Search results for: Jumps conditions

Authors: Dezhi Liu

Abstract:

In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.

Keywords: Impulsive, stochastic, delay, Markovian switching, Poisson jumps, mean square stability.

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper examines the problem of designing a robust H8 state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H8 performance are derived. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard nonlinear two-time scale systems. A numerical example is provided to illustrate the design developed in this paper.

Keywords: TS fuzzy, Markovian jumps, LMI, two-time scale systems.

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Authors: F. Rostami, M. Shahrokhi, M. A. Md Said, S.R. Sabbagh-Yazdi

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Undular hydraulic jumps are illustrated by a smooth rise of the free surface followed by a train of stationary waves. They are sometimes experienced in natural waterways and rivers. The characteristics of undular hydraulic jumps are studied here. The height, amplitude and the main characteristics of undular jump is depended on the upstream Froude number and aspect ratio. The experiments were done on the smooth bed flume. These results compared with other researches and the main characteristics of the undular hydraulic jump were studied in this article.

Keywords: Undular Hydraulic Jump, low Froude Number, wave characteristics

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Authors: Constantin Z. Leshan

Abstract:

Hole Vacuum theory is based on discontinuous spacetime that contains vacuum holes. Vacuum holes can explain gravitation, some laws of quantum mechanics and allow teleportation of matter. All massive bodies emit a flux of holes which curve the spacetime; if we increase the concentration of holes, it leads to length contraction and time dilation because the holes do not have the properties of extension and duration. In the limited case when space consists of holes only, the distance between every two points is equal to zero and time stops - outside of the Universe, the extension and duration properties do not exist. For this reason, the vacuum hole is the only particle in physics capable of describing gravitation using its own properties only. All microscopic particles must 'jump' continually and 'vibrate' due to the appearance of holes (impassable microscopic 'walls' in space), and it is the cause of the quantum behavior. Vacuum holes can explain the entanglement, non-locality, wave properties of matter, tunneling, uncertainty principle and so on. Particles do not have trajectories because spacetime is discontinuous and has impassable microscopic 'walls' due to the simple mechanical motion is impossible at small scale distances; it is impossible to 'trace' a straight line in the discontinuous spacetime because it contains the impassable holes. Spacetime 'boils' continually due to the appearance of the vacuum holes. For teleportation to be possible, we must send a body outside of the Universe by enveloping it with a closed surface consisting of vacuum holes. Since a material body cannot exist outside of the Universe, it reappears instantaneously in a random point of the Universe. Since a body disappears in one volume and reappears in another random volume without traversing the physical space between them, such a transportation method can be called teleportation (or Hole Teleportation). It is shown that Hole Teleportation does not violate causality and special relativity due to its random nature and other properties. Although Hole Teleportation has a random nature, it can be used for colonization of extrasolar planets by the help of the method called 'random jumps': after a large number of random teleportation jumps, there is a probability that the spaceship may appear near a habitable planet. We can create vacuum holes experimentally using the method proposed by Descartes: we must remove a body from the vessel without permitting another body to occupy this volume.

Keywords: Border of the universe, causality violation, perfect isolation, quantum jumps.

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper investigates the problem of designing a robust state-feedback controller for a class of uncertain Markovian jump nonlinear systems that guarantees the L2-gain from an exogenous input to a regulated output is less than or equal to a prescribed value. First, we approximate this class of uncertain Markovian jump nonlinear systems by a class of uncertain Takagi-Sugeno fuzzy models with Markovian jumps. Then, based on an LMI approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear systems to have an H performance are derived. An illustrative example is used to illustrate the effectiveness of the proposed design techniques.

Keywords: Robust H, Fuzzy Control, Markovian Jump Systems, LMI.

