International Journal of Modern Physics, Sep 10, 2011
We study the evolution of non-Gaussianity in multiple-field inflationary models, focusing on thre... more We study the evolution of non-Gaussianity in multiple-field inflationary models, focusing on three fundamental questions: (a) How is the sign and peak magnitude of the nonlinearity parameter f NL related to generic features in the inflationary potential? (b) How sensitive is f NL to the process by which an adiabatic limit is reached, where the curvature perturbation becomes conserved? (c) For a given model, what is the appropriate toolanalytic or numerical-to calculate f NL at the adiabatic limit? We summarise recent results obtained by the authors and further elucidate them by considering an inflection point model.
While the topology of the Universe is at present not specified by any known fundamental theory, i... more While the topology of the Universe is at present not specified by any known fundamental theory, it may in principle be determined through observations. In particular, a non-trivial topology will generate pairs of matching circles of temperature fluctuations in maps of the cosmic microwave background, the so-called circles-in-the-sky. A general search for such pairs of circles would be extremely costly and would therefore need to be confined to restricted parameter ranges. To draw quantitative conclusions from the negative results of such partial searches for the existence of circles we need a concrete theoretical framework. Here we provide such a framework by obtaining constraints on the angular parameters of these circles as a function of cosmological density parameters and the observer's position. As an example of the application of our results, we consider the recent search restricted to pairs of nearly back-to-back circles with negative results. We show that assuming the Universe to be very nearly flat, with its total matter-energy density satisfying the bounds 0 < |Ω0 − 1| 10 −5 , compatible with the predictions of typical inflationary models, this search, if confirmed, could in principle be sufficient to exclude a detectable non-trivial cosmic topology for most observers. We further relate explicitly the fraction of observers for which this result holds to the cosmological density parameters.
Anvar Shukurov and colleagues remember a theorist known for his work on stellar and galactic magn... more Anvar Shukurov and colleagues remember a theorist known for his work on stellar and galactic magnetism, who was also a prominent marine biologist.
British Journal For the Philosophy of Science, 1993
I INTRODUCTION In her challenging book How the Laws of Physics Lie, Nancy Cartwright [1983] expli... more I INTRODUCTION In her challenging book How the Laws of Physics Lie, Nancy Cartwright [1983] explicitly adopts a metaphysical position in support of her anti-realism with respect to the 'fundamental' laws of physics. She states: The metaphysical picture that underlies these ...
The Eleventh Marcel Grossmann Meeting - On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories - Proceedings of the MG11 Meeting on General Relativity, 2008
Among the most fundamental questions about the universe are those relating to its origin and earl... more Among the most fundamental questions about the universe are those relating to its origin and early evolution. Attempts at answering these questions within the classical relativistic framework have failed so far due to the presence of initial singularities, where the laws of physics break down. Recent results from Loop Quantum Cosmology, however, provide a framework where these questions can be
We investigate the detailed dynamics of a truncated αω dynamo model with a dynamic α effect. We f... more We investigate the detailed dynamics of a truncated αω dynamo model with a dynamic α effect. We find the presence of multiple attractors, including two chaotic attractors with a fractal basin boundary which merge to form a single attractor as the control parameter is increased. By considering phase portraits and the scaling of averaged times of transitions between the two attractors, we demonstrate that this merging is accompanied by a crisis-induced intermittency. We also find a range of parameter values over which the system has a fractal parameter dependence for fixed initial conditions. This is the first time this type of intermittency has been observed in a dynamo model and it could be of potential importance in accounting for some forms of intermittency in the solar and stellar output.
With the help of numerical experiments we find evidence for the existence of unique averaged comp... more With the help of numerical experiments we find evidence for the existence of unique averaged complex time singularities~Sfor dynamical systems subject to the same conditions as those required for Oseledec's multiplicative ergodic theorem to hold. By employing~and the leading resonances as the two analytical indicators of dynamical systems we study numerically the time invariant features of chaotic and fluid intermittent regimes. This in turn allows us to study the relationship between these two indicators themselves.
