Requirement engineering is both the hardest and critical part of software development since error... more Requirement engineering is both the hardest and critical part of software development since errors at this beginning stage propagate through the development process and are the hardest to repair later. The development of software systems depend totally on the accuracy of requirements.
The concept of clustering is to separate clusters based on the similarity which is greater within... more The concept of clustering is to separate clusters based on the similarity which is greater within cluster than among clusters. The similarity consists of two principles, namely, connectivity and cohesion. However, in partitional clustering, while some algorithms such as K-means and K-medians divides the dataset points according to the first principle (connectivity) based on centroid clusters without any regard to the second principle (cohesion), some others like K-medoids partially consider cohesion in addition to connectivity. This prevents to discover clusters with convex shape and results are affected negatively by outliers. In this paper a new Gravity Center Clustering (GCC) algorithm is proposed which depends on critical distance (λ) to define threshold among clusters. The algorithm falls under partition clustering and is based on gravity center which is a point within cluster that verifies both the connectivity and cohesion in determining the similarity of each point in the dataset. Therefore, the proposed algorithm deals with any shape of data better than K-means, K-medians and K-medoids. Furthermore, GCC algorithm does not need any parameters beforehand to perform clustering but can help user improving the control over clustering results and deal with overlapping and outliers providing two coefficients and an indicator. In this study, 22 experiments are conducted using different types of synthetic, and real healthcare datasets. The results show that the proposed algorithm satisfies the concept of clustering and provides great flexibility to get the optimal solution especially since clustering is considered as an optimization problem.
In this paper, we will use a BIonic solution for analyzing the holographic cosmology. A BIonic so... more In this paper, we will use a BIonic solution for analyzing the holographic cosmology. A BIonic solution is a configuration of a D3-brane and an anti-D3-brane connected by a wormhole, and holographic cosmology is a recent proposal to explain cosmic expansion by using the holographic principle. In our model, a BIonic configuration will be produced by the transition of fundamental black strings. The formation of a BIonic configuration will cause inflation. As the D3-brane moves away from the anti-D3-brane, the wormhole will get annihilated, and the inflation will end with the annihilation of this wormhole. However, it is possible for a D3-brane to collide with an anti-D3-brane. Such a collision will occur if the distance between the D3-brane and the anti-D3-brane reduces, and this will create tachyonic states. We will demonstrate that these tachyonic states will lead to the formation of a new wormhole, and this will cause acceleration of the universe before such a collision.
We will demonstrate that the generalized uncertainty principle exists because of the derivative e... more We will demonstrate that the generalized uncertainty principle exists because of the derivative expansion in the effective field theories. This is because in the framework of the effective field theories, the minimum measurable length scale has to be integrated away to obtain the low energy effective action. We will analyze the deformation of a massive free scalar field theory by the generalized uncertainty principle, and demonstrate that the minimum measurable length scale corresponds to a second more massive scale in the theory, which has been integrated away. We will also analyze CFT operators dual to this deformed scalar field theory, and observe that scaling of the new CFT operators indicates that they are dual to this more massive scale in the theory. We will use holographic renormalization to explicitly calculate the renormalized boundary action with counter terms for this scalar field theory deformed by generalized uncertainty principle, and show that the generalized uncertainty principle contributes to the matter conformal anomaly.
In this paper, we will propose the most general form of the deformation of Heisenberg algebra mot... more In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.
In this paper, we analyze Vaidya spacetime with an energy dependent metric in Galileon gravity's ... more In this paper, we analyze Vaidya spacetime with an energy dependent metric in Galileon gravity's rainbow. This will be done using the rainbow functions which are motivated from the results obtained in loop quantum gravity approach and noncommutative geometry. We will investigate the Gravitational collapse in this Galileon gravity's rainbow. We will discuss the behavior of singularities formed from the gravitational collapse in this rainbow deformed Galileon gravity.
In this paper, we analyze the clustering of galaxies using a modified Newtonian potential. This m... more In this paper, we analyze the clustering of galaxies using a modified Newtonian potential. This modification of the Newtonian potential occurs due to the existence of extra dimensions in brane world models. We will analyze a system of galaxies interacting with each other through this modified Newtonian potential. The partition function for this system of galaxies will be calculated, and this partition function will be used to calculate the free energy of this system of galaxies. The entropy and the chemical potential for this system will also be calculated. We will derive explicit expression for the clustering parameter for this system. This parameter will determine the behavior of this system, and we will be able to express various thermodynamic quantities using this clustering parameter. Thus, we will be able to explicitly analyze the effect that modifying the Newtonian potential can have on the clustering of galaxies. We also analyze the effect of extra dimensions on the two-point functions between galaxies.