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Authors: Kimou Kouadio Prosper, Souleymane Oumtanaga, Tety Pierre, Adou Kablan Jérôme

Abstract:

A satured liquid is warmed until boiling in a parallelepipedic boiler. The heat is supplied in a liquid through the horizontal bottom of the boiler, the other walls being adiabatic. During the process of boiling, the liquid evaporates through its free surface by deforming it. This surface which subdivides the boiler into two regions occupied on both sides by the boiled liquid (broth) and its vapor which surmounts it. The broth occupying the region and its vapor the superior region. A two- fluids model is used to describe the dynamics of the broth, its vapor and their interface. In this model, the broth is treated as a monophasic fluid (homogeneous model) and form with its vapor adiphasic pseudo fluid (two-fluid model). Furthermore, the interface is treated as a zone of mixture characterized by superficial void fraction noted α* . The aim of this article is to describe the dynamics of the interface between the boiled fluid and its vapor within a boiler. The resolution of the problem allowed us to show the evolution of the broth and the level of the liquid.

Keywords: Two-fluid models, homogeneous model, interface, averaged equations, Jumps conditions, void fraction.

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Authors: Mao Wei

Abstract:

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.

Keywords: Stochastic age-dependent population equations, poisson random measures, numerical solutions, exponential stability.

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Authors: Mahmoud E. Mohamed, Ahmed F. Shalash, Hanan A. Kamal

Abstract:

In communication systems, frequency jump is a serious problem caused by the oscillators used. Kalman filters are used to detect that jump, despite the tradeoff between the noise level and the speed of the detection. In this paper, an improvement is introduced in the Kalman filter, through a nonlinear change in the bandwidth of the filter. Simulation results show a considerable improvement in the filter speed with a very low noise level. Additionally, the effect on the response to false alarms is also presented and false alarm rate show improvement.

Keywords: Kalman Filter, Innovation, False Detection.

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Authors: Taiwo Olusoji Lawrence, Peace Mawo Aaron

Abstract:

Seismic analysis of bedforms has proven to be one of the best ways to study deepwater sedimentary features. Canyons are known to be sediment transportation conduit. Sediment wave are large-scale depositional bedforms in various parts of the world's oceans formed predominantly by suspended load transport. These undulating objects usually have tens of meters to a few kilometers in wavelength and a height of several meters. Cyclic steps have long long-wave upstream-migrating bedforms confined by internal hydraulic jumps. They usually occur in regions with high gradients and slope breaks. Cyclic steps and migrating sediment waves are the most common bedform on the seafloor. Cyclic steps and related sediment wave bedforms are significant to the morpho-dynamic evolution of deep-water depositional systems architectural elements, especially those located along tectonically active margins with high gradients and slope breaks that can promote internal hydraulic jumps in turbidity currents. This report examined sedimentary activities and sediment transportation in submarine canyons and provided distinctive insight into factors that created a complex seabed canyon system in the Ceara Fortaleza basin Brazilian Equatorial Margin (BEM). The growing importance of cyclic steps made it imperative to understand the parameters leading to their formation, migration, and architecture as well as their controls on sediment transport in canyon thalweg. We extracted the parameters of the observed bedforms and evaluated the aspect ratio and asymmetricity. We developed a relationship between the hydraulic jump magnitude, depth of the hydraulic fall and the length of the cyclic step therein. It was understood that an increase in the height of the cyclic step increases the magnitude of the hydraulic jump and thereby increases the rate of deposition on the preceding stoss side. An increase in the length of the cyclic steps reduces the magnitude of the hydraulic jump and reduces the rate of deposition at the stoss side. Therefore, flat stoss side was noticed at most preceding cyclic step and sediment wave.

Keywords: Ceara Fortaleza, sediment wave, cyclic steps, submarine canyons.

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Authors: Irwin Ma, Tony Wong, Thiagas Sankar

Abstract:

By systematically applying different engineering methods, difficult financial problems become approachable. Using a combination of theory and techniques such as wavelet transform, time series data mining, Markov chain based discrete stochastic optimization, and evolutionary algorithms, this work formulated a strategy to characterize and forecast non-linear time series. It attempted to extract typical features from the volatility data sets of S&P100 and S&P500 indices that include abrupt drops, jumps and other non-linearity. As a result, accuracy of forecasting has reached an average of over 75% surpassing any other publicly available results on the forecast of any financial index.

