Ayşe Hümeyra Bilge

Bilge, Ayşe Hümeyra

Name Variants

Bilge A.
BILGE, Ayşe Hümeyra
Bilge, AYŞE HÜMEYRA
Bilge, Ayse Humeyra
AYŞE HÜMEYRA BILGE
A. Bilge
Bilge,Ayse Humeyra
Ayşe Hümeyra Bilge
Bilge,A.H.
BILGE, AYŞE HÜMEYRA
Kupeli A.
B., Ayşe Hümeyra
Bilge, Ayşe Hümeyra
B.,Ayse Humeyra
Bilge, A. H.
Ayse Humeyra, Bilge
A. H. Bilge
B., Ayse Humeyra
Bilge, A.
Ayşe Hümeyra BILGE

Job Title

Prof. Dr.

Email Address

ayse.bilge@khas.edu.tr

ORCID ID

0000-0002-6043-0833

Scopus Author ID

7005981141

Full item page

Scholarly Output

52

Articles

36

Citation Count

195

Supervised Theses

9 Scholarly Output Search Results

Now showing 1 - 10 of 51

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: 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
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: 4
Assessment and simulation of water transfer for the megacity Istanbul
(Bellwether Publishing, Ltd., 2021) Bilge, Ayşe Hümeyra; Bilge, Ayşe Hümeyra; Ülker, Duygu
The population of Istanbul increased from three to fifteen million from 1970 to 2018. The city, which has no perennial fresh water resources within its metropolitan boundaries, has long imported water from other basins. In this study, the performance of a reservoir system fed by surface runoff and inter-basin water transfer is investigated and applied. Simulations are run for water demand estimates and with Gamma-distributed realizations of monthly precipitation, based on 105-year temperature and precipitation data. The research shows that after 2060, existing and transferred water alone will not be sufficient to meet demand and it is expected that the megacity Istanbul will be on a path towards water crisis after this date, if not before. It is concluded that it is vital to adopt a more diversified water supply and demand management portfolio with extensive Integrated Water Resources Management (IWRM) measures for “Water Sensitive Cities”. Strategies for reliable system operation that take foreseeable environmental problems into account are proposed.
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: 0
An Overview of Electricity Consumption in Europe: Models for Prediction of the Electricity Usage for Heating and Cooling
(Econjournals, 2024) Bilge, Ayşe Hümeyra; Aktunc,E.A.; Bilge,A.H.; Yucekaya,A.
Although aggregate electricity consumption provides valuable information for market analysis, demand composition, including industrial, residential, illumination, and other uses, and special days, such as national or religious holidays and annual industrial shutdowns, differ for each country. This paper analyzes the hourly electricity consumption of European countries in the European Transmission System Operation for Electricity (ENTSO-E) grid from 2006 to 2018. We propose an outlier detection method to identify special days and a modulated Fourier Series Expansion model to determine the breakdown of industrial versus household consumption and heating versus cooling consumption. The proposed outlier detection method uses the time series for each hour and checks whether a day has more than a threshold number of hours with exceptional electricity consumption levels. The proposed demand prediction model has a 3% average error when electricity usage for heating is not dominant. It also allows country classification based on consumption patterns to efficiently manage regional or country-based electricity markets. © 2024, Econjournals. All rights reserved.
Citation Count: 0
Epidemic Models for Chemical Gel Phase Transformation: Effect of Optical Measurements with Different Wavelengths
(Taylor & Francis Inc, 2023) Bilge, Ayşe Hümeyra; Bilge, Ayse Humeyra; Pekcan, Onder; Incegul, Metehan
In our previous work we characterized the sol-gel transition of chemical and physical gels in terms of epidemic models which describe the spread of a disease in a society. We have shown that gelation in chemical gels can be represented by the Susceptible-Infected-Recovered (SIR) model, while the gelation mechanism of physical gels can be represented by the Susceptible-Infected-Susceptible (SIS) model. These studies were based on optical measurements at a single wavelength. In the present work we studied the gelation mechanism for chemical gels obtained from experiments that have been carried out with acrylamide (AAm) and N,N0-methylenebis (acrylamide) (Bis) as base materials for chemical gel formation in water and with cross-linker. The transmitted light intensity was measured for various wavelengths from 440 nm to 690 nm during the gelation process. The data are modeled by the epidemic SIR process. The results indicate that the gelation processes obtained from the same Bis and water contents observed at different wavelengths obey different SIR models. This observation is explained by the scattering of light of different wavelengths depending on the sizes of the micro-gels formed.
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
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
Thornthwaite's Method for the Computation of the Water Balance
(Springer International Publishing Ag, 2022) Bilge, Ayşe Hümeyra; Bilge, Ayse Humeyra; Ulker, Duygu
Evapotranspiration is one of the crucial processes on water balance under the effect of meteorological and environmental factors and soil and vegetation characteristics. Thornhtwaite's method for the evaluation of the water balance at a given place is related to the temperature, precipitation data at monthly or daily intervals and on the information on the water holding capacity of the soil at that place. The method is based on equating the sum of evapotranspiration and runoff to the sum of precipitation and soil moisture. In Thornthwaite's method, most steps of the calculation are expressed by mathematical formulas but the values of the amount of water retained in the soil as a function of potential evapotranspiration (PE), for each value of the water holding capacity (WHC) of the soil are given by tables. In this paper we present an overview of the method and we present mathematical formulas that fit the data of the of these tables, to express the relation between water retained in soil and potential evapotranspiration (PE) for different water holding capacity (WHC).