Papers by Ayse Humeyra Bilge
arXiv (Cornell University), Mar 21, 2012
Fifth order, quasi-linear, non-constant separant evolution equations are of the form u t = A ∂ 5 ... more Fifth order, quasi-linear, non-constant separant evolution equations are of the form u t = A ∂ 5 u ∂x 5 + B, where A and B 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" ρ (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 = (αu 2 3 + βu 3 + γ) -1/2 , where α, β and γ 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 = 4αγ -β 2 > 0 and we give an explicit solution, showing that there are integrable fifth order non-polynomial evolution equations.
Frontiers in Physics, Nov 18, 2020
In the standard Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR... more 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) 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/c i , where 1/c i is the infectious period of the ith infectious stage, and we present numerical calculations that confirm this approximation.
American Scientific Research Journal for Engineering, Technology, and Sciences, Nov 27, 2015
Turkish power market has undergone a restructuring and deregulation to reach a competitive and re... more Turkish power market has undergone a restructuring and deregulation to reach a competitive and reliable electricity market. A typical day starts when the system operator announces the next day demand forecast for the electricity and participants submit offers in response to meet the demand. Accuracy in electricity demand forecast is essential for a reliable power system and successful market operation and mathematical models help market participants to forecast the electricity demand. We use hourly electricity demand data for Turkey, for the years 2012-2014 to make a linear model taking into account weekly and diurnal periodic variations modulated by seasonal effects. The model fits the data within %4 and predicts within %9.8 in the L 2 norm.
A R I, Oct 4, 1999
We show that the self-duality defined in [Trautman, Int.J.Theor.Phys.,16,561 (1977)] is equivalen... more We show that the self-duality defined in [Trautman, Int.J.Theor.Phys.,16,561 (1977)] is equivalent to strong self-duality defined in [Bilge, Dereli and Kocak, Lett.Math.Phys., 36, 301-309, (1996)] and we obtain an upper bound on (p 2) n , where p 2 is the second Pontrjagin class of an SO(N) bundle over a 8n dimensional manifold.
General Relativity and Gravitation, Apr 1, 1990
An asympototically flat algebraically general vacuum metric is obtained. The solution is characte... more An asympototically flat algebraically general vacuum metric is obtained. The solution is characterized by two commuting spacelike Killing vectors with flat integral surfaces and depends on one arbitrary function.
Journal of Natural Gas Science and Engineering, Jul 1, 2020
Demand for energy sources depends on several factors such as population growth, urbanization, ind... more 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.
Energy Strategy Reviews, Nov 1, 2019
The successful operation of a real time market is related to the planning in the day ahead market... more 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.
Phase Transitions, Feb 8, 2017
Carrageenan gels are characterized by reversible sol-gel and gel-sol transitions under cooling an... more 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 ; it is greater than T gs , i.e. later in time for low carrageenan contents and moves backward as carrageenan content increases.
Environmental earth sciences, 2022
Utilities Policy, 2022
The rapid spread of COVID-19 has severely impacted many sectors, including the electricity sector... more The rapid spread of COVID-19 has severely impacted many sectors, including the electricity sector. The reliability of the electricity sector is critical to the economy, health, and welfare of society; therefore, supply and demand need to be balanced in real-time, and the impact of unexpected factors should be analyzed. During the pandemic, behavioral restrictions such as lockdowns, closure of factories, schools, and shopping malls, and changing habits, such as shifted work and leisure hours at home, significantly affected the demand structure. In this research, the restrictions and their corresponding timing are classified and mapped with the Turkish electricity demand data to analyze the estimated impact of the restrictions on total demand and daily demand profile. A modulated Fourier Series Expansion evaluates deviations from normal conditions in the aggregate demand and the daily consumption profile. The aggregate demand shows a significant decrease in the early phase of the pandemic, during the period March–June 2020. The shape of the daily demand curve is analyzed to estimate how much demand shifted from daytime to night-time. A population-based restriction index is proposed to analyze the relationship between the strength and coverage of the restrictions and the total demand. The persistency of the changes in the daily demand curve in the post-contingency period is analyzed. These findings imply that new scheduling approaches for daily and weekly loads are required to avoid supply-demand mismatches in the future. The long-term policy implications for the energy transition and lessons learned from the COVID-19 pandemic experience are also presented.