Keywords: Discrete stochastic optimization, genetic algorithms, genetic programming, volatility forecast

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Authors: Dongdong Zhang, Deran Zhang

Abstract:

In this paper, a Markovian risk model with two-type claims is considered. In such a risk model, the occurrences of the two type claims are described by two point processes {Ni(t), t ¸ 0}, i = 1, 2, where {Ni(t), t ¸ 0} is the number of jumps during the interval (0, t] for the Markov jump process {Xi(t), t ¸ 0} . The ruin probability ª(u) of a company facing such a risk model is mainly discussed. An integral equation satisfied by the ruin probability ª(u) is obtained and the bounds for the convergence rate of the ruin probability ª(u) are given by using key-renewal theorem.

Keywords: Risk model, ruin probability, Markov jump process, integral equation.

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Authors: A. Abdalla, A. Kaltayev

Abstract:

This article presents the boundary conditions for the problem of turbulent supersonic gas flow in a plane channel with a perpendicular injection jets. The non-reflection boundary conditions for direct modeling of compressible viscous gases are studied. A formulation using the NSCBC (Navier- Stocks characteristic boundary conditions) through boundaries is derived for the subsonic inflow and subsonic non-reflection outflow situations. Verification of the constructed algorithm of boundary conditions is carried out by solving a test problem of perpendicular sound of jets injection into a supersonic gas flow in a plane channel.

Keywords: WENO scheme, non-reflection boundary conditions, NSCBC, supersonic flow.

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Authors: Hamid Mozafari, Andreas Öchsner, Amran Alias

Abstract:

Imperfect transmission conditions modeling a thin reactive 2D interphases layer between two dissimilar bonded strips have been extracted. In this paper, the soundness of these transmission conditions for heat conduction problems are examined by the finite element method for a strong temperature-dependent source or sink and non-monotonic temperature distributions around the faces..

Keywords: Imperfect interface, Transmission conditions, Finiteelement analysis, Interphase

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Authors: Tsugunosuke Sakai, Haruya Tamaki, Ryuichi Yoshida, Ryohei Egusa, Etsuji Yamaguchi, Shigenori Inagaki, Fusako Kusunoki, Miki Namatame, Masanori Sugimoto, Hiroshi Mizoguchi

Abstract:

We aim to develop a full-body interaction game that could let children cooperate and interact with other children in small groups. As the first step for our aim, the objective of the full-body interaction game developed in this study is to make interaction between children. The game requires two children to jump together with the same timing. We let children experience the game and answer the questionnaires. The children using several strategies to coordinate the timing of their jumps were observed. These included shouting time, watching each other, and jumping in a constant rhythm as if they were skipping rope. In this manner, we observed the children playing the game while cooperating with each other. The results of a questionnaire to evaluate the proposed interactive game indicate that the jumping game was a very enjoyable experience in which the participants could immerse themselves. Therefore, the game enabled children to experience cooperation with others by using body movements.

Keywords: Children, cooperation, full-body interaction game, kinect sensor.

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Authors: Kamil Aida-zade, C. Ardil

Abstract:

In this paper, some problem formulations of dynamic object parameters recovery described by non-autonomous system of ordinary differential equations with multipoint unshared edge conditions are investigated. Depending on the number of additional conditions the problem is reduced to an algebraic equations system or to a problem of quadratic programming. With this purpose the paper offers a new scheme of the edge conditions transfer method called by conditions shift. The method permits to get rid from differential links and multipoint unshared initially-edge conditions. The advantage of the proposed approach is concluded by capabilities of reduction of a parametric identification problem to essential simple problems of the solution of an algebraic system or quadratic programming.

Keywords: dynamic objects, ordinary differential equations, multipoint unshared edge conditions, quadratic programming, conditions shift

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Authors: L. Lundgren, S. Brorsson, A-L Osvalder

Abstract:

Participation in sporting activities can lead to injury. Sport injuries have been widely studied in many sports including the more extreme categories of aquatic board sports. Kitesurfing is a relatively new water surface action sport, and has not yet been widely studied in terms of injuries and stress on the body. The aim of this study was to get information about which injuries that are most common among kitesurfing participants, where they occur, and their causes. Injuries were studied using an international open web questionnaire (n=206). The results showed that many respondents reported injuries, in total 251 injuries to knee (24%), ankle (17%), trunk (16%) and shoulders (10%), often sustained while doing jumps and tricks (40%). Among the reported injuries were joint injuries (n=101), muscle/tendon damages (n=47), wounds and cuts (n=36) and bone fractures (n=28). Also environmental factors and equipment can influence the risk of injury, or the extent of injury in a hazardous situation. Conclusively, the information from this retrospective study supports earlier studies in terms of prevalence and site of injuries. Suggestively, this information should be used for to build a foundation of knowledge about the sport for development of applications for physical training and product development.