Journal of Cosmology and Astroparticle Physics, 2015
In this work, we investigate inflationary cosmology using scalar field theory deformed by the gen... more In this work, we investigate inflationary cosmology using scalar field theory deformed by the generalized uncertainty principle (GUP) containing a linear momentum term. Apart from being consistent with the existence of a minimum measurable length scale, this GUP is also consistent with doubly special relativity and hence with the existence of maximum measurable momentum. We use this deformed scalar field theory to analyze the tensor and scalar mode equations in a de Sitter background, and to calculate modifications to the tensor-to-scalar ratio. Finally, we compare our results for the tensor-to-scalar ratio with the Planck data to constrain the minimum length parameter in the GUP.
In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized un... more In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity shows very much different result.
International Journal of Geometric Methods in Modern Physics, 2015
In this paper, we will analyze the gravitational collapse in the framework of gravity's rainb... more In this paper, we will analyze the gravitational collapse in the framework of gravity's rainbow. We will demonstrate that the position of the horizon for a particle inside the black hole depends on the energy of that particle. It will also be observe that the position of the horizon for a particle falling radially into the black hole also depends on its energy. Thus, it is possible for a particle coming from outside to interact with a particle inside the black, and take some information outside the black hole. This is because for both these particles the position of horizon is different. So, even though the particle from inside the black hole is in its own horizon, it is not in the horizon of the particle coming from outside. Thus, we will demonstrate that in gravity's rainbow information can get out of a black hole.
Experimental and finite-element analyses for glass/epoxy composite I-beams were carried out to de... more Experimental and finite-element analyses for glass/epoxy composite I-beams were carried out to determine the effect of number of layers on load-carrying capacity and specific energy absorption. The loading modes used throughout this investigation were the axial compression, three and four point bending. The beams were fabricated from woven roving glass fibre and epoxy. The composite I-beams fabricated for axial compression tests were of 250 mm gauge length, 76 mm flange width and 125 mm web height, while the composite I-beams fabricated for three and four point bending tests were of 500 mm gauge length, 76 mm flange width and 125 mm web height. The matrix used was made of an epoxy resin (LECO 811-563-103) and a hardener (LECO 811-563-104) which were mixed at 8:1 ratio. Loading arrangements were also built to facilitate the experimental tests needed. The composite I-beams fabricated and tested were of 4, 6, 8 and 10 layers. Three samples were tested for each type and each load case. In addition, tensile samples were prepared and tested for the composite material used to evaluate the AINI IDERIS, Ph.D.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2011
Attempts to formulate a quantum theory of gravitation are collectively known as quantum gravity. ... more Attempts to formulate a quantum theory of gravitation are collectively known as quantum gravity. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special relativity theories predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called generalized uncertainty principle (GUP). We have proposed a GUP consistent with string theory, black hole physics and doubly special relativity theories and have showed that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it suggests that the space that confines it must be quantized, and in fact that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this may signal the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale. Because this influences all the quantum Hamiltonians in an universal way, it predicts quantum gravity corrections to various quantum phenomena. Therefore, in the present work we compute these corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current in a scanning tunneling microscope.
In this work, we investigate black hole (BH) physics in the context of gravity rainbow. We invest... more In this work, we investigate black hole (BH) physics in the context of gravity rainbow. We investigate this through rainbow functions that have been proposed by Amelino-Camelia, et el. in [1, 2]. This modification will give corrections to both the temperature and the entropy of BH and hence it changes the picture of Hawking radiation greatly when the size of BH approaches the Planck scale. It prevents BH from total evaporation, predicting the existence of BH remnant which may resolve the catastrophic behavior of Hawking radiation as the BH mass approaches zero.
It was shown recently that replacing classical geodesics with quantal (Bohmian) trajectories give... more It was shown recently that replacing classical geodesics with quantal (Bohmian) trajectories gives rise to a quantum corrected Raychaudhuri equation (QRE). In this article we derive the second order Friedmann equations from the QRE, and show that this also contains a couple of quantum correction terms, the first of which can be interpreted as cosmological constant (and gives a correct estimate of its observed value), while the second as a radiation term in the early universe, which gets rid of the big-bang singularity and predicts an infinite age of our universe.