We find concrete evidence for the presence of crisis-induced and Pomeau-Manneville Type-I intermi... more We find concrete evidence for the presence of crisis-induced and Pomeau-Manneville Type-I intermittencies in an axisymmetric PDE mean-field dynamo model. These findings are of potential importance for two different reasons. Firstly, as far as we are aware, this is the first time detailed evidence has been produced for the occurrence of these types of intermittency for such deterministic PDE models. And secondly, despite the rather idealised nature of these models, the concrete evidence for the occurrence of more than one type of intermittency in such models makes it in principle possible that different types of intermittency may occur in different solar-type stars or even in the same star over different epochs. In this way a multiple intermittency framework may turn out to be of importance in understanding the mechanisms responsible for grand-minima type behaviour in the Sun and solar-type stars and in particular in the interpretation of the corresponding observational and proxy evidence.
Despite its great successes in accounting for the current observations, the so called `standard' ... more Despite its great successes in accounting for the current observations, the so called `standard' model of cosmology faces a number of fundamental unresolved questions. Paramount among these are those relating to the nature of the origin of the universe and its early evolution. Regarding the question of origin, the main difficulty has been the fact that within the classical general relativistic framework, the `origin' is almost always a singular event at which the laws of physics break down, thus making it impossible for such an event, or epochs prior to it, to be studied. Recent studies have shown that Loop Quantum Cosmology may provide a non-singular framework where these questions can be addressed. The crucial role here is played by quantum effects, i.e.\ corrections to the classical equations of motion, which are incorporated in effective equations employed to develop cosmological scenarios. In this chapter we shall consider the three main types of quantum effects expected to be present within such a framework and discuss some of their consequences for the effective equations. In particular we discuss how such corrections can allow the construction of non-singular emergent scenarios for the origin of the universe, which are past-eternal, oscillating and naturally emerge into an inflationary phase. These scenarios provide a physically plausible picture for the origin and early phases of the universe, which is in principle testable. We pay special attention to the interplay between these different types of correction terms. Given the absence, so far, of a complete derivation of such corrections in general settings, it is important to bear in mind the questions of consistency and robustness of scenarios based on partial inclusion of such effects.
According to a theorem of RueUe and Takens, the occurrence ofquasiperiodic motion on T 4 should b... more According to a theorem of RueUe and Takens, the occurrence ofquasiperiodic motion on T 4 should be unlikely. Here with the help of numerical calculations, we give a concrete example for which such motion is shown to exist and survive under small perturbations.
The question is considered of whether the 'correct' theory of gravity is a metric theory. The met... more The question is considered of whether the 'correct' theory of gravity is a metric theory. The metric hypothesis is shown to place severe restrictions on the form of the equation of motion for the one-body problem. By relaxing these restrictions, nonmetric contributions to the equation of motion are included, and the solution in the post-Newtonian approximation is given. The solution given contains five arbitrary parameters in place of the usual two (beta, gamma) of metric theories. One of them produces a secular change in the eccentricity; the others contribute to the perihelion advance and to periodic terms. Only certain combinations of these parameters can be determined even from orbits with different eccentricities.
S u m m a r y : Calculations for mean field dynamo models (in both full spheres and spherical she... more S u m m a r y : Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic a-quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples.
In a recent work (Covas et al. 1997), the behaviour and the robustness of truncated $\alpha\Omega... more In a recent work (Covas et al. 1997), the behaviour and the robustness of truncated $\alpha\Omega$ dynamos with a dynamic $\alpha$ were studied with respect to a number of changes in the driving term of the dynamic $\alpha$ equation, which was considered previously by Schmalz and Stix (1991) to be of the form $\sim A_{\phi}B_{\phi}$. Here we review and extend our previous work and consider the effect of adding a quadratic quenching term of the form $\alpha|B|^2$. We find that, as before, such a change can have significant effects on the dynamics of the related truncated systems. We also find intervals of (negative) dynamo numbers, in the system considered by Schmalz and Stix (1991), for which there is sensitivity with respect to small changes in the dynamo number and the initial conditions, similar to what was found in our previous work. This latter behaviour may be of importance in producing the intermittent type of behaviour observed in the sun.
Calculations for mean field dynamo models (in both full spheres and spherical shells), with both ... more Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic $\alpha$--quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples. Overall, the effect of using a dynamic $\alpha$ appears to be complicated and is affected by the region of parameter space examined.