Keywords: Kitesurfing, injuries, injury cause, questionnaire.

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Authors: Arturs Macanovskis, Vitalijs Lusis, Andrejs Krasnikovs

Abstract:

This work had three stages. In the first stage was examined pull-out process for steel fiber was embedded into a concrete by one end and was pulled out of concrete under the angle to pulling out force direction. Angle was varied. On the obtained forcedisplacement diagrams were observed jumps. For such mechanical behavior explanation, fiber channel in concrete surface microscopical experimental investigation, using microscope KEYENCE VHX2000, was performed. At the second stage were obtained diagrams for load- crack opening displacement for breaking homogeneously reinforced and layered fiberconcrete prisms (with dimensions 10x10x40cm) subjected to 4-point bending. After testing was analyzed main crack. At the third stage elaborated prediction model for the fiberconcrete beam, failure under bending, using the following data: a) diagrams for fibers pulling out at different angles; b) experimental data about steel-straight fibers locations in the main crack. Experimental and theoretical (modeling) data were compared.

Keywords: Fiberconcrete, pull-out, fiber channel, layered fiberconcrete.

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Authors: K. Sudprasert, M. Precharattana, N. Nuttavut, D. Triampo, B. Pattanasiri, Y. Lenbury, W. Triampo

Abstract:

The study of non-equilibrium systems has attracted increasing interest in recent years, mainly due to the lack of theoretical frameworks, unlike their equilibrium counterparts. Studying the steady state and/or simple systems is thus one of the main interests. Hence in this work we have focused our attention on the driven lattice gas model (DLG model) consisting of interacting particles subject to an external field E. The dynamics of the system are given by hopping of particles to nearby empty sites with rates biased for jumps in the direction of E. Having used small two dimensional systems of DLG model, the stochastic properties at nonequilibrium steady state were analytically studied. To understand the non-equilibrium phenomena, we have applied the analytic approach via master equation to calculate probability function and analyze violation of detailed balance in term of the fluctuation-dissipation theorem. Monte Carlo simulations have been performed to validate the analytic results.

Keywords: Non-equilibrium, lattice gas, stochastic process

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Authors: Josip Visković, Josip Arnerić, Ante Rozga

Abstract:

Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models. When financial returns exhibit sudden jumps that are due to structural breaks, standard GARCH models show high volatility persistence, i.e. integrated behavior of the conditional variance. In such situations models in which the parameters are allowed to change over time are more appropriate. This paper compares different GARCH models in terms of their ability to describe structural changes in returns caused by financial crisis at stock markets of six selected central and east European countries. The empirical analysis demonstrates that Markov regime switching GARCH model resolves the problem of excessive persistence and outperforms uni-regime GARCH models in forecasting volatility when sudden switching occurs in response to financial crisis.

Keywords: Central and east European countries, financial crisis, Markov switching GARCH model, transition probabilities.

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Authors: Yoon-Hyuk Choi

Abstract:

Studies on the distribution of traffic demands have been proceeding by providing traffic information for reducing greenhouse gases and reinforcing the road's competitiveness in the transport section, however, since it is preferentially required the extensive studies on the driver's behavior changing routes and its influence factors, this study has been developed a discriminant model for changing routes considering driving conditions including traffic conditions of roads and driver's preferences for information media. It is divided into three groups depending on driving conditions in group classification with the CART analysis, which is statistically meaningful. And the extent that driving conditions and preferred media affect a route change is examined through a discriminant analysis, and it is developed a discriminant model equation to predict a route change. As a result of building the discriminant model equation, it is shown that driving conditions affect a route change much more, the entire discriminant hit ratio is derived as 64.2%, and this discriminant equation shows high discriminant ability more than a certain degree.