The Generalized Uncertainty Principle (GUP), which has been predicted by various theories of quan... more The Generalized Uncertainty Principle (GUP), which has been predicted by various theories of quantum gravity near the Planck scale is implemented on deriving the thermodynamics of ideal Quark-Gluon Plasma (QGP) consisting of two massless quark flavors at the hadron-QGP phase equilibrium and at a vanishing chemical potential. The effective degrees of freedom and MIT bag pressure are utilized to distinguish between the hadronic and partonic phases. We find that GUP makes a non-negligible contribution to all thermodynamic quantities, especially at high temperatures. The asymptotic behavior of corresponding QGP thermodynamic quantities characterized by the Stephan-Boltzmann limit would be approached, when the GUP approach is taken into consideration.
Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entro... more Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde’s proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde’s proposal and two known models of GUPs, we obtain modifications to Newton’s law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the p = ωp equation of state.
Inspired by Jacobson's thermodynamic approach [4], Cai et al. [5, 6] have shown the emergence of ... more Inspired by Jacobson's thermodynamic approach [4], Cai et al. [5, 6] have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation [6] of Friedmann equations to accommodate a general entropyarea law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure p(ρ, a) leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature k. As an example we study the evolution of the equation of state p = ωρ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.
The effects of Generalized Uncertainty Principle, which has been predicted by various theories of... more The effects of Generalized Uncertainty Principle, which has been predicted by various theories of quantum gravity replacing the Heisenberg's uncertainty principle near the Planck scale, on the thermodynamics of ideal Quark-Gluon Plasma (QGP) consisting of two and three flavors are included. There is a clear effect on thermodynamical quantities like the pressure and the energy density which means that a different effect from quantum gravity may be used in enhancement the theoretical results for Quark-Gluon Plasma state of matter. This effect looks like the technique used in lattice QCD simulation. We determine the value of the bag parameter from fitting lattice QCD data and a physical interpretation to the negative bag pressure is introduced.
We investigate the impact of the Generalized Uncertainty Principle (GUP), proposed by some approa... more We investigate the impact of the Generalized Uncertainty Principle (GUP), proposed by some approaches to quantum gravity such as String Theory and Doubly Special Relativity Theories (DSR) on the production of mini black holes, and show that the minimum black hole mass is formed at energies higher than the energy scales of LHC which possibly agrees with the recent experimental results of LHC [1, 2]
Requirement engineering is both the hardest and critical part of software development since error... more Requirement engineering is both the hardest and critical part of software development since errors at this beginning stage propagate through the development process and are the hardest to repair later. The development of software systems depend totally on the accuracy of requirements.
The concept of clustering is to separate clusters based on the similarity which is greater within... more The concept of clustering is to separate clusters based on the similarity which is greater within cluster than among clusters. The similarity consists of two principles, namely, connectivity and cohesion. However, in partitional clustering, while some algorithms such as K-means and K-medians divides the dataset points according to the first principle (connectivity) based on centroid clusters without any regard to the second principle (cohesion), some others like K-medoids partially consider cohesion in addition to connectivity. This prevents to discover clusters with convex shape and results are affected negatively by outliers. In this paper a new Gravity Center Clustering (GCC) algorithm is proposed which depends on critical distance (λ) to define threshold among clusters. The algorithm falls under partition clustering and is based on gravity center which is a point within cluster that verifies both the connectivity and cohesion in determining the similarity of each point in the dataset. Therefore, the proposed algorithm deals with any shape of data better than K-means, K-medians and K-medoids. Furthermore, GCC algorithm does not need any parameters beforehand to perform clustering but can help user improving the control over clustering results and deal with overlapping and outliers providing two coefficients and an indicator. In this study, 22 experiments are conducted using different types of synthetic, and real healthcare datasets. The results show that the proposed algorithm satisfies the concept of clustering and provides great flexibility to get the optimal solution especially since clustering is considered as an optimization problem.
In this paper, we will use a BIonic solution for analyzing the holographic cosmology. A BIonic so... more In this paper, we will use a BIonic solution for analyzing the holographic cosmology. A BIonic solution is a configuration of a D3-brane and an anti-D3-brane connected by a wormhole, and holographic cosmology is a recent proposal to explain cosmic expansion by using the holographic principle. In our model, a BIonic configuration will be produced by the transition of fundamental black strings. The formation of a BIonic configuration will cause inflation. As the D3-brane moves away from the anti-D3-brane, the wormhole will get annihilated, and the inflation will end with the annihilation of this wormhole. However, it is possible for a D3-brane to collide with an anti-D3-brane. Such a collision will occur if the distance between the D3-brane and the anti-D3-brane reduces, and this will create tachyonic states. We will demonstrate that these tachyonic states will lead to the formation of a new wormhole, and this will cause acceleration of the universe before such a collision.
