Core of the Magnetic Obstacle

Rich recirculation patterns have been recently discovered in the electrically conducting flow subject to a local external magnetic termed "the magnetic obstacle" [Phys. Rev. Lett. 98 (2007), 144504]. This paper continues the study of magnetic obstacles and sheds new light on the core of the magnetic obstacle that develops between magnetic poles when the intensity of the external field is very large. A series of both 3D and 2D numerical simulations have been carried out, through which it is shown that the core of the magnetic obstacle is streamlined both by the upstream flow and by the induced cross stream electric currents, like a foreign insulated insertion placed inside the ordinary hydrodynamic flow. The closed streamlines of the mass flow resemble contour lines of electric potential, while closed streamlines of the electric current resemble contour lines of pressure. New recirculation patterns not reported before are found in the series of 2D simulations. These are composed of many (even number) vortices aligned along the spanwise line crossing the magnetic gap. The intensities of these vortices are shown to vanish toward to the center of the magnetic gap, confirming the general conclusion of 3D simulations that the core of the magnetic obstacle is frozen. The implications of these findings for the case of turbulent flow are discussed briefly.Comment: 14 pages, 9 figures, submitted to Journal of Turbulenc

Smolyak's algorithm: A powerful black box for the acceleration of scientific computations

We provide a general discussion of Smolyak's algorithm for the acceleration of scientific computations. The algorithm first appeared in Smolyak's work on multidimensional integration and interpolation. Since then, it has been generalized in multiple directions and has been associated with the keywords: sparse grids, hyperbolic cross approximation, combination technique, and multilevel methods. Variants of Smolyak's algorithm have been employed in the computation of high-dimensional integrals in finance, chemistry, and physics, in the numerical solution of partial and stochastic differential equations, and in uncertainty quantification. Motivated by this broad and ever-increasing range of applications, we describe a general framework that summarizes fundamental results and assumptions in a concise application-independent manner

Kestabilan Solusi Numerik Sistem Berderajat Kebebasan Tunggal Akibat Gempa Dengan Metode Newmark (Studi Kasus: Menghitung Respons Bangunan Baja Satu Tingkat)

Metode Newmark merupakan salah satu prosedur numerik yang biasa digunakan untuk menganalisa respon struktur terhadap beban gempa. Metode ini mempunyai dua parameter penting yaitu β dan , yang menetapkan variasi dari percepatan terhadap selang waktu dan menentukan karakteristik kestabilan dan akurasi dari metode tersebut. Apabila dipakai nilai γ = dan β = , artinya digunakan prinsip metode percepatan rata-rata. Sedangkan apabila dipakai nilai γ = dan β = , maka digunakan prinsip metode percepatan linear. Dan seperti metode numerik yang lain pada umumnya, kedua prinsip ini masing-masing juga mempunyai tingkat kestabilan dan akurasi yang berbeda-beda. Kestabilan dan ketelitian/akurasi proses numerik akan terjaga apabila dipakai nilai selang waktu (Δt) yang relatif kecil. Tujuan dari penelitian ini adalah mencari seberapa kecil nilai Δt yang harus digunakan untuk mendapatkan respon struktur yang stabil dan akurat. Struktur dimodelkan menjadi sistem berderajat kebebasan tunggal (SDOF) dan dikenakan beban impuls setengah gelombang sinus. Perhitungan respons menggunakan kedua prinsip di atas, masing-masing dilakukan variasi untuk nilai Δt dan periode (T). Prosedur ini dilakukan dengan bantuan program MS Excel. Hasil perhitungan menunjukkan untuk rata-rata prosentase perbedaan nilai hasil simpangan ≤ 1 %, kurang lebih diperlukan rata-rata nilai Δt = 0,007 T bila menggunakan prinsip percepatan linear, dan Δt = 0,005 T bila menggunakan prinsip percepatan rata-rata. Dengan kata lain, metode percepatan linear lebih efisien dalam mendapatkan hasil yang akurat dibandingkan metode percepatan rata-rata. Sebaliknya, metode percepatan linear mempunyai syarat nilai Δt tertentu agar proses numerik dapat dikatakan stabil (conditionally stable). Ketika digunakan Δt > 0,551 T respons yang dihasilkan oleh metode percepatan linear semakin lama semakin besar seiring pertambahan waktu meskipun adanya efek redaman dan ciri khas dari beban impuls dimana respons yang dihasilkan seharusnya semakin lama semakin kecil. Metode ini dapat dikatakan stabil ketika digunakan Δt < 0,551 T. Sedangkan metode percepatan rata-rata tetap stabil untuk berapa pun nilai Δt yang digunakan

Jump at the onset of saltation

We reveal a discontinuous transition in the saturated flux for aeolian saltation by simulating explicitly particle motion in turbulent flow. The discontinuity is followed by a coexistence interval with two metastable solutions. The modification of the wind profile due to momentum exchange exhibits a second maximum at high shear strength. The saturated flux depends on the strength of the wind as $q_s=q_0+A(u_*-u_t)(u_*^2+u_t^2)$

