• Title/Summary/Keyword: first passage problem

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FIRST PASSAGE PROBLEM FOR WIENER PATHS CROSSING DIFFERENTIABLE CURVES

  • Jang, Yu-Seon;Kim, Sung-Lai;Kim, Sung-Kyun
    • Journal of applied mathematics & informatics
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    • v.19 no.1_2
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    • pp.475-484
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    • 2005
  • Let W(t) be a Wiener path, let $\xi\;:\;[0,\;{\infty})\;\to\;\mathbb{R}$ be a continuous and increasing function satisfying $\xi$(0) > 0, let $$T_{/xi}=inf\{t{\geq}0\;:\;W(t){\geq}\xi(t)\}$$ be the first-passage time of W over $\xi$, and let F denote the distribution function of $T_{\xi}$. Then the first passage problem has a unique continuous solution as following $$F(t)=u(t)+{\sum_{n=1}^\infty}\int_0^t\;H_n(t,s)u(s)ds$$, where $$u(t)=2\Psi(\xi(t)/\sqrt{t})\;and\;H_1(t,s)=d\Phi\;(\{\xi(t)-\xi(s)\}/\sqrt{t-s})/ds\;for\;0\;{\leq}\;s.

An Efficient Brownian Motion Simulation Method for the Conductivity of a Digitized Composite Medium

  • Kim, In-Chan
    • Journal of Mechanical Science and Technology
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    • v.17 no.4
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    • pp.545-561
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    • 2003
  • We use the first-passage-time formulation by Torquato, Kim and Cule [J. Appl. Phys., Vol. 85, pp. 1560∼1571 (1999) ], which makes use of the first-passage region in association with the diffusion tracer's Brownian movement, and develop a new efficient Brownian motion simulation method to compute the effective conductivity of digitized composite media. By using the new method, one can remarkably enhance the speed of the Brownian walkers sampling the medium and thus reduce the computation time. In the new method, we specifically choose the first-passage regions such that they coincide with two, four, or eight digitizing units according to the dimensionality of the composite medium and the local configurations around the Brownian walkers. We first obtain explicit solutions for the relevant first-passage-time equations in two-and three-dimensions. We then apply the new method to solve the illustrative benchmark problem of estimating the effective conductivities of the checkerboard-shaped composite media. for both periodic and random configurations. Simulation results show that the new method can reduce the computation time about by an order of magnitude.

CONTROLLING TRAFFIC LIGHTS AT A BOTTLENECK: THE OBJECTIVE FUNCTION AND ITS PROPERTIES

  • Grycho, E.;Moeschlin, O.
    • Journal of the Korean Mathematical Society
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    • v.35 no.3
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    • pp.727-740
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    • 1998
  • Controlling traffic lights at a bottleneck, in [5] a time of open passage is called optimal, if it minimizes the first moment of the asymptotic distribution of the queue length. The discussion of the first moment as function of the time of open passage is based on an analysis of the behavior of a fixed point when varying control parameters and delivers theoretical and computational aspects of the traffic problem.

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Connectivity and Conductivity of a Three-Dimensional Checkerboard-Shaped Composite Material (체커보드 형상을 가진 3차원 복합소재의 연결도와 전도율)

  • KIm, In-Chan
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.28 no.2
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    • pp.189-198
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    • 2004
  • We consider the problem of whether the three-dimensional checkerboard has the connectivity. For this purpose, we first consider the problem of determining the effective conductivity of a checkerboard-shaped composite material by the Brownian motion simulation method. Specifically, we use the efficient first-passage-time technique. Simulation results show that the effective conductivity of the three-dimensional checkerboard increases faster than the two-dimensional counterpart as the contrast between the phase conductivities increases. This implies that the three-dimensional checkerboard's connectivity is stronger than the two-dimensional checkerboard's and thus each phase material of the three-dimensional checkerboard is more likely to be connected than not to be connected.

Stochastic control approach to reliability of elasto-plastic structures

  • Au, Siu-Kui
    • Structural Engineering and Mechanics
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    • v.32 no.1
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    • pp.21-36
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    • 2009
  • An importance sampling method is presented for computing the first passage probability of elasto-plastic structures under stochastic excitations. The importance sampling distribution corresponds to shifting the mean of the excitation to an 'adapted' stochastic process whose future is determined based on information only up to the present. A stochastic control approach is adopted for designing the adapted process. The optimal control law is determined by a control potential, which satisfies the Bellman's equation, a nonlinear partial differential equation on the response state-space. Numerical results for a single-degree-of freedom elasto-plastic structure shows that the proposed method leads to significant improvement in variance reduction over importance sampling using design points reported recently.

