• Interaction and multiscale mechanics
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• v.5 no.2
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• pp.105-114
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• 2012

The study of rigid roadway pavement under dynamic traffic loads with variable velocity is investigated in this paper. Rigid roadway pavement is modeled as a rectangular damped orthotropic plate supported by elastic Pasternak foundation. The boundary supports of the plate are the steel dowels and tie bars which provide elastic vertical support and rotational restraint. The natural frequencies of the system and the mode shapes are solved using two transcendental equations, obtained from the solution of two auxiliary Levy's type problems, known as the Modified Bolotin Method. The dynamic moving traffic load is expressed as a concentrated load of harmonically varying magnitude, moving straight along the plate with a variable velocity. The dynamic response of the plate is obtained on the basis of orthogonality properties of eigenfunctions. Numerical example results show that the velocity and the angular frequency of the loads affected the maximum dynamic deflection of the rigid roadway pavement. It is also shown that a critical speed of the load exists. If the moving traffic load travels at critical speed, the rectangular plate becomes infinite in amplitude.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.99-115
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• 2022

The problem of Benard double diffusive Marangoni convection is investigated in a horizontally infinite composite layer system consisting of a two component fluid layer above a porous layer saturated with the same fluid, using Darcy-Brinkman model with constant heat sources/sink in both the layers. The lower boundary of the porous region is rigid and upper boundary of the fluid region is free with Marangoni effects. The system of ordinary differential equations obtained after normal mode analysis is solved in closed form for the eigenvalue, thermal Marangoni number for two types of thermal boundary combinations, Type (I) Adiabatic-Adiabatic and Type (II) Adiabatic -Isothermal. The corresponding two thermal Marangoni numbers are obtained and the essence of the different parameters on non-Darcy-Benard double diffusive Marangoni convection are investigated in detail.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.217-227
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• 2024

Let G be an infinite countable group and A be a finite set. If Σ ⊆ A^G is a strongly irreducible subshift of finite type and 𝓖 is the local conjugacy equivalence relation on Σ. We construct a decreasing sequence 𝓡 of unital C^*-subalgebras of C(Σ) and a sequence of faithful conditional expectations E defined on C(Σ), and obtain a Toeplitz algebra 𝓣 (𝓡, 𝓔) and a C^*-algebra C^*(𝓡, 𝓔) for the pair (𝓡, 𝓔). We show that C^*(𝓡, 𝓔) is *-isomorphic to the reduced groupoid C^*-algebra C^*_r(𝓖).

• Transactions of the Society of Information Storage Systems
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• v.1 no.1
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• pp.108-114
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• 2005

The generation of fine relics of suspensions is a significant interest as it holds the key to the fabrication of electronic devices. These processes offer opportunities for miniaturization of multilayer circuits, for production of functionally graded materials, ordered composites and far small complex-shaped components. Some novel printing methods of depositing ceramic and metal droplets were suggested in recent years. In an electro-hydrodynamic printing, the metallic capillary nozzle can be raised to several kilovolts with respect to the infinite ground plate or pin-type electrode positioned a few millimeters from the nozzle tip. Depending on the electrical and physical properties of the liquid, for a given geometry, it Is possible to generate droplets in any one of three modes, dripping, cone-jet and multi-jet. In this experiment, an alumina suspension flowing through a nozzle was subjected to electro-hydrodynamic printing using pin-type electrodes in the cone-jet mode at different applied voltages. The pin-type electrodes of 1, 100, 1000${\mu}m$ in diameter were used to form fine ceramic patterns onto the substrates. Various feature sizes with applied voltages and electrode diameters were measured. The feature sizes increased with the electrode diameter and applied voltages. The feature size was as fine as $30 {\mu}m$.

• Structural Engineering and Mechanics
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• v.62 no.1
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• pp.113-123
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• 2017

The bi-material elastic system consisting of the circular hollow cylinder and the infinite elastic medium surrounding this cylinder is considered and it is assumed that on the inner free face of the cylinder a point-located axisymmetric time harmonic force, with respect to the cylinder's axis and which is uniformly distributed in the circumferential direction, acts. The shear-spring type imperfect contact conditions on the interface between the constituents are satisfied. The mathematical formulation of the problem is made within the scope of the exact equations of linear elastodynamics. The focus is on the frequency-response of the interface normal and shear stresses and the influence of the problem parameters, such as the ratio of modulus of elasticity, the ratio of the cylinder thickness to the cylinder radius, and the shear-spring type parameter which characterizes the degree of the contact imperfectness, on these responses. Corresponding numerical results are presented and discussed. In particular, it is established that the character of the influence of the contact imperfection on the frequency response of the interface stresses depends on the values of the vibration frequency of the external forces.

