Search results for: Computational Fluid Dynamics.

Authors: Le Zhao, Alain Nogaret

Abstract:

We have built universal central pattern generator (CPG) hardware by interconnecting Hodgkin-Huxley neurons with reciprocally inhibitory synapses. We investigate the dynamics of neuron oscillations as a function of the time delay between current steps applied to individual neurons. We demonstrate stimulus dependent switching between spiking polyrhythms and map the phase portraits of the neuron oscillations to reveal the basins of attraction of the system. We experimentally study the dependence of the attraction basins on the network parameters: The neuron response time and the strength of inhibitory connections.

Keywords: Central pattern generator, winnerless competition principle.

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Authors: J. T. Manhire

Abstract:

A tax authority wants to take actions it knows will foster the greatest degree of voluntary taxpayer compliance to reduce the “tax gap.” This paper suggests that even if a tax authority could attain a state of complete knowledge, there are constraints on whether and to what extent such actions would result in reducing the macro-level tax gap. These limits are not merely a consequence of finite agency resources. They are inherent in the system itself. To show that this is one possible interpretation of the tax gap data, the paper formulates known results in a different way by analyzing tax compliance as a population with a single covariate. This leads to a standard use of the logistic map to analyze the dynamics of non-compliance growth or decay over a sequence of periods. This formulation gives the same results as the tax gap studies performed over the past fifty years in the U.S. given the published margins of error. Limitations and recommendations for future work are discussed, along with some implications for tax policy.

Keywords: Tax law, tax compliance, tax gap, income tax.

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Authors: M. Margarida Costa, Jorge Simão

Abstract:

The minimal condition for symmetry breaking in morphogenesis of cellular population was investigated using cellular automata based on reaction-diffusion dynamics. In particular, the study looked for the possibility of the emergence of branching structures due to mechanical interactions. The model used two types of cells an external gradient. The results showed that the external gradient influenced movement of cell type-I, also revealed that clusters formed by cells type-II worked as barrier to movement of cells type-I.

Keywords: Morphogenesis, branching structures, symmetrybreaking.

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Authors: Le Chi Cuong

Abstract:

X-ray diffraction is an effective mean for analyzing material properties. This paper developed a new computational software for determining the properties of crystalline materials such as elastic constants, residual stresses, surface hardness, phase components, and etc. The results computed from the X-ray diffraction method were compared to those from the traditional methods and they are in the 95% confidential limits, showing that the newly developed software has high reproducibility, opening a possibility of its commercialization.

Keywords: X-ray diffraction, Nondestructive evaluation, Hardness, Residual stress, Phase determination.

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Authors: C. C. Wang, N. S. Pai, H. T. Yau, T. T. Liao, M. J. Jang, C. W. Lee, W. M. Hong

Abstract:

Horizontal platform system (HPS) is popularly applied in offshore and earthquake technology, but it is difficult and time-consuming for regulation. In order to understand the nonlinear dynamic behavior of HPS and reduce the cost when using it, this paper employs differential transformation method to study the bifurcation behavior of HPS. The numerical results reveal a complex dynamic behavior comprising periodic, sub-harmonic, and chaotic responses. Furthermore, the results reveal the changes which take place in the dynamic behavior of the HPS as the external torque is increased. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of horizontal platform system.

Keywords: horizontal platform system, differentialtransformation method, chaotic.

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Authors: Luciana Montera

Abstract:

DNA shuffling is a powerful method used for in vitro evolute molecules with specific functions and has application in areas such as, for example, pharmaceutical, medical and agricultural research. The success of such experiments is dependent on a variety of parameters and conditions that, sometimes, can not be properly pre-established. Here, two computational models predicting DNA shuffling results is presented and their use and results are evaluated against an empirical experiment. The in silico and in vitro results show agreement indicating the importance of these two models and motivating the study and development of new models.

Keywords: Computer simulation, DNA shuffling, in silico andin vitro comparison.