Keywords: CART analysis, Diversion, Discriminant model, Driving conditions, and preferred media

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Authors: Hanaa M. Abdelgawad, Mona Safar, Ayman M. Wahba

Abstract:

Real time image and video processing is a demand in many computer vision applications, e.g. video surveillance, traffic management and medical imaging. The processing of those video applications requires high computational power. Thus, the optimal solution is the collaboration of CPU and hardware accelerators. In this paper, a Canny edge detection hardware accelerator is proposed. Edge detection is one of the basic building blocks of video and image processing applications. It is a common block in the pre-processing phase of image and video processing pipeline. Our presented approach targets offloading the Canny edge detection algorithm from processing system (PS) to programmable logic (PL) taking the advantage of High Level Synthesis (HLS) tool flow to accelerate the implementation on Zynq platform. The resulting implementation enables up to a 100x performance improvement through hardware acceleration. The CPU utilization drops down and the frame rate jumps to 60 fps of 1080p full HD input video stream.

Keywords: High Level Synthesis, Canny edge detection, Hardware accelerators, and Computer Vision.

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Authors: Ishtiaq A. Chaudhry, Zia R Tahir, F. A. Siddiqui, F. Noor, M. J. Rashid

Abstract:

It has experimentally been proved that the performance of compression ignition (C.I.) engine is spray characteristics related. In modern diesel engine the spray formation and the eventual combustion process are the vital processes that offer more challenges towards enhancing the engine performance. In the present work the numerical simulation has been carried out for evaporating diesel sprays using Fluent software. For computational fluid dynamics simulation “Meshing” is done using Gambit software before transmitting it into Fluent. The simulation is carried out using hot bomb conditions under varying chamber conditions such as gas pressure, nozzle diameter and fuel injection pressure. For comparison purpose, the numerical simulations the chamber conditions were kept the same as that of the experimental data. At varying chamber conditions the spray penetration rates are compared with the existing experimental results.

Keywords: Evaporating diesel sprays, Penetration rates, Hot bomb conditions.

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Authors: Afshin Ahmadi Nadooshan, Ebrahim Shirani

Abstract:

In this paper, the two-dimensional stagger grid interface pressure (SGIP) model has been generalized and presented into three-dimensional form. For this purpose, various models of surface tension force for interfacial flows have been investigated and compared with each other. The VOF method has been used for tracking the interface. To show the ability of the SGIP model for three-dimensional flows in comparison with other models, pressure contours, maximum spurious velocities, norm spurious flow velocities and pressure jump error for motionless drop of liquid and bubble of gas are calculated using different models. It has been pointed out that SGIP model in comparison with the CSF, CSS and PCIL models produces the least maximum and norm spurious velocities. Additionally, the new model produces more accurate results in calculating the pressure jumps across the interface for motionless drop of liquid and bubble of gas which is generated in surface tension force.

Keywords: Volume-of-Fluid; SGIP model; CSS model; CSF model; PCIL model; surface tension force; spurious currents.

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Authors: Dara Singh, Keikhosrow Firouzbakhsh, Mohammad Taghi Ahmadian

Abstract:

In this study, a validated 3D finite volume model of human eye is developed to study the fluid flow and heat transfer in the human eye at steady state conditions. For this purpose, discretized bio-heat transfer equation coupled with Boussinesq equation is analyzed with different anatomical, environmental, and physiological conditions. It is demonstrated that the fluid circulation is formed as a result of thermal gradients in various regions of eye. It is also shown that posterior region of the human eye is less affected by the ambient conditions compared to the anterior segment which is sensitive to the ambient conditions and also to the way the gravitational field is defined compared to the geometry of the eye making the circulations and the thermal field complicated in transient states. The effect of variation in material and boundary conditions guides us to the conclusion that thermal field of a healthy and non-healthy eye can be distinguished via computer simulations.

Keywords: Bio-heat, Boussinesq, conduction, convection, eye.

