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| 1.
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Xue, Peng ; Yamamoto, Shigeru
概要:
For a stochastic delay differential equation, the effects of noise and time delay are discussed in the sense of mean squ
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are stability. Neither time delay nor noise play bad roles for the differential equations and both of them are ubiquitous in nature. The so-called domain subdivision approach is taken to study the stability regions in terms of the parameters of a given equation and the Ito formula is employed to deal with the fluctuation noise. An interesting result demonstrated in this paper shows that noise with appropriate power could reduce the influence of time delay. © 2011 SICE.
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| 2.
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Hataue, Itaru
概要:
In the present paper, we study the structural stability of discrete dynamical system from the view point of influence of
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randomness added to deterministic difference equations. One-dimensional Burgers' equation is discretized by central difference method and the dependence of the asymptotic structure on forcibly added randomness is studied. Both of non-conservative and conservative forms are considered. The "Sample Mean Dynamical System(SMDS)" approach is applied in analyzing the degree of dynamical system. It is proposed that we should add a small amount of randomness to deterministic equations in order to make unstable incorrect invariant set removed in getting bifurcation diagrams. The discrete dynamical system in the case of conservative form is shown to be more unstable than that in the case of non-conservative form by analyses of SMDS. It is effective to study the structure of SMDS in evaluating the degree of structural stability of a discrete dynamical system. © 2011 International Information Institute.
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| 3.
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Nakayama, Kenji ; Nishimura, Katsuaki
概要:
金沢大学理工研究域電子情報学系<br />An associative memory using fixed and variable hysteresis thresholds in learning and recalling proc
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esses, respectively, has been proposed by authors. This model can achieve a large memory capacity and very low noise sensitivity. However, a relation between weight change Δ w and the hysteresis threshold ± T has not been well discussed. In this paper, a new learning algorithm is proposed, which is based on a delta rule. However, in order to stabilize the learning process, a method of using double hysteresis thresholds is proposed. Unit states are updated using ± T. The error, used for adjusting weights, is evaluated using ± (T+dT). This means 'over correction'. Stable and fast convergence can be obtained. Relations between η =dT/T and convergence rate and noise sensitivity are discussed, resulting the optimum selection for η. Furthermore, the order of presenting training data is optimized taking correlation, into account. In the recalling process, a threshold control method is further proposed in order to achieve fast recalling from noisy patterns.
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| 4.
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Nakata, Shunji ; Mutoh, Shin'ichiro ; Makino, Hiroshi ; Miyama, Masayuki ; Matsuda, Yoshio
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金沢大学理工研究域電子情報学系<br />We discuss the stability of an adiabatic stepwise-charging circuit with advanced series capacitors,
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which is effective for the reduction of the applied voltage to each capacitor. SPICE simulation shows that this circuit is stable even if the initial voltages are lower than zero. For the analytical discussion, we derive a matrix that connects charge and voltage in the circuit and show that the matrix is a positive-definite symmetric one. Therefore, the step voltage is generated spontaneously. We also derive energy dissipation analytically using tank capacitor voltage. Using this formula and SPICE simulation, we clarify that energy dissipation decreases monotonically as a function of time and finally reaches the minimum value. © IEICE 2010.
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| 5.
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Hataue, Itaru
概要:
金沢大学理工研究域電子情報学系<br />In the present paper, the dependencies of the numerical results of fluid simulations on forcibly ad
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ded randomness are discussed. The incompressible Navier-Stokes equations and the continuity equation are solved numerically by using the MAC (Maker-And-Cell) method and implicit temporal scheme. The model adopted in the present study is a flow around a two-dimensional circular cylinder and the Reynolds number is 1500. The randomness which is given by using the pseudo-random number is forcibly added in the time marching step of the discretized Navier-Stokes equations. Dependencies of the averaged structure of asymptotic numerical solutions on the randomness are discussed. Furthermore, the dependence of the qualitative structure of the asymptotic solution of each sample calculation on the amplitude of randomness is also studied. It is clarified that forcibly added random errors may cover the nonlinear errors which make the system unstable. © 2008 Elsevier B.V. All rights reserved.
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| 6.