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Authors: J. Urbánek Jiří, Krahulec Josef, Johanidesová Jitka, F. Urbánek Jiří

Abstract:

This paper deals with using of prevailing operation system MS Office (SmartArt...) for mathematical models, using DYVELOP (Dynamic Vector Logistics of Processes) method. It serves for crisis situations investigation and modelling within the organizations of critical infrastructure. In first part of paper, it will be introduced entities, operators, and actors of DYVELOP method. It uses just three operators of Boolean algebra and four types of the entities: the Environments, the Process Systems, the Cases, and the Controlling. The Process Systems (PrS) have five “brothers”: Management PrS, Transformation PrS, Logistic PrS, Event PrS and Operation PrS. The Cases have three “sisters”: Process Cell Case, Use Case, and Activity Case. They all need for the controlling of their functions special Ctrl actors, except ENV – it can do without Ctrl. Model´s maps are named the Blazons and they are able mathematically - graphically express the relationships among entities, actors and processes. In second part of this paper, the rich blazons of DYVELOP method will be used for the discovering and modelling of the cycling cases and their phases. The blazons need live PowerPoint presentation for better comprehension of this paper mission. The crisis management of energetic crisis infrastructure organization is obliged to use the cycles for successful coping of crisis situations. Several times cycling of these cases is necessary condition for the encompassment for both emergency events and the mitigation of organization´s damages. Uninterrupted and continuous cycling process brings for crisis management fruitfulness and it is good indicator and controlling actor of organizational continuity and its sustainable development advanced possibilities. The research reliable rules are derived for the safety and reliable continuity of energetic critical infrastructure organization in the crisis situation.

Keywords: Blazons, computational assistance, DYVELOP method, critical infrastructure.

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Authors: A. Heidarinasab, V. Moghaddam Nansa

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This paper deals with rheological behavior of tomato paste from the view point of time independent properties inclusive of processing variables such as sample temperature which influence on rheological properties as well as breaking temperature and concentration which beside the rheological properties, influence on the quality of final product. With this aim 10 tomato paste samples at various concentrations (17-25%) and breaking temperatures (65- 85 C o ) have been produced. The experimental results showed tomato paste behaves as a non-Newtonian semi-fluid which follows power law model that consistency coefficient (K) is supposed function of breaking temperature, concentration and sample temperature with consideration to superimpose function.

Keywords: Breaking temperature, Concentration, Power law, Rheology, Time independent.

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Authors: M. Vijaya Kini, R. S. Pai, D. Srikanth Rao, Satish Shenoy B, R. Pai

Abstract:

The stability characteristics of water lubricated journal bearings having three axial grooves are obtained theoretically. In this lubricant (water) is fed under pressure from one end of the bearing, through the 3-axial grooves (groove angles may vary). These bearings can use the process fluid as the lubricant, as in the case of feed water pumps. The Reynolds equation is solved numerically by the finite difference method satisfying the boundary conditions. The stiffness and damping coefficient for various bearing number and eccentricity ratios, assuming linear pressure drop along the groove, shows that smaller groove angles better results.

Keywords: 3-axial groove, dynamic characteristics, groovelocation, water lubricated bearings.

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Authors: Erna T. Herdiani, Maman A. Djauhari

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In recent years, the use of vector variance as a measure of multivariate variability has received much attention in wide range of statistics. This paper deals with a more economic measure of multivariate variability, defined as vector variance minus all duplication elements. For high dimensional data, this will increase the computational efficiency almost 50 % compared to the original vector variance. Its sampling distribution will be investigated to make its applications possible.

Keywords: Asymptotic distribution, covariance matrix, likelihood ratio test, vector variance.

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Authors: Y. Galerkin, O. Solovieva

Abstract:

Parameters of flow are calculated in vaneless diffusers with relative width 0,014–0,10. Inlet angles of flow and similarity criteria were varied. There is information on flow separation, boundary layer development, configuration of streamlines. Polytrophic efficiency, loss coefficient and recovery coefficient are used to compare effectiveness of diffusers. The sample of optimization of narrow diffuser with conical walls is presented. Three wide diffusers with narrowing walls are compared. The work is made in the R&D laboratory “Gas dynamics of turbo machines” of the TU SPb.

Keywords: Vaneless diffuser, relative width, flow angle, flow separation, loss coefficient, similarity criteria.

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Authors: Shorena Tsiklauri, Avtandil Sulaberidze, Nino Gomelauri

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In the years followed independence, an economic crisis and some conflicts led to the displacement of many people inside Georgia. The growing poverty, unemployment, low income and its unequal distribution limited access to basic social service have had a clear direct impact on Georgian population dynamics and its age-sex structure. Factors influencing the changing population age structure and urbanization include mortality, fertility, migration and expansion of urban. In this paper presents the main factors of changing the distribution by urban and rural areas. How different are the urban and rural age and sex structures? Does Georgia have the same age-sex structure among their urban and rural populations since 1950s?