It has recently been shown that nonlinear skew product dynamical systems with invariant subspaces... more It has recently been shown that nonlinear skew product dynamical systems with invariant subspaces which are capable of displaying on-off intermittency can show supersensitivity to small input signals. Here we show that this supersensitivity is absent for more general dynamical systems with non-skew product structure, capable of displaying a generalized form of on-off intermittency, and is therefore in this sense fragile. This absence of supersensitivity is of importance in view of the fact that dynamical systems are generically expected to be of non-skew product nature.
We consider the manner in which time-periodic solutions of an axisymmetric dynamo model can under... more We consider the manner in which time-periodic solutions of an axisymmetric dynamo model can undergo breaking of equatorial symmetry, i.e. loss of pure dipolar or quadrupolar symmetry. By considering the symmetry group underlying the solutions, we show that the fluctuations responsible for the symmetry-breaking can be constrained such that they are in resonance with the former solution. They can then be amplified until they are comparable in magnitude to the former solution. If the bifurcation is supercritical, the amplitude of the fluctuation is stabilised and a stable mixed parity limit cycle is formed. If it is subcritical it gives rise to a recently identified form of intermittency, called icicle intermittency. This produces episodes in which the original solution and the fluctuation are almost exactly synchronised and the fluctuation grows exponentially in amplitude, interrupted by brief episodes where synchronicity is lost and the amplitude of the fluctuation declines rapidly by several orders of magnitude. During these latter episodes there is a significant dip in the amplitude of the total magnetic field. This model-independent analysis can produce quantitative predictions for the behaviour of this bifurcation and we provide evidence for this behaviour by analysing timeseries from four different mean-field dynamo models, where intermittency is observed without the need for stochastic, or chaotically driven, forcing terms in the dynamo equations. We compare these results with recent work on intermittency in dynamo models and consider their relevance to the intermittency present in solar and stellar cycles.
The second of the annual BritGrav meetings on current research in Gravitational Physics in Britai... more The second of the annual BritGrav meetings on current research in Gravitational Physics in Britain took place at the School of Mathematical Sciences of Queen Mary, University of London on June 10/11, 2002. 47 plenary talks of 12min duration were given. We make available the abstracts of the talks and the references to the electronic preprints at arXiv.org where they exist.
International Journal of Modern Physics, Sep 10, 2011
We study the evolution of non-Gaussianity in multiple-field inflationary models, focusing on thre... more We study the evolution of non-Gaussianity in multiple-field inflationary models, focusing on three fundamental questions: (a) How is the sign and peak magnitude of the nonlinearity parameter f NL related to generic features in the inflationary potential? (b) How sensitive is f NL to the process by which an adiabatic limit is reached, where the curvature perturbation becomes conserved? (c) For a given model, what is the appropriate toolanalytic or numerical-to calculate f NL at the adiabatic limit? We summarise recent results obtained by the authors and further elucidate them by considering an inflection point model.
While the topology of the Universe is at present not specified by any known fundamental theory, i... more While the topology of the Universe is at present not specified by any known fundamental theory, it may in principle be determined through observations. In particular, a non-trivial topology will generate pairs of matching circles of temperature fluctuations in maps of the cosmic microwave background, the so-called circles-in-the-sky. A general search for such pairs of circles would be extremely costly and would therefore need to be confined to restricted parameter ranges. To draw quantitative conclusions from the negative results of such partial searches for the existence of circles we need a concrete theoretical framework. Here we provide such a framework by obtaining constraints on the angular parameters of these circles as a function of cosmological density parameters and the observer's position. As an example of the application of our results, we consider the recent search restricted to pairs of nearly back-to-back circles with negative results. We show that assuming the Universe to be very nearly flat, with its total matter-energy density satisfying the bounds 0 < |Ω0 − 1| 10 −5 , compatible with the predictions of typical inflationary models, this search, if confirmed, could in principle be sufficient to exclude a detectable non-trivial cosmic topology for most observers. We further relate explicitly the fraction of observers for which this result holds to the cosmological density parameters.
Anvar Shukurov and colleagues remember a theorist known for his work on stellar and galactic magn... more Anvar Shukurov and colleagues remember a theorist known for his work on stellar and galactic magnetism, who was also a prominent marine biologist.
