Endüstri Mühendisliği Bölümü Koleksiyonu

Permanent URI for this collectionhttps://gcris.khas.edu.tr/handle/20.500.12469/48

Browse

Now showing 1 - 20 of 25

Citation Count: 5
(3+3+2) warped-like product manifolds with Spin(7) holonomy
(Elsevier Science Bv, 2011) Bilge, Ayşe Hümeyra; Bilge, Ayşe Hümeyra
We consider a generalization of eight-dimensional multiply warped product manifolds as a special warped product by allowing the fiber metric to be non-block diagonal. We define this special warped product as a (3 + 3 + 2) warped-like manifold of the form M = F x B. where the base B is a two-dimensional Riemannian manifold and the fibre F is of the form F = F-1 x F-2 where the F-i(i = 1 2) are Riemannian 3-manifolds. We prove that the connection on M is completely determined by the requirement that the Bonan 4-form given in the work of Yasui and Ootsuka [Y. Yasui and T. Ootsuka Spin(7) holonomy manifold and superconnection Class. Quantum Gravity 18(2001)807-816] be closed. Assuming that the F-i are complete connected and simply connected it follows that they are isometric to S-3 with constant curvature k > 0 and the Yasui-Ootsuka solution is unique in the class of (3 + 3 + 2) warped-like product metrics admitting a specific Spin(7) structure. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.
Citation Count: 5
An analysis of price spikes and deviations in the deregulated Turkish power market
(Elsevier, 2019) Bilge, Ayşe Hümeyra; Yücekaya, Ahmet; Bilge, Ayşe Hümeyra
The successful operation of a real time market is related to the planning in the day ahead market. We analyze the day ahead and real time market data for the Turkish power market for the period 2012-2015 to classify price spikes and their causes. We also focus on the levels of deviation between the day ahead market values and the real time market values. We define price deviation and load deviation ratios to measure the level of deviation both in price and demand. The analysis for the load is based on load shedding and cycling values. We analyze the mean and standard deviation in market prices and we determine the price spike as a two sigma deviation from the mean value. It is shown that 60% of the price deviation ratios are in the range of ( +/- 20%), while 44% are in the range of ( +/- 10%) and 35% are in the range of (+/- 5%). We also show that 56.9% of the spikes are due to problems in the generation of natural gas based power plants which affect the day ahead and real time prices. A total of 29.2% of the spikes are due to power plant and system failures that affect only real time prices. The share of high temperature based spikes is 13.9% which is a result of air conditioner usage.
Citation Count: 10
Application of epidemic models to phase transitions
(Taylor & Francis Ltd, 2012) Bilge, Ayşe Hümeyra; Pekcan, Önder; Gürol, M. V.
The Susceptible-Infected-Recovered (SIR) and Susceptible-Exposed-Infected-Recovered (SEIR) models describe the spread of epidemics in a society. In the typical case, the ratio of the susceptible individuals fall from a value S-0 close to 1 to a final value S-f, while the ratio of recovered individuals rise from 0 to R-f = 1 - S-f. The sharp passage from the level zero to the level R-f allows also the modeling of phase transitions by the number of "recovered" individuals R(t) of the SIR or SEIR model. In this article, we model the sol-gel transition for polyacrylamide-sodium alginate (SA) composite with different concentrations of SA as SIR and SEIR dynamical systems by solving the corresponding differential equations numerically and we show that the phase transitions of "classical" and "percolation" types are represented, respectively, by the SEIR and SIR models.
Citation Count: 0
Canonical forms for families of anti-commuting diagonalizable linear operators
(Elsevier Science Inc, 2012) Bilge, Ayşe Hümeyra; Bilge, Ayşe Hümeyra
It is well known that a commuting family of diagonalizable linear operators on a finite dimensional vector space is simultaneously diagonalizable. In this paper we consider a family A = {A(a)} A(a) : V -> V a = 1... N of anti-commuting (complex) linear operators on a finite dimensional vector space. We prove that if the family is diagonalizable over the complex numbers then V has an A-invariant direct sum decomposition into subspaces V(alpha) such that the restriction of the family A to V(alpha) is a representation of a Clifford algebra. Thus unlike the families of commuting diagonalizable operators diagonalizable anti-commuting families cannot be simultaneously digonalized but on each subspace they can be put simultaneously to (non-unique) canonical forms. The construction of canonical forms for complex representations is straightforward while for the real representations it follows from the results of [A.H. Bilge S. Kocak S. Uguz Canonical bases for real representations of Clifford algebras Linear Algebra Appl. 419 (2006) 417-439]. (C) 2011 Elsevier Inc. All rights reserved.