A reliability-based criterion of structural performance for structures with linear damping

  • Kovaleva, Agnessa
    • Smart Structures and Systems
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    • v.2 no.4
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    • pp.313-320
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    • 2006
  • The reliability analysis of structures subjected to stochastic loading involves evaluation of time and probability of the system's residence in a reference domain. In this paper, we derive an asymptotic estimate of exit time for multi-degrees-of-freedom structural systems. The system's dynamics is governed by the Lagrangian equations with linear dissipation and fast additive noise. The logarithmic asymptotic of exit time is found explicitly as a sum of two terms dependent on kinetic and potential energy of the system, respectively. As an example, we estimate exit time and an associated structural performance for a rocking structure.

Low-Noise Design of Passage of Idle Speed Control Actuator in Automotive Engines Using Scaling Laws for Noise Prediction (소음예측 비례식을 이용한 자동차 엔진 공회전 속도 제어 장치 유로의 저소음 디자인)

  • Cheong, Cheol-Ung;Kim, Jae-Hyun;Park, Yong-Hwan;Lee, Soo-Gab
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.05a
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    • pp.283-290
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    • 2007
  • Recently, plastic products in air-intake parts of automotive engines have become very popular due to advantages that include reduced weight, constricted cost, and lower intake air temperature. However, flow-induced noise in air-intake parts becomes a more serious problem for plastic intake-manifolds than for conventional aluminum-made manifolds. This is due to the fact that plastic manifolds transmit more noise owing to their lower material density. Internal aerodynamic noise from an Idle Speed control Actuator (ISA) is qualitatively analyzed by using a scaling law, which is expressed with some flow parameters such as pressure drop, maximum flow velocity, and turbulence kinetic energy. First, basic flow characteristics through ISA passage are identified with the flow predictions obtained by applying Computational Fluid Dynamics techniques. Then, the effects on ISA passage noise of each design factors including the duct turning shape and vane geometries are assessed. Based on these results, the preliminary low noise design for the ISA passage are proposed. The current method for the prediction of internal aerodynamic noise consists of the steady CFD and the scaling laws for the noise prediction. This combination is most cost-effective, compared with other methods, and therefore is believed to be suited for the preliminary design tool in the industrial field.

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Low-noise Design of Passage of Idle Speed Control Actuator In Automotive Engines Using Scaling Laws for Noise Prediction (소음예측 비례식을 이용한 자동차 엔진 공회전 속도 제어 장치 유로의 저소음 설계)

  • Cheong, Cheol-Ung;Kim, Jae-Hyun;Kim, Sung-Tae;Park, Yong-Hwan;Lee, Soo-Gab
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.8
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    • pp.683-692
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    • 2007
  • Recently, plastic products in air-intake parts of automotive engines have become very popular due to advantages that include reduced weight, constricted cost, and lower intake air temperature. However, flow-induced noise in air-intake parts becomes a more serious problem for plastic intake-manifolds than for conventional aluminum-made manifolds. This is due to the fact that plastic manifolds transmit more noise owing to their lower material density. Internal aerodynamic noise from an idle speed control actuator(ISA) is qualitatively analyzed by using a scaling law, which is expressed with some flow parameters such as pressure drop, maximum flow velocity, and turbulence kinetic energy. First, basic flow characteristics through ISA passage are identified with the flow predictions obtained by applying computational fluid dynamics techniques. Then, the effects on ISA passage noise of each design factors including the duct turning shape and vane geometries are assessed. Based on these results, the preliminary low noise design for the ISA passage are proposed. The current method for the prediction of internal aerodynamic noise consists of the steady CFD and the scaling laws for the noise prediction. This combination is most cost-effective, compared with other methods, and therefore is believed to be suited for the preliminary design tool in the industrial field.