Keywords: Age and sex structure of population, Georgia, migration, urban-rural population.

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Authors: Moustafa Osman Mohammed

Abstract:

Integration sustainability outcomes give attention to construction ecology in the design review of urban environments to comply with Earth’s System that is composed of integral parts of the (i.e., physical, chemical and biological components). Naturally, exchange patterns of industrial ecology have consistent and periodic cycles to preserve energy flows and materials in Earth’s System. When engineering topology is affecting internal and external processes in system networks, it postulated the valence of the first-level spatial outcome (i.e., project compatibility success). These instrumentalities are dependent on relating the second-level outcome (i.e., participant security satisfaction). The construction ecology-based topology (i.e., as feedback energy system) flows from biotic and abiotic resources in the entire Earth’s ecosystems. These spatial outcomes are providing an innovation, as entails a wide range of interactions to state, regulate and feedback “topology” to flow as “interdisciplinary equilibrium” of ecosystems. The interrelation dynamics of ecosystems are performing a process in a certain location within an appropriate time for characterizing their unique structure in “equilibrium patterns”, such as biosphere and collecting a composite structure of many distributed feedback flows. These interdisciplinary systems regulate their dynamics within complex structures. These dynamic mechanisms of the ecosystem regulate physical and chemical properties to enable a gradual and prolonged incremental pattern to develop a stable structure. The engineering topology of construction ecology for integration sustainability outcomes offers an interesting tool for ecologists and engineers in the simulation paradigm as an initial form of development structure within compatible computer software. This approach argues from ecology, resource savings, static load design, financial other pragmatic reasons, while an artistic/architectural perspective, these are not decisive. The paper described an attempt to unify analytic and analogical spatial modeling in developing urban environments as a relational setting, using optimization software and applied as an example of integrated industrial ecology where the construction process is based on a topology optimization approach.

Keywords: Construction ecology, industrial ecology, urban topology, environmental planning.

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Authors: H. R. Goshayeshi, M. Mansori, M. Ahmady, M. Khaloyi

Abstract:

This paper presents the result of an experimental investigation regarding the use of Fe2O3 nanoparticles added to kerosene as a working fluid, under magnetic field for Copper Oscillating Heat pipe with inclination angle of 0°(horizontal), 15°, 30°,45°, 60°,75° and 90° (vertical). The following were examined; measure the temperature distribution and heat transfer rate on Oscillating Heat Pipe (OHP), with magnetic field under different angles. Results showed that the addition of Fe2O3 nanoparticles under magnetic field improved thermal performance of OHP especially in 75°.

Keywords: Copper oscillating heat pipe, Fe2O3, magnetic field, inclination angles.

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Authors: Narasimham Challa, Jayaram Pradhan

Abstract:

Cryptographic algorithms play a crucial role in the information society by providing protection from unauthorized access to sensitive data. It is clear that information technology will become increasingly pervasive, Hence we can expect the emergence of ubiquitous or pervasive computing, ambient intelligence. These new environments and applications will present new security challenges, and there is no doubt that cryptographic algorithms and protocols will form a part of the solution. The efficiency of a public key cryptosystem is mainly measured in computational overheads, key size and bandwidth. In particular the RSA algorithm is used in many applications for providing the security. Although the security of RSA is beyond doubt, the evolution in computing power has caused a growth in the necessary key length. The fact that most chips on smart cards can-t process key extending 1024 bit shows that there is need for alternative. NTRU is such an alternative and it is a collection of mathematical algorithm based on manipulating lists of very small integers and polynomials. This allows NTRU to high speeds with the use of minimal computing power. NTRU (Nth degree Truncated Polynomial Ring Unit) is the first secure public key cryptosystem not based on factorization or discrete logarithm problem. This means that given sufficient computational resources and time, an adversary, should not be able to break the key. The multi-party communication and requirement of optimal resource utilization necessitated the need for the present day demand of applications that need security enforcement technique .and can be enhanced with high-end computing. This has promoted us to develop high-performance NTRU schemes using approaches such as the use of high-end computing hardware. Peer-to-peer (P2P) or enterprise grids are proven as one of the approaches for developing high-end computing systems. By utilizing them one can improve the performance of NTRU through parallel execution. In this paper we propose and develop an application for NTRU using enterprise grid middleware called Alchemi. An analysis and comparison of its performance for various text files is presented.