Citation Count: 1
The critical point of a sigmoidal curve
(Babeș-Bolyai University, 2020) Bilge, Ayşe Hümeyra; Özdemir, Yunus
Let y(t) be a monotone increasing curve with lim(t ->+/-infinity) y((n))(t) = 0 for all n and let t(n) be the location of the global extremum of the nth derivative y((n))(t). Under certain assumptions on the Fourier and Hilbert transforms of y(t), we prove that the sequence {t(n)} is convergent. This implies in particular a preferred choice of the origin of the time axis and an intrinsic definition of the even and odd components of a sigmoidal function. In the context of phase transitions, the limit point has the interpretation of the critical point of the transition as discussed in previous work [3].
Citation Count: 1
Determination of epidemic parameters from early phase fatality data: A case study of the 2009 A(H1N1) pandemic in Europe
(World Scientific Publ Co Pte Ltd, 2018) Bilge, Ayşe Hümeyra; Samanlıoğlu, Funda
This paper demonstrates that the susceptible-infected-removed (SIR) model applied to the early phase of an epidemic can be used to determine epidemic parameters reliably. As a case study the SIR model is applied to the fatality data of the 2009 fall wave cycle of the A(H1N1) pandemic in 12 European countries. It is observed that the best estimates of the basic reproduction number R-0 and the mean duration of the infection period 1/eta lie on a curve in the scatterplots indicating the existence of a nearly-invariant quantity which corresponds to the duration of the epidemic. Spline interpolation applied to the early phase of the epidemic an approximately 10-week period together with a future control point in the stabilization region is sufficient to estimate model parameters. The SIR model is run over a wide range of parameters and estimates of R0 in the range 1.2-2.0 match the values in the literature. The duration of the infection period 1/eta is estimated to be in the range 2.0-7.0 days. Longer infection periods are tied to spatial characteristics of the spread of the epidemic.
Citation Count: 5
Epidemic models for phase transitions: application to a physical gel
(Taylor & Francis Ltd, 2017) Bilge, Ayşe Hümeyra; Pekcan, Önder; Kara, Selim; Öğrenci, Arif Selçuk
Carrageenan gels are characterized by reversible sol-gel and gel-sol transitions under cooling and heating processes and these transitions are approximated by generalized logistic growth curves. We express the transitions of carrageenan-water system as a representative of reversible physical gels in terms of a modified Susceptible-Infected-Susceptible epidemic model as opposed to the Susceptible-Infected-Removed model used to represent the (irreversible) chemical gel formation in the previous work. We locate the gel point T-c of sol-gel and gel-sol transitions and we find that for the sol-gel transition (cooling) T-c > T-sg (transition temperature) i.e. T-c is earlier in time for all carrageenan contents and moves forward in time and gets closer to T-sg as the carrageenan content increases. For the gel-sol transition (heating) T-c is relatively closer to T-gs
Citation Count: 2
An equivalence class decomposition of finite metric spaces via Gromov products
(Elsevier Science Bv, 2017) Bilge, Ayşe Hümeyra; Çelik, Derya; Koçak, Şahin
Let (X, d) be a finite metric space with elements P-i, i = 1,..., n and with the distance functions d(ij) The Gromov Product of the "triangle" (P-i, P-j, P-k) with vertices P-t, P-j and P-k at the vertex Pi is defined by Delta(ijk) = 1/2(d(ij) + d(ik) - d(jk)). We show that the collection of Gromov products determines the metric. We call a metric space Delta-generic, if the set of all Gromov products at a fixed vertex P-i has a unique smallest element (for i = 1,., n). We consider the function assigning to each vertex P-i the edge {P-i, P-k} of the triangle (P-i, P-j, P-k) realizing the minimal Gromov product at P-i and we call this function the Gromov product structure of the metric space (X, d). We say two Delta-generic metric spaces (X, d) and (X, d') to be Gromov product equivalent, if the corresponding Gromov product structures are the same up to a permutation of X. For n = 3, 4 there is one (Delta-generic) Gromov equivalence class and for n = 5 there are three (Delta-generic) Gromov equivalence classes. For n = 6 we show by computer that there are 26 distinct (Delta-generic) Gromov equivalence classes. (C) 2017 Elsevier B.V. All rights reserved.