A Study on the Planning Characteristics of Interior Space Aiming for the Exterior Space in Mixed-Use Development (복합용도개발 내부공간의 외부공간 지향성에 관한 계획특성 연구)

  • Kim, Suk-Ki;Sung, Lee-Yong
    • Korean Institute of Interior Design Journal
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    • v.22 no.3
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    • pp.43-51
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    • 2013
  • The purpose of this study is analysing the characteristics of interior space aiming for the exterior space in mixed-used development. The range of this study is limited as passage, department store, shoppingmall and Mixed Use Development. The method of this study is as follows. First, analysing the 7 samples of the interior space aiming for the exterior space in MXD through the framework of public character categorized as 5 factors, accessibility, openness, comfort properties, connectivity, convenience in use. Second, drawing a conclusion from the precedent step. The result of this study is as follows. First, the interior space has become bigger with time. And the public character is expanded with having the same structure of the city space. Second, the interior space solves the problem of the exterior space of city but prefers the same factors with the exterior space. Third, the street in the interior space has the characteristics of openness and comfort properties through diversification. And the open space is planned in various parts of the MXD and has the character of accessibility and connectivity.

"Legal Study on Boundary between Airspace and Outer Space" (영공(領空)과 우주공간(宇宙空間)의 한계(限界)에 관한 법적(法的) 고찰(考察))

  • Choi, Wan-Sik
    • The Korean Journal of Air & Space Law and Policy
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    • v.2
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    • pp.31-67
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    • 1990
  • One of the first issues which arose in the evolution of air law was the determination of the vertical limits of airspace over private property. In 1959 the UN in its Ad Hoc Committee on the Peaceful Uses of Outer Space, started to give attention to the question of the meaning of the term "outer space". Discussions in the United Nations regarding the delimitation issue were often divided between those in favour of a functional approach ("functionalists"), and those seeking the delineation of a boundary ("spatialists"). The functionalists, backed initially by both major space powers, which viewed any boundary as possibly restricting their access to space(Whether for peaceful or military purposes), won the first rounds, starting with the 1959 Report of the Ad Hoc Committee on the Peaceful Uses of Outer Space which did not consider that the topic called for priority consideration. In 1966, however, the spatialists, were able to place the issue on the agenda of the Outer Sapce Committee pursuant to Resolution 2222 (xxx1). However, the spatialists were not able to present a common position since there existed a variety of propositions for delineation of a boundary. Over the years, the funtionalists have seemed to be losing ground. As the element of location is a decisive factor for the choice of the legal regime to be applied, a purely functional approach to the regulation of activities in the space above the Earth does not offer a solution. It is therefore to be welcomed that there is clear evidence of a growing recognition of the defect inherent to such an approach and that a spatial approach to the problem is gaining support both by a growing number of States as well as by publicists. The search for a solution of the problem of demarcating the two different legal regimes governing the space above the Earth has undoubtedly been facilitated, and a number of countries, among them Argentina, Belgium, France, Italy and Mexico have already advocated the acceptance of the lower boundary of outer space at a height of 100km. The adoption of the principle of sovereignty at that height does not mean that States would not be allowed to take protective measures against space activities above that height which constitute a threat to their security. A parallel can be drawn with the defence of the State's security on the high seas. Measures taken by States in their own protection on the high seas outside the territorial waters-provided that they are proportionate to the danger-are not considered to infringe the principle of international law. The most important issue in this context relates to the problem of a right of passage for space craft through foreign air space in order to reach outer space. In the reports to former ILA Conferences an explanation was given of the reasons why no customary rule of freedom of passage for aircraft through foreign territorial air space could as yet be said to exist. It was suggested, however, that though the essential elements for the creation of a rule of customary international law allowing such passage were still lacking, developments apperaed to point to a steady growth of a feeling of necessity for such a rule. A definite treaty solution of the demarcation problem would require further study which should be carried out by the UN Outer Space Committee in close co-operation with other interested international organizations, including ICAO. If a limit between air space and outer space were established, air space would automatically come under the regime of the Chicago Convention alone. The use of the word "recognize" in Art. I of chicago convention is an acknowledgement of sovereignty over airspace existing as a general principle of law, the binding force of which exists independently of the Convention. Further it is important to note that the Aricle recognizes this sovereignty, as existing for every state, holding it immaterial whether the state is or is not a contracting state. The functional criteria having been created by reference to either the nature of activity or the nature of the space object, the next hurdle would be to provide methods of verification. With regard to the question of international verification the establishment of an International Satelite Monitoring Agency is required. The path towards the successful delimitation of outer space from territorial space is doubtless narrow and stony but the establishment of a precise legal framework, consonant with the basic principles of international law, for the future activities of states in outer space will, it is still believed, remove a source of potentially dangerous conflicts between states, and furthermore afford some safeguard of the rights and interests of non-space powers which otherwise are likely to be eroded by incipient customs based on at present almost complete freedom of action of the space powers.

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