Abstract: Abstract The authors are trying to develop an ultrasonic CT technique for concrete structures. As the first step of its development, we study how the ultrasonic waves propagate in concrete structures and pose a problem to develop ultrasonic CT, applying which we give a non-destructive inspection technique for concrete cover by application of the idea of the ultrasonic CT. The authors claim that this study gives the foundation of the theory of ultrasonic CT for concrete structures. PubDate: 2018-09-06

Abstract: Abstract A 3-D continuum mixture model describing the corrosion of concrete with sulfuric acid is built. Essentially, the chemical reaction transforms slaked lime (calcium hydroxide) and sulfuric acid into gypsum releasing water. The model incorporates the evolution of chemical reaction, diffusion of species within the porous material and mechanical deformations. This model is applied to a 1-D problem of a plate-layer between concrete and sewer air. The influx of slaked lime from the concrete and sulfuric acid from the sewer air sustains a gypsum creating chemical reaction (sulfatation or sulfate attack). The combination of the influx of matter and the chemical reaction causes a net growth in the thickness of the gypsum layer on top of the concrete base. The model allows for the determination of the plate layer thickness h=h(t) as function of time, which indicates both the amount of gypsum being created due to concrete corrosion and the amount of slaked lime and sulfuric acid in the material. The existence of a parameter regime for which the model yields a non-decreasing plate layer thickness h(t) is identified numerically. The robustness of the model with respect to changes in the model parameters is also investigated. PubDate: 2018-08-31

Abstract: Abstract We give an algebraic description of screw dislocations in a crystal, especially simple cubic (SC) and body centered cubic (BCC) crystals, using free abelian groups and fibering structures. We also show that the strain energy of a screw dislocation based on the spring model is expressed by the Epstein-Hurwitz zeta function approximately. PubDate: 2018-08-31

Abstract: Abstract In this paper, we formulate a method for minimising the expectation value of the procurement cost of electricity in two popular spot markets: day-ahead and intra-day, under the assumption that expectation value of unit prices and the distributions of prediction errors for the electricity demand traded in two markets are known. The expectation value of the total electricity cost is minimised over two parameters that change the amounts of electricity. Two parameters depend only on the expected unit prices of electricity and the distributions of prediction errors for the electricity demand traded in two markets. That is, even if we do not know the predictions for the electricity demand, we can determine the values of two parameters that minimise the expectation value of the procurement cost of electricity in two popular spot markets. We demonstrate numerically that the estimate of two parameters often results in a small variance of the total electricity cost, and illustrate the usefulness of the proposed procurement method through the analysis of actual data. PubDate: 2018-08-31

Abstract: Abstract The objective of this article is to present the seminal concepts and techniques of Sub-Riemannian geometry and Hamiltonian dynamics, complemented by adapted software to analyze the dynamics of the copepod micro-swimmer, where the model of swimming is the slender body approximation for Stokes flows in fluid dynamics. In this context, the copepod model is a simplification of the 3-link Purcell swimmer and is relevant to analyze more complex micro-swimmers. The mathematical model is validated by observations performed by Takagi’s team of Hawaii laboratory, showing the agreement between the predicted and observed motions. Sub-Riemannian geometry is introduced, assuming that displacements are minimizing the expanded mechanical energy of the micro-swimmer. This allows to compare different strokes and different micro-swimmers and minimizing the expanded mechanical energy of the micro-swimmer. The objective is to maximize the efficiency of a stroke (the ratio between the displacement produced by a stroke and its length). Using the Maximum Principle in the framework of Sub-Riemannian geometry, this leads to analyze family of periodic controls producing strokes to determine the most efficient one. Graded normal forms introduced in Sub-Riemannian geometry to evaluate spheres with small radius is the technique used to evaluate the efficiency of different strokes with small amplitudes, and to determine the most efficient stroke using a numeric homotopy method versus standard direct computations based on Fourier analysis. Finally a copepod robot is presented whose aim is to validate the computations and very preliminary results are given. PubDate: 2018-06-22

Abstract: Abstract In this paper, in view of application to pricing of Barrier options under a stochastic volatility model, we study a reflection principle for the hyperbolic Brownian motion, and introduce a hyperbolic version of Imamura-Ishigaki-Okumura’s symmetrization. Some results of numerical experiments, which imply the efficiency of the numerical scheme based on the symmetrization, are given. PubDate: 2018-01-11

Authors:Stephen W. Taylor; Shixiao Wang Abstract: Abstract Annealing furnaces are used to heat steel in order to change its chemical structure. In this paper we model an electric radiant furnace. One of the major defects in steel strips processed in such furnaces is a wave-like pattern near the edges of the strip, apparently due to extra heating near the edges. The aim of the paper is to model this effect and provide a way to calculate the elevated temperatures near the edges. We analyse two processes that are suspected to contribute to uneven heating. The modelling involves an asymptotic analysis of the effect of heat flux at the edges and a detailed analysis of the integral equations associated with radiant heat transfer in the furnace. PubDate: 2017-04-27 DOI: 10.1186/s40736-017-0030-7 Issue No:Vol. 9, No. 1 (2017)