Citation Count: 68
Forecasting electricity demand for Turkey: Modeling periodic variations and demand segregation
(Elsevier, 2017) Bilge, Ayşe Hümeyra; Yücekaya, Ahmet; Bilge, Ayşe Hümeyra
In deregulated electricity markets the independent system operator (ISO) oversees the power system and manages the supply and demand balancing process. In a typical day the ISO announces the electricity demand forecast for the next day and gives participants an option to prepare offers to meet the demand. In order to have a reliable power system and successful market operation it is crucial to estimate the electricity demand accurately. In this paper we develop an hourly demand forecasting method on annual weekly and daily horizons using a linear model that takes into account the harmonics of these variations and the modulation of diurnal periodic variations by seasonal variations. The electricity demand exhibits cyclic behavior with different seasonal characteristics. Our model is based solely on sinusoidal variations and predicts hourly variations without using any climatic or econometric information. The method is applied to the Turkish power market on data for the period 2012-2014 and predicts the demand over daily and weekly horizons within a 3% error margin in the Mean Absolute Percentage Error (MAPE) norm. We also discuss the week day/weekend/holiday consumption profiles to infer the proportion of industrial and domestic electricity consumption. (C) 2017 Elsevier Ltd. All rights reserved.
Citation Count: 6
Forecasting Models For Daily Natural Gas Consumption Considering Periodic Variations And Demand Segregation
(Elsevier Ltd, 2020) Bilge, Ayşe Hümeyra; Ağca Aktunç, Esra; Bilge, Ayşe Hümeyra; Ağca Aktunç, Esra
Due to expensive infrastructure and the difficulties in storage, supply conditions of natural gas are different from those of other traditional energy sources like petroleum or coal. To overcome these challenges, supplier countries require take-or-pay agreements for requested natural gas quantities. These contracts have many pre-clauses; even if they are not met due to low/high consumption or other external factors, buyers must completely fulfill them. A similar contract is then imposed on distributors and wholesale consumers. It is, thus, important for all parties to forecast their daily, monthly, and annual natural gas demand to minimize their risk. In this paper, a model consisting of a modulated expansion in Fourier series, supplemented by deviations from comfortable temperatures as a regressor is proposed for the forecast of monthly and weekly consumption over a one-year horizon. This model is supplemented by a day-ahead feedback mechanism for the forecast of daily consumption. The method is applied to the study of natural gas consumption for major residential areas in Turkey, on a yearly, monthly, weekly, and daily basis. It is shown that residential heating dominates winter consumption and masks all other variations. On the other hand, weekend and holiday effects are visible in summer consumption and provide an estimate for residential and industrial use. The advantage of the proposed method is the capability of long term projections, reflecting causality, and providing accurate forecasts even with minimal information.
Citation Count: 1
'Level grading' a new graded algebra structure on differential polynomials: application to the classification of scalar evolution equations
(IOP Publishing Ltd, 2013) Bilge, Ayşe Hümeyra; Bilge, Ayşe Hümeyra
We define a new grading which we call the 'level grading' on the algebra of polynomials generated by the derivatives u(k+i) over the ring K-(k) of C-infinity functions of x t u u(1) ... u(k) where . This grading has the property that the total derivative and the integration by parts with respect to x are filtered algebra maps. In addition if u satisfies the evolution equation u(j) = F[u] where F is a polynomial of order m = k + p and of level p then the total derivative with respect to t D-t is also a filtered algebra map. Furthermore if the separant partial derivative F/partial derivative u(m) belongs to K-(k) then the canonical densities (i) are polynomials of level 2i + 1 and (i) is of level 2i + 1 + m. We define 'KdV-like' evolution equations as those equations for which all the odd canonical densities rho((i)) are non-trivial. We use the properties of level grading to obtain a preliminary classification of scalar evolution equations of orders m = 7 9 11 13 up to their dependence on x t u u(1) and u(2). These equations have the property that the canonical density rho((-1)) is (alpha u(3)(2) + beta u(3) + gamma)(1/2) where alpha beta and gamma are functions of x t u u(1) u(2). This form of rho((-1)) is shared by the essentially nonlinear class of third order equations and a new class of fifth order equations.