We will demonstrate that the generalized uncertainty principle exists because of the derivative e... more We will demonstrate that the generalized uncertainty principle exists because of the derivative expansion in the effective field theories. This is because in the framework of the effective field theories, the minimum measurable length scale has to be integrated away to obtain the low energy effective action. We will analyze the deformation of a massive free scalar field theory by the generalized uncertainty principle, and demonstrate that the minimum measurable length scale corresponds to a second more massive scale in the theory, which has been integrated away. We will also analyze CFT operators dual to this deformed scalar field theory, and observe that scaling of the new CFT operators indicates that they are dual to this more massive scale in the theory. We will use holographic renormalization to explicitly calculate the renormalized boundary action with counter terms for this scalar field theory deformed by generalized uncertainty principle, and show that the generalized uncertainty principle contributes to the matter conformal anomaly.
In this paper, we will propose the most general form of the deformation of Heisenberg algebra mot... more In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.
In this paper, we analyze Vaidya spacetime with an energy dependent metric in Galileon gravity's ... more In this paper, we analyze Vaidya spacetime with an energy dependent metric in Galileon gravity's rainbow. This will be done using the rainbow functions which are motivated from the results obtained in loop quantum gravity approach and noncommutative geometry. We will investigate the Gravitational collapse in this Galileon gravity's rainbow. We will discuss the behavior of singularities formed from the gravitational collapse in this rainbow deformed Galileon gravity.
In this paper, we analyze the clustering of galaxies using a modified Newtonian potential. This m... more In this paper, we analyze the clustering of galaxies using a modified Newtonian potential. This modification of the Newtonian potential occurs due to the existence of extra dimensions in brane world models. We will analyze a system of galaxies interacting with each other through this modified Newtonian potential. The partition function for this system of galaxies will be calculated, and this partition function will be used to calculate the free energy of this system of galaxies. The entropy and the chemical potential for this system will also be calculated. We will derive explicit expression for the clustering parameter for this system. This parameter will determine the behavior of this system, and we will be able to express various thermodynamic quantities using this clustering parameter. Thus, we will be able to explicitly analyze the effect that modifying the Newtonian potential can have on the clustering of galaxies. We also analyze the effect of extra dimensions on the two-point functions between galaxies.
Journal of Cosmology and Astroparticle Physics, 2015
In this work, we investigate inflationary cosmology using scalar field theory deformed by the gen... more In this work, we investigate inflationary cosmology using scalar field theory deformed by the generalized uncertainty principle (GUP) containing a linear momentum term. Apart from being consistent with the existence of a minimum measurable length scale, this GUP is also consistent with doubly special relativity and hence with the existence of maximum measurable momentum. We use this deformed scalar field theory to analyze the tensor and scalar mode equations in a de Sitter background, and to calculate modifications to the tensor-to-scalar ratio. Finally, we compare our results for the tensor-to-scalar ratio with the Planck data to constrain the minimum length parameter in the GUP.
In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized un... more In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity shows very much different result.
International Journal of Geometric Methods in Modern Physics, 2015
In this paper, we will analyze the gravitational collapse in the framework of gravity's rainb... more In this paper, we will analyze the gravitational collapse in the framework of gravity's rainbow. We will demonstrate that the position of the horizon for a particle inside the black hole depends on the energy of that particle. It will also be observe that the position of the horizon for a particle falling radially into the black hole also depends on its energy. Thus, it is possible for a particle coming from outside to interact with a particle inside the black, and take some information outside the black hole. This is because for both these particles the position of horizon is different. So, even though the particle from inside the black hole is in its own horizon, it is not in the horizon of the particle coming from outside. Thus, we will demonstrate that in gravity's rainbow information can get out of a black hole.
Experimental and finite-element analyses for glass/epoxy composite I-beams were carried out to de... more Experimental and finite-element analyses for glass/epoxy composite I-beams were carried out to determine the effect of number of layers on load-carrying capacity and specific energy absorption. The loading modes used throughout this investigation were the axial compression, three and four point bending. The beams were fabricated from woven roving glass fibre and epoxy. The composite I-beams fabricated for axial compression tests were of 250 mm gauge length, 76 mm flange width and 125 mm web height, while the composite I-beams fabricated for three and four point bending tests were of 500 mm gauge length, 76 mm flange width and 125 mm web height. The matrix used was made of an epoxy resin (LECO 811-563-103) and a hardener (LECO 811-563-104) which were mixed at 8:1 ratio. Loading arrangements were also built to facilitate the experimental tests needed. The composite I-beams fabricated and tested were of 4, 6, 8 and 10 layers. Three samples were tested for each type and each load case. In addition, tensile samples were prepared and tested for the composite material used to evaluate the AINI IDERIS, Ph.D.