Authors:Volker Branding; Wayne Rossman Abstract: Abstract We focus on the numerical study of magnetic geodesics on surfaces, including surfaces with singularities. In addition to the numerical investigation, we give restrictive necessary conditions for tangency directions of magnetic geodesics passing through certain types of singularities. PubDate: 2017-03-06 DOI: 10.1186/s40736-017-0028-1 Issue No:Vol. 9, No. 1 (2017)

Authors:Khanh Duy Trinh Abstract: Abstract The convergence of the expectations of Betti numbers of Čech complexes built on binomial point processes in the thermodynamic regime is established. PubDate: 2017-03-06 DOI: 10.1186/s40736-017-0029-0 Issue No:Vol. 9, No. 1 (2017)

Authors:Denis Gilbert; Iraj Mortazavi; Olivier Piller; Hervé Ung Abstract: Abstract Water distribution networks are subject to potential intentional contaminations to cause harm to the consumer. Reliable transport models are needed to detect, trace and follow any contaminant transported inside the network. For now, the transport of contaminants in pipes has been mostly modeled assuming perfect mixing conditions at T-junction. However, some studies have shown that it is not always the case when crosses or double T-junctions are involved. In this paper an imperfect mixing at Double T-junction model is developed considering 3-D mixing behavior. A reduced model is then constructed in the form of a 1-D law to apply it to current 1-D transport models for water distribution networks. The methodology to create such law is detailed and can be applied to any reduced model problem including multi parameters and time consuming simulations. The procedure is composed of three steps: first calibrate the Kriging interpolation method parameters; then couple it with the Delaunay triangulation method to select simulation points with maximum gain; and finally implement a 1-D law based on the simulation results and the interpolation. PubDate: 2017-01-20 DOI: 10.1186/s40736-016-0026-8 Issue No:Vol. 9, No. 1 (2017)

Authors:Hayato Waki; Florin Nae Abstract: Abstract When using the convex hull approach in the boundary modeling process, Model-Based Calibration (MBC) software suites – such as Model-Based Calibration Toolbox from MathWorks – can be computationally intensive depending on the amount of data modeled. The reason for this is that the half-space representation of the convex hull is used. We discuss here another representation of the convex hull, the vertex representation, which proves capable to reduce the computational cost. Numerical comparisons in this article are executed in MATLAB by using MBC Toolbox commands, and show that for certain conditions, the vertex representation outperforms the half-space representation. PubDate: 2017-01-05 DOI: 10.1186/s40736-016-0027-7 Issue No:Vol. 9, No. 1 (2017)

Abstract: Abstract We apply innovative mathematical tools coming from optimal control theory to improve theoretical and experimental techniques in Magnetic Resonance Imaging (MRI). This approach allows us to explore and to experimentally reach the physical limits of the corresponding spin dynamics in the presence of typical experimental imperfections and limitations. We study in this paper two important goals, namely the optimization of image contrast and the maximization of the signal to noise per unit time. We anticipate that the proposed techniques will find practical applications in medical imaging in a near future to help the medical diagnosis. PubDate: 2017-10-17

Abstract: Abstract This article deals with applications of optimal control to aerospace problems with a focus on modern geometric optimal control tools and numerical continuation techniques. Geometric optimal control is a theory combining optimal control with various concepts of differential geometry. The ultimate objective is to derive optimal synthesis results for general classes of control systems. Continuation or homotopy methods consist in solving a series of parameterized problems, starting from a simple one to end up by continuous deformation with the initial problem. They help overcoming the difficult initialization issues of the shooting method. The combination of geometric control and homotopy methods improves the traditional techniques of optimal control theory. A nonacademic example of optimal attitude-trajectory control of (classical and airborne) launch vehicles, treated in details, illustrates how geometric optimal control can be used to analyze finely the structure of the extremals. This theoretical analysis helps building an efficient numerical solution procedure combining shooting methods and numerical continuation. Chattering is also analyzed and it is shown how to deal with this issue in practice. PubDate: 2017-07-20

Abstract: Abstract When a massive disaster occurs, to repair the damaged part of lifeline networks, planning is needed to appropriately allocate tasks to two or more restoration teams and optimize their traveling routes. However, precedence and synchronization constraints make restoration teams interdependent of one another, and impede a successful solution by standard local search. In this paper, we propose an indirect local search method using the product set of team-wise permutations as an auxiliary search space. It is shown that our method successfully avoids the interdependence problem induced by the precedence and synchronization constraints, and that it has the big advantage of non-deteriorating perturbations being available for iterated local search. PubDate: 2017-07-05