Keywords: Alchemi, GridNtru, Ntru, PKCS.

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Authors: Fatma Khaled, Khaoula Hidouri, Bechir Chaouachi

Abstract:

Desalination using solar energy coupled with membrane techniques such as vacuum membrane distillation (VMD) is considered as an interesting alternative for the production of pure water. During this work, a developed model of a polytetrafluoroethylene (PTFE) hollow fiber membrane module of a VMD unit of seawater was carried out. This simulation leads to establishing a comparison between the effects of two different equations of the vaporization latent heat on the membrane surface temperature and on the unit productivity. Besides, in order to study the effect of putting membrane modules in series on the outlet fluid temperature and on the productivity of the process, a simulation was executed.

Keywords: Vacuum membrane distillation, membrane module, membrane temperature, productivity.

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Authors: Vai Kuong Sin

Abstract:

Non-isothermal stagnation-point flow with consideration of thermal radiation is studied numerically. A set of partial differential equations that governing the fluid flow and energy is converted into a set of ordinary differential equations which is solved by Runge-Kutta method with shooting algorithm. Dimensionless wall temperature gradient and temperature boundary layer thickness for different combinaton of values of Prandtl number Pr and radiation parameter NR are presented graphically. Analyses of results show that the presence of thermal radiation in the stagnation-point flow is to increase the temperature boundary layer thickness and decrease the dimensionless wall temperature gradient.

Keywords: Stagnation-point flow, Similarity solution, Thermal radiation.

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Authors: Zhang Linan, Jihwan Song, Dongchoul Kim

Abstract:

In this study, a three-dimensional haptotaxis model to simulate the migration of a population of cancer cells has been proposed. The invasion of cancer cells is related with the hapto-attractant and the effect of the interface energies between the cells and the ECM. The diffuse interface model, which incorporates the haptotaxis mechanism and interface energies, is employed. The semi-implicit Fourier spectral scheme is adopted for efficient evaluation of the simulation. The simulation results thoroughly reveal the dynamics of cancer-cell migration.

Keywords: Haptotaxis, Cancer Cells, Cell Migration, Interface Energy, Diffuse Interface Model

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Authors: G. Candel, D. Naccache

Abstract:

t-SNE is an embedding method that the data science community has widely used. It helps two main tasks: to display results by coloring items according to the item class or feature value; and for forensic, giving a first overview of the dataset distribution. Two interesting characteristics of t-SNE are the structure preservation property and the answer to the crowding problem, where all neighbors in high dimensional space cannot be represented correctly in low dimensional space. t-SNE preserves the local neighborhood, and similar items are nicely spaced by adjusting to the local density. These two characteristics produce a meaningful representation, where the cluster area is proportional to its size in number, and relationships between clusters are materialized by closeness on the embedding. This algorithm is non-parametric. The transformation from a high to low dimensional space is described but not learned. Two initializations of the algorithm would lead to two different embedding. In a forensic approach, analysts would like to compare two or more datasets using their embedding. A naive approach would be to embed all datasets together. However, this process is costly as the complexity of t-SNE is quadratic, and would be infeasible for too many datasets. Another approach would be to learn a parametric model over an embedding built with a subset of data. While this approach is highly scalable, points could be mapped at the same exact position, making them indistinguishable. This type of model would be unable to adapt to new outliers nor concept drift. This paper presents a methodology to reuse an embedding to create a new one, where cluster positions are preserved. The optimization process minimizes two costs, one relative to the embedding shape and the second relative to the support embedding’ match. The embedding with the support process can be repeated more than once, with the newly obtained embedding. The successive embedding can be used to study the impact of one variable over the dataset distribution or monitor changes over time. This method has the same complexity as t-SNE per embedding, and memory requirements are only doubled. For a dataset of n elements sorted and split into k subsets, the total embedding complexity would be reduced from O(n2) to O(n2/k), and the memory requirement from n2 to 2(n/k)2 which enables computation on recent laptops. The method showed promising results on a real-world dataset, allowing to observe the birth, evolution and death of clusters. The proposed approach facilitates identifying significant trends and changes, which empowers the monitoring high dimensional datasets’ dynamics.

Keywords: Concept drift, data visualization, dimension reduction, embedding, monitoring, reusability, t-SNE, unsupervised learning.