Citation Count: 8
Managing natural gas demand for free consumers under uncertainty and limited storage capacity
(Elsevier, 2020) Bilge, Ayşe Hümeyra; Yükseltan, Ergün; Yücekaya, Ahmet; Bilge, Ayşe Hümeyra
Demand for energy sources depends on several factors such as population growth, urbanization, industrialization, and climate. Among fundamental energy sources, natural gas is characterized by storage limitations and take-or-pay contracts, which makes it especially critical to forecast the demand accurately for cost management policies. Suppliers of natural gas require take-or-pay contracts to ensure that consumers pay for any unused amount up front; and if the demand exceeds the agreed amount, they pay for over-use as well. Consumers with a demand above the eligible consumer limit are categorized as free consumers; and they have to specify their daily, monthly, and annual demand in these take-or-pay contracts. In residential areas, natural gas is used predominantly for heating, hence its consumption has a strong seasonality. In winter, the variability in the atmospheric temperature leads to fluctuations in the demand, while in summer, weekend effects dominate. In order to take these features into account, a demand forecasting model based on a modulated expansion in Fourier series, supplemented by deviations from comfortable temperatures, is used in this study to determine the threshold value for the onset of natural gas usage for heating purposes. The upper and lower bounds for consumption are obtained as a function of temperature only, after analyzing the details of the temperature-consumption relationship using historical data. Moreover, a temperature-based simulation methodology is proposed and simulation results that provide guidelines to manage the costs of storage under uncertainty are presented by suggesting the minimum storage capacity required and showing the distribution of the costs.
Citation Count: 3
A mathematical characterization of the gel point in sol-gel transition
(IOP Publishing Ltd, 2015) Bilge, Ayşe Hümeyra; Pekcan, Önder
We model the sol-gel transition in terms of Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models and compare with experimental results. We show, numerically, that the "gel point" described as the onset of the gelation phenomena and measured experimentally, corresponds to an accumulation point of the extreme values of the derivatives of the gelation curve. We define the "critical point of a sigmoidal curve" as the limit of the points where the derivatives reach their extreme values, provided that this limit exists.
Citation Count: 8
Mathematical Characterization of Thermo-reversible Phase Transitions of Agarose Gels
(Taylor & Francis Inc, 2018) Bilge, Ayşe Hümeyra; Pekcan, Önder; Kara, Selim; Bilge, Ayşe Hümeyra
The thermal phase transition temperatures of high (HMP) and low melting point (LMP) agarose gels were investigated by using UV-vis spectroscopy techniques. Transmitted light intensities from the gel samples with different agarose concentrations were monitored during the heating (gel-sol) and cooling (sol-gel) processes. It was observed that the transition temperatures T-m defined as the location of the maximum of the first derivative of the sigmoidal transition paths obtained from the UV-vis technique slightly increased by increasing the agarose concentration in both the HMP and LMP samples. Here we express the phase transitions of the agar-water system as a representative of reversible physical gels in terms of a modified Susceptible-Infected-Susceptible epidemic model whose solutions are the well-known 5-point sigmoidal curves. The gel point is hard to determine experimentally and various computational techniques are used for its characterization. Based on previous work we locate the gel point T-0 of sol-gel and gel-sol transitions in terms of the horizontal shift in the sigmoidal transition curve. For the gel-sol transition (heating) T-0 is greater than T-m i.e. later in time and the difference between T-0 and T-m is reduced as the agarose content increases. For the sol-gel transition (cooling) T-0 is again greater than T-m but it is earlier in time for all agarose contents and moves forward in time and gets closer to T-m as the agarose content increases.