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Authors: A. Shebani, S. Iwnicki

Abstract:

Understanding the nature of wheel and rail wear in the railway field is of fundamental importance to the safe and cost effective operation of the railways. Twin disc wear testing is used extensively for studying wear of wheel and rail materials. The University of Huddersfield twin disc rig was used in this paper to examine the effect of surface conditions on wheel and rail wear measurement under a range of wheel/rail contact conditions, with and without contaminants. This work focuses on an investigation of the effect of dry, wet, and lubricated conditions and the effect of contaminants such as sand on wheel and rail wear. The wheel and rail wear measurements were carried out by using a replica material and an optical profilometer that allows measurement of wear in difficult location with high accuracy. The results have demonstrated the rate at which both water and oil reduce wheel and rail wear. Scratches and other damage were seen on the wheel and rail surfaces after the addition of sand and consequently both wheel and rail wear damage rates increased under these conditions. This work introduced the replica material and an optical instrument as effective tools to study the effect of surface conditions on wheel and rail wear.

Keywords: Railway wheel/rail wear, surface conditions, twin disc test rig, replica material, Alicona profilometer.

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Authors: E. Shahhaidar

Abstract:

In this paper we present a novel design of a wearable electronic textile. After defining a special application, we used the specifications of some low power, tiny elements including sensors, microcontrollers, transceivers, and a fault tolerant special topology to have the most reliability as well as low power consumption and longer lifetime. We have considered two different conditions as normal and bodily critical conditions and set priorities for using different sensors in various conditions to have a longer effective lifetime.

Keywords: ECG, E-Textile, Fault Tolerance, Powerconsumption.

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Authors: Salah Alrabeei, Mohammad Yousuf

Abstract:

The goal of option pricing theory is to help the investors to manage their money, enhance returns and control their financial future by theoretically valuing their options. Modeling option pricing by Black-School models with jumps guarantees to consider the market movement. However, only numerical methods can solve this model. Furthermore, not all the numerical methods are efficient to solve these models because they have nonsmoothing payoffs or discontinuous derivatives at the exercise price. In this paper, the exponential time differencing (ETD) method is applied for solving partial integrodifferential equations arising in pricing European options under Merton’s and Kou’s jump-diffusion models. Fast Fourier Transform (FFT) algorithm is used as a matrix-vector multiplication solver, which reduces the complexity from O(M2) into O(M logM). A partial fraction form of Pad`e schemes is used to overcome the complexity of inverting polynomial of matrices. These two tools guarantee to get efficient and accurate numerical solutions. We construct a parallel and easy to implement a version of the numerical scheme. Numerical experiments are given to show how fast and accurate is our scheme.

Keywords: Integral differential equations, L-stable methods, pricing European options, Jump–diffusion model.

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Authors: Fahimeh Golestani, Mohammad Kazemeini, Moslem Fattahi, Ali Amjadian

Abstract:

In this research a mathematical model for direct oxidization of hydrogen sulfide into elemental sulfur in a fluidized bed reactor with external circulation was developed. As the catalyst is deactivated in the fluidized bed, it might be placed in a reduction tank in order to remove sulfur through heating above its dew point. The reactor model demonstrated via MATLAB software. It was shown that variations of H2S conversion as well as; products formed were reasonable in comparison with corresponding results of a fixed bed reactor. Through analyzing results of this model, it became possible to propose the main optimized operating conditions for the process considered. These conditions included; the temperature range of 100-130ºC and utilizing the catalyst as much as possible providing the highest bed density respect to dimensions of bed, economical aspects that the bed ever remained in fluidized mode. A high active and stable catalyst under the optimum conditions exhibited 100% conversion in a fluidized bed reactor.

Keywords: Direct oxidization, Fluidized bed, H2S, Mathematical modeling, Optimum conditions.

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

Abstract:

Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: Absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation.

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Authors: Seung-Yeon Kim

Abstract:

The square-lattice Ising model is the simplest system showing phase transitions (the transition between the paramagnetic phase and the ferromagnetic phase and the transition between the paramagnetic phase and the antiferromagnetic phase) and critical phenomena at finite temperatures. The exact solution of the squarelattice Ising model with free boundary conditions is not known for systems of arbitrary size. For the first time, the exact solution of the Ising model on the square lattice with free boundary conditions is obtained after classifying all ) spin configurations with the microcanonical transfer matrix. Also, the phase transitions and critical phenomena of the square-lattice Ising model are discussed using the exact solution on the square lattice with free boundary conditions.

Keywords: Phase transition, Ising magnet, Square lattice, Freeboundary conditions, Exact solution.

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