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Authors: Johannes Nywlt, Julian Becker, Sebastian Bertsch

Abstract:

Due to high dynamics in current markets the expectations regarding logistics increase steadily. However, the complexity and variety of products and production make it difficult to understand the interdependencies between logistical objectives and their determining factors. Therefore specific models are needed to meet this challenge. The Logistic Operating Curves Theory is such a model. With its aid the basic correlations between the logistic objectives can be described. Within this model the capacity flexibility represents an important parameter. However, a proper mathematical description for this parameter is still missing. Within this paper such a description will be developed in order to make the Logistic Operating Curves Theory more accurate.

Keywords: Capacity flexibility, Production controlling, Production logistics, Production management.

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Authors: N. Sopipan, A. Intarasit, K. Chuarkham

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 In this paper, we forecast the volatility of Baht/USDs using Markov Regime Switching GARCH (MRS-GARCH) models. These models allow volatility to have different dynamics according to unobserved regime variables. The main purpose of this paper is to find out whether MRS-GARCH models are an improvement on the GARCH type models in terms of modeling and forecasting Baht/USD volatility. The MRS-GARCH is the best performance model for Baht/USD volatility in short term but the GARCH model is best perform for long term.

Keywords: Volatility, Markov Regime Switching, Forecasting.

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Authors: Hari Mohan Kushwaha, Santosh K. Sahu

Abstract:

In the present study, analysis of heat transfer is carried out in the slip flow region for the fluid flowing between two parallel plates by employing the asymmetric heat fluxes at surface of the plates. The flow is assumed to be hydrodynamically and thermally fully developed for the analysis. The second order velocity slip and viscous dissipation effects are considered for the analysis. Closed form expressions are obtained for the Nusselt number as a function of Knudsen number and modified Brinkman number. The limiting condition of the present prediction for Kn = 0, Kn2 = 0, and Brq1 = 0 is considered and found to agree well with other analytical results.

Keywords: Knudsen Number, Modified Brinkman Number, Slip Flow, Velocity Slip.

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Authors: K. Vakhshouri, M.M. Y. Motamed Hashemi

Abstract:

A rigorous two-dimensional model is developed for simulating the operation of a less-investigated type steam reformer having a considerably lower operating Reynolds number, higher tube diameter, and non-availability of extra steam in the feed compared with conventional steam reformers. Simulation results show that reasonable predictions can only be achieved when certain correlations for wall to fluid heat transfer equations are applied. Due to severe operating conditions, in all cases, strong radial temperature gradients inside the reformer tubes have been found. Furthermore, the results show how a certain catalyst loading profile will affect the operation of the reformer.

Keywords: Steam reforming, direct reduction, heat transfer, two-dimensional model, simulation.

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Authors: Sol-Kil Oh, Hye-Jin Lee, Jung-Han Song, Kyoung-Tae Kim, Nak-Kyu Lee, Jong-Ho Kim

Abstract:

This paper deals with a novel technique for the fabrication of Spiral grooves in a dynamic thrust bearing. The main scheme proposed in this paper is to fabricate the microgrooves using desktop forming system. This process has advantages compared to the conventional electro-chemical machining in the viewpoint of a higher productivity. For this reason, a new testing apparatus is designed and built for press forming microgrooves on a surface of the thrust bearing. The material used in this study is sintered Cu-Fe alloy. The effects of the forming load on the performance of micro press forming are experimentally investigated. From the experimental results, formed depths are closed to the target ones with increasing the forming load.

Keywords: Desktop forming system, Fluid dynamic bearing, Thrust bearing, Microgroove.

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Authors: Moghadazadeh Zahra, Towfighi Jafar, Mofarahi Masoud

Abstract:

This article is presented an experimental and modeling study of a four-bed pressure swing adsorption process using zeolite13X to provide oxygen-enriched air. The binary mixture N2/O2 (79/21 vol %) was used as a feed stream. The effects of purge/feed ratio (P/F), adsorption pressure, cyclic time and product flow rate on product purity and recovery under nonisothermal condition were studied. The adsorption dynamics of process were determined using a mathematical model incorporated mass and energy balances. A Mathlab code using finite difference method was developed to solve the set of coupled differential-algebraic equations, and the simulation results are agreed well with experimental results.

Keywords: Pressure swing adsorption (PSA), Oxygen, Zeolite 13X.