Citation Count: 10
A MATHEMATICAL DESCRIPTION OF THE CRITICAL POINT IN PHASE TRANSITIONS
(World Scientific Publ Co Pte Ltd, 2013) Bilge, Ayşe Hümeyra; Pekcan, Önder
Let y(x) be a smooth sigmoidal curve, y((n)) be its nth derivative and {x(m,i)} and {x(a,i)}, i = 1, 2, ... , be the set of points where respectively the derivatives of odd and even order reach their extreme values. We argue that if the sigmoidal curve y(x) represents a phase transition, then the sequences {x(m,i)} and {x(a,i)} are both convergent and they have a common limit x(c) that we characterize as the critical point of the phase transition. In this study, we examine the logistic growth curve and the Susceptible-Infected-Removed (SIR) epidemic model as typical examples of symmetrical and asymmetrical transition curves. Numerical computations indicate that the critical point of the logistic growth curve that is symmetrical about the point (x(0), y(0)) is always the point (x(0), y(0)) but the critical point of the asymmetrical SIR model depends on the system parameters. We use the description of the sol-gel phase transition of polyacrylamide-sodium alginate (SA) composite (with low SA concentrations) in terms of the SIR epidemic model, to compare the location of the critical point as described above with the "gel point" determined by independent experiments. We show that the critical point t(c) is located in between the zero of the third derivative t(a) and the inflection point t(m) of the transition curve and as the strength of activation (measured by the parameter k/eta of the SIR model) increases, the phase transition occurs earlier in time and the critical point, t(c), moves toward t(a).
Citation Count: 2
Maximal linear subspaces of strong self-dual 2-forms and the Bonan 4-form
(Elsevier Science Inc, 2011) Bilge, Ayşe Hümeyra; Dereli, Tekin; Koçak, Şahin
The notion of self-duality of 2-forms in 4-dimensions plays an eminent role in many areas of mathematics and physics, but although the 2-forms have a genuine meaning related to curvature and gauge-field-strength in higher dimensions also, their "self-duality" is something which is almost avoided above 4-dimensions. We show that self-duality of 2-forms is a very natural notion in higher (even) dimensions also and we prove the equivalence of some scattered and rarely used definitions in the literature. We demonstrate the usefulness of this higher self-duality by studying it in 8-dimensions and we derive a natural expression for the Bonan form in terms of self-dual 2-forms and we give an explicit expression of the local action of SO(8) on the Bonan form. (C) 2010 Elsevier Inc. All rights reserved.
Citation Count: 1
Modeling of Wind Effects on Stratified Flows in Open Channels: A Model for the Istanbul Strait (Bosphorus)
(2016) Bilge, Ayşe Hümeyra; Kirkil, Gökhan; Burak, Selmin; İncegül, Metehan
Stratified flows in open channels arise as a result of density or surface level differences. If the channel is connected to a basin at one or both ends, strong winds originating from the basin cause the "wind setup" effect that increases the water level at the entrance of the channel. On the other hand, along the channel, persistent winds in the upper layer flow direction lead to an increase of the drift velocity and to a decrease in upper layer flow depth. The Istanbul Strait (Bosphorus) connecting the Black and the Marmara Seas, is characterized by a stratified flow caused by the surface level and salinity difference between these basins, consisting of a southward upper layer flow and a northward lower layer flow. Along the strait, there are three hydraulic control points; the north sill, a midway contraction reach and the south sill. Under wind effects, the northern and southern entrances of the strait behave as an estuary whereas the midway reach to the south of the contraction acts as as an open channel. In winter, when the sea level difference is relatively low, the wind setup due to southerly winds may cause a blockage and even reversal of the upper layer flow. On the other hand in spring when there is excessive river discharge, northerly winds increase the influx of Black Sea waters into the strait and may lead to a blockage of the lower layer. We claim that strong northerly winds may cause a decrease of the upper layer depth beyond the contraction and we propose a simple model for its estimation in terms of the wind and water flow speeds.