British Journal For the Philosophy of Science, 1993
I INTRODUCTION In her challenging book How the Laws of Physics Lie, Nancy Cartwright [1983] expli... more I INTRODUCTION In her challenging book How the Laws of Physics Lie, Nancy Cartwright [1983] explicitly adopts a metaphysical position in support of her anti-realism with respect to the 'fundamental' laws of physics. She states: The metaphysical picture that underlies these ...
The Eleventh Marcel Grossmann Meeting - On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories - Proceedings of the MG11 Meeting on General Relativity, 2008
Among the most fundamental questions about the universe are those relating to its origin and earl... more Among the most fundamental questions about the universe are those relating to its origin and early evolution. Attempts at answering these questions within the classical relativistic framework have failed so far due to the presence of initial singularities, where the laws of physics break down. Recent results from Loop Quantum Cosmology, however, provide a framework where these questions can be
We investigate the detailed dynamics of a truncated αω dynamo model with a dynamic α effect. We f... more We investigate the detailed dynamics of a truncated αω dynamo model with a dynamic α effect. We find the presence of multiple attractors, including two chaotic attractors with a fractal basin boundary which merge to form a single attractor as the control parameter is increased. By considering phase portraits and the scaling of averaged times of transitions between the two attractors, we demonstrate that this merging is accompanied by a crisis-induced intermittency. We also find a range of parameter values over which the system has a fractal parameter dependence for fixed initial conditions. This is the first time this type of intermittency has been observed in a dynamo model and it could be of potential importance in accounting for some forms of intermittency in the solar and stellar output.
With the help of numerical experiments we find evidence for the existence of unique averaged comp... more With the help of numerical experiments we find evidence for the existence of unique averaged complex time singularities~Sfor dynamical systems subject to the same conditions as those required for Oseledec's multiplicative ergodic theorem to hold. By employing~and the leading resonances as the two analytical indicators of dynamical systems we study numerically the time invariant features of chaotic and fluid intermittent regimes. This in turn allows us to study the relationship between these two indicators themselves.
We find concrete evidence for the presence of crisis-induced and Pomeau-Manneville Type-I intermi... more We find concrete evidence for the presence of crisis-induced and Pomeau-Manneville Type-I intermittencies in an axisymmetric PDE mean-field dynamo model. These findings are of potential importance for two different reasons. Firstly, as far as we are aware, this is the first time detailed evidence has been produced for the occurrence of these types of intermittency for such deterministic PDE models. And secondly, despite the rather idealised nature of these models, the concrete evidence for the occurrence of more than one type of intermittency in such models makes it in principle possible that different types of intermittency may occur in different solar-type stars or even in the same star over different epochs. In this way a multiple intermittency framework may turn out to be of importance in understanding the mechanisms responsible for grand-minima type behaviour in the Sun and solar-type stars and in particular in the interpretation of the corresponding observational and proxy evidence.
Despite its great successes in accounting for the current observations, the so called `standard' ... more Despite its great successes in accounting for the current observations, the so called `standard' model of cosmology faces a number of fundamental unresolved questions. Paramount among these are those relating to the nature of the origin of the universe and its early evolution. Regarding the question of origin, the main difficulty has been the fact that within the classical general relativistic framework, the `origin' is almost always a singular event at which the laws of physics break down, thus making it impossible for such an event, or epochs prior to it, to be studied. Recent studies have shown that Loop Quantum Cosmology may provide a non-singular framework where these questions can be addressed. The crucial role here is played by quantum effects, i.e.\ corrections to the classical equations of motion, which are incorporated in effective equations employed to develop cosmological scenarios. In this chapter we shall consider the three main types of quantum effects expected to be present within such a framework and discuss some of their consequences for the effective equations. In particular we discuss how such corrections can allow the construction of non-singular emergent scenarios for the origin of the universe, which are past-eternal, oscillating and naturally emerge into an inflationary phase. These scenarios provide a physically plausible picture for the origin and early phases of the universe, which is in principle testable. We pay special attention to the interplay between these different types of correction terms. Given the absence, so far, of a complete derivation of such corrections in general settings, it is important to bear in mind the questions of consistency and robustness of scenarios based on partial inclusion of such effects.
According to a theorem of RueUe and Takens, the occurrence ofquasiperiodic motion on T 4 should b... more According to a theorem of RueUe and Takens, the occurrence ofquasiperiodic motion on T 4 should be unlikely. Here with the help of numerical calculations, we give a concrete example for which such motion is shown to exist and survive under small perturbations.