Physical Review D - Particles, Fields, Gravitation and Cosmology, 2011
Attempts to formulate a quantum theory of gravitation are collectively known as quantum gravity. ... more Attempts to formulate a quantum theory of gravitation are collectively known as quantum gravity. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special relativity theories predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called generalized uncertainty principle (GUP). We have proposed a GUP consistent with string theory, black hole physics and doubly special relativity theories and have showed that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it suggests that the space that confines it must be quantized, and in fact that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this may signal the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale. Because this influences all the quantum Hamiltonians in an universal way, it predicts quantum gravity corrections to various quantum phenomena. Therefore, in the present work we compute these corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current in a scanning tunneling microscope.
In this work, we investigate black hole (BH) physics in the context of gravity rainbow. We invest... more In this work, we investigate black hole (BH) physics in the context of gravity rainbow. We investigate this through rainbow functions that have been proposed by Amelino-Camelia, et el. in [1, 2]. This modification will give corrections to both the temperature and the entropy of BH and hence it changes the picture of Hawking radiation greatly when the size of BH approaches the Planck scale. It prevents BH from total evaporation, predicting the existence of BH remnant which may resolve the catastrophic behavior of Hawking radiation as the BH mass approaches zero.
It was shown recently that replacing classical geodesics with quantal (Bohmian) trajectories give... more It was shown recently that replacing classical geodesics with quantal (Bohmian) trajectories gives rise to a quantum corrected Raychaudhuri equation (QRE). In this article we derive the second order Friedmann equations from the QRE, and show that this also contains a couple of quantum correction terms, the first of which can be interpreted as cosmological constant (and gives a correct estimate of its observed value), while the second as a radiation term in the early universe, which gets rid of the big-bang singularity and predicts an infinite age of our universe.
The Generalized Uncertainty Principle (GUP), which has been predicted by various theories of quan... more The Generalized Uncertainty Principle (GUP), which has been predicted by various theories of quantum gravity near the Planck scale is implemented on deriving the thermodynamics of ideal Quark-Gluon Plasma (QGP) consisting of two massless quark flavors at the hadron-QGP phase equilibrium and at a vanishing chemical potential. The effective degrees of freedom and MIT bag pressure are utilized to distinguish between the hadronic and partonic phases. We find that GUP makes a non-negligible contribution to all thermodynamic quantities, especially at high temperatures. The asymptotic behavior of corresponding QGP thermodynamic quantities characterized by the Stephan-Boltzmann limit would be approached, when the GUP approach is taken into consideration.
Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entro... more Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde’s proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde’s proposal and two known models of GUPs, we obtain modifications to Newton’s law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the p = ωp equation of state.
Inspired by Jacobson's thermodynamic approach [4], Cai et al. [5, 6] have shown the emergence of ... more Inspired by Jacobson's thermodynamic approach [4], Cai et al. [5, 6] have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation [6] of Friedmann equations to accommodate a general entropyarea law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure p(ρ, a) leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature k. As an example we study the evolution of the equation of state p = ωρ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.
The effects of Generalized Uncertainty Principle, which has been predicted by various theories of... more The effects of Generalized Uncertainty Principle, which has been predicted by various theories of quantum gravity replacing the Heisenberg's uncertainty principle near the Planck scale, on the thermodynamics of ideal Quark-Gluon Plasma (QGP) consisting of two and three flavors are included. There is a clear effect on thermodynamical quantities like the pressure and the energy density which means that a different effect from quantum gravity may be used in enhancement the theoretical results for Quark-Gluon Plasma state of matter. This effect looks like the technique used in lattice QCD simulation. We determine the value of the bag parameter from fitting lattice QCD data and a physical interpretation to the negative bag pressure is introduced.
We investigate the impact of the Generalized Uncertainty Principle (GUP), proposed by some approa... more We investigate the impact of the Generalized Uncertainty Principle (GUP), proposed by some approaches to quantum gravity such as String Theory and Doubly Special Relativity Theories (DSR) on the production of mini black holes, and show that the minimum black hole mass is formed at energies higher than the energy scales of LHC which possibly agrees with the recent experimental results of LHC [1, 2]
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Papers by Farag ali Ali