Citation Count: 2
On the Classification of Fifth Order Quasi-linear Non-constant Separant Scalar Evolution Equations of the KdV-Type
(Physical Soc Japan, 2012) Bilge, Ayşe Hümeyra; Bilge, Ayşe Hümeyra
Fifth order, quasi-linear, non-constant separant evolution equations are of the form u(t) = A(partial derivative(5)u/partial derivative x(5)) + (B) over tilde, where A and (B) over tilde are functions of x, t, u and of the derivatives of u with respect to x up to order 4. We use the existence of a "formal symmetry'', hence the existence of "canonical conservation laws'' rho((i)), i = -1, . . . , 5 as an integrability test. We define an evolution equation to be of the KdV-Type, if all odd numbered canonical conserved densities are nontrivial. We prove that fifth order, quasi-linear, non-constant separant evolution equations of KdV type are polynomial in the function a = A(1/5); a = (alpha u(3)(2) + beta u(3) + gamma)(-1/2), where alpha, beta, and gamma are functions of x, t, u and of the derivatives of u with respect to x up to order 2. We determine the u(2) dependency of a in terms of P = 4 alpha gamma - beta(2) > 0 and we give an explicit solution, showing that there are integrable fifth order non-polynomial evolution equations.
Citation Count: 0
On the classification of scalar evolution equations with non-constant separant
(IOP Publishing Ltd, 2017) Bilge, Ayşe Hümeyra; Mizrahi, Eti
The ` separant' of the evolution equation u(t) = F where F is some differentiable function of the derivatives of u up to order m is the partial derivative partial derivative F/partial derivative u(m) where um u(m) = partial derivative(m)u/partial derivative x(m). As an integrability test we use the formal symmetry method of Mikhailov-Shabat-Sokolov which is based on the existence of a recursion operator as a formal series. The solvability of its coefficients in the class of local functions gives a sequence of conservation laws called the 'conserved densities' rho((i)) i = -1 1 2 3 ... We apply this method to the classification of scalar evolution equations of orders 3 <= m <= 15 for which rho((-)) = [partial derivative F/partial derivative u(m)](-1/m) and rho((1)) are non-trivial i.e. they are not total derivatives and rho((-1)) is not linear in its highest order derivative. We obtain the 'top level' parts of these equations and their ` top dependencies' with respect to the 'level grading' that we defined in a previous paper as a grading on the algebra of polynomials generated by the derivatives u(b+i) over the ring of C-infinity functions of u u(1) .. u(b). In this setting b and i are called 'base' and 'level' respectively. We solve the conserved density conditions to show that if rho((-)) depends on u u(1) ... u(b) then these equations are level homogeneous polynomials in u(b+i) ... u(m) i >= 1. Furthermore we prove that if rho((3)) is nontrivial then rho((-)) = (alpha mu(2)(b) (3) is trivial then ub 1/3 where b similar to 5 and a .. and mu are functions of u. ub-1. We show that the equations that we obtain form commuting flows and we construct their recursion operators that are respectively of orders 2 and 6 for non-trivial and trivial (3) respectively. Omitting lower order dependencies we show that equations with non-trivial (3) and b = 3 are symmetries of the ` essentially non-linear third order equation'
Citation Count: 1
On the Time Shift Phenomena in Epidemic Models
(Frontiers Media Sa, 2020) Bilge, Ayşe Hümeyra; Demirci, Ali; Bilge, Ayşe Hümeyra; Ahmetolan, Semra
In the standard Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models, the peak of infected individuals coincides with the inflection point of removed individuals. Nevertheless, a survey based on the data of the 2009 H1N1 epidemic in Istanbul, Turkey displayed a time shift between the hospital referrals and fatalities. An analysis of recent COVID-19 data and the records for Spanish flu (1918-1919) and SARS (2002-2004) epidemics confirm this observation. We use multistage SIR and SEIR models to provide an explanation for this time shift. Numerical solutions of these models present strong evidence that the delay between the peak of R' (t) and the peak of J(t) = Sigma I-i(i)(t) is approximately half of the infectious period of the epidemic disease. In addition, we use a quadratic approximation to show that the distance between successive peaks of I-i is 1/gamma(i) , where 1/gamma(i) is the infectious period of the ith infectious stage, and we present numerical calculations that confirm this approximation.

Browse

Browsing Endüstri Mühendisliği Bölümü Koleksiyonu by Author "Bilge, Ayşe Hümeyra"