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Iwata, Yoshio ; Takeda, Masaki ; Sato, Hidenori ; Komatsuzaki, Toshihiko ; Shako, Eiji
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A method for analyzing steady state vibration of a system with localized nonlinear springs by convolution integral is pr
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oposed. Scale of the nonlinear problem can be reduced by using localization of the nonlinear springs in the method. First, equation of motion with the convolution integral of nonlinear restoring force which is treated as an external force is made, second, a set of nonlinear algebraic equations on discrete-time history of unit period is derived and finally the nonlinear algebraic equations is solved with the harmonic balance method. Stable and unstable condition of the steady state vibration can be distinguished by the present method and the impulse response required can be also measured in the experiment because of the merit of the convolution integral. Two examples are shown and the validity of the method is discussed in comparison with Runge-Kutta-Gill method or the experiment. © 2000, The Japan Society of Mechanical Engineers. All rights reserved.
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| 7.
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Tanahashi, Hiroshi ; Kito, Keiji ; Ito, Takashi ; Yoshioka, Katsuji
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金沢大学がん研究所がん分子細胞制御<br />MafB is a basic leucine zipper transcription factor that plays important roles in development and
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differentiation processes. During osteoclastogenesis, its expression is downregulated at the transcriptional level via the JNK and p38 MAP kinase pathways. In the present study, we demonstrated that MafB protein stability is regulated by JNK and identified a phosphorylation site, Thr62. The expression of a constitutively active form of JNK (a fusion protein MKK7α1-JNK1β1) promoted the degradation of MafB in COS7 cells, and a T62A substitution significantly reduced the instability of MafB. The introduction of a fourfold (T58A/T62A/S70A/S74A) substitution in an acidic transcription-activating domain almost protected the instability resulting from the activation of JNK. Furthermore, treatment with proteasome inhibitors increased the MafB level, and a high-molecular-weight smear, characteristic of polyubiquitination, was observed in lysates from cells in which MafB, ubiquitin, and MKK7α1-JNK1β1 were co-expressed. These results suggest that phosphorylation of MafB by JNK confers susceptibility to proteasomal degradation. © 2009 Elsevier Inc. All rights reserved.
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| 8.
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畑上, 到 ; Hataue, Itaru
概要:
発展方程式の数値解の信頼性の向上を目的として,誤差移入による解の構造の変化に対する,統計的な挙動の考察を行った.特に本研究では,まず一様乱数等によるランダムな様式での誤差を発生させてランダムネスを付加した場合の数値解の構造について,ロジステ
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ィック方程式やローレンツ方程式等の比較的単純な非線型発展方程式系を離散化した差分方程式系に対して,確率論的および力学的な見地から理論的考察を行った.同時に数値実験をおこなうことによって,その理論の正当性を実証することを試みた.さらに,反復収束過程を有する流体シミュレーションにおける数値解と構造についての類似点について詳細に議論した.また,ランダムネスを負荷した場合の数値解の平均値としての力学的挙動がもとの差分方程式の構造とどのような差異があるかについて理論的に考察した.これにより,反復解法の収束条件による精度の低下(誤差移入の増大)により計算される系が安定化され,より次元の低い幻影解の発現を誘起する可能性があるとともに,解の分岐過程にランダムネスが大きく影響していることがわかった.この結果をもとに,流体モデルを応用した交通流モデルによる渋滞形成についての応用問題への展開を行い,渋滞形成時における走行車線と追い越し車線の同期現象や平均速度の逆転現象などの再現に成功した.また,混ざらない非圧縮性の2流体問題に対する高い質量保存性を有するフラックス・フリー有限要素法について,収束性を示す際の不連続な粘性係数および密度を有する一般化Stokes方程式を考察し,これらの解の正則性の仮定の下でフラックス・フリー有限要素法の収束性を示した.<br />For the purpose of development of reliability evaluation system for numerical solutions, we tried to discuss how structure of numerical solutions of a stochastic difference equation changes by the insertion of errors with the random style from the viewpoints of probabilistic approaches. Errors in solving the nonlinear systems are inserted randomly and structure of solutions becomes very complicated We try to investigate the dependence of the structure of numerical solutions on insertion of random errors As a fundamental study, the stochastic differential equation based on the deterministic logistic differential equation and the Lorenz equations are considered. A new approach, sample mean dynamical system (SMDS), is proposed in order to analyze the dependence of the structure of numerical solutions of discretized dynamical system on insertion of random errors