Journal of Physics: Conference Series, 2016
Stratified flows in open channels arise as a result of density or surface level differences. If t... more 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.
Journal of Physics: Conference Series, 2016
View the article online for updates and enhancements. You may also like Formation and Eruption of... more View the article online for updates and enhancements. You may also like Formation and Eruption of Sigmoidal Structure from a Weak Field Region of NOAA 11942 N. Vasantharaju, P. Vemareddy, B. Ravindra et al.
arXiv (Cornell University), Mar 31, 2017
Thermal phase transition temperatures of high and low melting point agarose gels were investigate... more Thermal phase transition temperatures of high and low melting point agarose gels were investigated by using the 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 Tm, defined as the location of the maximum of the first derivative of the sigmoidal transition paths obtained from UV-vis technique, slightly increased with the agarose type and concentration. Here, we express the phase transitions of 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 T0 of sol-gel and gel-sol transitions in terms of the horizontal shift in the sigmoidal transition curve. For the gel-sol transition (heating), T0 is greater than Tm, i.e. later in time, and the difference between T0 and Tm is reduced as agarose content increases. For the sol-gel transition (cooling), T0 is again greater than Tm, but it is earlier in time for all agarose contents and moves forward in time and gets closer to Tm as the agarose content increases.
International Journal of Modern Physics C, Sep 17, 2013
Journal of Macromolecular Science, Part B, Apr 27, 2018
Thermal phase transition temperatures of high and low melting point agarose gels were investigate... more Thermal phase transition temperatures of high and low melting point agarose gels were investigated by using the 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 Tm, defined as the location of the maximum of the first derivative of the sigmoidal transition paths obtained from UV-vis technique, slightly increased with the agarose type and concentration. Here, we express the phase transitions of 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 T0 of sol-gel and gel-sol transitions in terms of the horizontal shift in the sigmoidal transition curve. For the gel-sol transition (heating), T0 is greater than Tm, i.e. later in time, and the difference between T0 and Tm is reduced as agarose content increases. For the sol-gel transition (cooling), T0 is again greater than Tm, but it is earlier in time for all agarose contents and moves forward in time and gets closer to Tm as the agarose content increases.
Journal of Macromolecular Science, Part B, Apr 27, 2023
Modern Physics Letters B, Mar 30, 2019
It has been shown that reversible and irreversible phase transitions of biogels can be represente... more It has been shown that reversible and irreversible phase transitions of biogels can be represented by epidemic models. The irreversible chemical sol–gel transitions are modeled by the Susceptible-Exposed-Infected-Removed (SEIR) or Susceptible-Infected-Removed (SIR) epidemic systems whereas reversible physical gels are modeled by a modification of the Susceptible-Infected-Susceptible (SIS) system. Measured sol–gel and gel–sol transition data have been fitted to the solutions of the epidemic models, either by solving the differential equations directly (SIR and SEIR models) or by nonlinear regression (SIS model). The gel point is represented as the “critical point of sigmoid,” defined as the limit point of the locations of the extreme values of its derivatives. Then, the parameters of the sigmoidal curve representing the gelation process are used to predict the gel point and its relative position with respect to the transition point, that is, the maximum of the first derivative with respect to time. For chemical gels, the gel point is always located before the maximum of the first derivative and moves backward in time as the strength of the activation increases. For physical gels, the critical point for the sol–gel transition occurs before the maximum of the first derivative with respect to time, that is, it is located at the right of this maximum with respect to temperature. For gel–sol transitions, the critical point is close to the transition point; the critical point occurs after the maximum of the first derivative for low concentrations whereas the critical point occurs after the maximum of the first derivative for higher concentrations.
Journal of physics, Jan 21, 2015
We model the sol-gel transition in terms of Susceptible-Infected-Removed (SIR) and Susceptible-Ex... more 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.
Journal of Geometry and Physics, Jun 1, 2011
We consider a generalization of eight-dimensional multiply warped product manifolds as a special ... more 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× B, where ...
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Papers by Ayse Humeyra Bilge