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Articles 1 - 11 of 11
Full-Text Articles in Physical Sciences and Mathematics
Renormalized Stress-Energy Tensor For Scalar Fields In Hartle-Hawking, Boulware, And Unruh States In The Reissner-Nordström Spacetime, Julio Arrechea, Cormac Breen, Adrian Ottewill, Peter Taylor
Renormalized Stress-Energy Tensor For Scalar Fields In Hartle-Hawking, Boulware, And Unruh States In The Reissner-Nordström Spacetime, Julio Arrechea, Cormac Breen, Adrian Ottewill, Peter Taylor
Articles
In this paper, we consider a quantum scalar field propagating on the Reissner-Nordström black hole spacetime. We compute the renormalized stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh states. When the field is in the Hartle-Hawking state, we renormalize using the recently developed “extended coordinate” prescription. This method, which relies on Euclidean techniques, is very fast and accurate. Once, we have renormalized in the Hartle-Hawking state, we compute the stress-energy tensor in the Boulware and Unruh states by leveraging the fact that the difference between stress-energy tensors in different quantum states is already finite. We consider a …
Determining The Proportionality Of Ischemic Stroke Risk Factors To Age, Elizabeth Hunter, John D. Kelleher
Determining The Proportionality Of Ischemic Stroke Risk Factors To Age, Elizabeth Hunter, John D. Kelleher
Articles
While age is an important risk factor, there are some disadvantages to including it in a stroke risk model: age can dominate the risk score and lead to over-or under-predictions in some age groups. There is evidence to suggest that some of these disadvantages are due to the non-proportionality of other risk factors with age, eg, risk factors contribute differently to stroke risk based on an individual’s age. In this paper, we present a framework to test if risk factors are proportional with age. We then apply the framework to a set of risk factors using Framingham heart study data …
A Mode Sum Regularization Prescription In Quantum Field Theory In Curved Spacetimes In Higher Dimensions And For Charged Scalar Fields, Eoin Scanlon
Academic Posters Collection
Semi-classical gravity combines classical treatment of the gravitational field with quantum mechanical treatment of matter fields. A significant challenge however is the divergence contained within the stress-energy tensor when solving the semi-classical Einstein equations. This work extends to higher dimensions an extremely efficient method for renormalizing the stress-energy tensor of a quantum scalar field in spherically-symmetric black hole spacetimes, thereby removing the divergences. The method applies to a scalar field with arbitrary field parameters. The utility of the method is demonstrated by computing the renormalized stress-energy tensor for a scalar field in the Schwarzschild black hole spacetime for odd dimensions.
Integrable Systems On Symmetric Spaces From A Quadratic Pencil Of Lax Operators, Rossen Ivanov
Integrable Systems On Symmetric Spaces From A Quadratic Pencil Of Lax Operators, Rossen Ivanov
Conference papers
The article surveys the recent results on integrable systems arising from quadratic pencil of Lax operator L, with values in a Hermitian symmetric space. The counterpart operator M in the Lax pair defines positive, negative and rational flows. The results are illustrated with examples from the A.III symmetric space. The modeling aspect of the arising higher order nonlinear Schrödinger equations is briefly discussed.
