Spatially partitioned embedded Runge-Kutta Methods

We study spatially partitioned embedded Runge–Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different part of the spatial domain. Such methods may be convenient for problems in which the smoothness of the solution or the magnitudes of the PDE coefficients vary strongly in space. We focus on embedded partitioned methods as they offer greater efficiency and avoid the order reduction that may occur in non-embedded schemes. We demonstrate that the lack of conservation in partitioned schemes can lead to non-physical effects and propose conservative additive schemes based on partitioning the fluxes rather than the ordinary differential equations. A variety of SPERK schemes are presented, including an embedded pair suitable for the time evolution of fifth-order weighted non-oscillatory (WENO) spatial discretizations. Numerical experiments are provided to support the theory

Strong Stability Preserving Two-Step Runge-Kutta Methods

We investigate the strong stability preserving (SSP) property of two-step Runge– Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple\ud subclass of TSRK methods, in which stages from the previous step are not used. We derive simple order conditions for this subclass. Whereas explicit SSP Runge–Kutta methods have order at most four, we prove that explicit SSP TSRK methods have order at most eight. We present TSRK methods of up to eighth order that were found by numerical search. These methods have larger SSP coefficients than any known methods of the same order of accuracy, and may be implemented in a form with relatively modest storage requirements. The usefulness of the TSRK methods is demonstrated through numerical examples, including integration of very high order WENO discretizations

University of Glasgow at WebCLEF 2005: experiments in per-field normalisation and language specific stemming

We participated in the WebCLEF 2005 monolingual task. In this task, a search system aims to retrieve relevant documents from a multilingual corpus of Web documents from Web sites of European governments. Both the documents and the queries are written in a wide range of European languages. A challenge in this setting is to detect the language of documents and topics, and to process them appropriately. We develop a language specific technique for applying the correct stemming approach, as well as for removing the correct stopwords from the queries. We represent documents using three fields, namely content, title, and anchor text of incoming hyperlinks. We use a technique called per-field normalisation, which extends the Divergence From Randomness (DFR) framework, to normalise the term frequencies, and to combine them across the three fields. We also employ the length of the URL path of Web documents. The ranking is based on combinations of both the language specific stemming, if applied, and the per-field normalisation. We use our Terrier platform for all our experiments. The overall performance of our techniques is outstanding, achieving the overall top four performing runs, as well as the top performing run without metadata in the monolingual task. The best run only uses per-field normalisation, without applying stemming

Effective order strong stability preserving Runge–Kutta methods

We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. The relaxed order conditions allow for greater freedom in the design of effective order methods. We show that this allows the construction of four-stage SSP methods with effective order four (such methods cannot have classical order four). However, we also prove that effective order five methods—like classical order five methods—require the use of non-positive weights and so cannot be SSP. By numerical optimization, we construct explicit SSP Runge–Kutta methods up to effective order four and establish the optimality of many of them. Numerical experiments demonstrate the validity of these methods in practice

Jack polynomials with prescribed symmetry and hole propagator of spin Calogero-Sutherland model

We study the hole propagator of the Calogero-Sutherland model with SU(2) internal symmetry. We obtain the exact expression for arbitrary non-negative integer coupling parameter $\beta$ and prove the conjecture proposed by one of the authors. Our method is based on the theory of the Jack polynomials with a prescribed symmetry.Comment: 12 pages, REVTEX, 1 eps figur

Bilinear identities on Schur symmetric functions

A series of bilinear identities on the Schur symmetric functions is obtained with the use of Pluecker relations.Comment: Accepted to Journal of Nonlinear Mathematical Physics. A reference to a connected result is adde

Rising minimum daily flows in northern Eurasian rivers: A growing influence of groundwater in the high‐latitude hydrologic cycle

A first analysis of new daily discharge data for 111 northern rivers from 1936–1999 and 1958–1989 finds an overall pattern of increasing minimum daily flows (or “low flows”) throughout Russia. These increases are generally more abundant than are increases in mean flow and appear to drive much of the overall rise in mean flow observed here and in previous studies. Minimum flow decreases have also occurred but are less abundant. The minimum flow increases are found in summer as well as winter and in nonpermafrost as well as permafrost terrain. No robust spatial contrasts are found between the European Russia, Ob\u27, Yenisey, and Lena/eastern Siberia sectors. A subset of 12 unusually long discharge records from 1935–2002, concentrated in south central Russia, suggests that recent minimum flow increases since ∼1985 are largely unprecedented in the instrumental record, at least for this small group of stations. If minimum flows are presumed sensitive to groundwater and unsaturated zone inputs to river discharge, then the data suggest a broad‐scale mobilization of such water sources in the late 20th century. We speculate that reduced intensity of seasonal ground freezing, together with precipitation increases, might drive much of the well documented but poorly understood increases in river discharge to the Arctic Ocean

The quantum Casimir operators of \Uq and their eigenvalues

We show that the quantum Casimir operators of the quantum linear group constructed in early work of Bracken, Gould and Zhang together with one extra central element generate the entire center of \Uq. As a by product of the proof, we obtain intriguing new formulae for eigenvalues of these quantum Casimir operators, which are expressed in terms of the characters of a class of finite dimensional irreducible representations of the classical general linear algebra.Comment: 10 page

Some Properties of the Calogero-Sutherland Model with Reflections

We prove that the Calogero-Sutherland Model with reflections (the BC_N model) possesses a property of duality relating the eigenfunctions of two Hamiltonians with different coupling constants. We obtain a generating function for their polynomial eigenfunctions, the generalized Jacobi polynomials. The symmetry of the wave-functions for certain particular cases (associated to the root systems of the classical Lie groups B_N, C_N and D_N) is also discussed.Comment: 16 pages, harvmac.te

Spin-dependent Seebeck coefficients of Ni_{80}Fe_{20} and Co in nanopillar spin valves

We have experimentally determined the spin-dependent Seebeck coefficient of permalloy (Ni_{80}Fe_{20}) and cobalt (Co) using nanopillar spin valve devices. The devices were specifically designed to completely separate heat related effects from charge related effects. A pure heat current through the nanopillar spin valve, a stack of two ferromagnetic layers (F) separated by a non-magnetic layer (N), leads to a thermovoltage proportional to the spin-dependent Seebeck coefficient S_{S}=S_{\uparrow}-S_{\downarrow} of the ferromagnet, where S_{\uparrow} and S_{\downarrow} are the Seebeck coefficient for spin-up and spin-down electrons. By using a three-dimensional finite-element model (3D-FEM) based on spin-dependent thermoelectric theory, whose input material parameters were measured in separate devices, we were able to accurately determine a spin-dependent Seebeck coefficient of -1.8 microvolt/Kelvin and -4.5 microvolt/Kelvin for cobalt and permalloy, respectively corresponding to a Seebeck coefficient polarization P_{S}=S_{S}/S_{F} of 0.08 and 0.25, where S_{F} is the Seebeck coefficient of the ferromagnet. The results are in agreement with earlier theoretical work in Co/Cu multilayers and spin-dependent Seebeck and spin-dependent Peltier measurements in Ni_{80}Fe_{20}/Cu spin valve structures