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Authors: N. Targui, H. Kahalerras

Abstract:

The present work is a numerical simulation of nanofluids flow in a double pipe heat exchanger provided with porous baffles. The hot nanofluid flows in the inner cylinder, whereas the cold nanofluid circulates in the annular gap. The Darcy- Brinkman-Forchheimer model is adopted to describe the flow in the porous regions, and the governing equations with the appropriate boundary conditions are solved by the finite volume method. The results reveal that the addition of metallic nanoparticles enhances the rate of heat transfer in comparison to conventional fluids but this augmentation is accompanied by an increase in pressure drop. The highest heat exchanger performances are obtained when nanoparticles are added only to the cold fluid.

Keywords: Double pipe heat exchanger, Nanofluids, Nanoparticles, Porous baffles.

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Authors: Francois T. Pronk, Steven J. Hulshoff

Abstract:

A study of various turbulent inflow generation methods was performed to compare their relative effectiveness for LES computations of turbulent boundary layers. This study confirmed the quality of the turbulent information produced by the family of recycling and rescaling methods which take information from within the computational domain. Furthermore, more general inflow methods also proved applicable to such simulations, with a precursor-like inflow and a random inflow augmented with forcing planes showing promising results.

Keywords: Boundary layer, Flat plate, Inflow modeling, LES

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Authors: Lenka Krulikovská, Jaroslav Polec, Tomáš Hirner

Abstract:

In this paper we present a novel method, which reduces the computational complexity of abrupt cut detection. We have proposed fast algorithm, where the similarity of frames within defined step is evaluated instead of comparing successive frames. Based on the results of simulation on large video collection, the proposed fast algorithm is able to achieve 80% reduction of needed frames comparisons compared to actually used methods without the shot cut detection accuracy degradation.

Keywords: Abrupt cut, fast algorithm, shot cut detection, Pearson correlation coefficient.

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Authors: Corneliu Sofronie, Roxana Zubcov

Abstract:

Cognitive Science appeared about 40 years ago, subsequent to the challenge of the Artificial Intelligence, as common territory for several scientific disciplines such as: IT, mathematics, psychology, neurology, philosophy, sociology, and linguistics. The new born science was justified by the complexity of the problems related to the human knowledge on one hand, and on the other by the fact that none of the above mentioned sciences could explain alone the mental phenomena. Based on the data supplied by the experimental sciences such as psychology or neurology, models of the human mind operation are built in the cognition science. These models are implemented in computer programs and/or electronic circuits (specific to the artificial intelligence) – cognitive systems – whose competences and performances are compared to the human ones, leading to the psychology and neurology data reinterpretation, respectively to the construction of new models. During these processes if psychology provides the experimental basis, philosophy and mathematics provides the abstraction level utterly necessary for the intermission of the mentioned sciences. The ongoing general problematic of the cognitive approach provides two important types of approach: the computational one, starting from the idea that the mental phenomenon can be reduced to 1 and 0 type calculus operations, and the connection one that considers the thinking products as being a result of the interaction between all the composing (included) systems. In the field of psychology measurements in the computational register use classical inquiries and psychometrical tests, generally based on calculus methods. Deeming things from both sides that are representing the cognitive science, we can notice a gap in psychological product measurement possibilities, regarded from the connectionist perspective, that requires the unitary understanding of the quality – quantity whole. In such approach measurement by calculus proves to be inefficient. Our researches, deployed for longer than 20 years, lead to the conclusion that measuring by forms properly fits to the connectionism laws and principles.

Keywords: complementary methodology, connection approach, networks without scaling, quantum psychology.

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Authors: D. H. Kim, Y. H. Kim, T. Kim

Abstract:

A new method identifies coupled fluid-structure system with a reduced set of state variables is presented. Assuming that the structural model is known a priori either from an analysis or a test and using linear transformations between structural and aeroelastic states, it is possible to deduce aerodynamic information from sampled time histories of the aeroelastic system. More specifically given a finite set of structural modes the method extracts generalized aerodynamic force matrix corresponding to these mode shapes. Once the aerodynamic forces are known, an aeroelastic reduced-order model can be constructed in discrete-time, state-space format by coupling the structural model and the aerodynamic system. The resulting reduced-order model is suitable for constant Mach, varying density analysis.

Keywords: ROM (Reduced-Order Model), aero elasticity, AGARD 445.6 wing.

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