinberg equation) and its Green's function. Such an approach allows for the consistent treatment of the non-wave function vertex (but rules out the case of phenomenological wave functions derived from ad hoc potentials). Our investigation centers around checking internal consistency by demonstrating time-reversal invariance and continuity between valence and non-valence regimes. We derive our expressions by assuming the effective qq potential is independent of the mass squared, and verify the sum rule in a non-relativistic approximation in which the potential is energy independent. We consider bare-coupling as well as interacting skewed parton distributions and develop approximations for the Green's function which preserve the general properties of these distributions. Lastly we apply our approach to time-like form factors and find similar expressions for the related generalized distribution amplitudes.Comment: 25 pages, 12 figures, revised (minor changes but essential to consistency

    Felsic crust development in the Kaapvaal Craton, South Africa: A reference sample collection to investigate a billion years of geological history

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    The crust of the Kaapvaal craton accreted throughout the Archaean over nearly 1 billion years. It provides a unique example of the various geological processes that shape Earth's continental crust, and is illustrated by a reference collection of granitoids and mafic rocks (SWASA collection). This sample collection is fully characterised in term of age, major and trace elements, and documents the following multistage history of the craton. In the Barberton area, the initial stages of accretion (stage B·I, > 3.33 Ga and B.II, 3.28—3.21 Ga) correspond to the formation of a sodic (TTG) crust extracted from a near-chondritic reservoir. Stage B.III (ca. 3.1 Ga) corresponds to reworking of this crust, either through intracrustal melting, or via recycling of some material into the mantle and melting of this enriched mantle. Stage B.IV (2.85—2.7 Ga) corresponds to the emplacement of small, discrete plutons involving limited intracrustal reworking. The Northern Kaapvaal craton corresponds to a mobile belt flanking the Barberton cratonic core to the North. Stage NK·I (> 3.1 Ga) resembles stages B·I and B.II: formation of a TTG crust from a chondritic reservoir. In contrast, stage NK.II. (2.97–2.88 Ga) witnesses probable rifting of a cratonic fragment and formation of greenstone basins as well as a new generation of TTGs with both the mafic and felsic magmatism extracted from an isotopically depleted mantle (super-chondritic) reservoir. Intra-crustal reworking dominates stage NK.III (2.88–2.71 Ga), whereas sanukitoids and related granites, involving a mantle contaminated by recycled crustal material, are common during stage NK.IV (ca. 2.67 Ga)

    Supersymmetric string model with 30 kappa--symmetries in an extended D=11 superspace and 30/ 32 BPS states

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    A supersymmetric string model in the D=11 superspace maximally extended by antisymmetric tensor bosonic coordinates, Σ(52832)\Sigma^{(528|32)}, is proposed. It possesses 30 κ\kappa-symmetries and 32 target space supersymmetries. The usual preserved supersymmetry-κ\kappa-symmetry correspondence suggests that it describes the excitations of a BPS state preserving all but two supersymmetries. The model can also be formulated in any Σ(n(n+1)2n)\Sigma^{({n(n+1)\over 2}|n)} superspace, n=32 corresponding to D=11. It may also be treated as a `higher--spin generalization' of the usual Green--Schwarz superstring. Although the global symmetry of the model is a generalization of the super--Poincar\'e group, Σ(n(n+1)2n)×Sp(n){\Sigma}^{({n(n+1)\over 2}|n)}\times\supset Sp(n), it may be formulated in terms of constrained OSp(2n|1) orthosymplectic supertwistors. We work out this supertwistor realization and its Hamiltonian dynamics. We also give the supersymmetric p-brane generalization of the model. In particular, the Σ(52832)\Sigma^{(528|32)} supersymmetric membrane model describes excitations of a 30/32 BPS state, as the Σ(52832)\Sigma^{(528|32)} supersymmetric string does, while the supersymmetric 3-brane and 5-brane correspond, respectively, to 28/32 and 24/32 BPS states.Comment: 23 pages, RevTex4. V2: minor corrections in title and terminology, some references and comments adde

    Trans-Amazon Drilling Project (TADP): origins and evolution of the forests, climate, and hydrology of the South American tropics

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    This article presents the scientific rationale for an ambitious ICDP drilling project to continuously sample Late Cretaceous to modern sediment in four different sedimentary basins that transect the equatorial Amazon of Brazil, from the Andean foreland to the Atlantic Ocean. The goals of this project are to document the evolution of plant biodiversity in the Amazon forests and to relate biotic diversification to changes in the physical environment, including climate, tectonism, and the surface landscape. These goals require long sedimentary records from each of the major sedimentary basins across the heart of the Brazilian Amazon, which can only be obtained by drilling because of the scarcity of Cenozoic outcrops. The proposed drilling will provide the first long, nearly continuous regional records of the Cenozoic history of the forests, their plant diversity, and the associated changes in climate and environment. It also will address fundamental questions about landscape evolution, including the history of Andean uplift and erosion as recorded in Andean foreland basins and the development of west-to-east hydrologic continuity between the Andes, the Amazon lowlands, and the equatorial Atlantic. Because many modern rivers of the Amazon basin flow along the major axes of the old sedimentary basins, we plan to locate drill sites on the margin of large rivers and to access the targeted drill sites by navigation along these rivers
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