Numerical Simulation of Rotating Accretion Disk Around the Schwarzschild Black Hole Using GRH Code

The 2D time dependent solution of thin accretion disk in a close binary system have been presented on the equatorial plane around the Schwarzschild black hole. To do that, the special part of the General Relativistic Hydrodynamical(GRH) equations are solved using High Resolution Shock Capturing (HRSC) schemes. The spiral shock waves on the accretion disk are modeled using perfect fluid equation of state with adiabatic indices $\gamma = 1.05, 1.2$ and 5/3. The results show that the spiral shock waves are created for gammas except the case $\gamma=5/3$. These results consistent with results from Newtonian hydrodynamic code except close to black hole. Newtonian approximation does not give good solution while matter closes to black hole. Our simulations illustrate that the spiral shock waves are created close to black hole and the location of inner radius of spiral shock wave is around $10M$ and it depends on the specific heat rates. We also find that the smaller $\gamma$ is the more tightly the spiral winds.Comment: 19 pages 11 figure

Quasi Periodic Oscillations (QPOs) and frequencies in an accretion disk and comparison with the numerical results from non-rotating black hole computed by the GRH code

The shocked wave created on the accretion disk after different physical phenomena (accretion flows with pressure gradients, star-disk interaction etc.) may be responsible observed Quasi Periodic Oscillations (QPOs) in $X-$ray binaries. We present the set of characteristics frequencies associated with accretion disk around the rotating and non-rotating black holes for one particle case. These persistent frequencies are results of the rotating pattern in an accretion disk. We compare the frequency's from two different numerical results for fluid flow around the non-rotating black hole with one particle case. The numerical results are taken from our papers Refs.\refcite{Donmez2} and \refcite{Donmez3} using fully general relativistic hydrodynamical code with non-selfgravitating disk. While the first numerical result has a relativistic tori around the black hole, the second one includes one-armed spiral shock wave produced from star-disk interaction. Some physical modes presented in the QPOs can be excited in numerical simulation of relativistic tori and spiral waves on the accretion disk. The results of these different dynamical structures on the accretion disk responsible for QPOs are discussed in detail.Comment: 13 figures, added reference, accepted for publication in Modern Physics Letters

Karadeniz'in karanlıkta kalan seyr-i

Taha Toros Arşivi, Dosya Adı: Samiye Bilhanİstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

Aristotelian Reasoning in the 13th Century Latin Medieval Age and a Philosophical Assessment on Latin Avicenousness

In this article, Aristotelian Intelligence in the 13th Century Latin Medieval Era was evaluated on the basis of Ibn Rushd. In this context, the philosophical movement which is known as Latin Averroism is discussed. The concept of reason, which has begun to be discussed by the philosopher Ibn Rushd in the Middle Middle Age through the recognition of the annotations he wrote on Aristotle's works in the Middle Ages, seems to have gained a theological and political aspect with differentiated readings

Meromorphic Functions

Bu çalışmada, homojen diferansiyel polinomlar Nevanlinna kuramına uygulandı ve bu homojen polinomlarla bazı genelleştirmeler verildi.In this paper, we have given the applications of homogeneous differential polynomials to the Nevanlinna’s theory of meromorphic functions in the finite complex plane and given some generalizations by these polynomials

Some Paradoxes in Mathematics

Matematiğin kümeler kuramındaki bazı paradoksları inceledik.We have explained some paradoxes in the set theory of mathematics

Catalytic combustion of methanol on structured catalysts for direct methanol fuel cell

Thesis (Master)--Izmir Institute of Technology, Energy Engineering, Izmir, 2011Includes bibliographical references (leaves: 46-50)Text in English; Abstract: Turkish and Englishx, 59 leavesThe major goal of this study is to investigate the effect of metal loading, space velocity and the outside temperature on both the steady state temperature of the alumina supported platinum catalysts and on time to reach at the temperature of 60 oC of a typical direct methanol fuel cell operating temperature in methanol combustion reaction. Alumina supported platinum catalysts were synthesized by using impregnation method and sol-gel made alumina. The methanol combustion reaction was performed in a tubular reactor.The characterization of the catalysts was performed by XRD and BET techniques. Particle size of Pt and surface area of the catalysts were compared before and after the reaction. In this study, it was found that the pure alumina was not active in methanol combustion whereas Pt/Al2O3 catalysts with varying loadings were active starting at room temperature. 2, 3 and 5% Pt loading catalysts showed the similar activity so it is possible that the average crystallite size and the crystallite size distribution of Pt on these catalysts would be similar. The space velocity tests indicated that low space velocity is required to quickly reach at 60 oC and also to achieve the highest steady state temperature for fresh catalyst whereas high space velocity is required to quickly reach at 60 oC and to achieve the highest steady state temperature for reused catalyst. The activity of the catalyst was also tested at sub-room temperatures. It was observed that the steady state temperature of the catalyst decreased and the time to reach at 60 oC increased when the outside temperature was below the room temperature. In addition to the tubular reactor, plate reactor was prepared for the methanol combustion. For this purpose, varying concentration alumina sols were coated on the stainless steel plates. However, optimum coating thickness could not be obtained because of the crack formation and peeling offs; thus, further detailed studies are necessary for obtaining stable coating suitable for the catalytic combustion

Some Paradoxes in Mathematics

Matematiğin kümeler kuramındaki bazı paradoksları inceledik.We have explained some paradoxes in the set theory of mathematics

Women Mathematicians

Herhangi bir matematik tarihi kitabında kadın matematikçilere az rastlanılır. İnsan bunun neden bu kadar az olduğunu merak eder. Bu soruya yanıt verebilmek için bilinenlerin bazılarının yaşam öykülerinin bilinmesi gerekir. Bu yazının ilk kısmı farklı ülkelerin kadın matematikçilerine ayrılmıştır. Bunlardan ilki 370 yılında doğmuş ve sonuncusu da 1935 yılında ölmüştür. Bunlarla ilgili bazı sorular vardır. Yirminci yüzyıldan önce çok az kadın matematikçi varsa yirminci yüzyılda daha fazla olması için ne yapılabilirdi? 2001 yılları için ne tahmin yapılabilir? Kadın matematikçilerin matematikte neler yaptıklarını burada anlatacak kadar yer yoktur. Çok güçlükler çeken bu kadın matematikçilerin ilki Hypatia’dır.In any book on the history of mathematics, mention about women mathematicians is hardly found. One wonders if there were any and, if any, why so few? The lives of some women mathematicians from different countries, the first who was born in 370 AD and the last who died in 1935. If there were only a few women mathematicians before the 20th Century, why have there been more in the 21th century what has been done, and what is being done, to increase their number? There is no enough space in this paper to examine the details of the mathematical research being conducted by these eight women. Instead the main interest will be the difficulties involved and the struggles they underwent while fulfilling their desire to become mathematicians, the first one of them who had a tragic end