Abstract: Abstract We present an algorithm for solving an infinite horizon discrete time lot sizing problem with deterministic non-stationary demand and discounting of future cost. Besides non-negativity and finite supremum over infinite horizon, no restrictions are placed on single period demands. (In particular, they need not follow any cyclical pattern). Variable procurement cost, fixed ordering cost, and holding cost can be different in different periods. The algorithm uses forward induction and its essence lies in the use of critical periods. Period j following t is the critical period of t if satisfying demands in any subset of the set of periods between t and j, including j and excluding t, from an order in t is not more expensive than satisfying it from an order in a later period and j is the last period with this property. When deciding whether to place an order in period t, all demands from t to its critical period are taken into account. PubDate: 2017-06-14

Authors:Hidekazu Yoshioka; Yuta Yaegashi Abstract: Abstract As an application of mathematics to engineering problems, this paper formulates a simple optimal stopping problem to decide the opening time of harvesting farmed fishery resources that maximizes an economic objective function. A sufficient condition for unique existence of the internal optimal opening time is provided and its concrete mathematical analysis is carried out. Comparative statics of the optimal opening time clearly reveals its dependence on the parameters of the farming environment. The problem is finally applied to analyzing management of a commercially important fishery resource in Japan. PubDate: 2016-10-28 DOI: 10.1186/s40736-016-0025-9 Issue No:Vol. 8, No. 1 (2016)

Authors:Yuta Umezu; Hidetoshi Matsuoka; Hiroshi Ikeda; Yoshiyuki Ninomiya Abstract: Abstract In questionnaire studies for evaluating objects such as manufacturing products, evaluators are required to respond to several evaluation items for the objects. When the number of objects is large, a part of the objects is often assigned randomly to each evaluator, and the response becomes a matrix with missing components. To handle this kind of data, we consider a model by using a dummy matrix representing the existence of the missing components, which can be interpreted as an extension of the GMANOVA model. In addition, to cope with the case where the numbers of the object and evaluation items are large, we consider a ridge-type estimator peculiar to our model to avoid instability in estimation. Moreover, we derive a C p criterion in order to select the tuning parameters included in our estimator. Finally, we check the validity of the proposed method through simulation studies and real data analysis. PubDate: 2016-08-30 DOI: 10.1186/s40736-016-0024-x Issue No:Vol. 8, No. 1 (2016)

Authors:Hyoung-In Lee; Jinsik Mok Abstract: Abstract Cylindrical electromagnetic waves have been examined mostly with a radiation condition applied at the radial far field. In modern optical technology, there are however growing number of applications where both radiation and absorption of energy should be taken into account. In order to illustrate the ramifications of such energy balance, we take plasmonic waves propagating around a metallic nanowire as an example. Hence, we provide both key mathematical formulas and corresponding numerical results for the collective electronic motions in resonance with electromagnetic waves. Firstly, we show theoretically why a net Poynting energy flow is directed inward to the cylindrical axis. Secondly, we invoke a Cauchy-Schwarz inequality for complex variables in deriving an upper bound on the specific transverse light spin along the axial direction. Thirdly, we could identify both first- and second-order polarizations. Overall, loss-induced and gain-compensated characteristics are illustrated for a dissipative system. In addition, the stability of neutral states are examined by relaxing the angular periodicity. PubDate: 2016-04-04 DOI: 10.1186/s40736-016-0023-y Issue No:Vol. 8, No. 1 (2016)

Authors:Kenji Kajiwara; Toshinobu Kuroda; Nozomu Matsuura Abstract: Abstract We study deformations of plane curves in the similarity geometry. It is known that continuous deformations of smooth curves are described by the Burgers hierarchy. In this paper, we formulate the discrete deformation of discrete plane curves described by the discrete Burgers hierarchy as isogonal deformations. We also construct explicit formulas for the curve deformations by using the solution of linear diffusion differential/difference equations. PubDate: 2016-03-16 DOI: 10.1186/s40736-016-0022-z Issue No:Vol. 8, No. 1 (2016)

Authors:Evgeny Verbitskiy Abstract: Abstract We study a hidden Markov process which is the result of a transmission of the binary symmetric Markov source over the memoryless binary symmetric channel. This process has been studied extensively in Information Theory and is often used as a benchmark case for the so-called denoising algorithms. Exploiting the link between this process and the 1D Random Field Ising Model (RFIM), we are able to identify the Gibbs potential of the resulting Hidden Markov process. Moreover, we obtain a stronger bound on the memory decay rate. We conclude with a discussion on implications of our results for the development of denoising algorithms. PubDate: 2016-03-14 DOI: 10.1186/s40736-015-0021-5 Issue No:Vol. 8, No. 1 (2016)