The question is considered of whether the 'correct' theory of gravity is a metric theory. The met... more The question is considered of whether the 'correct' theory of gravity is a metric theory. The metric hypothesis is shown to place severe restrictions on the form of the equation of motion for the one-body problem. By relaxing these restrictions, nonmetric contributions to the equation of motion are included, and the solution in the post-Newtonian approximation is given. The solution given contains five arbitrary parameters in place of the usual two (beta, gamma) of metric theories. One of them produces a secular change in the eccentricity; the others contribute to the perihelion advance and to periodic terms. Only certain combinations of these parameters can be determined even from orbits with different eccentricities.
S u m m a r y : Calculations for mean field dynamo models (in both full spheres and spherical she... more S u m m a r y : Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic a-quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples.
In a recent work (Covas et al. 1997), the behaviour and the robustness of truncated $\alpha\Omega... more In a recent work (Covas et al. 1997), the behaviour and the robustness of truncated $\alpha\Omega$ dynamos with a dynamic $\alpha$ were studied with respect to a number of changes in the driving term of the dynamic $\alpha$ equation, which was considered previously by Schmalz and Stix (1991) to be of the form $\sim A_{\phi}B_{\phi}$. Here we review and extend our previous work and consider the effect of adding a quadratic quenching term of the form $\alpha|B|^2$. We find that, as before, such a change can have significant effects on the dynamics of the related truncated systems. We also find intervals of (negative) dynamo numbers, in the system considered by Schmalz and Stix (1991), for which there is sensitivity with respect to small changes in the dynamo number and the initial conditions, similar to what was found in our previous work. This latter behaviour may be of importance in producing the intermittent type of behaviour observed in the sun.
Calculations for mean field dynamo models (in both full spheres and spherical shells), with both ... more Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic $\alpha$--quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples. Overall, the effect of using a dynamic $\alpha$ appears to be complicated and is affected by the region of parameter space examined.
It has recently been shown that nonlinear skew product dynamical systems with invariant subspaces... more It has recently been shown that nonlinear skew product dynamical systems with invariant subspaces which are capable of displaying on-off intermittency can show supersensitivity to small input signals. Here we show that this supersensitivity is absent for more general dynamical systems with non-skew product structure, capable of displaying a generalized form of on-off intermittency, and is therefore in this sense fragile. This absence of supersensitivity is of importance in view of the fact that dynamical systems are generically expected to be of non-skew product nature.
We consider the manner in which time-periodic solutions of an axisymmetric dynamo model can under... more We consider the manner in which time-periodic solutions of an axisymmetric dynamo model can undergo breaking of equatorial symmetry, i.e. loss of pure dipolar or quadrupolar symmetry. By considering the symmetry group underlying the solutions, we show that the fluctuations responsible for the symmetry-breaking can be constrained such that they are in resonance with the former solution. They can then be amplified until they are comparable in magnitude to the former solution. If the bifurcation is supercritical, the amplitude of the fluctuation is stabilised and a stable mixed parity limit cycle is formed. If it is subcritical it gives rise to a recently identified form of intermittency, called icicle intermittency. This produces episodes in which the original solution and the fluctuation are almost exactly synchronised and the fluctuation grows exponentially in amplitude, interrupted by brief episodes where synchronicity is lost and the amplitude of the fluctuation declines rapidly by several orders of magnitude. During these latter episodes there is a significant dip in the amplitude of the total magnetic field. This model-independent analysis can produce quantitative predictions for the behaviour of this bifurcation and we provide evidence for this behaviour by analysing timeseries from four different mean-field dynamo models, where intermittency is observed without the need for stochastic, or chaotically driven, forcing terms in the dynamo equations. We compare these results with recent work on intermittency in dynamo models and consider their relevance to the intermittency present in solar and stellar cycles.
The second of the annual BritGrav meetings on current research in Gravitational Physics in Britai... more The second of the annual BritGrav meetings on current research in Gravitational Physics in Britain took place at the School of Mathematical Sciences of Queen Mary, University of London on June 10/11, 2002. 47 plenary talks of 12min duration were given. We make available the abstracts of the talks and the references to the electronic preprints at arXiv.org where they exist.
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Papers by Reza Tavakol