53,450 research outputs found
Small-amplitude perturbations of shape for a nearly spherical bubble in an inviscid straining flow (steady shapes and oscillatory motion)
The method of domain perturbations is used to study the problem of a nearly spherical bubble in an inviscid, axisymmetric straining flow. Steady-state shapes and axisymmetric oscillatory motions are considered. The steady-state solutions suggest the existence of a limit point at a critical Weber number, beyond which no solution exists on the steady-state solution branch which includes the spherical equilibrium state in the absence of flow (e.g. the critical value of 1.73 is estimated from the third-order solution). In addition, the first-order steady-state shape exhibits a maximum radius at θ = 1/6π which clearly indicates the barrel-like shape that was found earlier via numerical finite-deformation theories for higher Weber numbers. The oscillatory motion of a nearly spherical bubble is considered in two different ways. First, a small perturbation to a spherical base state is studied with the ad hoc assumption that the steady-state shape is spherical for the complete Weber-number range of interest. This analysis shows that the frequency of oscillation decreases as Weber number increases, and that a spherical bubble shape is unstable if Weber number is larger than 4.62. Secondly, the correct steady-state shape up to O(W) is included to obtain a rigorous asymptotic formula for the frequency change at small Weber number. This asymptotic analysis also shows that the frequency decreases as Weber number increases; for example, in the case of the principal mode (n = 2), ω^2 = ω_0^0(1−0.31W), where ω_0 is the oscillation frequency of a bubble in a quiescent fluid
Bubble dynamics in time-periodic straining flows
The dynamics and breakup of a bubble in an axisymmetric, time-periodic straining flow has been investigated via analysis of an approximate dynamic model and also by time-dependent numerical solutions of the full fluid mechanics problem. The analyses reveal that in the neighbourhood of a stable steady solution, an O(ϵ1/3) time-dependent change of bubble shape can be obtained from an O(ε) resonant forcing. Furthermore, the probability of bubble breakup at subcritical Weber numbers can be maximized by choosing an optimal forcing frequency for a fixed forcing amplitude
Integral-method analysis for a hypersonic viscous shock layer with mass injection
Integral method analysis for hypersonic viscous shock layer with mass injectio
Top-N Recommendation on Graphs
Recommender systems play an increasingly important role in online
applications to help users find what they need or prefer. Collaborative
filtering algorithms that generate predictions by analyzing the user-item
rating matrix perform poorly when the matrix is sparse. To alleviate this
problem, this paper proposes a simple recommendation algorithm that fully
exploits the similarity information among users and items and intrinsic
structural information of the user-item matrix. The proposed method constructs
a new representation which preserves affinity and structure information in the
user-item rating matrix and then performs recommendation task. To capture
proximity information about users and items, two graphs are constructed.
Manifold learning idea is used to constrain the new representation to be smooth
on these graphs, so as to enforce users and item proximities. Our model is
formulated as a convex optimization problem, for which we need to solve the
well-known Sylvester equation only. We carry out extensive empirical
evaluations on six benchmark datasets to show the effectiveness of this
approach.Comment: CIKM 201
Crystal Interpretation of Kerov-Kirillov-Reshetikhin Bijection II. Proof for sl_n Case
In proving the Fermionic formulae, combinatorial bijection called the
Kerov--Kirillov--Reshetikhin (KKR) bijection plays the central role. It is a
bijection between the set of highest paths and the set of rigged
configurations. In this paper, we give a proof of crystal theoretic
reformulation of the KKR bijection. It is the main claim of Part I
(math.QA/0601630) written by A. Kuniba, M. Okado, T. Takagi, Y. Yamada, and the
author. The proof is given by introducing a structure of affine combinatorial
matrices on rigged configurations.Comment: 45 pages, version for publication. Introduction revised, more
explanations added to the main tex
Box ball system associated with antisymmetric tensor crystals
A new box ball system associated with an antisymmetric tensor crystal of the
quantum affine algebra of type A is considered. This includes the so-called
colored box ball system with capacity 1 as the simplest case. Infinite number
of conserved quantities are constructed and the scattering rule of two olitons
are given explicitly.Comment: 15 page
Stabilizing the forming process in unipolar resistance switching using an improved compliance current limiter
The high reset current IR in unipolar resistance switching now poses major
obstacles to practical applications in memory devices. In particular, the first
IR-value after the forming process is so high that the capacitors sometimes do
not exhibit reliable unipolar resistance switching. We found that the
compliance current Icomp is a critical parameter for reducing IR-values. We
therefore introduced an improved, simple, easy to use Icomp-limiter that
stabilizes the forming process by drastically decreasing current overflow, in
order to precisely control the Icomp- and subsequent IR-values.Comment: 15 pages, 4 figure
Scattering Rule in Soliton Cellular Automaton associated with Crystal Base of
In terms of the crystal base of a quantum affine algebra ,
we study a soliton cellular automaton (SCA) associated with the exceptional
affine Lie algebra . The solitons therein are labeled
by the crystals of quantum affine algebra . The scatteing rule
is identified with the combinatorial matrix for -crystals.
Remarkably, the phase shifts in our SCA are given by {\em 3-times} of those in
the well-known box-ball system.Comment: 25 page
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