Nonlinear Two-Dimensional Water Waves With Arbitrary Vorticity, Delia Ionescu-Kruse, Rossen Ivanov
Nonlinear Two-Dimensional Water Waves With Arbitrary Vorticity, Delia Ionescu-Kruse, Rossen Ivanov
Articles
We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed with the aid of the Dirichlet-Neumann operator and the Green function of the Laplace operator in the fluid domain. Moreover, we provide new explicit expressions for both objects. The field of a point vortex and its interaction with the free surface is studied as an example. In the small-amplitude long-wave Boussinesq and KdV regimes, we obtain appropriate systems of coupled equations for …
The Lagrangian Formulation For Wave Motion With A Shear Current And Surface Tension, Conor Curtin, Rossen Ivanov
The Lagrangian Formulation For Wave Motion With A Shear Current And Surface Tension, Conor Curtin, Rossen Ivanov
Articles
The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant vorticity, which arises for example when a shear current is present, the separation of the energy into kinetic and potential is not at all obvious and neither is the Lagrangian formulation of the problem. Nevertheless, we use the known Hamiltonian formulation of the problem in this case to obtain the Lagrangian density function, and utilising the Euler-Lagrange equations we proceed to derive some …
On The Modelling Of Short And Intermediate Water Waves, Rossen Ivanov
On The Modelling Of Short And Intermediate Water Waves, Rossen Ivanov
Articles
Most of the model equations for water waves are approximations for the long-wave propagation regimes, since most of the energy of the wave motion is concentrated in these waves. Long waves (or shallow-water waves) are defined usually as the depth to wavelength ratio δ = h/λ < 0.05. Several famous integrable nonlinear equations, like the K d V equation [1,2], are models for long waves of small amplitude. The short waves (or waves over deep water) are usually defined with δ > 0.5, and the intermediate waves (or transitional waves) - with 0.05 < δ < 0.5. The intermediate and short waves received a lot less attention, and one reason is perhaps the fact that the corresponding approximations lead to more complicated, nonlinear and nonlocal equations. In [3] an integral equation for surface waves has been proposed for arbitrary wavelengths and finite depth. The problem has been studied in [4] and model equations both for long and short waves are derived from the governing equations as well. The short-wave effects usually compete with the capillarity effects and then resonances can be observed — these have been studied quite a lot, see for example [5–12]. For the intermediate long waves or for waves on deep water the so-called Benjamin–Ono (BO) [13–15] and the Intermediate Long Wave Equation (ILWE) [16–18] are derived for the internal waves below a flat surface, which leads to some simplifications and these models are in fact integrable.
The Pierce Decomposition And Pierce Embedding Of Endomorphism Rings Of Abelian P-Groups, Brendan Goldsmith, Luigi Salce
The Pierce Decomposition And Pierce Embedding Of Endomorphism Rings Of Abelian P-Groups, Brendan Goldsmith, Luigi Salce
Articles
We prove that more classes of groups than those described by Pierce have the property that the map Ψ is surjective, and we furnish examples of groups which do not have this property. Several results connecting the Pierce decomposition and the Pierce embedding of End(G) are obtained that allow one to derive general conditions on a group G which ensure that the Pierce embedding of End(G) is not surjective.
On The Cubic Equation With Its Siebeck–Marden–Northshield Triangle And The Quartic Equation With Its Tetrahedron, Emil Prodanov
On The Cubic Equation With Its Siebeck–Marden–Northshield Triangle And The Quartic Equation With Its Tetrahedron, Emil Prodanov
Articles
The real roots of the cubic and quartic polynomials are studied geometrically with the help of their respective Siebeck–Marden–Northshield equilateral triangle and regular tetrahedron. The Viète trigonometric formulæ for the roots of the cubic are established through the rotation of the triangle by variation of the free term of the cubic. A very detailed complete root classification for the quartic 𝑥4 + 𝑎𝑥3 + 𝑏𝑥2 + 𝑐𝑥 + 𝑑 is proposed for which the conditions are imposed on the individual coefficients 𝑎, 𝑏, 𝑐, and 𝑑. The maximum and minimum lengths of the interval containing the four real roots of …
Turbulence Phenomena In Magnetohydrodynamic Phase Transitions, Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
Turbulence Phenomena In Magnetohydrodynamic Phase Transitions, Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden
Articles
The model developed in (Fabrizio in J. Eng. Math., 2023) and (Fabrizio in Int. J. Eng. Sci. 44:529–539, 2006), involving the use of a local Reynolds number, is applied to describe phase transitions in a fluid. Specifically, it is applied in a magnetohydrodynamics context to study the evolution of turbulence in certain phenomena. The relevant equations describing the system are those of Navier-Stokes, Ginzburg-Landau and the magnetohydrodynamic equations, all suitably interconnected.
Feedback, Learning Outcomes And Mathematics Anxiety In A Digital Game Based Learning Approach In Mathematics Education, André Almo
Academic Posters Collection
Feedback is a crucial part of learning, and an essential element in digital game-based learning approaches, in which digital games - known as 'serious games' - are used to deliver educational content. Feedback features respond to players' actions within the game, providing them with information and guidance, as well as potentially impacting their learning, motivation and engagement. However, these features may be designed differently, since they include various distinct characteristics and dimensions. This work proposes a new taxonomy for feedback features in serious games, with an emphasis in game design aspects, in order to provide clearer descriptions and distinctions of …