• Journal of the Korean Vacuum Society
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• v.17 no.5
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• pp.419-425
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• 2008

In previous study, it was reported that the anomalous skin effect should be considered in the low pressure condition(<10 mTorr). However there is the problem that the filament type antenna model of which size is 0 makes the non-physical phenomena that the electric field at the antenna point is infinite. Therefore, in this work, using the surface current model the electric field in antenna region is calculated and compared with the case of filament type antenna model in various conditions.

• Structural Engineering and Mechanics
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• v.74 no.1
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• pp.91-104
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• 2020

A mathematical analysis has been carried out for understanding the traversal attributes of torsional waves in a Voigt-type viscoelastic porous layer bounded with corrugated surfaces resting over a heterogeneous transversely isotropic gravitating semi-infinite medium. Both the media are assumed to be under the effect of initial stresses acting along horizontal directions. In the presumed geometry, continuous and periodic type of corrugation has been considered. The condensed form of dispersion relation has been obtained analytically with the aid of the Whittaker's function and suitable boundary conditions. The influence of viscoelasticity, porosity, initial stresses, heterogeneity, gravity, undulation and position parameters on the phase and damped velocities has been illustrated graphically. In addition, relative examination investigating the impact of corrugated and planar bounded surfaces on the dispersion and damping characteristics is one of the important highlights of this study.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.32 no.9
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• pp.315-324
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• 1983

Dynamic stability problems have been experienced with a generator connected to an infinite bus through a long transmission line. Nuclear turbine-generator units #1 and #2 at the Winsconsin Electric Power Point Baech Station were found to be dynamically unstable when one unit is isolated on one of the lines to Milwaukee or when two units are isolaed on the lines to milwaukee. Power System Stabilizers(PSS) were applied to the excitation system to provide stable operation under these conditions. Suitable settings for the PSS were predetetermined analytically by computer method and root licus analysis of an equivalent single machine-infinite bus configuration. This procedure allows graphical approach to the design of power stabilizers and serves as assynthesis procedure when the design constraints are relaxed so the the speed stabilizer is required ro provide animprovement in system damping. A simplified model of the complete exciter generator system is shown to be adequate for this type of analysis.

• Interaction and multiscale mechanics
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• v.3 no.1
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• pp.95-110
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• 2010

In recent years, study of the static response of pavements to moving vehicle and aircraft loads has received significant attention because of its relevance to the design of pavements and airport runways. The static response of beams resting on an elastic foundation and subjected to moving loads was studied by several researchers in the past. However, most of these studies were limited to steady-state analytical solutions for infinitely long beams resting on Winkler-type elastic foundations. Although the modelling of subgrade as a continuum is more accurate, such an approach can hardly be incorporated in analysis due to its complexity. In contrast, the two-parameter foundation model provides a better way for simulating the underlying soil medium and is conceptually more appealing than the one-parameter (Winkler) foundation model. The finite element method is one of the most suitable mathematical tools for analysing rigid pavements under moving loads. This paper presents an improved solution algorithm based on the finite element method for the static analysis of rigid pavements under moving vehicular or aircraft loads. The concrete pavement is discretized by finite and infinite beam elements, with the latter for modelling the infinity boundary conditions. The underlying soil medium is modelled by the Pasternak model allowing the shear interaction to exist between the spring elements. This can be accomplished by connecting the spring elements to a layer of incompressible vertical elements that can deform in transverse shear only. The deformations and forces maintaining equilibrium in the shear layer are considered by assuming the shear layer to be isotropic. A parametric study is conducted to investigate the effect of the position of moving loads on the response of pavement.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.251-267
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• 2015

The Indian Buffet Process is a stochastic process on equivalence classes of binary matrices having finite rows and infinite columns. The Indian Buffet Process can be imposed as the prior distribution on the binary matrix in an infinite feature model. We describe the derivation of the Indian buffet process from a finite feature model, and briefly explain the relation between the Indian buffet process and the beta process. Using a Gaussian linear model, we describe three algorithms: Gibbs sampling algorithm, Stick-breaking algorithm and variational method, with application for finding features in image data. We also illustrate the use of the Indian Buffet Process in various type of analysis such as dyadic data analysis, network data analysis and independent component analysis.