On the analogy between streamlined magnetic and solid obstacles

Analogies are elaborated in the qualitative description of two systems: the magnetohydrodynamic (MHD) flow moving through a region where an external local magnetic field (magnetic obstacle) is applied, and the ordinary hydrodynamic flow around a solid obstacle. The former problem is of interest both practically and theoretically, and the latter one is a classical problem being well understood in ordinary hydrodynamics. The first analogy is the formation in the MHD flow of an impenetrable region -- core of the magnetic obstacle -- as the interaction parameter $N$, i.e. strength of the applied magnetic field, increases significantly. The core of the magnetic obstacle is streamlined both by the upstream flow and by the induced cross stream electric currents, like a foreign insulated insertion placed inside the ordinary hydrodynamic flow. In the core, closed streamlines of the mass flow resemble contour lines of electric potential, while closed streamlines of the electric current resemble contour lines of pressure. The second analogy is the breaking away of attached vortices from the recirculation pattern produced by the magnetic obstacle when the Reynolds number $Re$, i.e. velocity of the upstream flow, is larger than a critical value. This breaking away of vortices from the magnetic obstacle is similar to that occurring past a real solid obstacle. Depending on the inlet and/or initial conditions, the observed vortex shedding can be either symmetric or asymmetric.Comment: minor changes, accepted for PoF, 26 pages, 7 figure

KESTABILAN SOLUSI NUMERIK SISTEM BERDERAJAT KEBEBASAN TUNGGAL AKIBAT GEMPA DENGAN METODE NEWMARK (Studi Kasus: Menghitung Respons Bangunan Baja Satu Tingkat)

Metode Newmark merupakan salah satu prosedur numerik yang biasa digunakan untuk menganalisa respon struktur terhadap beban gempa. Metode ini mempunyai dua parameter penting yaitu β dan , yang menetapkan variasi dari percepatan terhadap selang waktu dan menentukan karakteristik kestabilan dan akurasi dari metode tersebut. Apabila dipakai nilai γ = dan β = , artinya digunakan prinsip metode percepatan rata-rata. Sedangkan apabila dipakai nilai γ = dan β = , maka digunakan prinsip metode percepatan linear. Dan seperti metode numerik yang lain pada umumnya, kedua prinsip ini masing-masing juga mempunyai tingkat kestabilan dan akurasi yang berbeda-beda. Kestabilan dan ketelitian/akurasi proses numerik akan terjaga apabila dipakai nilai selang waktu (Δt) yang relatif kecil. Tujuan dari penelitian ini adalah mencari seberapa kecil nilai Δt yang harus digunakan untuk mendapatkan respon struktur yang stabil dan akurat. Struktur dimodelkan menjadi sistem berderajat kebebasan tunggal (SDOF) dan dikenakan beban impuls setengah gelombang sinus. Perhitungan respons menggunakan kedua prinsip di atas, masing-masing dilakukan variasi untuk nilai Δt dan periode (T). Prosedur ini dilakukan dengan bantuan program MS Excel. Hasil perhitungan menunjukkan untuk rata-rata prosentase perbedaan nilai hasil simpangan ≤ 1 %, kurang lebih diperlukan rata-rata nilai Δt = 0,007 T bila menggunakan prinsip percepatan linear, dan Δt = 0,005 T bila menggunakan prinsip percepatan rata-rata. Dengan kata lain, metode percepatan linear lebih efisien dalam mendapatkan hasil yang akurat dibandingkan metode percepatan rata-rata. Sebaliknya, metode percepatan linear mempunyai syarat nilai Δt tertentu agar proses numerik dapat dikatakan stabil (conditionally stable). Ketika digunakan Δt > 0,551 T respons yang dihasilkan oleh metode percepatan linear semakin lama semakin besar seiring pertambahan waktu meskipun adanya efek redaman dan ciri khas dari beban impuls dimana respons yang dihasilkan seharusnya semakin lama semakin kecil. Metode ini dapat dikatakan stabil ketika digunakan Δt < 0,551 T. Sedangkan metode percepatan rata-rata tetap stabil untuk berapa pun nilai Δt yang digunakan. Kata kunci : Metode Newmark, SDOF, kestabilan dan akurasi numeri

Regularity for eigenfunctions of Schr\"odinger operators

We prove a regularity result in weighted Sobolev spaces (or Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\"odinger operator. More precisely, let K_{a}^{m}(\mathbb{R}^{3N}) be the weighted Sobolev space obtained by blowing up the set of singular points of the Coulomb type potential V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N} \frac{c_{ij}}{|x_i-x_j|}, x in \mathbb{R}^{3N}, b_j, c_{ij} in \mathbb{R}. If u in L^2(\mathbb{R}^{3N}) satisfies (-\Delta + V) u = \lambda u in distribution sense, then u belongs to K_{a}^{m} for all m \in \mathbb{Z}_+ and all a \le 0. Our result extends to the case when b_j and c_{ij} are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a<3/2.Comment: to appear in Lett. Math. Phy

The generalized Robinson-Foulds metric

The Robinson-Foulds (RF) metric is arguably the most widely used measure of phylogenetic tree similarity, despite its well-known shortcomings: For example, moving a single taxon in a tree can result in a tree that has maximum distance to the original one; but the two trees are identical if we remove the single taxon. To this end, we propose a natural extension of the RF metric that does not simply count identical clades but instead, also takes similar clades into consideration. In contrast to previous approaches, our model requires the matching between clades to respect the structure of the two trees, a property that the classical RF metric exhibits, too. We show that computing this generalized RF metric is, unfortunately, NP-hard. We then present a simple Integer Linear Program for its computation, and evaluate it by an all-against-all comparison of 100 trees from a benchmark data set. We find that matchings that respect the tree structure differ significantly from those that do not, underlining the importance of this natural condition.Comment: Peer-reviewed and presented as part of the 13th Workshop on Algorithms in Bioinformatics (WABI2013

Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.Comment: 21 pages, 9 figure

An adaptive numerical method for the Vlasov equation based on a multiresolution analysis.

International audienceIn this paper, we present very first results for the adaptive solution on a grid of the phase space of the Vlasov equation arising in particles accelarator and plasma physics. The numerical algorithm is based on a semi-Lagrangian method while adaptivity is obtained using multiresolution analysis