and the relation between the size of noise and characteristics of obtained numerical solutions is discussed.In addition, we appli ed them to the issues of real fluid calculation and the problem of traffic jam in order to analyze several factors which govern nonlinear phenomena. First, we tried to discuss the dependence of the structure of numerical solutions of incompressible fluid equations on insertion of random errors in solving simultaneous equations. Dependence of the averaged structure of numerical solutions of fluid simulations on forcibly added random errors are discussed. Next, we give some theoretical considerations on the flux-free finite-element method for the generalized Stokes interface problem arising from the immiscible two-fluid flow problems. In the flux-free finite-element method, the flux constraint is posed as another Lagrange multiplier to keep the zero-flux on the interface. As a result, the mass of each fluid is expected to be preserved at every time step. We fast study the effect of discontinuous coefficients(viscosity and density)on the error of the standard finite element approximations very carefully. Then, the analysis is extended to the flux-free finite element method. As for the problem of traffic jam, the formation of the traffic congestion in two-lane traffic flow is studied. The two-lane macroscopic model using the optimal velocity model which has been introduced in the microscopic model is constructed on the basis of the one-lane model. We adopt different optimal velocity function to each lane and new rules of changing lanes are introduced. Numerical simulations are performed in order to investigate the characteristic phenomena of two-lane traffic flow In particular, we concentrate the discussion about the property of "Synchronized flow', one of the most characteristic phenomena of two-lane traffic flow Furthermore, the fundamental diagrams from the simulations are compared with those observed in a highway.<br />研究課題/領域番号:18540118, 研究期間(年度):2006-2007<br />出典：「確率論的アプローチを融合した数値解の信頼性評価システム開発と複雑流体計算への展開」研究成果報告書 課題番号18540118 (KAKEN：科学研究費助成事業データベース（国立情報学研究所）) 本文データは著者版報告書より作成
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| 9.
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宮川, 鉄朗 ; Miyakawa, Tetsuro
概要:
金沢大学自然科学研究科<br />代表者宮川は,2次元と3次元の外部領域における非圧縮粘性流を扱い,流れの時間・空間減衰度と運動方程式の解の対称性の関係を明らかにした.特に2次元外部問題においてほぼ最終的な結果を得た.その研究の副産物として
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,2次元外部領域での非圧縮完全流体に関するダランベールの逆理と,対応する圧力場の可積分性との間の明確かつ密接な関係を見出した.この方向での3次元流の研究を現在進めている.分担者福本は,粘性渦の運動と形状変化を研究し,非局所誘導モデルを採用して特異摂動の手法をそれに適用し,渦糸や渦輪の位相的形状変化について考察し,渦の安定性に対して渦の曲率等の幾何学的性質がどのように寄与するかという問題に関して新しい知見を得た.分担者菱田は,回転物体の周囲の流れを初めて数学的に厳密に考察し,新しい特異積分作用素のクラスを発見してその詳しい解析を行い,その結果を駆使して,当該問題に対し,定常流と非定常流に関する新しい存在定理を証明した.同時にまた有限個の穴で結ばれた半空間での流れの問題を扱い,非定常流の存在について従来知られた結果を改良した.分担者井口は,気体の1次元運動方程式を考察し,流れの自由境界面の研究から得た知見を応用して,この方程式の新しい解法を見出し,それが従来の方法にくらべて物事の本質により迫るものであって,従ってより広い応用範囲を持つことを示した.この研究は気体の運動方程式を取り扱う際の本質的な難点がどこにあるかを明らかにしたもので,注目に値する.さらに井口は周期的な底をもつ浅い流れの自由表面の形状を,分岐理論を用いて分類した.<br />MIYAKAWA studied the flows of a viscous incompressible fluid in two and three-dimensional exterior domains and clarified explicit relationship between the space-time decay rates of flows and the symmetry of solutions of the equations of motion. He obtained almost complete results in the case of two space dimensions. FUKUMOTO studied the evolution of viscous vortices, applying the singular perturbation method to the non-local induction model, and obtained new results on the topological change of vortex filaments and rings. HISHIDA studied the viscous flow around a rotating body and proved for the first time the existence of stationary and nonstationary flows by finding a new class of singular integral operators. He also gave a new existence result for flows in domains with apertures. IGUCHI applied the method for treating free-surface problem to the equation of one-dimensional gas dymanics and gave a completely new approach to this problem which has wide applications to equations of similar types. He also classified the shape of free surfaces associated with shallow water flow with periodic bottom, applying the bifurcation theory.<br />研究課題/領域番号:15340054, 研究期間(年度):2003 – 2005<br />出典：「流れに伴う渦と波動のパターン変化の研究」研究成果報告書 課題番号15340054（KAKEN：科学研究費助成事業データベース（国立情報学研究所））（https://kaken.nii.ac.jp/ja/report/KAKENHI-PROJECT-15340054/153400542005kenkyu_seika_hokoku_gaiyo/)を加工して作成
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